]> Towards the Design of Carnitine Acyltransferase Inhibitors: Modeling the Conformational Behavior of (<em>R</em>)-Carnitine, (<em>R</em>)-Acetylcarnitine, Morpholinium rings, and 2-Oxo-1,3,6-dioxazaphosphacinium rings. <author> <given>Víctor Manuel <surname>Rosas-García <submission>Dissertation <school>Virginia Polytechnic Institute and State University <degree>Doctor of Philosophy <major>Chemistry <approvals> <name>Richard D. Gandour <name>Mark Anderson <name>David Bevan <name>Harry Gibson <name>Thomas Hudliçky <name>James Tanko <date> <city>Blacksburg <state>Virginia <keywords> <keyword>carnitine <keyword>acylcarnitine <keyword>modeling of morpholinium rings <keyword>phosphonate <keyword>modeling of medium-sized rings <keyword>conformational analysis </keywords> <copyright>Copyright 1997, Víctor M. Rosas-García <abstract> <p>Full grid-search semiempirical calculations (AM1 and AM1/COSMO) on zwitterionic acetylcarnitine and carnitine, cationic acetylcholine and choline, and 3-acetoxypropanoate and 3-hydroxypropanoate in the gas phase and solution were performed. The calculated δH°<sub>hydr</sub> for hydrolyses of acetylcarnitine to carnitine and of acetylcholine to choline show reasonable agreement with the experimental values in unbuffered solution (acetylcarnitine: -4.63 kcal/mol calc. vs. -7.43 kcal/mol exp.; acetylcholine: -3.20 kcal/mol calc. vs. -3.06 kcal/mol exp.) The results suggest that a change in the conformational populations of acetylcarnitine-carnitine upon hydrolysis maintains a nearly constant polarity, which keeps the work of desolvation of the products to a minimum. Acetylcholine-choline and acetoxypropanoate-hydroxypropanoate present a much higher work of desolvation, therefore yielding a lower free enthalpy of hydrolysis. Ab initio calculations at the RHF/6-31G* level for the carnitines and the cholines, and RHF/6-31+G for the propanoates, were done to calibrate the quality of the AM1 results for both the gas phase and in solution. The calculations in the gas phase involved full optimization of the AM1-optimized structures at the RHF/6-31G* level and RHF/6-31+G level, and single points at the MP2//RHF/6-31G* and MP2//RHF/6-31+G level to estimate correlation effects. The ab initio calculations in solution were single points on the AM1-optimized geometries and used the Tomasi solvent model. The ab initio results confirmed the qualitative reliability of the semiempirical results. <p>The conformational behavior of several 4,4-dimethylmorpholinium rings and 4,4-dimethyl-2-oxo-1,3,6-dioxazaphosphacinium rings was examined by molecular mechanics (AMBER* and AMBER*-GB/SA). The contrast between the behavior of these heterocycles and that of the parent saturated hydrocarbon systems formed a picture of the conformational behavior of these six- and eight-membered heterocycles. Influences of factors such as shortened bond lengths, varied bond angles, presence or absence of lone pairs and substituents, and dipolar alignment are described. Morpholinium rings show increased stabilization of the twist-boat with 1,1,3,3-di<em>gem</em> substitution, as compared to the parent cyclohexane systems. In the gas phase, the lowest chair/twist-boat energy gap is found in 2-(hydroxymethyl)-2,4,4-trimethylmorpholinium at 1.14 kcal/mol. The gap in the congruent hydrocarbon system is 5.23 kcal/mol. Differential solvation destabilizes the lowest energy twist-boat found in the gas phase, increasing the energy gap to 2.62 kcal/mol. The lowest chair/twist-boat energy gap in GB/SA water amounts to 1.45 kcal/mol, stabilized by solvation from an initial 2.13 kcal/mol in the gas phase. <p>In the dioxazaphosphacinium rings, the preferred conformation in the gas phase is the boat-chair (BC) and the populations are conformationally heterogeneous. As substituents approach a 1,1,3,3-di<em>gem</em> pattern, the twist-chair (TC) and twist-boat (TB) conformers are stabilized. Solvation favors boat-boat (BB) conformers, with the substituents exerting influence on the conformational preference only to stabilize the TB in two instances ( <link goesto="tableCompP3"><em>cis</em>-substituted ring</> and <link goesto="tableCompP5">disubstituted ring</>). Solvation reduces the heterogeneity of the conformational populations. <p>Modeling of phosphonate moieties required development of molecular mechanics parameters for dimethyl methylphosphonate. Dimethyl methylphosphonate conformations were calculated at the RHF/6-31+G* level. Charges were calculated by the CHelpG scheme. The results were used to generate AMBER* parameters for modeling of alkylphosphonates in the gas phase and in solution. Comparison of the results of our AMBER* parameters against three other common force fields (MM2*, MMX and UFF) showed that AMBER* reproduced better the ab initio results when comparing absolute deviations in bond lengths, bond angles and torsion angles. The modified AMBER* reproduced better than the other three force fields several X-ray geometries of alkylphosphonates. </abstract> <grant>Part of this work was supported by NIH Grant GM 42016 <dedication> <p>A mis padres, que me enseńaron el buen camino. <blockquote> <q>(. . .)I had an extreme desire to acquire instruction. But so soon as I had achieved the entire course of study at the close of which one is usually received into the ranks of the learned, I entirely changed my opinion. For I found myself embarrassed with so many doubts and errors that it seemed to me that the effort to instruct myself had no effect other than the increasing discovery of my own ignorance.</q></blockquote> <attrib>Rene Descartes, <worktitle>Discourse on the Method, ed. James Fieser (Internet Release, 1996)</> <acknowledgments> <p>I want to thank many people: first comes Rich, who provided guidance and taught me the intellectual habits that make a good scientist. Also my friends from Baton Rouge, especially Guillermo (G-man) and Renee Morales, for all the fun we had together and for their support. Here at Virginia Tech I cannot forget Brett Kite, for providing an always challenging environment; Alex Lostetter, Dan Lough and the people in the Newman Communities (LSU and Va Tech) for helping me keep my sanity. I thank Ms. Paige Phillips for her friendship and support, and for all those discussions about chemistry. <p>I extend my appreciation also to my professors back in UANL (Monterrey), especially Alejandro García, Celso Rodríguez and Ricardo Flores for their exhaustive teaching and for encouraging me to pursue advanced studies. <p>Quentin MacDonald (Columbia Univ.) provided invaluable help by teaching me the how-to of parameter development for molecular mechanics force fields. The Computing Center at Virginia Tech gave me a generous allocation of CPU time in the IBM SP2 and SMP machines. Without these contributions, many of my calculations would have been impossible. <p>I thank Jan Labanowski (Ohio Supercomputer Center) for his excellent job running the Computational Chemistry List (CCL) and the members of the CCL for the high quality of their discussions about computational chemistry. Interacting with them has been (and still is) a great educational experience. <p>Steve Young from MDL Information Systems, Inc. provided a free copy of the software used for the chemical drawings in this dissertation (ISIS/Draw v.1.2). <p>This has been a time of growth and change, and many people, too numerous to list here, have influenced my life. To those that go unmentioned, I express my deepest thanks. Rest assured that the seed you planted in me will not be lost. </front> <!--Body matter --> <body> <chapter> <head>Introduction. <p>This research attempted to determine the conformational behavior of several building blocks employed in our group for the design of enzymatic inhibitors. To this effect, this dissertation covers three main projects: <ol> <li>A computational study of the energetics of the hydrolysis of acetylcarnitine, accounting for the effects of changes in the predominant conformation due to solvation.</li> <li>Effect of substitution on the conformational behavior of 4,4-dimethylmorpholinium rings, studied by computational techniques. <!-- README The full captions for a figures is always kept in the same line, and is not indented, for an easier compilation of a "List of Figures". --> <float id=morpholinium> <mm entity=fig.morph>fig.morph.gif, 0.44k</mm> <caption>4,4-dimethylmorpholinium ring. </float></li> <li>Development of parameters for AMBER* force field, and modeling of the conformational behavior of 4,4-dimethyl-2-oxo-1,3,6-dioxazaphosphacinium rings. <float id=phosphacinium> <mm entity=fig.phosp>fig.phosp.gif, 0.591KB</mm> <caption>2,4,4,-trimethyl-2-oxo-1,3,6-dioxazaphosphacinium ring. </float></li> </ol> <section> <head>Purpose of study. <p>Our group designs and synthesizes transition-structure analogs (TSA) as inhibitors for carnitine acetyl-, octanoyl- and palmitoyltransferases (CAT, COT and, CPT-I and CPT-II). Normally the designer of an inhibitor tries to imitate the geometry of the transition structure <link goesto="j.Wolfenden69">Wolfenden, 1969</> for the reaction catalyzed by the enzyme. Ideally, knowing the shape of the active site in an enzyme would enable us to design strong inhibitors. Presently, we only know the aminoacid sequences for CAT, COT, CPT-I and CPT-II, but their tertiary structures remain unknown. Until the resolution of the tertiary structures, only indirect methods can yield information about the shape of the active site. Knowledge of the preferred conformations adopted by TSAs, together with their measured inhibitory potency, can shed some light on the shape of the active site of these enzymes. <p>Inhibitors for CAT, COT and CPT can help us understand the role of each carnitine acyltransferase in the cell. Such understanding will help us in the design of potentially therapeutic compounds for diseases like diabetes and myocardial ischemia. <p>As the costs of experimentation and waste disposal continue to increase, it is imperative to find more efficient ways to choose targets for synthesis, especially those compounds with a greater chance of success as inhibitors. Computer modeling allows us to examine many compounds before choosing a target. The question then becomes: are there any modeling methods refined to the point they can yield reliable results for charged species? In particular, modeling of species with charges such as morpholinium, and zwitterions as that of carnitine in solution is difficult. <!-- README All the footnotes are referred to as "Note."s. It would be desirable to have a reformatter that used more standard designations: superscript arabic numbers (Journal of American Chemical Society-style), or a standard sequence of characters (such as the ones specified in the journals "Science" or the "Proceedings of the National Academy of Sciences of the USA" --> <link goesto="f.Solvation">Note.</> <footnote id=f.Solvation>Cramer and Truhlar <link goesto="b.Cramer95">Cramer, 1995</> have reviewed the performance of several solvation models and critically analyzed their implementations. One of their conclusions is that few software packages take into account both the contributions of charge and of multipolar moments, such as dipole, quadrupole, octapole and hexadecapole moments. </footnote> We need, however, such modeling to understand the conformational preferences of the reactants --acetylcarnitine, carnitine-- and the enzymic reaction intermediate to achieve a more rational design of inhibitors. As several of our inhibitors include phosphonate substructures, we require methods able to deal with them. Such methods are not widely available; modeling of phosphonates has certainly lagged behind that of more popular phosphorus species, such as phosphates. <p>For these purposes we want to assess the ability of current state-of-the-art computational methods to model the compounds of our concern. We put particular emphasis on the inclusion of solvent effects, so we want to see the abilities of methods such as COSMO to reproduce properties such as dipole moments and heats of formation in solution. As we need to consider hundreds of conformations and configurations in crowded, charged species, optimization of computer resources is essential. We therefore need to evaluate the applicability of ab initio, semiempirical and molecular mechanics methods so that we spend a minimum of resources without undermining the quality of the predictions. <p>Among the problems we face are: the high free energy of hydrolysis of acetylcarnitine, which qualifies it as a high-energy molecule. This high energy has remained unexplained for about three decades. <link goesto="j.Friedman55">Friedman, 1955</> The conformational dynamics of six- and eight-membered heterocycles are still imperfectly understood. <link goesto="b.Eliel94">Eliel, 1994</> All these pieces of information can help us understand the mode of action of the inhibitors already available to us. <p>We can take two approaches to deal with modeling: <ol> <li>As a tool oriented to engineering of results, meaning that achieving experimental accuracy is the most important matter, even though the methods may not have full theoretical justification.</li> <li>As a research tool, where the theoretical basis of the method can provide insight on the mechanisms underlying the phenomenon of interest, even if the approximation to experiment is only qualitative.</li> </ol> <p>In general, molecular modelers use a combination of the two approaches, and it would be difficult to find examples of <q>pure</q> techniques, (techniques that adhere strictly to only one approach). Regardless of the <q>purity</q> of the technique employed, if we can model experimental results, we can gain confidence on the predictions generated for systems that have not been tested yet. How closely should the modeling results approach the experimental results to render the modeling as reliable? This is a somewhat subjective matter, as there are no hard guidelines to make such a decision. <chapter> <head>Historical. <section> <head>Introduction. <p>This review reproduces the latest advances in the design of carnitine acyltransferase inhibitors, and provides only the background necessary for a fruitful discussion of the conformational behavior of the inhibitors mentioned below. <section> <head>Acyltransferase inhibitors. <p>One common strategy to design enzymatic inhibitors is to use transition-structure-analog theory <link goesto="j.Wolfenden69">Wolfenden, 1969</> to design a compound that the enzyme can recognize. Binding of the following tetrahedral intermediate is commonly considered important in the transfer of acyl groups to CoA: <float id=gandour93> <mm entity=fig.gandour93>fig.gandour93.gif, 1.231KB </mm> <caption>Tetrahedral intermediate for Carnitine-CoA acyl transfer. </float> <p>We can classify enzymatic inhibitors according to their observed effects on enzymatic activity (reversible or irreversible) or by their mechanism of action (competitive or noncompetitive). Irreversible inhibitors eliminate enzymatic activity in such a way that the enzyme does not recover its original activity. Reversible inhibitors allow the recovery of catalytic activity after elimination of the inhibitor. Competitive inhibitors bind to the active site instead of the substrate, while noncompetitive inhibitors do not attach themselves to the active site, so the substrate can still bind to the enzyme. Thus we have four main types of enzymatic inhibitors: <ol> <li>Competitive reversible</li> <li>Competitive irreversible</li> <li>Noncompetitive reversible</li> <li>Noncompetitive irreversible</li> </ol> Competitive carnitine analogs constitute our primary concern, but we include summaries of the other types for the sake of completeness. We offer only a brief description of each, as Colucci and Gandour <link goesto="j.Colucci88">Colucci, 1988</> have reviewed extensively CAT inhibitors. <subsection> <head>Competitive reversible inhibitors. <p><chemname>(<em>S</em>)-Carnitine</chemname> and <chemname>(<em>S</em>)-acetylcarnitine</chemname> inhibit competitively pigeon CAT. <link goesto="j.Tipton69">Tipton, 1969</> Tipton and Chase justified the recognition of the <em>S</em> isomers by postulating a two-point recognition site that binds only to carboxylate and ammonium. CATs extracted from bovine heart, pig heart and mouse-liver peroxisomes discriminated substantially between the (<em>R</em>) and the (<em>S</em>) isomers. The authors postulated a more restricted two-point recognition site, or a three-point recognition site for these CATs. <p>Aminocarnitine <float id=aminocarn> <mm entity=fig.aminocarn>fig.aminocarn.gif, 0.595KB. <caption>Aminocarnitine. </float> is a weak reversible competitive inhibitor for CAT, although it inhibits strongly both CPT-I and CPT-II. <link goesto="j.Kanamaru85">Kanamaru, 1985</> <link goesto="j.Jenkins85">Jenkins, 1985</> <link goesto="j.Jenkins86">Jenkins, 1986</> Due to the isosteric relationship to carnitine, <em>N</em>-Acylated derivatives of racemic aminocarnitine can also inhibit reversibly carnitine acyltransferases, as shown by the great inhibitory potency of D,L-acetylaminocarnitine. <link goesto="j.Jenkins85">Jenkins, 1985</> (<em>R</em>)-acetylaminocarnitine --named <q>emeriamine</q> because it was isolated from a culture filtrate of <em>Emericella quadrilineata</em>-- showed even stronger inhibitory action than the racemic compound. <link goesto="j.Shinagawa87">Shinagawa, 1987</> <p>Gandour <em>et al.</em> <link goesto="j.Gandour86">Gandour, 1986</> <link goesto="j.Gandour92">Gandour, 1992</> showed good inhibition of CAT by hemiacylcarnitinium (HAC). Later, the same authors <link goesto="j.Gandour88">Gandour, 1988</> <link goesto="j.Gandour93">Gandour, 1993</> demonstrated the strong activity of hemipalmitoylcarnitinium (HPC) as a competitive inhibitor of CPT-I. HAC inhibits CAT, but not CPT. HPC inhibits CPT, but not CAT. It seemed that CPT requires a long chain for proper recognition of the substrate. These differences in the specificity of the inhibitors allowed for a partial mapping of the topographies of the active sites in both enzymes. The design of all these inhibitors relied on making them analogs of the <link goesto="gandour93">tetrahedral intermediate</> mentioned previously by means of restricting the conformations with a morpholinium moiety: <float id=HAC> <mm entity=fig.HAC>fig.HAC.gif, 0.740KB <caption>Hemiacylcarnitinium moiety. </float> <p>The morpholinium ring locks the N-CH<sub>2</sub>-CH-OH(Ac) torsion of the carnitine backbone in the <em>gauche</em> conformation. The authors stated the difficulty of excluding selective binding of the open form of the hemiacetal, but "presumably" hemiacylcarnitiniums bind as cyclic structures. NMR did not detect any open form of the compound in solution. <p>Saeed <em>et al.</em> <link goesto="j.Saeed93">Saeed, 1993</> showed that 3-hydroxy-5,5-dimethylhexanoic acid <float id=saeed93> <mm entity=fig.saeed93>fig.saeed93.gif, 0.581KB <caption>3-hydroxy-5,5-dimethylhexanoic acid. </float> competitively inhibited CAT, CPT-I and CPT-II, indicating that these enzymes require a positively charged center to show catalysis. Saeed <em>et al.</em> <link goesto="j.Saeed94">Saeed, 1994</> later reported the inhibitory properties of 3-amino-5,5-dimethylhexanoic acid. <float id=saeed94> <mm entity=fig.saeed94>fig.saeed94.gif, 0.585KB <caption>3-amino-5,5-dimethylhexanoic acid. </float> Both 3-hydroxy- and 3-amino-5,5-dimethylhexanoic acid are alternative substrates for CAT. <p>Gandour's group evaluated Protein Kinase C, COT and CPT inhibitors based on a 2-oxo-1,3,6-dioxazaphosphacinium moiety. <link goesto="j.Kumaravel94">Kumaravel, 1994</> <float id=kumaravel94> <mm entity=fig.kumaravel94>fig.kumaravel94.gif, 0.743KB <caption>4-hexadecyl-2,4,4-trimethyl-2-oxo-1,3,6-dioxazaphosphacinium bromide. </float> The authors tested racemic mixtures (2<em>S</em>, 4<em>S</em>)/(2<em>R</em>, 4<em>R</em>) and (2<em>S</em>, 4<em>R</em>)/(2<em>R</em>, 4<em>S</em>) and found they inhibited COT and CPT-II moderately. <p>Gandour's group also reported several CAT inhibitors incorporating a methylenecarboxylate substructure on a morpholinium ring. <link goesto="j.Sun95">Sun, 1995</> <float id=sun95> <mm entity=fig.sun95>fig.sun95.gif, 1.157KB <caption>6-(Carboxylatomethyl)-2-(hydroxymethyl)-2,4,4-trimethylmorpholinium. </float> All four stereoisomers were evaluated for inhibitory activity and the authors concluded that <q>CAT recognizes both configurations at C2 and C6 in the analogues.</q> <p>Anderson <em>et al.</em> <link goesto="j.Anderson95">Anderson, 1995</> reported on the potency of a series of CPT-I inhibitors based on a phosphonate moiety designed by transition-structure-analog theory. <float id=anderson951> <mm entity=fig.anderson951>fig.anderson951.gif, 0.842KB <caption>Anderson's phosphonate. </float> This compound showed appreciable inhibitory activity. After trying systematic structural variations, they found that the following phosphate: <float id=anderson952> <mm entity=fig.anderson952>fig.anderson952.gif, 0.980KB <caption>Anderson's phosphate. </float> inhibited to a level comparable to the phosphonate. Both the phosphonate and the phosphate could show similar detergency, thus explaining the similar inhibition. The authors discarded such an explanation due to the stronger inhibition shown by the <em>R</em> enantiomers when compared to the <em>S</em> enantiomers. <subsection> <head>Competitive irreversible inhibitors. <!-- README The words between <term> tags are kept in the same line for an easier compilation of a glossary. --> <p>We can visualize the enzyme and the substrates as part of a ternary complex. <!-- --><term>Bisubstrate inhibitors</term> resemble the spatial disposition of the substrates, leaving the enzyme as the "third" component. One of the earliest examples of a bisubstrate inhibitor is <chemname><em>S</em>-carboxymethyl-CoA-(<em>R</em>)-carnitine ester</chemname>, reported by Chase and Tubbs. Bromoacetyl-CoA and bromoacetyl-(<em>R</em>)-carnitine are also bisubstrate inhibitors for CAT. <link goesto="j.Chase69">Chase, 1969</> <p>Fritz and Schultz <link goesto="j.Fritz65">Fritz, 1965</> reported inhibition of CAT by <em>p</em>-hydroxymercuribenzoate (HMB) at a concentration of 2.6 µM. Such inhibition was prevented or <em>partially</em> reversed by addition of acetyl-CoA, which suggested to these authors that HMB may bind to the active site. <p>Several groups have reported compounds possessing inhibitory activity towards carnitine acyltransferases. Etomoxir <chemname>(2-[6-(4-chlorophenoxy)hexyl]oxirane-2-carboxylate)</chemname> is an irreversible inhibitor of CPT-I. <link goesto="j.Eistetter82">Eistetter, 1982</> Tetradecylglycidate (TDGA) is also an oxirane-based irreversible competitive inhibitor of CPT-I. <link goesto="j.Tutwiler85">Tutwiler, 1985</> <p>Another competitive inhibitor is methoxycarbonylCoA disulfide, <link goesto="j.Venkatraghavan83">Venkatraghavan, 1983</> which modifies selectively a sulfhydryl group in the active site. Dithioerythritol or thiocholine can partially reverse its action. <subsection> <head>Noncompetitive reversible inhibitors. <p>5,5'-Dithiobis(2-nitrobenzoic acid) (DTNB), reacts with sulfhydryl groups in a non-specific way. It inhibits pig heart CAT <link goesto="j.Fritz63">Fritz, 1963</> and pigeon breast CAT. <link goesto="j.Venkatraghavan83">Venkatraghavan, 1983</> Because this reagent forms disulfide linkages, adding a disulfide exchange reagent such as dithiothreitol, dithioerythritol or thiocholine can restore enzymatic activity. <p>Derrick and Ramsay <link goesto="j.Derrick89">Derrick, 1989</> showed that malonylCoA is a reversible inhibitor of peroxisomal CPT-I, but does not show competitive behavior. These authors estimated that peroxisomal palmitoyltransferase activity constituted up to 20% of the peroxisomal + overt-mitochondrial pool in fed-rat liver. A concentration lower than 10µM of malonyl-CoA was enough to show 90% inhibition of the peroxisomal palmitoyltranferase. <subsection> <head>Noncompetitive irreversible inhibitors. <p>Fritz and Schultz <link goesto="j.Fritz65">Fritz, 1969</> reported the inhibitory activity of ZnCl<sub>2</sub>, HgCl<sub>2</sub>, <em>N</em>-ethylmaleimide and iodoacetamide. Addition of ethanethiol prevented or partially reversed HgCl<sub>2</sub> inhibition. The authors did not cite the values of K<sub><em>i</em></sub> for these compounds. </section> <chapter> <head>Acetylcarnitine hydrolysis. <section> <head>Review of literature. <subsection> <head>Acylcarnitines in cellular metabolism. <p>Carnitine transports long-chain fatty acids across the mitochondrial membrane; thus, it is essential for lipid metabolism. Bieber reviewed the metabolic roles of acylcarnitine. <link goesto="b.Bieber92">Bieber, 1992</> In microsomes and peroxisomes, carnitine transports medium-chain fatty acids into the cytosol. Non-Insulin-Dependent Diabetes (NIDD) and myocardial ischemia are among the diseases thought to bear a relationship to carnitine. Carnitine abounds in semen, although the reason for its presence remains a matter of speculation. <p>CAT catalyzes the acetylation of carnitine. <link goesto="j.Colucci88">Colucci, 1988</> Acetylated carnitine has a large group-transfer potential, which makes it an active form of acetate that the mitochondria can use efficiently for oxidation. A carrier of acetyl groups is necessary, because the inner mitochondrial membrane is impermeable to Coenzyme A (CoA) and AcetylCoenzyme A (AcCoA). <p>There are (at least) two kinds of CPT, usually designated as CPT-I and CPT-II. CPT-I resides inside the inner mitochondrial membrane, while CPT-II is attached to the outside of the outer mitochondrial membrane. MalonylCoA, CPT-I and fatty acylCoA form part of a mechanism that regulates glucose levels. Inhibition of CPT-I by high malonylCoA levels suppresses fatty acid synthesis and oxidation in the liver, while a high level of fatty acylCoA lowers malonylCoA levels. Thus, CPT inhibitors are potential therapeutic agents for diabetes. <p>COT is the long-chain carnitine acyltransferase on peroxisomes. Peroxisomes have the ability to oxidize fatty acids. COT is likely the enzyme responsible for forming carnitine esters of aromatic and branched alkyl acids, which form in the metabolism of drugs. <subsection> <head>Thermodynamics of acetylcarnitine hydrolysis. <block> <head>High-energy compounds. <p>The high energy of hydrolysis of acetylcarnitine places it in the <q>energy-rich</q> category, like ATP, but the body does not use acetylcarnitine for energy storage. Two basic questions are: <ol> <li>How does acetylcarnitine store chemical energy?</li> <li>Why the need for such a high energy?</li> </ol> In this work we shall address mostly the first question, but first a note on terminology: we use the definition of <term>energy-rich compound</term> (also called <q>high-energy</q> compound) suggested by Jencks: <link goesto="j.Jencks60">Jencks, 1960</> <blockquote><q>(. . .)an <q>energy-rich</q> compound is one which will react, <em>under physiological conditions</em>, with a substance that is commonly present in the environment, to liberate a large amount of free energy.</q></blockquote> A free energy of hydrolysis is <q>high-energy</q> if it releases more than -7.0 kcal/mol, according to Jencks. In addition to ATP, other biomolecules qualify as energy-rich compounds. <p>Burton <link goesto="j.Burton54">Burton, 1954</> measured the free energy of hydrolysis of the thioester bond in AcCoA, reaching a value close to -8 kcal/mol. Burton noticed that this high free energy of hydrolysis puts AcCoA in the same category of <q>high-energy molecule</q> as ATP. Later, after determining the free energy of hydrolysis of thiol esters and aminoacid esters, Jencks <em>et al.</em> <link goesto="j.Jencks60">Jencks, 1960</> concluded that both qualified as energy-rich compounds. Thiol esters had a free energy of hydrolysis of approx. -7.7 kcal/mol. They reported that, in general, the difference in free energies of hydrolyses between oxygen esters and thiol esters, was approx. 2.5 kcal/mol. This lower value of free energy of hydrolysis placed the oxygen esters outside the energy-rich range. Aminoacids seemed a special case, given that hydrolysis of glycine ethyl ester to the dissociated acid (zwitterionic form) had a free energy change of -8.4 kcal/mol <em>at pH=7.0</em>. As a comparison, hydrolysis of glycine ethyl ester to the undissociated acid yielded a free energy change of -1.97 kcal/mol, very similar to that of ethyl acetate. Jencks ascribed the high free energy of hydrolysis of glycine ethyl ester to a destabilizing effect of the positively charged ammonium group, rather than to the high acidity of glycine. <p>The first indication of the high-energy status of acetylcarnitine came from Friedman and Fraenkel <link goesto="j.Friedman55">Friedman, 1955</> who reported on the ability of acetylcarnitine to transfer an acetyl group to CoA. They studied the effects of added carnitine on the enzymatic acetylation of <em>p</em>-aminobenzoic acid. Carnitine inhibited the acetylation reaction, while neither the zwitterion of glycine, choline or β-hydroxybutyrate showed any inhibitory activity. Acetylcarnitine reversed the inhibition produced by carnitine, while an equivalent amount of acetate added to a carnitine-inhibited system failed to restore enzymatic activity. A few years later, Fritz <em>et al.</em> <link goesto="j.Fritz63">Fritz, 1963</> were the first to measure the high free energy change in the hydrolysis of acetylcarnitine. They reported a value of -7.9 kcal/mol at pH=7.0. This value changed little when using chains longer than acetyl. Acetylcarnitine participated in an acetyl group exchange equilibrium with AcCoA, with an equilibrium constant approximately equal 0.6. Their results indicated that acetylcarnitine required a free carboxylate group to show activity and they postulated <a href="reviews/fig.fritz63.gif">anchimeric assistance of the carboxylate (fig.fritz63.gif, 2.362KB)</a> as a step in the acetyl hydrolysis. <p><target id=revMuller>Müller and Strack</target> <link goesto="j.Muller73">Müller, 1973</> determined the enthalpies of hydrolysis of a series of acylcarnitines, acetylcholine <link goesto="hydrolysis2">see figure</>, glycine methyl ester and acetyl-β-methylcholine by microcalorimetry. Their results show that the enthalpic term contributes the most to the free energy of hydrolysis. For the acylcarnitines, the entropic term is relatively small and invariant with chain length. Glycine methyl ester, acetyl-β-methylcholine, and acetylcarnitine methyl ester had less negative enthalpies of hydrolysis than acetylcarnitine, at pH=7.0, by about 2 kcal/mol. <float id=hydrolysis2> <mm entity=fig.hydrolysis2>fig.hydrolysis2.gif, 2.714KB <caption>Comparison of free energies of hydrolysis between acetylcarnitine and acetylcholine. </float> The previous values were determined at buffered pH=7.0. For the process at pH=4.0 (producing HOAc instead of <sup>-</sup>OAc), the values are -4.63 kcal/mol for acetylcarnitine, and -3.20 kcal/mol for acetylcholine. The difference (1.43 kcal/mol) does not depend on pH. <p>Pierlik and Guynn <link goesto="j.Pierlik75">Pierlik, 1975</> compared the group-transfer potential of acetylcarnitine and acetylcholine under physiological conditions. They found the free energy of hydrolysis of acetylcarnitine only 1.21 kcal/mol more negative than that for the hydrolysis of acetylcholine: -8.20 kcal/mol for acetylcarnitine vs. -6.99 kcal/mol for acetylcholine. <block> <head>Effects of solvation on thermodynamic quantities. <p>George <em>et al.</em> <link goesto="j.George70">George, 1970</> called attention to solvation effects in the hydrolysis of ATP. Their work remarked the influence of differential solvation between reactants and products as a <q>(. . .) major factor contributing to the thermodynamic reactivity (. . .)</q>. They found that, as the charge increased, water solvation could stabilize multiply charged species such as phosphates, compensating for the increased electrostatic repulsion of the multiple negative charges present in such anions as pyrophosphate, tripolyphosphate, and glucose-6-phosphate. <p>Wolfenden discussed a similar question about the contributions of solvent effects in group-transfer potentials of uncharged species, mostly of mixed anhydrides of phosphoric and carboxylic acids, <link goesto="j.Wolfenden89">Wolfenden, 1989</> as well as carbohydrates. <link goesto="j.Wolfenden88">Wolfenden, 1988</> He pointed to the role of solvation energy of the products as a driving force for the reaction when he inquired <q>(. . .)whether the large negative change in free energy, that normally accompanies conversion of mixed phosphoric-carboxylic anhydrides to the products of their hydrolysis in dilute aqueous solution, may depend on differences in free energy of solvation between the reactants and the products.</q> One of his findings was that <q>(. . .)the uncharged products of hydrolysis of acetyl dimethyl phosphate are solvated much more strongly by water than are the reactants.</q> <p>Hayes <em>et al.</em> <link goesto="j.Hayes78">Hayes, 1978</> did ab initio calculations on hydrolytic reactions of several high-energy molecules. Their results, which included <q>a crude reaction field solvent model</q>, pointed out that the greatest contributions to the energies of hydrolysis came from the relative solvation energies of reactants and products. The relative solvation energies were <q>by far the most important factors in determining the energies</q>, especially in those cases of greatest importance in energy storage and transduction, namely, <pre> ATP --> ADP + orthophosphate </pre> and <pre> phosphocreatine + ADP --> creatine + ATP </pre> <p>Marsh <em>et al.</em> <link goesto="j.Marsh80">Marsh, 1980</> applied ab initio methods together with molecular mechanics to the study of AMP derivatives. The greater exothermicity of 3',5'-cyclic AMP vs. trimethylene phosphate was attributed to: strain due to <em>trans</em> fusion in 3',5'-cyclic AMP (4-5 kcal/mol), an unfavorable O-C-C-O interaction relieved by ring opening (1-2 kcal/mol, because the interaction depends on the solvent), and 1-2 kcal/mol ascribable to differential solvation between reactants and products. <block> <head>Relationship between conformational preference and thermodynamics. <p>Colucci <em>et al.</em> <link goesto="j.Colucci86">Colucci, 1986</> conducted NMR measurements in D<sub>2</sub>O and MM2 calculations that showed that, upon hydrolysis, the predominant conformation of the carnitine skeleton changes from <q>folded</q> to <q>extended</q>. The N-CH<sub>2</sub>-CH-OH(Ac) torsion angle remained <em>g-</em> throughout. <section> <head>Results and Discussion. <p>The carnitine backbone can present two major conformations: <float id=folded> <mm entity=fig.folded>fig.folded.gif, 0.510KB <caption><q>Folded</q> conformer of carnitine. </float> <float id=extended> <mm entity=fig.extended>fig.extended.gif, 0.608KB <caption><q>Extended</q> conformer of carnitine. </float> <p>We can break down the process of hydrolysis to that of individual conformers: <float id=hydrolysis1> <mm entity=fig.hydrolysis1>fig.hydrolysis1.gif, 2.491KB <caption>Hydrolyses of extended and folded conformers. </float> In general, the ratios extended:folded before and after hydrolysis are not the same. <p>We studied the thermodynamics of acetylcarnitine hydrolysis by semiempirical and ab initio methods both in the gas phase and solvent. <subsection> <head>Conformational analyses in gas phase. <p>We calculated the enthalpies of formation and dipole moments of acetylcarnitine, carnitine, acetylcholine, choline, 3-acetoxypropanoate and 3-hydroxypropanoate in gas phase (see tables). We justified our use of enthalpies instead of free energies on the results reported by Müller and Strack. <link goesto="revMuller">See review of literature.</> <ul> <li> <a href="carnitine/TableAcCarnAM1Gas.html">Acetylcarnitine in gas phase.</></li> <li> <a href="carnitine/TableCarnAM1Gas.html">Carnitine in gas phase.</></li> <li> <a href="carnitine/TableAcCholAM1Gas.html">Acetylcholine in gas phase.</></li> <li> <a href="carnitine/TableCholAM1Gas.html">Choline in gas phase.</></li> <li> <a href="carnitine/TableOAcPrAM1Gas.html">3-Acetoxypropanoate in gas phase.</></li> <li> <a href="carnitine/TableOHPrAM1Gas.html">3-Hydroxypropanoate in gas phase.</></li> </ul> The labels for torsion angles in the tables are as follows: <float id=torsions> <mm entity=fig.torsions>fig.torsions.gif, 0.731KB <caption>Labels for torsion angles used in acetylcarnitine. </float> <dl> <dt>A</dt> <dd>N-CH<sub>2</sub><strong>-</strong>CH-OH(Ac)</dd> <dt>B</dt> <dd>CH<sub>2</sub>-CH<strong>-</strong>CH<sub>2</sub>COO<sup>-</sup></dd> <dt>C</dt> <dd>C-C<strong>-</strong>C(O)-O<sup>-</sup></dd> <dt>D</dt> <dd>CH<sub>2</sub>-CH<strong>-</strong>O-H(Ac)</dd> <dt>E</dt> <dd>C-O<strong>-</strong>C(O)-CH<sub>3</sub></dd> </dl> The hydrolyses of acetylcholine to choline and of 3-acetoxypropanoate to 3-hydroxypropanoate constituted our reference points. <p>Acetylcholine and choline cannot show an extended or a folded conformation because they lack the methylenecarboxylate group, so they helped us assess the importance of the gauche effect <link goesto="gaucheeff">(see section below) </> <link goesto="j.Sundaralingam68">Sundaralingam, 1968</> <link goesto="j.Wiberg90">Wiberg, 1990</> and of the CH<sub>2</sub>-CH-O-H(Ac) torsion in the energetics of the hydrolysis. The propanoates can show folded and extended conformations, but are not affected by the gauche effect. <block> <head>Acetylcarnitine vs. carnitine. <p><em>Anti</em> conformers of N-CH<sub>2</sub>-CH-OH(Ac) account for nearly 50% of the population of acetylcarnitine but only 1% for carnitine. The CH<sub>2</sub>-CH-CH<sub>2</sub>-COO<sup>-</sup> torsion angle always prefers <em>gauche +</em> (<em>g+</em>) in carnitine and <em>gauche -</em> (<em>g-</em>) in acetylcarnitine, so folded conformations comprise 100% of the populations. We can explain this preference by Coulombic attraction between the negatively charged carboxylate and the positively charged tetramethylammonium moiety: the <em>gauche</em> conformation allows the closest approach of the charged centers. <p>Given that the distance between the charged centers does not change much because the conformation is always folded, we expect only a small change in the dipole moment when hydrolyzing acetylcarnitine to carnitine (the dipole moments depend on charge separation). The results of the calculations confirm this suspicion; the global minimum in acetylcarnitine has a dipole moment of 12.15 D, and the global minimum in carnitine a dipole moment of 12.74 D. The hydroxyl group in carnitine could hydrogen bond to the carboxylate. A distance of 2.1 Ĺ separates a carboxylate oxygen from the hydroxylic proton. This indicates a weak hydrogen bond. <block> <head>Acetylcholine vs. choline. <p>The calculations reproduce the gauche effect: in both cases, the N-CH<sub>2</sub><strong>-</strong>CH-OH(Ac) torsion angle prefers a <em>gauche</em> conformation. The <em>gauche</em>/<em>anti</em> energy gap in choline is 1.76 kcal/mol, but in acetylcholine is only 0.28 kcal/mol. Conformers with the N-CH<sub>2</sub><strong>-</strong>CH-OH(Ac) torsion angle as <em>anti</em> make up about 15% of the population in acetylcholine compared to the 0.01% in choline. Differences in the inductive effects of a hydroxylic oxygen vs. an ester oxygen might explain the difference, given that the gauche effect relates to the electronegativity of the atoms X and Y that form the fragment X-C-C-Y. Conjugation of the ester oxygen with the carbonyl group can decrease the inductive effect exerted on the carbon. Such effect does not appear in the hydroxylic oxygen. <p>The dipole moments have a good correlation with stability: in both cases the global minimum has the lowest dipole moment, 5.9 D in acetycholine and 2.34 D in choline. <block> <head>Acetoxypropanoate vs. hydroxypropanoate. <p>Acetoxypropanoate prefers a folded conformation <link goesto="f.torsion">Note.</> in gas phase. This means that torsion B prefers a <em>gauche</em> conformation, but this should not be construed as an example of gauche effect because carboxylates do not have an inductive effect strong enough to cause gauche effect. <link goesto="b.Juaristi95">Juaristi, 1995</> 3-Hydroxypropanoate shows equal proportions of <em>g+</em> and <em>anti</em>. Hydrogen bonding between the carboxylate and the hydroxyl group seems to favor the <em>anti</em> conformation. The expected dipole moment decreases from 6.8 D to 5.4 D upon hydrolysis. <footnote id=f.torsion> We defined torsion angle B in the propanoates as H-C-C-COO<sup>-</sup>, taking the pro-R hydrogen. We did this to keep consistency with the terms <q>folded</q> and <q>extended</q>, and to yield an easier comparison of the torsions between different compounds. </footnote> <p>Steric effects and dipole moment reduction seem to control the conformational preference: the bulkiest groups (acetoxy and carboxylate) stay <em>anti</em> to each other, and the global minimum has the lowest dipole moment in acetoxypropanoate, 6.8 D and one of the lowest in hydroxypropanoate, 5.4 D. <block> <head>Carnitines vs. cholines. <p>The N-CH<sub>2</sub>-CH-OH(Ac) torsion is <em>anti</em> in 15% of the population of acetylcholine, while this conformation makes up approx. 50% of the population in acetylcarnitine. Torsion angles CH<sub>2</sub>-CH-O-H(Ac) and C-O-C(O)-CH<sub>3</sub> show parallel behavior: CH<sub>2</sub>-CH-O-H(Ac) prefers <em>g</em>, although in acetylcarnitine nearly 35% of the conformers have this torsion as <em>anti</em>. C-O-C(O)-CH<sub>3</sub> prefers <em>syn</em> (<em>s</em>) in all cases. <p>For carnitine vs. choline we observe no major differences in the preferred conformations: N-CH<sub>2</sub>-CH-OH(Ac) prefers <em>gauche</em>, although carnitine shows 1% of <em>anti</em> vs. the 0.01% for choline. CH<sub>2</sub>-CH-O-H(Ac) always prefers the <em>anti</em>. <block> <head>Carnitines vs. propanoates. <p>Acetylcarnitine has 100% of the population folded, acetoxypropanoate has 92% folded. Torsion CH<sub>2</sub>-CH-O-H(Ac) shows some variation, mostly because of the presence of several <em>anti</em> torsion angles in acetylcarnitine. Torsion angle C-O-C(O)-CH<sub>3</sub> shows opposite behavior in the two molecules: E prefers <em>s</em> in acetylcarnitine and <em>anti</em> in acetoxypropanoate. However, the global minima have the <q>same</q> conformation, as long as all the torsions in acetoxypropanoate have a corresponding torsion in acetylcarnitine. <p>In carnitine, 99% of the population is folded, vs. only 51% in hydroxypropanoate. <subsection> <head>Ab initio results in the gas phase. <p>We calculated the predominant conformations, found by AM1, at the RHF/6-31G* level of theory for both the zwitterions and the cations. Calculations for the anions used the 6-31+G basis set. We conducted full optimizations in the gas phase (see tables). In the following tables, the conformer designated as "1" is the global minimum by AM1, and "2" is the conformer next in energy above the global minimum. <link goesto="tableAM1631Gas">Table AM1 vs 6-31G* (gas)</> <float id=tableAM1631Gas> <table> <rowhead>Compound <row> <c>δE AM1 (kcal/mol) <c>δE HF/6-31G* (kcal/mol) <c>δE MP2 (kcal/mol) <c>μ AM1 (D) <c>μ HF/6-31G* (D) <c>μ MP2 (D) <rowhead>Acetylcarnitine 1 <row> <c>0.00 <c>0.00 <c>0.00 <c>12.15 <c>10.72 <c>10.72 <rowhead>Acetylcarnitine 2 <row> <c>0.20 <c>-0.66 <c>0.86 <c>12.66 <c>12.81 <c>12.81 <rowhead>Carnitine 1 <row> <c>0.00 <c>0.00 <c>0.00 <c>12.74 <c>12.22 <c>12.22 <rowhead>Carnitine 2 <row> <c>0.94 <c>-0.86 <c>-0.50 <c>13.42 <c>12.54 <c>12.54 <rowhead>Acetylcholine 1 <row> <c>0.00 <c>0.00 <c>0.00 <c>5.92 <c>6.16 <c>6.16 <rowhead>Acetylcholine 2 <row> <c>0.45 <c>0.55 <c>1.83 <c>6.20 <c>6.95 <c>6.95 <rowhead>Choline 1 <row> <c>0.00 <c>0.00 <c>0.00 <c>2.34 <c>1.86 <c>1.86 <rowhead>Choline 2 <row> <c>4.89 <c>4.46 <c>5.76 <c>4.10 <c>3.64 <c>3.64 <caption>Comparison of AM1 vs. 6-31G* calculations on carnitines and cholines in the gas phase. </float> <subsection> <head>Comparison of AM1 vs. ab initio. <p>We observe several differences between the ab initio and the semiempirical results. The acetylcarnitine global minimum by AM1 is a local minimum in the HF/6-31G* hypersurface, but the inclusion of electronic correlation reverses the effect. The dipole moments calculated by HF/6-31G* follow the same trend as those calculated by AM1. Most of the ab initio dipole moments approach closely the values obtained by AM1, with one exception (Acetylcarnitine 1), where the ab initio value is nearly 1.4 D lower than the semiempirical. The difference may be due to the lack of geometric optimization, meaning that we do not have a stationary point on the HF/6-31G* hypersurface, or probably due to the adjustment in the number of surface points included in the calculation. For more details, <link goesto="abinitio">refer to the Methods section</>. <float id=table2AM1631Gas> <table> <rowhead>Compound <row> <c>δE AM1 (kcal/mol) <c>δE HF/6-31+G (kcal/mol) <c>δE MP2 (kcal/mol) <c>μ AM1 (D) <c>μ HF/6-31+G* (D) <c>μ MP2 (D) <rowhead>Acetoxypropanoate 1 <row> <c>0.00 <c>0.00 <c>0.00 <c>6.68 <c>8.41 <c>8.41 <rowhead>Acetoxypropanoate 2 <row> <c>0.24 <c>0.00 <c>0.00 <c>6.64 <c>8.41 <c>8.41 <rowhead>Hydroxypropanoate 1 <row> <c>0.00 <c>0.00 <c>0.00 <c>5.37 <c>5.82 <c>5.82 <rowhead>Hydroxypropanoate 2 <row> <c>0.01 <c>0.00 <c>0.00 <c>5.37 <c>5.82 <c>5.82 <caption>Comparison of AM1 vs 6-31+G calculations on propanoates in the gas phase. </float> <p>The table shows that in the anions, correlation effects <link goesto="f.correl">Note.</> <footnote id=f.correl> The Hartree-Fock approximation does not include the Coulombic repulsion between the electrons of different spins. The Coulombic repulsion of the electrons makes the motions of the electrons depend on one another (<q>correlates</q> the motions). Inclusion of electronic correlation requires schemes that consider configuration interaction. For more details on the procedures, see the book by Szabo and Ostlund <link goesto="b.Szabo96">Szabo, 1996</>. </footnote> do not exert a great influence. Given that we did not use succesively higher levels of theory in the ab initio calculations to assess convergence, we cannot guarantee that correlation effects are not likely to change with higher levels of theory. More importantly to us, we observe that the trends of the MP2 calculations are the same as that of HF. We notice that the same geometries that AM1 calculated as different in energy, are degenerate by ab initio. This may be a reflection of the numerous convergence problems found when using AM1 on these anions. <subsection> <head>Conformational analyses including the effect of solvent. <p>We calculated the enthalpies of formation and dipole moments of acetylcarnitine, carnitine, acetylcholine, choline, 3-acetoxypropanoate and 3-hydroxypropanoate including the effect of solvent. We used full optimization in MOPAC93 using the COSMO solvent model, while the ab initio calculations involved single points at the RHF/6-31G* level of theory employing the solvent model developed by Tomasi. <link goesto="j.Miertus82">Miertus, 1982</>, <link goesto="j.Miertus81">Miertus, 1981</> <p>The following tables gather the semiempirical results: <ul> <li> <a href="carnitine/TableAcCarnAM1Wat.html">Acetylcarnitine in water.</></li> <li> <a href="carnitine/TableCarnAM1Wat.html">Carnitine in water.</></li> <li> <a href="carnitine/TableAcCholAM1Wat.html">Acetylcholine in water.</></li> <li> <a href="carnitine/TableCholAM1Wat.html">Choline in water.</></li> <li> <a href="carnitine/TableOAcPrAM1Wat.html">3-Acetoxypropanoate in water.</></li> <li> <a href="carnitine/TableOHPrAM1Wat.html">3-Hydroxypropanoate in water.</></li> </ul> <block> <head>Acetylcarnitine vs. carnitine <p>The N-CH<sub>2</sub>-CH-OH(Ac) torsion remains fairly constant, although we still see a slight favoring of the <em>anti</em> conformation in acetylcarnitine: conformers with the N-CH<sub>2</sub>-CH-OH(Ac) torsion angle <em>anti</em> make up almost 9% of the population in aceytlcarnitine, while in carnitine they account for less than 4%. <p>Regarding the CH<sub>2</sub>-CH-CH<sub>2</sub>-COO<sup>-</sup>, the extended conformation constitutes 39% of the population, almost as much as the 43% of the folded. In carnitine we see the situation reversed, with the extended predominating over the folded (61% vs. 27% respectively). Differences in solvation can explain this reversal, as solvation differences relate to polarity: as the distance between the charged centers in the molecule differs between the folded and the extended, we expect the calculated dipole moments to differ as well. In acetylcarnitine, the folded has a dipole moment of 26.67 D vs. the 29.90 D of the extended. In carnitine, the folded conformation has a dipole moment of 23.89 D vs. the 29.17 D of the extended. <p>There is little support for hydrogen bonding between the carboxylate and the hydroxyl groups in carnitine. In the global minimum (extended conformer), the carboxylic oxygen closest to the hydroxylic proton is 3.8 Ĺ away from it. The only conformer showing a O-HˇˇˇO distance adequate for hydrogen bonding (2.8 Ĺ) accounts for < 4% of the population. <block> <head>Acetylcholine vs. choline. <p><em>Anti</em> conformers of N-CH<sub>2</sub>-CH<sub>2</sub>-OH(Ac) make up about 4% of the population in acetylcholine. In choline, these conformers account for more than 9% of the population. Differential solvation might hold the key to this reversal in the conformational preference: the global minimum in acetylcholine (N-CH<sub>2</sub>-CH-OAc <em>g-</em>) has a dipole moment of 10.85 D, while the <em>anti</em> conformation of N-CH<sub>2</sub>-CH-OAc has a dipole moment of 9.24 D, a difference of 1.6 D. In choline, on the other hand, the global minimum (N-CH<sub>2</sub>-CH-OH <em>g-</em>) has a dipole moment of 5.25 D, while the <em>anti</em> conformer has a dipole moment of 5.07 D. The difference is now less than 0.2 D. We can see that solvation stabilizes the choline conformers to an almost equal extent, while in acetylcholine, the lower polarity of the <em>anti</em>-containing conformer increases the energy gap, by solvating more the global minimum. <block> <head>Acetoxypropanoate vs. hydroxypropanoate. <p>The H-C-C-COO- torsion prefers <em>g-</em>, although the <em>anti</em> and the <em>g+</em> each make up about 12% of the population. The C-C-C(O)-O- torsion does not change much upon hydrolysis, although hydroxypropanoate shows a much lower percentage of <em>g+</em>. The H-C-O-H(Ac) torsion prefers <em>anti</em> in both cases. Acetoxypropanoate in solution differs from gas phase by a greater stabilization of <em>anti</em> conformations in torsions CH<sub>2</sub>-CH-CH<sub>2</sub>-COO<sup>-</sup>, CH<sub>2</sub>-CH-O-H(Ac) and C-O-C(O)-CH<sub>3</sub>. <em>Anti</em> conformers of these torsion angles have the highest dipole moments in the gas phase (10 >μ< 14), so solvation reduces the energy gap to the point that the global minimum in solution accounts only for 0.06% of the population in the gas phase. The population of 3-hydroxypropanoate in solution differs from that in the gas phase because of a lower presence of the extended conformer. The dipole moment decreases from 16.07 D in acetoxypropanoate to 8.93 D in hydroxypropanoate. <block> <head>Carnitines vs. cholines. <p>Both acetylcarnitine and acetylcholine show gauche effects in the N-CH<sub>2</sub>-CH-OAc torsion. The CH<sub>2</sub>-CH-O-Ac torsion angle is <em>g-</em> in both global minima, but in acetylcarnitine it shows a greater population of <em>anti</em>. The CH-O-C(O)-CH<sub>3</sub> torsion angle is <em>syn</em>, with only one high energy conformer in acetylcarnitine that shows it in <em>anti</em>. The main difference between carnitine and choline is due to the chirality of carnitine: the N-CH<sub>2</sub>-CH-OH(Ac) torsion angle prefers the <em>g-</em> over the <em>g+</em>, while choline shows equal populations of <em>g+</em> and <em>g-</em>. The CH<sub>2</sub>-CH-O-H torsion angle is always <em>anti</em> in choline, but it prefers <em>g-</em> in carnitine. <block> <head>Carnitines vs. propanoates. <p>In general, the carnitines show a greater proportion of <em>anti</em> torsions than the propanoates. The conformer that corresponds to the global minimum in acetoxypropanoate, accounts for 0.01% of the population in acetylcarnitine. <em>Anti</em> torsion CH<sub>2</sub>-CH-CH<sub>2</sub>COO<sup>-</sup> comprises 50% of the population in acetylcarnitine, 60% in carnitine, 23% in acetoxypropanoate and 48% in hydroxypropanoate. <subsection> <head>Ab initio results including solvent. <p>We compare AM1/COSMO vs. 6-31G*/Tomasi in the following <link goesto="table1AM1631Wat">table</> <float id=table1AM1631Wat> <table> <colhead>Compound <column> <c>Acetylcarnitine folded <c>Acetylcarnitine extended <c>Carnitine extended <c>Carnitine folded <c>Acetylcholine 1 <c>Acetylcholine 2 <c>Choline 1 <c>Choline 2 <colhead>δE AM1/COSMO <column> <c>0.00 <c>0.10 <c>0.00 <c>0.60 <c>0.00 <c>0.15 <c>0.00 <c>0.94 <colhead>δE 6-31G*/Tomasi <column> <c>0.00 <c>5.24 <c>0.00 <c>-4.63 <c>0.00 <c>2.05 <c>0.00 <c>0.82 <colhead>μ AM1/COSMO <column> <c>26.7 <c>29.9 <c>29.2 <c>23.9 <c>10.9 <c>9.4 <c>5.3 <c>5.1 <colhead>μ 6-31G*/Tomasi <column> <c>26.7 <c>29.5 <c>28.9 <c>23.6 <c>10.4 <c>9.0 <c>5.0 <c>4.7 <caption>Comparison of AM1 vs. 6-31G* calculations on carnitines and cholines in water. </float> <link goesto="table2AM1631Wat">table</> <float id=table2AM1631Wat> <table> <colhead>Compound <column> <c>Acetoxypropanoate 1 <c>Acetoxypropanoate 2 <c>Hydroxypropanoate 1 <c>Hydroxypropanoate 2 <colhead>δE AM1/COSMO <column> <c>0.00 <c>0.18 <c>0.00 <c>0.10 <colhead>δE 6-31+G/Tomasi <column> <c>0.00 <c>0.90 <c>0.00 <c>1.51 <colhead>μ AM1/COSMO <column> <c>17.4 <c>14.65 <c>9.2 <c>9.1 <colhead>μ 6-31+G/Tomasi <column> <c>18.65 <c>15.67 <c>9.92 <c>9.81 <caption>Comparison of AM1 vs. 6-31+G calculations on propanoates in water. </float> <p>The 6-31G* calculations were single points on the geometries optimized by AM1/COSMO. We wanted to assess the ability of the combination AM1/COSMO to reproduce the change in dipole moment when going from gas phase to solution. The <link goesto="tableAM1631Gas">gas phase results</> indicate the need for inclusion of correlation effects. We found such optimization prohibitively long, and the full conformational search by ab initio is at present beyond the computational resources available to us. <subsection> <head>Thermochemical calculations from semiempirical results. <p>We can calculate the expected enthalpies of hydrolysis. (See <link goesto="tableHhyd">table.</>) <float id=tableHhyd> <table> <colhead>Compound <column> <c>Acetylcarnitine <c>Acetylcholine <c>Acetoxypropanoate <colhead>AM1 <column> <c>-7.43 <c>-3.06 <c>-4.02 <colhead>Exp. unbuffered H<sub>2</sub>O <column> <c><link goesto="j.Muller73">-4.63</> <c><link goesto="j.Muller73">-3.20</> <c>n.a. <colhead>Exp. buffered pH=7.0 <column> <c><link goesto="j.Muller73">-14.67</> <c><link goesto="j.Muller73">-13.00</> <c>n.a. <caption>Comparison of δH<sub>hydr</sub> (kcal/mol) calculated at ε=78.3 vs. calorimetric values. </float> From the previous table, we observe that the semiempirical results for the carnitines agree moderately well with the experimental values in unbuffered solution. The results for the cholines show good agreement with the experimental values. <p>The expectation values for both dipole moments and solvation energies, calculated by using Boltzmann's equation are displayed in the following <link goesto="tableDipvsHF">table</>. <float id=tableDipvsHF> <table> <colhead>Compound <column> <c>Acetylcarnitine <c>Carnitine <c>Acetylcholine <c>Choline <c>Acetoxypropanoate <c>Hydroxypropanoate <c>Acetic acid <c>Water <colhead>μ (D) <column> <c>27.90 <c>27.12 <c>9.89 <c>4.79 <link goesto="j.Maurel71">2.65 exp.</> <c>16.07 <c>8.93 <c>6.40 <c>2.22 <colhead>δH°<sub>solv</sub> (kcal/mol) <column> <c>-64.76 <c>-62.35 <c>-59.30 <c>-54.87 <c>-94.54 <c>-90.06 <c>-17.02 <link goesto="j.Wilson91">-12.7 exp.</> <c>-9.22 <link goesto="b.BenNaim87">-9.98 exp.</> <caption>Expectation values for Dipoles (μ) and Enthalpies of Solvation (δH°<sub>solv</sub>) </float> <p>The variation in the enthalpies of solvation parallels that in the dipole moments: a smaller decrease in dipole moment upon hydrolysis (0.78 D for acetylcarnitine vs. 5.1 D for acetylcholine and 7.1 D in acetoxypropanoate) corresponds to a smaller decrease in enthalpy of solvation (-2.41 kcal/mol in acetylcarnitine vs. -4.43 kcal/mol for acetylcholine and -4.48 kcal/mol in acetoxypropanoate). <p>The calculated <term>Boltzmann factors (F)</term> for the conformers indicate that the N-CH<sub>2</sub>-CH-OH(Ac) torsion prefers <em>g-</em> (>90%) for both acetylcarnitine and carnitine, thus we focus mostly on the CH<sub>2</sub>-CH-CH<sub>2</sub>-COO<sup>-</sup> torsion: AM1 shows that in acetylcarnitine 37% of the population is extended, and 41% of the population is folded. The values for carnitine are 57% extended and 18% folded. As acetylcarnitine loses its acetyl group through hydrolysis, the carnitine backbone goes from folded to extended. Such conformational change implies a change in the dipole moment, reflected by the AM1 calculations. The expectation values for the dipole moments of these compounds are gathered in the <link goesto="tableDipvsHF">table</> <p>We can highlight the results stated above for acetylcarnitine in the following figure: <float id=highlight> <mm entity=fig.highlight>fig.highlight.gif, 4.852KB <caption>Changes in population and dipole moments upon hydrolysis. </float> <p>We cannot draw a similar figure for acetylcholine and 3-acetoxypropanoate because of the lack of the methylenecarboxylate group, but we present the differences in expectation values for the enthalpies of solvation of the three acetates in the following figure: <float id=solvation> <mm entity=fig.solvation>fig.solvation.gif, 4.823KB <caption>Differences in the energies of solvation for acetylcarnitine, acetylcholine and 3-acetoxypropanoate. </float> The values between brackets are expectation values calculated using the complete Boltzmann populations. The upper values are enthalpies of hydration in kcal/mol, while the lower values are the expectation values for the dipole moments in Debyes. <p>We see that the dipole moment stays nearly constant for the carnitines (change <0.8 D). For the cholines, the dipole moment suffers a reduction of about 5.0 D, while for the propanoates the dipole reduction amounts to approximately 7.0 D. These lower polarities in choline and hydroxypropanoate imply an additional work (of desolvation) that consumes part of the free energy available from these reactions. Change in free energy measures the work obtainable from a process; thus, <em>the hydrolysis of acetylcholine yields a lower available work than that of acetylcarnitine because part of the free energy change in acetylcholine hydrolysis is spent desolvating the product (lower polarity choline).</em> We could apply a similar argument to acetoxypropanoate, but we cannot compare against experiment due to lack of experimental data. <p><strong>Summary</strong>: Changes in polarity coupled to conformational changes can influence deeply the thermodynamics of reactions through differential solvation. Electroneutrality does not guarantee small solvation effects. Calculations have to account for the presence of charged centers, together with the influence in molecular polarity that such centers exert, to understand correctly the thermodynamics of charged systems. <subsection> <head>Modeling of tetrahedral intermediate: preliminary results. <p>We modeled the tetrahedral intermediate suggested by Gandour <link goesto="j.Gandour85">Gandour, 1985</> to see the geometry of the preferred conformation. Because the attack of the sulfide on the carbonyl group generates a chiral center, we considered both diastereomers generated by the (<em>R</em>) configuration of carnitine (<em>R,R</em>) and (<em>R,S</em>) in GB/SA water. These results are preliminary, because we looked only for the global minimum, not concerning ourselves with finding all the conformers within 3.0 kcal/mol. <p>The conformational searches yielded the following global minima: <float id=RSWat> <mm entity=fig.RSWat>fig.RSWat.gif, 0.807KB <caption>Global minimum for (<em>R,S</em>) tetrahedral intermediate in GB/SA water. </float> <float id=vrmlRSWat> <mm entity=VR.RSWat>RSWat.wrl, 16.938KB <caption>3D Model of the <em>R,S</em> tetrahedral intermediate in GB/SA water. </float> <float id=RRWat> <mm entity=fig.RRWat>fig.RRWat.gif, 0.801KB <caption>Global minimum for (<em>R,R</em>) tetrahedral intermediate in GB/SA water. </float> <float id=vrmlRRWat> <mm entity=VR.RRWat>RRWat.wrl, 17.048KB <caption>3D Model of the <em>R,R</em> tetrahedral intermediate in GB/SA water. </float> <p>We then determined the RMS deviations after least-squares fit to the global minima obtained from the <link goesto="ConfPhosp">conformational searches for the phosphonate rings</>. The results are displayed in the table below: <float id=tableTIWat1> <table> <colhead>Diastereomer <column> <c><em>R,S</em> <c><em>R,R</em> <colhead>Unsubstituted ring. <column> <c>0.438, 0.685 <c>0.619, 0.600 <colhead><em>Cis</em>-substituted ring. <column> <c>0.384, 0.809 <c>0.716, 0.548 <colhead><em>Trans</em>-substituted ring. <column> <c>0.767, 0.822 <c>0.931, 1.017 <colhead>Dimethyl substituted ring. <column> <c>0.322, 0.834 <c>0.731, 0.537 <caption>RMS deviation after least-squares fitting of global minimum of rings to global minimum of intermediate in GB/SA water. </float> <p>The first value in each cell corresponds to the fitting of the <em>oxo</em> oxygen on the phosphorus to the negatively charged oxygen (for the <em>R,S</em> isomer) or the methyl group on the TI (for the <em>R,R</em> isomer) in the tetrahedral intermediate. The second value corresponds to the matching of the <em>oxo</em> oxygen on the phosphorus to the sulfur atom in the intermediate (for both diastereomers). This is equivalent to saying that both halves of the ring compounds were used in the fit. The atoms used were: <float id=FitTI> <mm entity=fig.fitTI>fig.fitTI.gif, 1.511KB</mm> <caption>Atom pairs used in the least squares fit between the phosphonate rings and the tetrahedral intermediate. </float> The <em>oxo</em> oxygen on the phosphorus could be matched to any of the atoms marked with asterisks. For more details, see the <link goesto="LSFit">Methods</> section. <p>The greater RMS values obtained when matching oxygen to sulfur atom should not be discarded offhand. S-C bonds (1.85 Ĺ) are longer than C=O bonds (1.46 Ĺ), so the difference influences significantly the final RMS value. <p>The following table displays the RMS values for the second most populated conformation in GB/SA water and the global minimum of the TI. The first value in each cell corresponds to the fitting of the <em>oxo</em> oxygen on the phosphorus to the methyl group on the TI, unless specified otherwise. The second value on each cell corresponds to the matching of the <em>oxo</em> oxygen on the phosphorus to the sulfur atom in the intermediate (in all cases). <float id=tableTIWat2> <table> <colhead>Diastereomer <column> <c><em>R,S</em> <c><em>R,R</em> <colhead>Unsubstituted ring. <column> <c>0.471, 0.630 <c>0.975, 1.009 <colhead><em>Cis</em>-substituted ring. <column> <c>0.740, 0.935 <c>0.975, 1.011 <colhead><em>Trans</em>-substituted ring. <column> <c>0.388, 0.747 <c>0.652, 0.577 <colhead>Dimethyl substituted ring. <column> <c>1.201, 1.032 <c>1.097, 1.092 <caption>RMS deviation after least-squares fitting of second most populated conformer of ring to global minimum of intermediate in GB/SA water. </float> <p>To give us an idea of the best possible fit, we did a least-squares fitting of the tetrahedral center in the intermediate to dimethyl methylphosphonate. If we match the <em>oxo</em> group on phosphorus to the negatively charged oxygen in the intermediate, the RMS value is 0.227. If we match the <em>oxo</em> oxygen to the sulfur atom on the intermediate, the RMS value is 0.203. We note that the conformation around the tetrahedral center matched the <link goesto="tableRelEn"><em>g+,a</em></> conformer of dimethyl methylphosphonate, which is not a stationary point either by ab initio, or by AMBER*. The fit included only the heavy atoms around the phosphorus, not including the carbons attached to the oxygens. <chapter> <head>Effects of heteroatoms on conformational stability. <p>Here follows a general exposition of the changes in conformational behavior induced by the introduction of heteroatoms, according to the following scheme: <ul> <li>General effects of introduction of heteroatoms.</li> <li>The anomeric effect.</li> <li>The gauche effect.</li> </ul> <section> <head>General effects of introduction of heteroatoms. <p>The first difference between hydrocarbon rings and their hetero-substituted analogs resides in the different bond lengths and bond angles involving the heteroatoms. Shorter distances, such as those of C-N and C-O bonds, increase the van der Waals repulsion among substituents in the ring. Longer distances between substituents, as those provided by C-P and C-S bonds, relieve van der Waals repulsions. Heteroatoms differ from carbon in the number of substituents they can bond to. This difference affects directly the energies of eclipsing interactions within the ring. <p>Differences in electronegativity introduce dipolar bonds, and the orientation of the resulting dipoles can change the relative stabilities within a series of conformers (<em>e.g.</em>, in side-by-side dipoles, antiparallel orientation reduces Coulombic repulsions, yielding a lower energy than a parallel orientation). In general, dipoles interact to yield the smallest possible total dipole. The lowest energy conformers tend to have the smallest dipole moments. <link goesto="f.Perrin95">Note.</> <footnote id=f.Perrin95>However, Perrin <link goesto="j.Perrin95">Perrin, 1995</> has shown two counterexamples to the commonly accepted assertion that the conformer with the <em>largest</em> dipole moment is always the <em>least</em> stable. </footnote> Polar solvents better stabilize conformers of greater polarity as compared to the least polar ones. Given that the solvation of a molecule depends strongly on its polarity, solvation affects the energy gap between conformations possessing opposing dipoles and the ones containing parallel dipoles, (see p.747 on Eliel, Wilen and Mander's book <link goesto="b.Eliel94">Eliel, 1994</>). As different atoms have orbitals with different energies, accounting for stereoelectronic factors, such as orbital overlap, can help understand the conformations of heterocycles. The anomeric effect provides the best known case of such an interaction. <p>Consideration of the lone pairs present on certain heteroatoms requires an interaction model. The debate centers on the best description of the lone pairs density: as unhybridized n<sub>σ</sub> and n<sub>p</sub> orbitals, or as <em>sp<sup>3</sup></em> hybrids. Although equivalent in many respects, the models differ in the directionality of the lone pairs. <em>sp<sup>3</sup></em>-Hybridized orbitals are directionally equivalent, while the unhybridized orbitals are not. Each model requires different spatial dispositions for optimal overlap. Laing has compiled theoretical and experimental evidence <link goesto="j.Laing87">Laing, 1987</> supporting the nonequivalence of the lone pairs. Kirby <link goesto="b.Kirby83">Kirby, 1983</> has discussed the differences that arise between the two models, concluding that both are equivalent energetically speaking, so the choice of a particular description is done better on a <foreign>per case</foreign> basis. <section> <head>The anomeric effect. <p>This review follows the main lines of a similar one in the book by Juaristi and Cuevas. <link goesto="b.Juaristi95">Juaristi, 1995</> Edward <link goesto="j.Edward55">Edward, 1955</> <link goesto="b.Chu59">Chu, 1959</> reported on the axial preference of an alkoxy substituent in pyranoses, instead of the equatorial orientation one would expect from comparison with hydrocarbon systems. This behavior received the designation of <term>anomeric effect</term>. Later experimental results pointed to the existence of a similar phenomenon in compounds other than sugars, calling this effect the <term>generalized anomeric effect</term>. The generalized anomeric effect appears whenever a molecule possesses a fragment with the formula: R-Z-X-Y, where R is an alkyl group or hydrogen, X is an atom of intermediate electronegativity (C, Si, P, S among others), Y is an atom of stronger electronegativity than X (usually O, N or halogen (Hal)) and Z is an atom with lone pairs. By the previous criteria, we can suggest several common molecular fragments expected to show an anomeric effect: <strong>R-O-C-O</strong>, R-O-C-N, R-O-C-S, R-O-C-Hal, R-N-C-O, R-N-C-Hal, <strong>R-S-C-O</strong>, <strong>R-O-P-O</strong>, R-O-P-N and R-O-P-Hal among others. <p>In addition to the marked axial preference of oxygenated substituents on pyranose rings, some researchers report <link goesto="j.Lemieux69">Lemieux, 1969</> that polar solvents preferentially stabilize the more polar conformer (equatorial). The anomeric effect results in altered bond lengths and bond angles, specifically, the axial bond is shorter than usual, while the equatorial bond is longer. An electronic model, proposed early by Edward <link goesto="j.Edward55">Edward, 1955</> suggests that the repulsive interaction between the ring dipole and nearly parallel polar bonds in the equatorial conformer constitute the dominating forces in the preference for the axial position. Juaristi <link goesto="b.Juaristi95">Juaristi, 1955</> has criticized Edward's hypothesis on the grounds that it cannot explain the variations on bond lengths and angles. Juaristi favors a stereoelectronic interpretation suggested by Altona. <link goesto="j.Altona63">Altona, 1963</> <link goesto="b.Romers69">Romers, 1969</> The stereoelectronic hypothesis attributes the anomeric effect to mixing of the nonbonding electrons on oxygen with the antiperiplanar antibonding σ<sup>*</sup> orbital in C-Y, involving a stereoelectronic interaction of type n<sub>Z</sub> ----> σ<sup>*</sup><sub>C-Y</sub>. Hyperconjugation (no-bond/double-bond resonance) can help us visualize the effect of the electron transfer involved in this interaction. Kirby <link goesto="b.Kirby83">Kirby, 1983</> expressed this as <q>there is a stereoelectronic preference for conformations in which the best donor lone pair is antiperiplanar to the best acceptor bond.</q> <float id=anomeric> <mm entity=fig.anomeric>fig.anomeric.gif, 1.774KB <caption>Orbital and hyperconjugation description of the anomeric effect. </float> <section> <head>The gauche effect. <!-- README It would be nice to be able to <target> a <head>. In this case I had to target the term itself, instead of the head of the section, although the target should actually point to the whole section. --> <p>Polar factors can markedly bias a conformation, such as in the case of the well-known gauche effect. <link goesto="j.Sundaralingam68">Sundaralingam, 1968</> <target id=gaucheeff>The <term>gauche effect</term> is the preference, usually 1-2 kcal/mol, that 1,2-disubstituted ethanes show for the <em>gauche</em> conformation, as opposed to the <em>anti</em> conformation preferred by butane</target>. Wolfe <link goesto="j.Wolfe72">Wolfe, 1972</> has described it as: <blockquote><q>(. . .)when electron pairs or polar bonds are placed on adjacent pyramidal atoms, <em>syn</em>- or <em>anti</em>-periplanar orientations are disfavoured energetically with respect to that structure which contains the maximum number of <em>gauche</em> interactions.</q></blockquote> <p>Based on steric grounds, the <em>anti</em> conformation has greater stability. The gauche effect shows up in molecules containing the unit: X-C-C-Y, where X and Y are groups more electronegative than carbon (N, O or halogen). Wolfe rationalized the gauche effect by postulating that nuclear-electron attraction between X and Y dominated over nuclear-nuclear and electron-electron repulsions. Baddeley preferred to extend Altona's explanation of the anomeric effect, arguing that the gauche effect arises from σ ---> σ<sup>*</sup> orbital interactions that stabilize the <em>gauche</em> conformation. This interaction implies a no-bond/double-bond resonance model. Dionne and St-Jacques <link goesto="j.Dionne87">Dionne, 1987</> used Baddeley's argument to justify the preference for the twist-boat conformation in 3-substituted-1,5-benzodioxepines in CHF<sub>2</sub>Cl. Based on calculated bond paths, Wiberg and Murcko <link goesto="j.Wiberg90">Wiberg, 1990</> have suggested that the gauche effect originates in "bent" bonds, due to the greater electronegativity of the 1,2 substituents. This model implies a destabilization of the <em>anti</em> conformer, as opposed to the stabilization of the <em>gauche</em> conformer suggested by hyperconjugation. <section> <head>Conformational analysis of heterocycles. <subsection> <head>Six-membered rings. <p>The conformational analysis of compounds containing six-membered rings has been a favorite topic for organic research; thus, we have not attempted an exhaustive coverage of the literature. This section only summarizes the background needed for an understanding of the conformational behavior described in this dissertation. The interested reader can find the fundamentals in the excellent textbook by Eliel, Wilen and Mander <link goesto="b.Eliel94">Eliel, 1994</> while some finer points regarding conformational interconversion between chair and non-chair conformers are covered by Kellie and Riddell, <link goesto="b.Kellie74">Kellie 1974</> and Anderson. <link goesto="b.Anderson74">Anderson, 1974</> <p>We can assign steric energies to any substituent attached to a six-membered ring. These steric energies are usually additive, a scheme that aids in the estimation of conformational stabilities. However, geminal substitution tends to break simple additivity: one group interferes with the free rotation of its geminal neighbor so the optimal conformation of a substituent may change when adding a geminal neighbor. <p>Weiser <em>et al.</em> <link goesto="j.Weiser96">Weiser, 1996</> employed MM3(92) to study the conformational behavior of polyalkylated cyclohexanes, focusing mostly on how substituents affect the chair/twist-boat energy gap. They determined that <blockquote>(. . .) two methyls and two isopropyl groups are sufficient for rendering the twist-boat form the minimum energy conformation (. . .)</blockquote> and determined <em>cis,trans,trans</em>-1,2-diisopropyl-3,4-dimethylcyclohexane; <em>cis,syn,cis</em>-1,2-diisopropyl-4,5-dimethylcyclohexane and <em>cis,syn,cis</em>-1,4-diisopropyl-2,5-dimethylcyclohexane as the less crowded cyclohexanes that prefer a twist-boat (0.8 kcal/mol lower in energy than the chair). <p>For geminally substituted cyclohexanes, the magnitudes of the energy gaps calculated by MM3 were: cyclohexane, 6.2 kcal/mol; <link goesto="j.Aped92">Aped, 1992</> 1,1-dimethylcyclohexane, 5.7 kcal/mol; 1,1,3,3-tetramethylcyclohexane, 5.0 kcal/mol. <p>Mursakulov <em>et al.</em> <link goesto="j.Mursakulov84">Mursakulov, 1984</> used MM2 to study 2-substituted-1,1-dimethylcyclohexanes. They found that <em>gem</em> substitution flattens the ring. They also found a <q>negligibly small</q> amount of twist-boat in 1,1,2-trimethylcyclohexane (4.6 kcal/mol higher in energy than the chair). All these calculations simulated gas phase. Dalling's <link goesto="j.Dalling67">Dalling, 1967</> NMR results in solution, indicate an appreciable contribution of the twist-boat. <p>Kolossváry and Guida <link goesto="j.Kolossvary93">Kolossváry, 1993</> did a comprehensive conformational search on cyclohexane using MM2*. <footnote id=mm2mac> MM2* is the modification of the MM2 force field included in the package MacroModel. </footnote> Some of their results are gathered in the <link goesto="tableCyclohex">table below</>. <float id=tableCyclohex> <table> <colhead>Conformation <column> <c>Chair <c>Twist-boat <c>Boat <c>Half-chair <colhead>MM3(92) <column> <c>0.00 <c>6.2 <c>n.d.<link goesto="ND">*</> <c>n.d.<link goesto="ND">*</> <colhead>MM2* <column> <c>0.00 <c>5.35 <c>6.45 <c>10.51 <caption>Comparison of relative energies in the gas phase (kcal/mol) of cyclohexane conformations. </float> <footnote id=ND> *not determined </footnote> <p>Sieburth <link goesto="j.Sieburth94">Sieburth, 1994</> analyzed crystal structures and molecular mechanics evidence on cyclohexene-like cyclohexanes and observed a correlation between the internal bond angles and the preference for a boat over a half-chair. He concluded that partially flattened cyclohexanes prefer a boat conformation when the average value of the internal bond angles approaches 114°. As the same average approaches 117.5°, the half-chair becomes preferred. <subsection> <head>Eight-membered rings. <p> <link goesto="f.eightname">Note.</> <footnote id=f.eightname> We discuss the behavior of eight-membered heterocycles by using cyclooctane as a reference structure. A note on nomenclature is in order: Hendrickson developed the most generally employed nomenclature for cyclooctane conformations. <link goesto="j.Hendrickson64">Hendrickson, 1964</> His system visualizes the conformations of cyclooctane as formed by cyclohexane components. Anet <link goesto="b.Anet74">Anet, 1974</> prefers the scheme suggested by Roberts <link goesto="j.Anderson69">Anderson, 1969</> because Hendrickson's scheme leaves the S<sub>4</sub> conformer without an appropriate name. For that reason, we prefer Roberts's naming scheme throughout this dissertation. The naming of the S<sub>4</sub> conformer is the only difference between Hendrickson's and Roberts's schemes. </footnote> <p>Molecular mechanics calculations in the gas phase show that the conformational hypersurface of cyclooctane has at least ten possible stationary points. <link goesto="j.Hendrickson64">Hendrickson, 1964</> <link goesto="j.Hendrickson67">Hendrickson, 1967</> <link goesto="j.Kolossvary93">Kolossváry, 1993</> We can split these conformers into three families: chair-chair, boat-boat and boat-chair. We depict the conformers of cyclooctane by the usual perspective drawings and by their Weiler plots <link goesto="j.Ounsworth87">Ounsworth, 1987</> as Weiler plots are specially clear bidimensional representations of ring conformation. <term>Weiler plots</term> depict the internal torsion angles of a ring in the form of a radar plot. We took all the values of the torsions from Hendrickson's paper to use in the <q>standard</q> Weiler plots. <link goesto="j.Hendrickson67">Hendrickson, 1967</> <p><term>Chair-chair</term>. <ul> <li> <float id=crown> <mm entity=fig.crown>fig.crown.gif, 3.852KB <caption><strong>Crown</strong> (D<sub>4<em>d</em></sub>) </float> <li> <float id=chair-chair> <mm entity=fig.cc>fig.cc.gif, 2.539KB <caption>Chair-chair, <strong>CC</strong> (C<sub>2<em>v</em></sub>) </float> <li> <float id=twist-chair-chair> <mm entity=fig.tcc>fig.tcc.gif, 2.446KB <caption>Twist-chair-chair, <strong>TCC</strong> (D<sub>2</sub>) </float> <li> <float id=twist-chair> <mm entity=fig.tc>fig.tc.gif, 2.500KB <caption>Twist-chair, <strong>TC</strong> (C<sub>2<em>v</em></sub>) </float> <li> <float id=chair> <mm entity=fig.c>fig.c.gif, 2.416KB <caption>Chair, <strong>C</strong> (C<sub>2<em>h</em></sub>) </float> </ul> <term>Boat-chair</term>. <ul> <li> <float id=boat-chair> <mm entity=fig.bc>fig.bc.gif, 2.304KB <caption>Boat-chair, <strong>BC</strong> (C<sub><em>s</em></sub>) </float> <li> <float id=twist-boat-chair> <mm entity=fig.tbc1>fig.tbc1.gif, 2.639KB</mm> <mm entity=fig.tbc-1>fig.tbc-1.gif, 2.601KB</mm> <caption>Twist-boat-chair, <strong>TBC</strong> (C<sub>2</sub>) </float> </ul> <term>Boat-boat</term>. <ul> <li> <float id=boat-boat> <mm entity=fig.bb>fig.bb.gif, 2.486KB <caption>Boat-boat, <strong>BB</strong> (D<sub>2<em>d</em></sub>) </float> <li> <float id=twist-boat> <mm entity=fig.tb>fig.tb.gif, 2.426KB <caption>Twist-boat, <strong>TB</strong> (S<sub>4</sub>) </float> <li> <float id=boat> <mm entity=fig.b>fig.b.gif <caption>Boat, <strong>B</strong> (D<sub>2<em>d</em></sub>) </float> </ul> <p>Most calculations indicate BC as the global minimum in cyclooctane. <link goesto="j.Bixon67">Bixon, 1967</> <link goesto="j.Hendrickson67">Hendrickson, 1967</> <link goesto="j.Allinger68">Allinger, 1968</> <link goesto="j.Kolossvary93">Kolossváry, 1993</> This agrees with X-ray structural determinations of substituted cyclooctane rings, where the BC conformation predominates. Wiberg constitutes the exception, <link goesto="j.Wiberg65">Wiberg, 1965</> finding the BC 0.25 kcal/mol higher in energy than the TCC. After reviewing dynamic NMR, X-ray and computational results for cyclooctanes, Anet <link goesto="b.Anet74">Anet, 1974</> concluded that <blockquote> (. . .) most 'simple' cyclooctanes, including ketones and heterocyclic analogues, exist predominantly in BC conformations.</blockquote> <p>Reports differ, though, in the energetic ranking of other conformers. The latest results by Kolossváry and Guida, <link goesto="j.Kolossvary93">Kolossváry, 1993</> who employed the MM2* <link goesto="j.Allinger77">Allinger, 1997</> force field, indicated the TCC approximately 1.0 kcal/mol above the BC. Other researchers have reported the TCC form as 1.7 <link goesto="j.Hendrickson67">Hendrickson, 1967</>, 1.89 <link goesto="j.Bixon67">Bixon, 1967</>, -0.25 <link goesto="j.Wiberg65">Wiberg, 1965</> and 2.20 <link goesto="j.Anet71">Anet, 1971</> kcal/mol higher in energy than the BC. <p>The crown is another conformation thought to be significantly populated in cyclooctane. Again, we find differences in the reported energies relative to the BC: 2.8 <link goesto="j.Hendrickson67">Hendrickson, 1967</>, 3.62 <link goesto="j.Bixon67">Bixon, 1967</>, 0.26 <link goesto="j.Wiberg65">Wiberg, 1965</> and 2.09 <link goesto="j.Anet71">Anet, 1971</> kcal/mol higher in energy than the BC. Kolossváry did not report finding the crown conformer. <p>Anet and Yavari <link goesto="j.Anet72">Anet, 1972</> studied <a href="reviews/fig.oxo.gif">oxocane (fig.oxo.gif, 0.414KB)</a>, <a href="reviews/fig.dioxo.gif">1,3-dioxocane (fig.dioxo.gif, 0.411KB)</a>, <a href="reviews/fig.trioxo.gif">1,3,6-trioxocane (fig.trioxo.gif, 0.420KB)</a>, <a href="reviews/fig.tetraoxo.gif">1,3,5,7-tetraoxocane (fig.tetraoxo.gif, 0.432KB)</a>, by <sup>1</sup>H NMR. 1,3-dioxocane showed a single BC conformation, while the two other compounds showed a mixture of two conformations. The authors could not identify positively the conformations, but they argued for a TCC or a crown, in equilibrium with a distorted BC. They reasoned that transannular repulsions between the oxygen atoms would destabilize the BC conformers. <p>Dale <em>et al.</em> <link goesto="j.Dale72">Dale, 1972</> studied by <sup>1</sup>H NMR the conformational behavior in CDCl<sub>3</sub> and CHFCl<sub>2</sub> of 1,3,5,7-tetraoxocane, 2,2- or 6,6-disubstituted-1,3,6-trioxocanes and 2,2,6,6-tetrasubstituted-1,3-dioxocanes, including <a href="reviews/fig.22dioxo.gif">2,2-dimethyl-1,3-dioxocane (fig.22dioxo.gif, 0.516KB)</a>, <a href="reviews/fig.66dioxo.gif">6,6-dimethyl-1,3-dioxocane (fig.66dioxo.gif, 0.530KB)</a> and <a href="reviews/fig.2266dioxo.gif">2,2,6,6-tetramethyl-1,3-dioxocane (fig.2266dioxo.gif, 0.573KB)</a>. Their findings led them to conclude that incorporation of a 1,3-dioxa moiety does not suffice to favor the BB over the BC, but geminal substitution at position 6 is also necessary. Geminal substitution on the 2 position had little effect on determining the preferred conformer. <p>Armarego reviewed extensively the stereochemistry of heterocyclic compounds. <link goesto="b.Armarego77">Armarego, 1977</> He showed that oxocanes, in general, prefer a BC conformation, sometimes with substantial amount of the crown. Special substitution patterns, such as in 2,4,6,8-tetrakis(trischloromethyl)-1,3,5,7-tetraoxocane can bias the global minimum to the crown form. Thiocanes also prefer the BC, but the crown form is destabilized, as compared to oxocanes. <p>Riddell discussed briefly the conformational behavior of eight-membered rings, both saturated and heterocyclic. <link goesto="b.Riddell80">Riddell, 1980</> Based on X-ray data, he concluded that, in general, heterocyclic eight-membered rings adopt either a crown or a BC conformation. Both conformations are generally regarded as the most populated conformations in cyclooctane. <p>Moore and Anet reviewed the dynamics of hydrocarbon and heteroatom-substituted eight-membered rings. <link goesto="b.Moore84">Moore, 1984</> The BC conformer predominated in oxocane, according to NMR data, although the position of the oxygen was not well-defined, opening the possibility for several BC conformations coexisting in solution. The crown conformer constituted a minor part of the population. <p>Quin thoroughly reviewed conformational analyses of medium-sized heterocycles. <link goesto="b.Quin88">Quin, 1988</> 1,3,6-Dioxaza- and 1,3,6-dioxaphospha-2-oxide phosphocanes preferred to crystallize as crowns. In 2-oxo-1,3,6-trioxaphosphocane a CC conformation predominated at room temperature, as determined by <sup>31</sup>P NMR. In 1,3-dioxa-6-thia-2-phosphocane the most abundant conformer was the crown. <p>In their review of nitrogen heterocycles, Alder and White conclude that azacanes with one nitrogen atom prefer the BC. <link goesto="b.Alder88">Alder, 1988</> Nevertheless, additional heteroatoms give rise to a preference for other conformations, such as in the case of the explosive HMX. HMX prefers a CC global minimum. <float id=hmx> <mm entity=fig.hmx>fig.hmx.gif, 0.823KB <caption>Structure of explosive HMX. </float> <p>Kolossváry and Guida <link goesto="j.Kolossvary93">Kolossváry, 1993</> did a comprehensive conformational search on cyclooctane. They reported the energetic ranking as follows: BC, 0.00; TCC, 0.96; CC, 1.14; TBC (minimum), 1.67; TBC (saddle), 2.80; TB, 3.13; BB, 3.56; C, 7.50 kcal/mol. <p>In summary, eight-membered rings prefer a BC conformer as global minimum, but heteroatom substitution can shift the preference towards a member of the chair-chair family or to a BB conformer. <section> <head>Conformational analyses of morpholinium rings. <p>Previous modeling results from our group <link goesto="j.Savle97">Savle, 1997</> on the following compound <float id=savleMeOH> <mm entity=fig.savle97>fig.savle97.gif, 0.583KB</mm> <caption>2-(Hydroxymethyl)-2,4,4-trimethylmorpholinium studied by Savle <em>et al.</em> </float> pointed to a predominant chair conformation, the same as in solid state. The calculations also showed that twist-boat conformations accounted for approximately 14% of the total population. To support this finding and to gain a better understanding of the conformational behavior of these rings, we analyzed by computational methods the conformational behavior of: <ol> <li><chemname>1,1-dimethylcyclohexane</chemname> <a href="cyclohexane/TableDiMeCyclohGas.html"> in the gas phase</a></li> <li><chemname>(<em>R</em>)-1,1,3-trimethylcyclohexane</chemname> <a href="cyclohexane/TableTriMeCyclohGas.html"> in the gas phase</a></li> <li><chemname>1,1,3,3-tetramethylcyclohexane</chemname> <a href="cyclohexane/TableTetraMeCyclohGas.html"> in the gas phase</a></li> <li><chemname>(<em>R</em>)-1-ethyl-1,3,3-trimethylcyclohexane</chemname> <a href="cyclohexane/TableEtTriMeCyclohGas.html"> in the gas phase</a></li> </ol> as a reference framework to understand: <ol> <li><chemname>4,4-dimethylmorpholinium</chemname> <a href="morpholinium/TableMorpholGas.html"> in the gas phase</a> and <a href="morpholinium/TableMorpholWat.html"> in solution</a></li> <li><chemname>(<em>S</em>)-2,4,4-trimethylmorpholinium</chemname> <a href="morpholinium/TableSMeMorpholGas.html">in the gas phase</a> and <a href="morpholinium/TableSMeMorpholWat.html"> in solution</a></li> <li><chemname>2,2,4,4-tetramethylmorpholinium</chemname> <a href="morpholinium/TableDiMeMorpholGas.html"> in the gas phase</a> and <a href="morpholinium/TableDiMeMorpholWat.html"> in solution</a></li> <li><chemname>(<em>R</em>)-2-hydroxymethyl-2,4,4-trimethylmorpholinium</chemname> <a href="morpholinium/TableMeOHMorpholGas.html"> in the gas phase</a> and <a href="morpholinium/TableMeOHMorpholWat.html"> in solution</a></li> </ol> respectively. <subsection> <head>Modeling in the gas phase. <p>We tried to get a complete picture of the energy hypersurface by means of MonteCarlo conformational searches. We chose MonteCarlo instead of Grid Search because the number of torsion angles involved made the Grid Search less efficient. For more details about the procedures, see the Methods section. Conformational energies always refer to the global minimum as 0.00 kcal/mol, unless specified otherwise. <p>The following figure summarizes the nomenclature we use for cyclohexane conformers: <float id=hexConfs> <mm entity=fig.hexConfs>fig.hexConfs.gif, 3.085KB <caption>Labeling of substituent positions in cyclohexane. </float> <block> <head>Cyclohexanes. <p> <a href="cyclohexane/TableDiMeCyclohGas.html">1,1-Dimethylcyclohexane</a> yielded five minima: a chair (global minimum) and four twist-boats (pairs at 5.09 and 6.12 kcal/mol). Introducing <em>gem</em> substitutents in a chair destabilizes it by worsening 1,3-diaxial interactions, both because of the greater volume of the methyl group and because of <term>Allinger buttressing</term>, where an equatorial substituent pushes its axial neighbor into closer proximity with the other 1,3 axial substituents. As the chair constitutes our zero-energy reference, we can only <em>deduce</em> the changes in stability of the chair after analyzing the behavior of other higher-energy conformers. <p>We find a boat at 6.51 kcal/mol. We observe a smaller chair/boat energy gap than in cyclohexane: 6.95 kcal/mol. This boat has the methyl groups on an in-plane carbon so this increases the strain due to eclipsing interactions with the hydrogens on the adjacent in-plane carbon, and possibly with the hydrogens on the in-plane carbon connected through the out-of-plane carbon. We have now the first indication of a destabilized chair: <em>if</em> the increase in 1,3-diaxial strain in the chair is greater than the increase due to 1,2 and 1,3 eclipsing strain, the resulting destabilization of the chair yields a smaller energy-gap. A second boat appears at 9.99, a much greater energy gap than in cyclohexane. This boat has the methyl substituents in bowsprit-flagpole positions. The crowding of a methyl group with the flagpole hydrogen can account for almost 3 kcal/mol of conformational energy. <p>The hypersurface shows four twist-boats, two enantiomeric pairs at 5.09 and 6.12 kcal/mol. The pair at 5.09 has the <em>gem</em> substitution on an in-plane carbon. Again, we find a smaller energy gap than the 5.82 kcal/mol in cyclohexane. We can apply an argument similar to the one used for the boats: a greater destabilization of the chair than of the twist-boat, to explain the reduced gap. The twist-boats at 6.12 have flagpole-flagpole interactions strong enough to destabilize this conformer even more than the chair. Apparently, flagpole-flagpole interactions are at least 2 kcal/mol stronger than the 1,3-diaxial. We can justify this by pointing out that 1,3-diaxial interactions involve mostly changes in torsion angles, while flagpole-flagpole interactions involve compression of bonds. Bonds have usually much stiffer potentials and narrower energy wells than torsions. <p>Six half-chairs determine three distinguishable barriers to chair/twist-boat interconversion with values of 10.98, 11.91 and 12.12 kcal/mol. All these values are close to the 11.25 kcal/mol found in cyclohexane. Both 1,3-diaxial as well as eclipsing interactions are still at work within the appropriate substitution patterns. On the other hand, flagpole-flagpole interactions are eliminated, because there is only one out-of-plane carbon. This eliminates one of the sources of strong destabilization. <p> <a href="cyclohexane/TableTriMeCyclohGas.html">Trimethylcyclohexane</a> shows eight minima: two chairs (0.00 and 3.61 kcal/mol) and six twist-boats. 1,3-Diaxial interactions (worsened by Allinger buttressing) raise the chair to 3.61 kcal/mol. The lowest energy boat appears at 6.68 kcal/mol, slightly higher than the lowest boat in dimethylcyclohexane (6.51), but still lower than the 6.95 kcal/mol in cyclohexane. This boat has 1,3(in-plane) diaxial interactions with one of the <em>gem</em> methyls. The third methyl group is in the equatorial orientation on one in-plane carbon. At this energy, this boat splits the twist-boats in two triads. The first three twist-boats have the third methyl group either in bowsprit or in equatorial orientation, thus reducing van der Waals interactions. The other three have the methyl group in flagpole or axial orientation, so van der Waals repulsions increase. This increased repulsion affects the bond angles: when the methyl group is equatorial, the H<sub>ax</sub>-C-R bond angle approaches 109° very closely. When the same methyl group is axial, the H<sub>ax</sub>-C-R bond angle approaches 112°, being <q>pushed out</q> by the bulk of the methyl group. Higher in energy than these twist-boats, we find three boats. All have 1,3-diaxial methyl-methyl interactions, or methyl-hydrogen flagpole interactions. <p>Trimethylcyclohexane shows four half-chairs, three of them with energies close to the half-chair in cyclohexane: 11.22, 11.57 and 11.83 vs. 11.25. The first two half-chairs show a small energetic difference between the pseudoaxial and pseudoequatorial positions in the half-chair when the <em>gem</em> substituents are on the out-of-plane carbon, about 0.35 kcal/mol. The fourth chair has an energy of 17.05, and vibrational analysis characterized it as a higher-order saddle point. This half-chair has 1,3-diaxial methyl-methyl repulsions, justifying its high energy. <p> <a href="cyclohexane/TableTetraMeCyclohGas.html">1,1,3,3-Tetramethylcyclohexane</a> shows the effects of crowding substituents, now in a 1,1,3,3 di<em>gem</em> pattern. We see only one chair as the global minimum. The bond angles indicate strain due to 1,3-diaxial repulsions: the Me<sub>ax</sub>-C-C angles are 113.3°, compared to the 109.2° of the H<sub>ax</sub>-C-C angles. The change in the bond angles also affects the torsions according to the equation reported by Romers <em>et al.</em> <link goesto="b.Romers69">Romers, 1969</>: <pre> cos(ω) = -cos(θ)/(1+cos(θ)) </pre> where ω is the torsion angle, and θ is the adjacent bond angle. Measuring the torsion adjacent to the 113.3° angle yields a value of 46.8°; the value calculated with the equation is 49.1°. We can attribute the deviation to the uncommon steric crowding produced by the 1,1,3,3 di<em>gem</em> substitution pattern which induces severe 1,3-diaxial stress. <p>After the chair, we find four twist-boats in enantiomeric pairs. The first pair shows up at 3.93 kcal/mol and the second at 4.75. Both values, 3.93 and 4.75, are lower than the 5.82 kcal/mol gap in cyclohexane. In the first one, all the methyl groups are on in-plane carbons, the second pair has two methyls in bowsprit-flagpole positions. We infer that the reduction of the gap has to do with the severe strain present in the chair, although the twist-boats have strain as evidenced by the flatter torsions found. The average of the (absolute) values of the torsions in the cyclohexane twist-boat is 42.8°. The same average in tetramethylcyclohexane comes out as 39.8° and 37.3°. <p>Two boats, corresponding to the two pairs of twist-boats, have energies of 5.23 and 6.57 kcal/mol. Again, the highest energy boat has flagpole-equatorial methyl-methyl interactions, increasing its energy over the boat with axial-axial methyl-methyl interactions. <p>At first sight, <a href="cyclohexane/TableEtTriMeCyclohGas.html">(<em>R</em>)-1-ethyl-1,3,3-trimethylcyclohexane</a> shows a very complex energy hypersurface, due to the additional degree of freedom introduced by the ethyl group. We can formally generate this hypersurface by splitting each conformer of 1,1,3,3-tetramethylcyclooctane into a family of three conformers, because of the three positions the ethyl group can take (<em>g+</em>, <em>g-</em> and <em>anti</em>). Closer examination reveals that some families are missing a member, namely, the one with the ethyl group pointing inside the ring. <p>All the minima within 3.5 kcal/mol above the global minimum are exclusively chairs. The first saddle point comes at 3.72 kcal/mol, and it involves rotation of the ethyl group. After that, we find a series of twist-boats, differing in most cases only in the ethyl torsion. The first ten twist-boats are spread over a range from 4.10 kcal/mol to 4.92 kcal/mol. With an average of 4.52 kcal/mol, the chair/twist-boat energy gap is somewhat greater than the 4.34 kcal/mol in 1,1,3,3-tetramethylcyclohexane, in agreement with a greater strain produced by the ethyl group. The first boat appears at 5.33 kcal, higher than its corresponding conformer in 1,1,3,3-tetramethylcyclohexane at 5.23 kcal/mol. 1,1,3,3-tetramethylcyclohexane has another boat at 6.57 kcal/mol, the corresponding conformer here shows up at 6.77 kcal/mol. The lowest energy chair in 1,1,3,3-tetramethylcyclohexane has an energy of 8.09 kcal/mol; the corresponding stationary point in this molecule is at 8.29. <p><strong>To summarize,</strong> destabilization of the chair plays heavily in the determination of the chair/twist-boat energy gap because of the presence of six 1,3-diaxial interactions in the chair. Geminal substitution increases the diaxial strain due to Allinger buttressing. Flagpole-flagpole interactions in twist-boats account for more of the increase in strain energy than diaxial interactions. Flagpole-flagpole interactions in boats are stronger than both eclipsing and axial interactions on the in-plane carbons. Flagpole-axial interactions dominate the stability of the half-chairs, followed by eclipsing and 1-3 diaxial interactions. Our results agree with those obtained by Weiser <em>et al.</em> <link goesto="j.Weiser96">Weiser, 1996</> who employed the MM3(92) force field. This agreement gives us confidence in the ability of AMBER* to model crowded systems. <p>Cyclohexanes have helped us develop a picture of the changes in energy and strain due to steric effects. In the following sections we use the insights obtained from the analysis of these hydrocarbons as a framework for the inclusion of steric effects due to heteroatom substitution, dipolar effects and the effects of solvation. <block> <head>Morpholinium rings. <p><mm entity=fig.Morphtags></mm> <a href="morpholinium/TableMorpholGas.html">4,4-Dimethylmorpholinium</a> yielded five minima: one chair (global minimum) and four twist-boats grouped in two degenerate pairs with energies equal to 4.51 and 7.12 kcal/mol, respectively. A boat at 5.38 kcal/mol separates these pairs. The other two twist-boats interconvert through a boat at 7.55 kcal/mol. The half-chairs at 10.80 and 11.11 can collapse to the chair or to any of the two twist-boats at 4.51. The half-chair at 10.80 kcal/mol has a plane of symmetry that passes through the N and the O, so it provides a symmetric path for chair-chair interconversion or for the generation of the lowest energy twist-boats. The half-chairs at 11.11 can collapse to any of the lowest energy twist-boats, but they are distorted as compared to the half-chair at 10.80. They represent asymmetric paths for chair-chair interconversion or for the generation of the twist-boats. <p>Comparing <link goesto="tableCompDi">dimethylcyclohexane vs. 4,4-dimethylmorpholinium</>, one change is the lowering of the energy of one of the cyclohexane boats, from 9.99 to 5.38 kcal/mol. This corresponds to the boat having the methyl groups in bowsprit-flagpole positions. Crowding with the nearby hydrogen strains the dimethylcyclohexane molecule. Dimethylmorpholinium, having an oxygen atom that eliminates the hydrogen atoms at position 4, relieves that strain. The other boat in dimethylmorpholinium (7.55 kcal/mol) corresponds to the boat at 6.51 kcal/mol in dimethylcyclohexane. These conformers have the methyl substituents on one in-plane carbon. These methyl groups eclipse the adjacent pair of hydrogens so, the greater bulk of the methyl groups, together with the shorter C-N bond, increases the strain by steric hindrance. The asymmetric half-chairs do not have analogs in dimethylcyclohexane, but in the symmetric ones we observe only small changes to lower energies. We can ascribe them to the loss of the hydrogen atoms opposite to the nitrogen, relieving flagpole-flagpole, axial, and eclipsing interactions. <float id=tableCompDi> <table> <rowhead>Conformer <row> <c>Dimethylcyclohexane <c>4,4-Dimethylmorpholinium <rowhead>chair <row> <c>0.00 <c>0.00 <rowhead>twist-boat <row> <c>5.09 <c>4.51 <rowhead>twist-boat <row> <c>5.09 <c>4.51 <rowhead>twist-boat <row> <c>6.12 <c>7.12 <rowhead>twist-boat <row> <c>6.12 <c>7.12 <rowhead> <row> <c> <c> <rowhead>boat <row> <c>6.51 <c>7.55 <rowhead>boat <row> <c>9.99 <c>5.38 <rowhead>half-chair <row> <c>10.98 <c>10.80 <rowhead>half-chair <row> <c>10.98 <c>NA <rowhead>half-chair <row> <c>11.19 <c>11.11 <rowhead>half-chair <row> <c>11.19 <c>11.11 <rowhead>half-chair <row> <c>12.12 <c>11.67 <rowhead>half-chair <row> <c>12.12 <c>NA <caption>Comparison of morpholinium vs. dimethylcyclohexane in the gas phase. </float> <p> <a href="morpholinium/TableSMeMorpholGas.html">Trimethylmorpholinium</a> shows a total of eight minima: two chairs (the global minimum and a chair at 4.73 kcal/mol), and six twist-boats. The global minimum is a chair, followed by a twist boat at 4.49 kcal/mol. This twist-boat has the non-<em>gem</em> methyl group in equatorial. The lower destabilization of the global minimum can justify the greater energy gap here. Another chair, now with the non-<em>gem</em> methyl group axial, shows up at 4.73 kcal/mol. A combination of increased 1,3-diaxial repulsions due to bulkier groups held closer by the shorter C-N and C-O bonds can explain this higher energy (Let us not forget the lower strain present in the global minimum). The lowest energy boat appears at 7.55 kcal/mol with the non-<em>gem</em> methyl in bowsprit and the <em>gem</em> substituents on an in-plane carbon. The shape is somewhat distorted from an ideal boat, leaving the equatorial <em>gem</em> methyl in an orientation closer to axial and distorting the H<sub>ax</sub>-C-C angles from the ideal 109.5°, making them as open as 111°. The lowest energy half-chair is at 10.91 kcal/mol. As with dimethylmorpholinium, we find several asymmetric half-chairs. The presence of a boat at 11.68 kcal/mol is very noticeable, as the highest energy boat we have found so far. <p>Drawing a <link goesto="tableCompTri">comparison of trimethylmorpholinium and trimethylcyclohexane</> we see that the second chair is destabilized, going from 3.61 to 4.73 kcal/mol. We can ascribe part of this increased energy gap to a less strained global minimum. From the study of cyclohexanes we learned that 1,3-diaxial interactions could justify the reduced energy gaps found. Since morpholinium compounds lack a pair of hydrogens, that reduces the total number of 1,3-diaxial contacts from six to four, thus reducing the strain introduced by substituents on the ring. A similar observation comes from the boat at 10.09 in trimethylcyclohexane, which goes as low as 5.35 kcal/mol in the trimethylmorpholinium. The loss of flagpole-flagpole crowding helps this lowering of the energy. Additionally, even though this structure does not have any elements of symmetry because of its chirality, the ring conformation is the same as we found in dimethylmorpholinium (with the heteroatoms split by a mirror plane). Given that none of the methyl substituents on the ring have any heteroatoms, the dipolar picture approaches very closely that of dimethylmorpholinium. This results in a reduction of the overall dipole moment due to a symmetric disposition of the dipoles. <float id=tableCompTri> <table> <rowhead> <row> <c>Trimethylcyclohexane <c>Trimethylmorpholinium <rowhead>Chair <row> <c>0.00 <c>0.00 <rowhead>Chair <row> <c>3.61 <c>4.73 <rowhead>Twist-boat <row> <c>5.10 <c>7.04 <rowhead>Twist-boat <row> <c>6.14 <c>4.49 <rowhead>Twist-boat <row> <c>6.28 <c>6.84 <rowhead>Boat <row> <c>6.68 <c>7.55 <rowhead>Twist-boat <row> <c>7.44 <c>4.89 <rowhead>Twist-boat <row> <c>7.63 <c>9.06 <rowhead>Twist-boat <row> <c>8.53 <c>5.37 <rowhead>Boat <row> <c>10.09 <c>5.35 <rowhead>Half-chair <row> <c>11.22 <c>10.91 <rowhead>Half-chair <row> <c>11.57 <c>11.11 <rowhead>Half-chair <row> <c>11.83 <c>12.22 <rowhead> <row> <c> <c> <rowhead>Boat <row> <c>8.76 <c>n.f.<link goesto="NF">*</><link goesto="NF">*</> <rowhead>Boat <row> <c>10.52 <c>n.f.<link goesto="NF">*</> <rowhead>Boat <row> <c>10.09 <c>n.f.<link goesto="NF">*</> <rowhead>Boat <row> <c>10.52 <c>n.f.<link goesto="NF">*</> <rowhead>Half-chair <row> <c>17.05 <c>n.f.<link goesto="NF">*</> <rowhead>Boat <row> <c>n.f.<link goesto="NF">*</> <c>9.41 <rowhead>Boat <row> <c>n.f.<link goesto="NF">*</> <c>11.68 <rowhead>Half-chair <row> <c>n.f.<link goesto="NF">*</> <c>11.61 <caption>Comparison of energies of trimethylmorpholinium vs. trimethylcyclohexane in the gas phase (kcal/mol). </float> <p>The gap between the first twist-boat in trimethylcyclohexane and its chair (5.10 kcal/mol) increases in the morpholinium to 7.04. Flagpole-flagpole hydrogen-hydrogen repulsion can partly justify this result, even more because the non-<em>gem</em> methyl in bowsprit forces Allinger buttressing, but examination of the internal angles of the ring reveals that they are distorted, having an average value of 111.9°. <p> <a href="morpholinium/TableDiMeMorpholGas.html">Tetramethylmorpholinium</a> has a two enantiomeric chairs as global minima. These enantiomers arise because the introduction of nitrogen and oxygen into the global minimum in 1,1,3,3-tetramethylcyclohexane eliminates a plane of symmetry. After the chairs we find three enantiomeric pairs of twist-boats. The energies are remarkably low if compared to the other morpholinium rings: 1.25, 1.56 and 3.93 kcal/mol vs. the lowest twist-boat at 4.51 kcal/mol in morpholinium; or the lowest twist-boat in trimethylmorpholinium at 4.49 kcal/mol. Because of the 1,3 substitution pattern, two of the twist-boat pairs have two methyl groups in bowsprit-flagpole orientations. These are the lowest energy pairs. The third pair has all methyl groups on in-plane carbons, and corresponds to the highest energy pair. We indicated above that flagpole-flagpole interactions weighed heavily among the contributions to strain, followed by diaxial and eclipsing. The lowest energy twist-boats have a methyl in flagpole, but they lack the opposite flagpole atom, leaving only 1,3-diaxial and eclipsing repulsions to induce strain. The third twist-boat pair shows flagpole-flagpole HˇˇˇH contacts, plus 1,3-diaxial MeˇˇˇMe contacts, therefore increasing the strain. <p>At 6.69 kcal/mol we find the lowest energy half-chair in all the cases analyzed so far. It shows some distortion from a perfect half-chair, and lacks strong flagpole interactions because of the absence of hydrogens on position 1,4 to the out-of-plane carbon. Higher in energy we see a pair of enantiomeric boats at 6.86 kcal/mol. These have the methyl groups on nitrogen in bowsprit-flagpole, so flagpole-flagpole interactions do not destabilize it. By analyzing the possible permutations of the substituents on the basic boat framework, we realize that another boat, with all four methyl groups on in-plane carbons, is possible. Under the conditions of our minimizations, AMBER* could not find those stationary points in the search, nor refine the gradients under acceptable cutoffs when the structures were generated by hand and increased the number of iterations for the minimization routine (Full Matrix Newton Raphson) to 2000. <strong>This is probably the first indication of a significant shortcoming in this model chemistry.</strong> After this result, we consider that the results obtained at higher energies may be less reliable, so we mention only the presence of three more half-chairs, one of them classified as a multiple maximum by AMBER* although there are no methyl rotations that could justify the additional imaginary frequencies. <p>We can <link goesto="tableCompTetra">contrast tetramethylmorpholinium vs. tetramethylcyclohexane</>. About half of the stationary points found in morpholinium have a cyclohexane analog. Most of the conformers lose strain in the morpholinium analog, due to the loss of 1,3-diaxial or flagpole interactions. There are only two cases of more highly strained morpholinium analogs: the boat at 6.57 kcal/mol in the cyclohexane rises to 6.86 kcal/mol in the morpholinium, and the enantiomeric half-chairs that go from 8.25 to 8.73 kcal/mol. Both increases correspond to increased eclipsing interactions brought about by the shorter C-N bonds. The presence of so many conformers without an analog, casts some doubt on the ability of AMBER* to model such <strong>highly crowded, charged</strong> systems. <float id=tableCompTetra> <table> <rowhead>Conformer <row> <c>Tetramethylcyclohexane <c>Tetramethylmorpholinium <rowhead>Chair <row> <c>0.00 <c>0.00 <rowhead>Twist-boat <row> <c>4.75 <c>1.25 & 1.56 <rowhead>Twist-boat <row> <c>4.75 <c>1.25 & 1.56 <rowhead>Boat <row> <c>6.57 <c>6.86 <rowhead>Half-chair <row> <c>8.09 <c>6.98 <rowhead>Half-chair <row> <c>8.25 <c>8.73 <rowhead>Half-chair <row> <c>8.25 <c>8.73 <rowhead>Half-chair <row> <c>9.60 <c>6.69 <rowhead> <row> <c> <c> <rowhead>Twist-boat <row> <c>3.93 <c>n.f.<link goesto="NF">*</> <rowhead>Twist-boat <row> <c>3.93 <c>n.f.<link goesto="NF">*</> <rowhead>Boat <row> <c>5.23 <c>n.f.<link goesto="NF">*</> <rowhead>Half-chair <row> <c>14.07 <c>n.f.<link goesto="NF">*</> <rowhead>Half-chair <row> <c>14.07 <c>n.f.<link goesto="NF">*</> <rowhead>Twist-boat <row> <c>n.f.<link goesto="NF">*</> <c>3.93 <rowhead>Twist-boat <row> <c>n.f.<link goesto="NF">*</> <c>3.93 <rowhead>Half-chair <row> <c>n.f.<link goesto="NF">*</> <c>13.32 <caption>Comparison of energies of tetramethylcyclohexane vs. tetramethylmorpholinium in the gas phase (kcal/mol). </float> <p>The introduction of a hydroxymethyl group complicates the hypersurface of the molecule, by adding the degrees of freedom, in the -CH<sub>2</sub>-CH<sub>2</sub>-O-H fragment. Additionally, the new N-CH-CH<sub>2</sub>-OH fragment shows a gauche effect. Given the risks involved in modeling such crowded systems uncovered by the results on tetramethylmorpholinium, we content ourselves with discussing only the lowest energy conformers, namely, those within 3.0 kcal/mol above the global minimum. <p>In <a href="morpholinium/TableMeOHMorpholGas.html">(<em>R</em>)-2-hydroxymethyl-2,4,4-trimethylmorpholinium</a>, the global minimum is a chair. Within 3.0 kcal/mol we observe a mixture of chairs and twist-boats. <link goesto="tableCompEt">Comparing ethyltrimethylcyclohexane vs. hydroxymethyl trimethylmorpholinium</> shows the effects of polar influences on conformation. These comparisons take into account seven torsions: the six internal torsions of the ring and the torsion of the bond that connects the ethyl group to the ring because we cannot compare the C-C-O-H torsion to the C-C-CH<sub>2</sub>-H. The table shows many changes in the energetic ranking of the conformers, the most noticeable of which is the change in global minimum. Both conformations are chairs, but they differ in the orientation of the ethyl/hydroxymethyl substituent. The ethyl prefers an <em>anti</em> conformation, while the hydroxymethyl prefers <em>gauche</em>. Some conformers show substantial stabilization by the presence of heteroatoms, like in the case of a twist-boat at 7.00 kcal/mol in the cyclohexane. The morpholinium analog has an energy of 2.18 kcal/mol. The gauche effect comes into play here: a <em>gauche</em> ethyl group has a much higher energy than a <em>gauche</em> hydroxymethyl subject to gauche effect. Most conformers in this morpholinium ring are highly distorted, and the identification of analog pairs was difficult. <float id=tableCompEt> <table> <rowhead>Conformer <row> <c>Ethyltrimethylcyclohexane <c>(Hydroxymethyl)trimethylmorpholinium <rowhead>Chair <row> <c>0.00 <c>2.19 <rowhead>Chair <row> <c>0.35 <c>1.77 <rowhead>Chair <row> <c>0.74 <c>1.60 <rowhead>Chair <row> <c>0.74 <c>0.81 <rowhead>Chair <row> <c>1.64 <c>0.00 <rowhead>Twist-boat <row> <c>4.10 <c>2.20 <rowhead>Twist-boat <row> <c>4.83 <c>2.13 <rowhead>Twist-boat <row> <c>5.23 <c>1.14 <rowhead>Twist-boat <row> <c>5.39 <c>2.71 <rowhead>Twist-boat <row> <c>7.00 <c>2.18 <rowhead> <row> <c> <c> <rowhead>Twist-boat <row> <c>n.f.<link goesto="NF">*</> <c>1.20 <rowhead>Chair <row> <c>n.f.<link goesto="NF">*</> <c>2.01 <rowhead>Twist-boat <row> <c>n.f.<link goesto="NF">*</> <c>2.35 <rowhead>Chair <row> <c>n.f.<link goesto="NF">*</> <c>2.56 <rowhead>Chair <row> <c>n.f.<link goesto="NF">*</> <c>2.73 <caption>Comparison of energies of ethyltrimethylcyclohexane vs. (hydroxymethyl)trimethylmorpholinium in the gas phase (kcal/mol). </float> <p><strong>In summary,</strong> morpholinium rings follow the same general trends regarding steric interactions uncovered by the study of hydrocarbon systems, but the shorter bond lengths associated with heteroatoms increase steric crowding. In analyzing these conformational energies one has to take into consideration the reduced number of diaxial or flagpole interactions, due to the absence of substituents on atoms like oxygen. Dipole-dipole interactions do not seem to play an important role in the gas phase. We might have pushed AMBER* over its limit of applicability by modeling this highly crowded, charged species. <subsection> <head>Modeling in GB/SA water. <p>MacroModel does not calculate dipole moments, but all calculations including solvent report a <q>Solvation</q> component. We use this term in lieu of a dipole moment. The table for <a href="morpholinium/TableMorpholWat.html">dimethylmorpholinium in water</a> displays all the minima found including GB/SA water. The <link goesto="tableCompDiWat">comparison between gas phase and water</> <float id=tableCompDiWat> <table> <rowhead>Conformer <row> <c>Energy in the gas phase <c>Energy in GB/SA water <c>δH<sub>solv</sub> <rowhead>Chair <row> <c>0.00 <c>0.00 <c>-56.66 <rowhead>Twist-boat <row> <c>4.51 <c>4.92 <c>-55.35 <rowhead>Boat <row> <c>5.38 <c>5.93 <c>-54.91 <rowhead>Twist-boat <row> <c>7.12 <c>6.66 <c>-57.52 <rowhead>Boat <row> <c>7.55 <c>7.23 <c>-57.06 <rowhead>Half-chair <row> <c>10.80 <c>10.66 <c>-56.22 <rowhead>Half-chair <row> <c>11.11 <c>11.07 <c>-56.47 <caption>Conformational and solvation energies (kcal/mol) of dimethylmorpholinium in the gas phase and GB/SA water. </float> shows the differences brought about by solvation. The chair is the global minimum, two twist-boats have energies of 4.92 kcal/mol, having increased its energy by 0.41 kcal/mol from the 4.51 it had in the gas phase. The other pair has an energy of 6.66 kcal/mol. Solvation has stabilized these structures by 0.46 kcal/mol from their 7.12 kcal/mol in the gas phase. The energy gap between the twist-boats has decreased from 2.61 kcal/mol to 1.74 kcal/mol. The difference in solvation is 2.17 kcal/mol, which explains, at least qualitatively, the difference. One of the boats, at 5.38 kcal/mol in the gas phase, has an energy of 5.93 in solution. The energetic ranking in solution follows closely that in the gas phase, although the highest energy half-chair (pair) in solution does not show up in the gas phase. The saddle points have among the highest solvation terms in the set of conformers, to the exception of the first boat. The first boat has the nitrogen and the oxygen in out-of-plane positions; thus they are part of a plane of symmetry of the molecule. This symmetric arrangement makes for a partial cancellation of the dipoles, thereby reducing the overall molecular dipole moment, and yielding the smallest δH<sub>solv</sub>. <p> <a href="morpholinium/TableSMeMorpholWat.html">Trimethylmorpholinium in water</a> shows eight minima, two chairs and six twist-boats. The chairs follow the same energetic ranking as in the gas phase. So do most of the twist-boats. There is only one crossover in the ranking, as the twist-boat at 6.84 kcal/mol in the gas phase increases its energy to 7.54 kcal/mol in water, while the one at 7.04 is lowered to 6.63 kcal/mol by solvation. The solvation terms fit that behavior, given that the twist-boat at 6.63 kcal/mol in water has a solvation term equal to -56.08 kcal/mol, while the destabilized twist-boat has a solvation equal to -53.50. This destabilized twist-boat does not have any elements of symmetry because of its chirality, but the ring conformation is the same as we found in dimethylmorpholinium in solution (with the heteroatoms in out-of-plane positions). Thus the dipolar picture approaches closely that of dimethylmorpholinium. This results in a reduction of the overall dipole moment due to a symmetric disposition of the dipoles and in one of the lowest solvation terms in the table. <float id=tableCompTriWat> <table> <rowhead>Conformer <row> <c>Energy in the gas phase <c>Energy in GB/SA water <c>δH<sub>solv</sub> <rowhead>Chair <row> <c>0.00 <c>0.00 <c>-55.27 <rowhead>Twist-boat <row> <c>4.49 <c>4.87 <c>-53.97 <rowhead>Chair <row> <c>4.73 <c>4.88 <c>-54.98 <rowhead>Twist-boat <row> <c>4.89 <c>5.36 <c>-53.66 <rowhead>Boat <row> <c>5.35 <c>5.86 <c>-53.52 <rowhead>Twist-boat <row> <c>5.37 <c>5.76 <c>-54.12 <rowhead>Twist-boat <row> <c>6.84 <c>7.54 <c>-53.50 <rowhead>Twist-boat <row> <c>7.04 <c>6.63 <c>-56.08 <rowhead>Boat <row> <c>7.55 <c>12.57? <c>-55.59 <rowhead>Twist-boat <row> <c>9.06 <c>8.87 <c>-55.59 <rowhead>Boat <row> <c>9.41 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Half-chair <row> <c>10.91 <c>10.84, 14.93 <c>-54.76 <rowhead>Half-chair <row> <c>11.11 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Half-chair <row> <c>11.61 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Boat <row> <c>11.68 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Half-chair <row> <c>12.22 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Boat <row> <c>n.f.<link goesto="NF">*</> <c>7.33 <c>-55.54 <rowhead>Half-chair <row> <c>n.f.<link goesto="NF">*</> <c>11.15 <c>-55.02 <rowhead>Half-chair <row> <c>n.f.<link goesto="NF">*</> <c>18.28 <c>-55.73 <caption>Conformational and solvation energies (kcal/mol) of trimethylmorpholinium in the gas phase and GB/SA water. </float> <p>In <a href="morpholinium/TableDiMeMorpholWat.html">tetramethylmorpholinium</a>, all the stationary points we found had their corresponding structure in the gas phase. They keep the same energetic ranking as in the gas phase. We found two chairs (0.00 kcal/mol) and three pairs of enantiomeric twist-boats. The saddle points, however, deviate from the calculated behavior in the gas phase. One boat and two half-chairs could not be found, despite repeated attempts with increased energy windows (perhaps one more of the difficulties AMBER* has coping with charged, crowded molecules?). The boats have energies of 4.18 and 6.67 kcal/mol and the half-chairs have energies of 6.47 and 9.95 kcal/mol. <float id=tableCompTetraWat> <table> <rowhead>Conformer <row> <c>Energy in the gas phase <c>Energy in GB/SA water <c>δH<sub>solv</sub> <rowhead>Chair <row> <c>0.00 <c>0.00 <c>-53.71 <rowhead>Chair <row> <c>0.00 <c>0.00 <c>-53.71 <rowhead>Twist-boat <row> <c>1.25 <c>1.63 <c>-52.40 <rowhead>Twist-boat <row> <c>1.25 <c>1.63 <c>-52.40 <rowhead>Twist-boat <row> <c>1.56 <c>2.07 <c>-52.23 <rowhead>Twist-boat <row> <c>1.56 <c>2.07 <c>-52.23 <rowhead>Twist-boat <row> <c>3.93 <c>3.67 <c>-54.27 <rowhead>Twist-boat <row> <c>3.93 <c>3.67 <c>-54.27 <rowhead>Half-chair <row> <c>6.69 <c>6.47* <c>-53.57 <rowhead>Boat <row> <c>6.86 <c>6.67 <c>-53.85 <rowhead>Boat <row> <c>6.86 <c>6.67* <c>-53.85 <rowhead>Half-chair <row> <c>6.98 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Half-chair <row> <c>8.73 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Half-chair <row> <c>13.32 <c>n.f.<link goesto="NF">*</> <c>---- <caption>Conformational and solvation energies (kcal/mol) of tetramethylmorpholinium in the gas phase and GB/SA water. </float> <p> <a href="morpholinium/TableMeOHMorpholWat.html">(<em>R</em>)-2-Hydroxymethyl-2,4,4-trimethylmorpholinium in water</a> has a chair as the global minimum. The global minimum has the C-C-CH<sub>2</sub>-O-H fragment in <em>g-,g+</em>. There are two chairs within 1 kcal/mol above the global minimum. One differs only in the conformation of the C-C-CH<sub>2</sub>-O-H fragment: <em>g+,g-</em>. The other one is a conformational diastereomer with the ring torsion angles as "mirror images" of those in the global minimum. That chirality, plus that due to the chiral center already present in the molecule, give rise to diastereomers. The O-C-C-C torsion is <em>anti</em> in a few high energy (>4.9 kcal/mol) instances. The C-C-O-H torsion prefers a <em>gauche</em> conformation, which probably helps hydrogen bonding to the oxygen in the ring. The first conformer with an <em>anti</em> C-C-O-H is 3.20 kcal/mol above the global minimum. We cannot see a simple correlation between the solvation energy of the conformer and the torsions in the ring or those of the hydroxymethyl group. We found a total of 43 conformations, as in the gas phase. <a href="morpholinium/TableMeOHMorpholWat.html">See appendix for full listing of results</a> <float id=tableCompEtWat> <table> <rowhead>Conformer <row> <c>Energy in the gas phase <c>Energy in GB/SA water <c>δH<sub>solv</sub> <rowhead>Chair <row> <c>0.00 <c>0.00 <c>-59.59 <rowhead>Chair <row> <c>0.81 <c>0.81 <c>-56.84 <rowhead>Twist-boat <row> <c>1.14 <c>2.62 <c>-54.83 <rowhead>Twist-boat <row> <c>1.20 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Chair <row> <c>1.60 <c>0.86 <c>-59.57 <rowhead>Chair <row> <c>1.77 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Chair <row> <c>2.01 <c>4.42 <c>-52.24 <rowhead>Twist-boat <row> <c>2.13 <c>1.45 <c>-58.46 <rowhead>Twist-boat <row> <c>2.18 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Chair <row> <c>2.19 <c>4.95 <c>-53.66 <rowhead>Twist-boat <row> <c>2.20 <c>1.79 <c>-58.51 <rowhead>Twist-boat <row> <c>2.35 <c>1.90 <c>-58.34 <rowhead>Chair <row> <c>2.63 <c>3.20 <c>-55.44 <rowhead>Twist-boat <row> <c>2.71 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Chair <row> <c>2.73 <c> <c> <rowhead>Twist-boat <row> <c>3.66 <c>n.f.<link goesto="NF">*</> <c>---- <rowhead>Twist-boat <row> <c>3.90 <c>6.63 <c>-53.15 <rowhead>Twist-boat <row> <c>4.06 <c>4.57 <c>-57.10 <rowhead>Twist-boat <row> <c>4.11 <c>7.24 <c>-52.68 <rowhead>Twist-boat <row> <c>4.32 <c>7.88 <c>-52.85 <rowhead>Boat <row> <c>4.45 <c>n.f.<link goesto="NF">*</> <c>---- <caption>Conformational and solvation energies (kcal/mol) of (hydroxymethyl)trimethylmorpholinium in the gas phase and GB/SA water. </float> <section> <head>Conformational analyses of 2-oxo-1,3,6-dioxazaphosphacinium rings. <p>We analyzed by molecular mechanics the conformational behavior of: <ol><li><chemname>Cyclooctane</chemname> <a href="cyclooctane/TableCycloctGas.html">in the gas phase</a>.</li> <li><chemname>1,1,5,5-tetramethylcyclooctane</chemname> <a href="cyclooctane/Table4MeCyclooctGas.html">in the gas phase</a>.</li> <li><chemname>1,1,3,5,5-pentamethylcyclooctane</chemname> <a href="cyclooctane/Table5MeCyclooctGas.html">in the gas phase</a>.</li> <li><chemname>1,1,3,3,5,5-hexamethylcyclooctane</chemname> <a href="cyclooctane/Table6MeCyclooctGas.html">in the gas phase</a>.</li> </ol> as a reference frame to understand: <ol><li><chemname>6,6-dimethyl-2-oxo-1,3,6-dioxazaphosphacinium</chemname> <a href="phosphacinium/TableDioxPGas.html">in the gas phase</a> and <a href="phosphacinium/TableDioxPWat.html">in solution</a>.</li> <li><chemname><em>cis</em>-4,6,6-Trimethyl-2-oxo-1,3,6-dioxazaphosphacinium</chemname> <a href="phosphacinium/TableCisMedioxPGas.html">in the gas phase</a> and <a href="phosphacinium/TableCisMedioxPWat.html">in solution</a>.</li> <li><chemname><em>trans</em>-4,6,6-Trimethyl-2-oxo-1,3,6-dioxazaphosphacinium</chemname> <a href="phosphacinium/TableTransMedioxPGas.html">in the gas phase</a> and <a href="phosphacinium/TableTransMedioxPWat.html">in solution</a>.</li> <li><chemname>4,4,6,6-Tetramethyl-2-oxo-1,3,6-dioxazaphosphacinium</chemname> <a href="phosphacinium/TableDiMePGas.html">in the gas phase</a> and <a href="phosphacinium/TableDiMePWat.html">in solution</a>.</li> </ol> <subsection> <head>Modeling in the gas phase. <p>As previously indicated for the six-membered ring molecules, we repeated MonteCarlo runs until the searches converged. For details about the setup, refer to the Methods section. All energies refer to the global minimum as 0.00 kcal/mol unless specified otherwise. <block> <head>Cyclooctanes. <p>In <a href="cyclooctane/TableCycloctGas.html">cyclooctane</> we find 8 out of the ten conformations normally regarded as stationary points and which we have described previously in the review of the literature. We only miss the crown and the CC. The BC is the global minimum, in agreement with most of the previous determinations. After this, the TCC is the most populated, with an energy of 0.83 kcal/mol in the gas phase. Two kinds of TBC come at 1.77 kcal/mol (minimum) and at 2.88 kcal/mol (saddle). The TB shows up at 3.63 kcal/mol, a BB at 4.86, a C at 7.76. The TC is at 8.47 and the B at 10.55 kcal/mol. The AMBER* ordering agrees fairly well with that of Kolossváry and Guida <link goesto="j.Kolossvary93">Kolossváry, 1993</> giving us confidence in the ability of AMBER* to model these rings. <!-- README The following table contains only GIF images and VRML models. Substituting the extension "mol" instead of the "wrl" will access the MDL molfiles, displayable with Chime. It will also be necessary to move the *.mol files out of the MOL directory.In that case, the GIF images will be unnecessary, because molfiles in Chime yield both 2D and 3d views. This is likely to require human intervention, because a reformating script would have to be *really* smart to accomodate all these changes. The caption is all in one line to make it easier to use a utility like "grep" when gathering a "List of Tables" --> <float id=tableComp0O> <table> <colhead>Conformer <column> <c>BC <c>TCC <c>TCC' <c>TBC <c>TBC' <c>TBC <c>TBC' <colhead>Structure <column> <c><mm entity=fig.bc0O>fig.bc0O.gif, 0.249KB </mm> <mm entity=VR.bc>bc.wrl, 9.668KB </mm> </c> <c><mm entity=fig.tcc10O>fig.tcc10O.gif, 0.257KB </mm> <mm entity=VR.tcc1>tcc1.wrl, 9.651KB </mm></c> <c><mm entity=fig.tcc-10O>fig.tcc-10O.gif, 0.280KB </mm><mm entity=VR.tcc1>tcc1.wrl, 9.651KB </mm></c> <c><mm entity=fig.tbc10O>fig.tbc10O.gif, 0.311KB </mm> <mm entity=VR.tbc1>tbc1.wrl, 9.649KB </mm></c> <c><mm entity=fig.tbc-10O>fig.tbc-10O.gif, 0.307KB </mm><mm entity=VR.tbc2>tbc2.wrl, 9.654KB </mm></c> <c><mm entity=fig.tbc10O>fig.tbc10O.gif, 0.311KB </mm> <mm entity=VR.tbc3>tbc3.wrl, 9.667KB </mm></c> <c><mm entity=fig.tbc-10O>fig.tbc-10O.gif, 0.307KB </mm><mm entity=VR.tbc4>tbc4.wrl, 9.667KB </mm></c> <colhead>AMBER* (kcal/mol) <column> <c>0.00 <c>0.83 <c>0.83 <c>1.77 <c>1.77 <c>2.88 <c>2.88 <colhead>MM2* (kcal/mol) <column> <c>0.00 <c>0.96 <c>0.96 <c>1.67 <c>1.67 <c>2.80 <c>2.80 <caption>Conformers of <a href="cyclooctane/TableCycloctGas.html">cyclooctane</a> within 3.0 kcal/mol of global minima in the gas phase. </float> <p>In <a href="cyclooctane/Table4MeCyclooctGas.html">1,1,5,5-tetramethylcyclooctane</> the BCs are global minima with the methyl groups in positions 2 and 6. The introduction of two 1,5-<em>gem</em>-dimethyl groups lowers the symmetry, so we describe two different, enantiomeric BCs. See the <link goesto="rules1">appendix</> for a full description of the naming and numbering system used for <em>all</em> conformers. After the BC follows a lowered TCC (0.39 kcal/mol, possibly an indication of a destabilized BC) with methyl groups in 1,5. Now the TCC is followed by a 1,5 TB, not a TBC as in cyclooctane. The 1,5 TB is now only 0.45 kcal/mol higher in energy than the BC, as does the 3,7 TB, instead of the 3.63 kcal/mol it showed in cyclooctane. The 2,6 and 4,8 BB have an energy gap of 0.84, much smaller than 4.86 the BB showed in cyclooctane. A 1,5 CC appears at 1.12 kcal/mol. On the other hand, the 1,5 TBC has increased to 2.17 kcal/mol from the original 1.77 in cyclooctane. <float id=tableComp4O> <table> <colhead>Conformer <column> <c>2,2,6,6-BC <c>2,2,6,6-BC' <c>1,1,5,5-TCC <c>1,1,5,5-TCC' <c>1,1,5,5-TB <c>1,1,5,5-TB' <c>2,2,6,6-BB <c>2,2,6,6-BB' <c>1,1,5,5-CC <c>1,1,5,5-TBC <c>1,1,5,5-TBC' <colhead>Structure <column> <c><mm entity=fig.bc14O>fig.bc14O.gif, 0.301KB </mm> <mm entity=VR.bc14O>bc14O.wrl, 14.058KB </mm> </c> <c><mm entity=fig.bc24O>fig.bc24O.gif, 0.301KB </mm> <mm entity=VR.bc24O>bc24O.wrl, 14.074KB </mm> </c> <c><mm entity=fig.tcc14O>fig.tcc14O.gif, 0.365KB </mm><mm entity=VR.tcc14O>tcc14O.wrl, 14.027KB </mm></c> <c><mm entity=fig.tcc24O>fig.tcc24O.gif, 0.357KB </mm><mm entity=VR.tcc24O>tcc24O.wrl, 14.082KB </mm></c> <c><mm entity=fig.tb14O>fig.tb14O.gif,0.435KB </mm> <mm entity=VR.tb14O>tb14O.wrl, 14.069KB </mm> </c> <c><mm entity=fig.tb24O>fig.tb24O.gif, 0.427KB </mm> <mm entity=VR.tb24O>tb24O.wrl, 14.143KB </mm> </c> <c><mm entity=fig.bb14O>fig.bb14O.gif, 0.430KB </mm> <mm entity=VR.bb14O>bb14O.wrl 14.000KB </mm> </c> <c><mm entity=fig.bb24O>fig.bb24O.gif, 0.435KB </mm> <mm entity=VR.bb24O>bb24O.wrl, 14.195KB </mm> </c> <c><mm entity=fig.cc4O>fig.cc4O.gif, 0.324KB </mm> <mm entity=VR.cc4O>cc4O.wrl, 14.201KB </mm> </c> <c><mm entity=fig.tbc14O>fig.tbc14O.gif, 0.377KB </mm><mm entity=VR.tbc14O>tbc14O.wrl, 14.084KB </mm></c> <c><mm entity=fig.tbc24O>fig.tbc24O.gif, 0.379KB </mm><mm entity=VR.tbc24O>tbc24O.wrl, 14.084KB </mm></c> <colhead>AMBER* (kcal/mol) <column> <c>0.00 <c>0.00 <c>0.39 <c>0.39 <c>0.45 <c>0.45 <c>0.84 <c>0.84 <c>1.12 <c>2.17 <c>2.17 <caption>Conformers of <a href="cyclooctane/Table4MeCyclooctGas.html">tetramethylcyclooctane</a> within 3.0 kcal/mol of global minima in the gas phase. </float> <p>In <a href="cyclooctane/Table5MeCyclooctGas.html">1,1,3,5,5-pentamethylcyclooctane</> the global minimum is formed by a pair of enantiomeric BCs, followed at 0.43 kcal/mol by two enantiomeric TCCs. The barrier for TCC-TCC' interconversion is very low, 1.49 kcal/mol (CC). We then find a set of TBs at 1.55 and 1.59 kcal/mol, two BCs and two TBCs. These results continue the pattern started with 1,1,5,5-tetramethylcyclooctane: the BCs prefer to carry the <em>gem</em> substituents in positions 2 and 6 (sometimes 4 and 8), while the methyl group prefers positions 4<em>e</em> and, sometimes, 2<em>e</em>. Only in high energy cases we find the substituents in positions 1, 3 or 7. Apparently, this positions suffer strong axial-axial or flagpole-axial interactions. The TCC carries the substituents on positions 1, 3 and 5; as the CC does. Positions 2, 3, 6 and 7 are subject to stronger axial-axial repulsions. <link goesto="f.artifact1">Note</> <footnote id=f.artifact1> The absence of substitution patterns in carbons 4 and 8 may well be an artifact of the <link goesto="rules2">procedure to name the conformers</>. </footnote> <float id=tableComp5O> <table> <colhead>Conformer <column> <c>2,2,4,6,6-BC <c>2,2,4,6,6-BC' <c>1,1,3,5,5-TCC <c>1,1,3,5,5-TCC' <c>1,1,3,5,5-CC <c>2,2,4,6,6-TB <c>2,2,4,6,6-TB' <c>1,1,3,5,5-TB <c>1,1,3,5,5-TB' <c>2,4,4,8,8-BC <c>2,4,4,8,8-BC' <c>1,1,5,5,7-TBC <c>1,1,5,5,7-TBC' <c>2,4,4,8,8-BC <c>2,4,4,8,8-BC' <c>2,2,4,6,6-BB <c>1,1,3,5,5-TBC <c>1,1,3,5,5-TBC' <colhead>Structure <column> <c><mm entity=fig.bc15O>fig.bc15O.gif, 0.364KB </mm> <mm entity=VR.bc15O>bc15O.wrl, 15.236KB </mm> </c> <c><mm entity=fig.bc25O>fig.bc25O.gif, 0.365KB </mm> <mm entity=VR.bc25O>bc25O.wrl, 15.183KB </mm> </c> <c><mm entity=fig.tcc15O>fig.tcc15O.gif, 0.381KB </mm><mm entity=VR.tcc15O>tcc15O.wrl, 15.302KB </mm></c> <c><mm entity=fig.tcc25O>fig.tcc25O.gif, 0.405KB </mm><mm entity=VR.tcc25O>tcc25O.wrl, 15.238KB </mm></c> <c><mm entity=fig.cc5O>fig.cc5O.gif, 0.334KB </mm> <mm entity=VR.cc5O>cc5O.wrl, 15.181KB </mm> </c> <c><mm entity=fig.tb15O>fig.tb15O.gif, 0.435KB </mm> <mm entity=VR.tb15O>tb15O.wrl, 15.190KB </mm> </c> <c><mm entity=fig.tb25O>fig.tb25O.gif, 0.459KB </mm> <mm entity=VR.tb25O>tb25O.wrl, 15.177KB </mm> </c> <c><mm entity=fig.tb35O>fig.tb35O.gif, 0.481KB </mm> <mm entity=VR.tb35O>tb35O.wrl, 15.126KB </mm> </c> <c><mm entity=fig.tb45O>fig.tb45O.gif, 0.489KB </mm> <mm entity=VR.tb45O>tb45O.wrl, 15.168KB </mm> </c> <c><mm entity=fig.bc35O>fig.bc35O.gif, 0.402KB </mm> <mm entity=VR.bc35O>bc35O.wrl, 15.291KB </mm> </c> <c><mm entity=fig.bc45O>fig.bc45O.gif, 0.405KB </mm> <mm entity=VR.bc45O>bc45O.wrl, 15.037KB </mm> </c> <c><mm entity=fig.tbc15O>fig.tbc15O.gif, 0.394KB </mm><mm entity=VR.tbc15O>tbc15O.wrl, 15.276KB </mm></c> <c><mm entity=fig.tbc25O>fig.tbc25O.gif, 0.389KB </mm><mm entity=VR.tbc25O>tbc25O.wrl, 15.220KB </mm></c> <c><mm entity=fig.bc55O>fig.bc55O.gif, 0.434KB </mm> <mm entity=VR.bc55O>bc55O.wrl, 15.179KB </mm> </c> <c><mm entity=fig.bc65O>fig.bc65O.gif, 0.435KB </mm> <mm entity=VR.bc65O>bc65O.wrl, 15.200KB </mm> </c> <c><mm entity=fig.bb5O>fig.bb5O.gif, 0.489KB </mm> <mm entity=VR.bb5O>bb5O.wrl, 15.165KB </mm> </c> <c><mm entity=fig.tbc35O>fig.tbc35O.gif, 0.396KB </mm><mm entity=VR.tbc35O>tbc35O.wrl, 15.116KB </mm></c> <c><mm entity=fig.tbc45O>fig.tbc45O.gif, 0.392KB </mm><mm entity=VR.tbc45O>tbc45O.wrl, 15.141KB </mm></c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>0.00 <c>0.43 <c>0.43 <c>1.49 <c>1.55 <c>1.55 <c>1.59 <c>1.59 <c>1.65 <c>1.65 <c>1.92 <c>1.92 <c>2.09 <c>2.09 <c>2.34 <c>2.61 <c>2.61 <caption>Conformers of <a href="cyclooctane/Table5MeCyclooctGas.html">pentamethylcyclooctane</a> within 3.0 kcal/mol of global minima in the gas phase. </float> <p>The TB has a slight preference by 2,4 and 6 closely followed by 1,3 and 5. The single methyl group prefers the equatorial orientation in all cases and only in higher energy structures, (> 5.5 kcal/mol) do we find it in axial. TBC prefers a pattern 1,3,5, although a 2,6,8 pattern is also possible (2,2,6,6,8<em>e</em>). A saddle TBC shows a 2,2,4<em>e</em>,6,6 pattern. We did not name structures higher than 8.35 kcal/mol. Most of them show great distorsion, and neither by use of the Weiler plots nor direct examination of the structure could we assign them a name. We think it better to assign them a number, rather than trying to force a fit into our preconceived notions. We shall look back on them only if needed to understand the behavior of the systems that concern us. <p> <a href="cyclooctane/Table6MeCyclooctGas.html">1,1,3,3,5,5-Hexamethylcyclooctane</> shows a pair of TBs as global minima. The interconversion barrier, through a BB, is 0.82 kcal/mol. The BCs are now 1.21 kcal/mol higher in energy than the TBs. The TB prefers to carry its substituents in positions 2,4 and 6. The BC prefers positions 2,4, and 8; and 2,4, and 6. The TBC at 5.99 kcal/mol, prefers substitution on carbons 2,4 and 8. The conformational picture is somewhat simpler than that of 1,1,3,5,5-pentamethylcyclooctane because 1,1,3,3,5,5-hexamethylcyclooctane does not have an equatorial/axial option available as in the pentamethyl substituted ring. As we examine conformations higher in energy, we find many highly distorted structures difficult to name. The distortions seem to depend heavily on the number of substituents so, at present, we cannot see any trends emerging from the ordering of these conformers. <float id=tableComp6O> <table> <colhead>Conformer <column> <c>1,1,3,3,5,5-TB <c>1,1,3,3,5,5-TB' <c>2,2,4,4,8,8-BB <c>2,2,4,4,8,8-BC <c>2,2,4,4,8,8-BC' <colhead>Structure <column> <c><mm entity=fig.tb16O>fig.tb16O.gif, 0.511KB </mm><mm entity=VR.tb16O>tb16O.wrl, 16.172KB </mm></c> <c><mm entity=fig.tb26O>fig.tb26O.gif, 0.515KB </mm><mm entity=VR.tb26O>tb26O.wrl, 16.226KB </mm></c> <c><mm entity=fig.bb6O>fig.bb6O.gif, 0.449KB </mm> <mm entity=VR.bb6O>bb6O.wrl, 16.350KB </mm> </c> <c><mm entity=fig.bc16O>fig.bc16O.gif, 0.439KB </mm><mm entity=VR.bc16O>bc16O.wrl, 16.189KB </mm></c> <c><mm entity=fig.bc26O>fig.bc26O.gif, 0.441KB </mm><mm entity=VR.bc26O>bc26O.wrl, 16.221KB </mm></c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>0.00 <c>0.82 <c>1.21 <c>1.21 <caption>Conformers of <a href="cyclooctane/Table6MeCyclooctGas.html">hexamethylcyclooctane</a> within 3.0 kcal/mol of global minima in the gas phase. </float> <p>BCs accomodate substituents preferentially on an equatorial 2,4,6 pattern; a 2,4,8 pattern introduces more strain than a 2,4,6. Substituents on atom 1 can orient either as bowsprit or flagpole. The flagpole orientation suffers close contacts with the axial substituents on atoms 4 and 6. Axial substituents on atoms 2, 3, 7 and 8 produce strong axial-axial interactions among themselves. The most sterically unhindered positions are 1<em>b</em> and <em>equatorial</em> 2, 3, 4, 5, 6, 7 and 8. A 1,3,5 pattern becomes highly strained when adding <em>gem</em> substituents: in tetramethylcyclooctane, the 1,5 is 5.27 kcal/mol higher in energy than the 2,6; in pentamethylcyclooctane, the 1,3,5 pattern is 5.42 kcal/mol higher in energy than the 2,4,6 and 3.77 kcal/mol higher than the 2,4,8. We could not find this pattern in hexamethylcyclooctane. <p>TBs prefer a 2,4,6 pattern over a 1,3,5. Because of the high symmetry of the conformation, all the positions have similar steric hindrances. We see that in tetramethylcyclooctane the lowest energy TB is a 1,5; in pentamethylcyclooctane the preferred TB is a 2,4,6 followed closely by a 1,3,5 (0.4 kcal/mol gap); while in hexamethylcyclooctane the lowest TB is a 2,4,6. The TB/BC energy gap starts at 3.63 kcal/mol in cyclooctane, in tetramethylcyclooctane is only 0.45 kcal/mol; increases to 1.55 kcal/mol in pentamethylcyclooctane and becomes -1.21 kcal/mol in hexamethylcyclooctane. The best explanation for the decrease in the TB/BC gap when going from cyclooctane to tetramethylcyclooctane consists of destabilization of the BC. This argument also explains the increase in energy in the TBC conformers. <p>The TBCs prefer positions 1,3,5 for the substituents. Positions 2,3,6 and 7 generate some axial-flagpole repulsions with the flagpoles on carbons 1 and 4. The bowsprit orientations on atoms 1 and 5 present little steric hindrance, because they are directed away from the ring, so the justification for the preference on these positions becomes clear. The smallest TBC/BC energy gap in cyclooctane is 1.77 kcal/mol. This increases to 2.17 kcal/mol in tetramethylcyclooctane, goes down to 1.92 kcal/mol in pentamethylcyclooctane and then increases to 4.78 kcal/mol in hexamethylcyclooctane. <p><strong>To summarize,</strong> the conformations of substituted cyclooctanes are very sensitive to the positioning of the substituents on the ring. As the conformation of the ring skeleton becomes less symmetric, the sensitivity to positioning of the substituents increases, <em>e. g.</em>, the BC and TBC are more sensitive to the position of the substituents than the TCC or the C. More extended conformers, like the C or the TC, are less affected than more crowded conformers, like the TB or BB. As the number of <em>gem</em> substituent groups increases, the TB/BC energy gap tends to decrease until, with three <em>gem</em> dimethyl groups in a 1,3,5 pattern, the stabilities switch and the TB becomes the global minimum. <p>The positions with least steric hindrance are: 2, 4, 6 in the BC (the absence of 8 is an artifact of the rules used to name the conformers); 1 and 5, followed by 3, in the TCC; 2 and 6 in the TBC, although 1 and 5 are not much more hindered; all the positions in the TB are nearly equivalent in terms of steric hindrance; the TC prefers 1 and 3 (5 and 7 are equivalent to 1 and 3 respectively). <block> <head>Dioxazaphosphacinium rings. <p><target id=ConfPhosp>The conformational search on the unsubstituted phosphonate ring in the gas phase <a href="phosphacinium/TableDioxPGas.html">6,6-dimethyl-2-oxo-1,3,6-dioxazaphosphacinium</> showed that the global minimum is a pair of enantiomeric BCs with the nitrogen on position 2 and the phosphorus on 6. <link goesto="f.Dale72">Note.</> </target> <footnote id=f.Dale72> The results reported by Dale <em>et al.</em> <link goesto="j.Dale72">Dale, 1972</> show that 6,6-disubstituted-1,3-dioxocanes prefer the BB as the global minimum. Given the close analogy of this skeleton to that of 6,6-dimethyl-2-oxo-1,3,6-dioxazaphosphacinium, we wonder what are the reasons for this discrepancy. We defer this until we discuss the effects of solvation on the conformations of this ring. Dale carried out his determinations in CDCl<sub>3</sub> and CHFCl<sub>2</sub>. Our results including water solvation <em>may</em> compare better. </footnote> The more voluminous methyl group, compared to the <em>oxo</em> oxygen, prefers the least hindered equatorial position, as one would expect. Putting the methyl groups in any other position carries a very high energetic cost: the 1<em>b</em>,5,5 BC increases the energy 7.52 kcal/mol, 2<em>a</em>,6,6 increases the energy to 10.12 kcal/mol, while a 3<em>e</em>,7,7 pattern raises the energy to 11.18 kcal/mol. In these three cases, unfavorable 1,3-diaxial interactions are responsible for most of the increase in energy. We could not find examples of BCs with a 1<em>f</em>,5,5 or a 3<em>a</em>,7,7 substitution pattern. <p>As in the cyclooctanes, we found a minimum TBC and a saddle point TBC. The TBC (min) has an energy of 2.37 kcal/mol, compared to the 2.17 kcal/mol in tetramethylcyclooctane. The TBC (saddle) has an energy of 6.70 kcal/mol, compared to the 6.33 kcal/mol in tetramethylcyclooctane. <p>Two other conformers have energies within 3.0 kcal/mol above the global minimum: TB (pair at 2.55) and TC (2.75). This differs appreciably from tetramethylcyclooctane, which shows the TB at 0.45 and the TC at 4.42 kcal/mol. <float id=tableCompP2> <table> <colhead>Conformer <column> <c>2,2,6,6-BC <c>2,2,6,6-BC' <c>2,2,6,6-TBC <c>2,2,6,6-TBC' <c>1,1,5,5-TB <c>1,1,5,5-TB' <c>3,3,7,7-TC <colhead>Structure <column> <c><mm entity=fig.bc1P2>fig.bc1P2.gif, 0.451KB </mm> <mm entity=VR.bc1P2>bc1P2.wrl, 13.665KB </mm> </c> <c><mm entity=fig.bc2P2>fig.bc2P2.gif, 0.434KB </mm> <mm entity=VR.bc2P2>bc2P2.wrl, 13.653KB </mm> </c> <c><mm entity=fig.tbc2P2>fig.tbc2P2.gif, 0.460KB </mm><mm entity=VR.tbc2P2>tbc2P2.wrl, 13.697KB </mm></c> <c><mm entity=fig.tbc1P2>fig.tbc1P2.gif, 0.461KB </mm><mm entity=VR.tbc1P2>tbc1P2.wrl, 13.678KB </mm></c> <c><mm entity=fig.tb1P2>fig.tb1P2.gif, 0.522KB </mm> <mm entity=VR.tb1P2>tb1P2.wrl, 13.780KB </mm> </c> <c><mm entity=fig.tb2P2>fig.tb2P2.gif, 0.516KB </mm> <mm entity=VR.tb2P2>tb2P2.wrl, 13.732KB </mm> </c> <c><mm entity=fig.tcP2>fig.tcP2.gif, 0.477KB </mm> <mm entity=VR.tcP2>tcP2.wrl, 13.635KB </mm> </c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>0.00 <c>2.37 <c>2.37 <c>2.55 <c>2.55 <c>2.75 <caption>Conformers of <a href="phosphacinium/TableDioxPGas.html">dioxazaphosphacinium</a> within 3.0 kcal/mol of global minima in the gas phase. </float> <p> <a href="phosphacinium/TableCisMedioxPGas.html"><em>cis</em>-4,6,6-Trimethyl-2-oxo-1,3,6-dioxazaphosphacinium</> in the gas phase also shows a BC as the global minimum, but its conformational heterogeneity is much lower than that of the unsubstituted ring. Pentamethylcyclooctane has BCs as global minima, but the similarity ends there. Pentamethylcyclooctane shows a TCC at 0.43 kcal/mol (a reduced TCC/BC gap that we previously ascribed to destabilization of the BC), while this phosphorus ring has its lowest TCC at 5.59 kcal/mol. The CC originally at 1.49 kcal/mol in pentamethyl, now appears at 5.70 kcal/mol. The first TB in pentamethyl has increased from 1.55 to 4.10 kcal/mol. The second TB has gone from 1.59 to 5.59 kcal/mol. The TBC starting at 1.92 is now 4.94 kcal/mol above the global minimum. <float id=tableCompP3> <table> <colhead>Conformer <column> <c>2,2,4,6,6-BC' <c>1,3,3,7,7-TC <colhead>Structure <column> <c><mm entity=fig.bcP3>fig.bcP3.gif, 0.525KB </mm><mm entity=VR.bcP3>bcP3.wrl, 14.873KB </mm></c> <c><mm entity=fig.tcP3>fig.tcP3.gif, 0.504KB </mm><mm entity=VR.tcP3>tcP3.wrl, 14.910KB </mm></c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>2.89 <caption>Conformers of <a href="phosphacinium/TableCisMedioxPGas.html"><em>cis</em>-methyl dioxazaphosphacinium</a> within 3.0 kcal/mol of global minimum in the gas phase. </float> <p> <a href="phosphacinium/TableTransMedioxPGas.html"><em>trans</em>-4,6,6-Trimethyl-2-oxo-1,3,6-dioxazaphosphacinium</> in the gas phase shows a distorted TBC as the global minimum. Its conformational heterogeneity is much higher than that of the <em>cis</em> ring: the <em>cis</em> ring has only two conformers within 3.0 kcal/mol above the global minimum (inclusive), while the <em>trans</em> ring has seven. Both have fewer conformers than pentamethylcyclooctane, which has eight pairs of conformational enantiomers and two saddle points, all within 3.0 kcal/mol above the global minimum (inclusive). We find a BC (0.20 kcal/mol), two TCs (1.43 and 2.49), two TBs (1.50 and 2.84 kcal/mol) and another TBC (2.01 kcal/mol). <float id=tableCompP4> <table> <colhead>Conformer <column> <c>2,2,4,6,6-TBC <c>2,2,6,6,8-BC <c>1,3,3,7,7-TC <c>1,1,3,5,5-TB <c>2,2,6,6,8-TBC <c>3,3,5,7,7-TC <c>1,1,3,5,5-TB' <colhead>Structure <column> <c><mm entity=fig.tbc1P4>fig.tbc1P4.gif, 0.509KB </mm><mm entity=VR.tbc1P4>tbc1P4.wrl, 14.853KB </mm></c> <c><mm entity=fig.bcP4>fig.bcP4.gif, 0.517KB </mm> <mm entity=VR.bcP4>bcP4.wrl, 14.860KB </mm> </c> <c><mm entity=fig.tc1P4>fig.tc1P4.gif, 0.497KB </mm> <mm entity=VR.tc1P4>tc1P4.wrl, 14.841KB </mm> </c> <c><mm entity=fig.tb1P4>fig.tb1P4.gif, 0.497KB </mm> <mm entity=VR.tb1P4>tb1P4.wrl, 14.814KB </mm> </c> <c><mm entity=fig.tbc2P4>fig.tbc2P4.gif, 0.519KB </mm><mm entity=VR.tbc2P4>tbc2P4.wrl, 14.857KB </mm></c> <c><mm entity=fig.tc2P4>fig.tc2P4.gif, 0.511KB </mm> <mm entity=VR.tc2P4>tc2P4.wrl, 14.813KB </mm> </c> <c><mm entity=fig.tb2P4>fig.tb2P4.gif, 0.536KB </mm> <mm entity=VR.tb2P4>tb2P4.wrl, 14.881KB </mm> </c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>0.20 <c>1.43 <c>1.50 <c>2.01 <c>2.49 <c>2.84 <caption>Conformers of <a href="phosphacinium/TableTransMedioxPGas.html"><em>trans</em>-methyl dioxazaphosphacinium</a> within 3.0 kcal/mol of global minimum in the gas phase. </float> <p>The results in the gas phase for <a href="phosphacinium/TableDiMePGas.html">4,4,6,6-tetramethyl-2-oxo-1,3,6-dioxazaphosphacinium</> show a mixture of conformers. Five conformers show up within 3.0 kcal/mol above the global minimum. Now the global minimum is a TC, followed closely (0.58 kcal/mol) by a BC. In hexamethylcyclooctane, the global minimum is a TB, and the first TC has an energy of 7.26 kcal/mol. The first TB in this phosphonate ring appears at 2.58 kcal/mol and follows a TBC at 2.62, completing all the conformations within 3.0 kcal/mol. <float id=tableCompP5> <table> <colhead>Conformer <column> <c>1,1,3,3,7,7-TC <c>2,2,6,6,8,8-BC <c>2,2,4,4,6,6-BC' <c>3,3,5,5,7,7-TB <c>1,1,3,3,5,5-TB <c>2,2,6,6,8,8-TBC <colhead>Structure <column> <c><mm entity=fig.tcP5>fig.tcP5.gif, 0.529KB </mm> <mm entity=VR.tcP5>tcP5.wrl, 15.871KB </mm> </c> <c><mm entity=fig.bc1P5>fig.bc1P5.gif, 0.530KB </mm><mm entity=VR.bc1P5>bc1P5.wrl, 15.785KB </mm></c> <c><mm entity=fig.bc2P5>fig.bc2P5.gif, 0.521KB </mm><mm entity=VR.bc2P5>bc2P5.wrl, 15.646KB </mm></c> <c><mm entity=fig.tb1P5>fig.tb1P5.gif,0.570KB </mm> <mm entity=VR.tb1P5>tb1P5.wrl, 15.871KB </mm></c> <c><mm entity=fig.tb2P5>fig.tb2P5.gif, 0.552KB </mm><mm entity=VR.tb2P5>tb2P5.wrl, 15.844KB </mm></c> <c><mm entity=fig.tbcP5>fig.tbcP5.gif, 0.534KB </mm><mm entity=VR.tbcP5>tbcP5.wrl, 15.826KB </mm></c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>0.58 <c>1.71 <c>2.58 <c>2.61 <c>2.62 <caption>Conformers of <a href="phosphacinium/TableDiMePGas.html">dimethyl dioxazaphosphacinium</a> within 3.0 kcal/mol of global minimum in the gas phase. </float> <subsection> <head>Modeling in GB/SA water. <p>The conformational search for the <a href="phosphacinium/TableDioxPWat.html">6,6-dimethyl-2-oxo-1,3,6-dioxazaphosphacinium</> in water showed that the global minimum is a degenerate pair of BBs. These are followed by a degenerate pair of BC conformers, at 2.52 kcal/mol. All the other conformers are higher than 3.0 kcal/mol. The P-O bonds are longer than C-C bonds (1.59Ĺ vs. 1.54Ĺ), so this helps the relief of strain. The steric requirements of the oxygens and of the methyl groups are the same in both cases. <p>The dipole moments measured by Dale <link goesto="j.Dale72">Dale, 1972</> could fit both a BC or a BB, but he could not define unambiguously the positions of the oxygens. In the BBs, the oxygens could have taken positions 1,3 or 1,7; leaving the <em>gem</em>-dimethyls in positions 2,6. Our results agree with Dale's: in the BBs, the oxygens take positions 1,3 and 1,7 and the <em>gem</em> groups (dimethyl and methyl-oxo) are in 2,6. In the BCs at 2.52 kcal/mol (the only ones significantly populated at room temperature) the oxygens occupy positions 5,7 and the <em>gem</em> groups take 2,6. <float id=tableCompPWat2> <table> <colhead>Conformer <column> <c>2,2,6,6-BB <c>4,4,8,8-BB <c>2,2,6,6-BC <c>2,2,6,6-BC' <colhead>Structure <column> <c><mm entity=fig.bb1PW2>fig.bb1PW2.gif, 0.489KB </mm><mm entity=VR.bb1PW2>bb1PW2.wrl, 13.903KB </mm></c> <c><mm entity=fig.bb2PW2>fig.bb2PW2.gif, 0.457KB </mm><mm entity=VR.bb2PW2>bb2PW2.wrl, 13.751KB </mm></c> <c><mm entity=fig.bc1PW2>fig.bc1PW2.gif, 0.446KB </mm><mm entity=VR.bc1PW2>bc1PW2.wrl, 13.695KB </mm></c> <c><mm entity=fig.bc2PW2>fig.bc2PW2.gif, 0.437KB </mm><mm entity=VR.bc2PW2>bc2PW2.wrl, 13.702KB </mm></c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>0.00 <c>2.52 <c>2.52 <caption>Conformers of <a href="phosphacinium/TableDioxPWat.html">dioxazaphosphacinium</a> within 3.0 kcal/mol of global minimum in water. </float> <p> <a href="phosphacinium/TableCisMedioxPWat.html"><em>cis</em>-4,6,6-Trimethyl-2-oxo-1,3,6-dioxazaphosphacinium</> in water shows a TB' as the global minimum. It is closely followed (0.19 kcal/mol) by a BC. The enantiomeric conformer TB appears at 1.71 kcal/mol, and the last conformer within 3.0 kcal/mol is a BC. The second BC is not the conformational enantiomer of the one at 0.19 kcal/mol. <float id=tableCompPWat3> <table> <colhead>Conformer <column> <c>1,1,3,5,5-TB' <c>2,2,4,6,6-BC' <c>4,4,6,8,8-BB <c>2,2,4,6,6-BC <colhead>Structure <column> <c><mm entity=fig.tbPW3>fig.tbPW3.gif, 0.555KB </mm> <mm entity=VR.tbPW3>tbPW3.wrl, 14.900KB </mm> </c> <c><mm entity=fig.bc1PW3>fig.bc1PW3.gif, 0.477KB </mm><mm entity=VR.bc1PW3>bc1PW3.wrl, 14.847KB </mm></c> <c><mm entity=fig.bbPW3>fig.bbPW3.gif, 0.524KB </mm> <mm entity=VR.bbPW3>bbPW3.wrl, 14.764KB </mm> </c> <c><mm entity=fig.bc2PW3>fig.bc2PW3.gif, 0.482KB </mm><mm entity=VR.bc2PW3>bc2PW3.wrl, 14.796KB </mm></c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>0.19 <c>1.71 <c>2.84 <caption>Conformers of <a href="phosphacinium/TableCisMedioxPWat.html"><em>cis</em>-methyl dioxazaphosphacinium</a> within 3.0 kcal/mol of global minimum in water. </float> <p> <a href="phosphacinium/TableTransMedioxPWat.html"><em>trans</em>-4,6,6-Trimethyl-2-oxo-1,3,6-dioxazaphosphacinium</> in water shows a BB as the global minimum another BB is at 0.49 kcal/mol. The oxygens prefer positions 1,7 and 5,7; and the <em>gem</em> groups (Me, Me and Me, oxo) are in 4,8 and 2,6. A series of BCs show up in the region from 0.89 to 4.81 kcal/mol. The BCs have 2, 4, 6 as the preferred substitution sites. There are no TBCs lower than 5.4 kcal/mol. <float id=tableCompPWat4> <table> <colhead>Conformer <column> <c>4,4,6,8,8-BB <c>2,2,6,6,8-BB <c>2,2,4,6,6-BC' <c>2,2,6,6,8-BC <colhead>Structure <column> <c><mm entity=fig.bb1PW4>fig.bb1PW4.gif, 0.527KB </mm><mm entity=VR.bb1PW4>bb1PW4.wrl, 14.854KB </mm></c> <c><mm entity=fig.bb2PW4>fig.bb2PW4.gif, 0.519KB </mm><mm entity=VR.bb2PW4>bb2PW4.wrl, 14.818KB </mm></c> <c><mm entity=fig.bc1PW4>fig.bc1PW4.gif, 0.487KB </mm><mm entity=VR.bc1PW4>bc1PW4.wrl, 14.860KB </mm></c> <c><mm entity=fig.bc2PW4>fig.bc2PW4.gif, 0.481KB </mm><mm entity=VR.bc2PW4>bc2PW4.wrl, 14.924KB </mm></c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>0.49 <c>0.89 <c>2.98 <caption>Conformers of <a href="phosphacinium/TableTransMedioxPWat.html"><em>trans</em>-methyl dioxazaphosphacinium</a> within 3.0 kcal/mol of global minimum in water. </float> <p>The results in water for <a href="phosphacinium/TableDiMePWat.html">4,4,6,6-tetramethyl-2-oxo-1,3,6-dioxazaphosphacinium</> show TB (global minimum) and TB' (1.47 kcal/mol) as the only conformers within the 3.0 kcal/mol window. We could not characterize the lowest energy structure as either a minimum or as a saddle point. We attribute that to the different gradient-calculation algorithms used in the minimization routine and the vibrational frequencies routine. The higher gradient calculated by the frequencies routine terminated the calculation every time we attempted to characterize the stationary point. The energy minimization yielded a gradient well below 0.05 and we did not find any eclipsing methyl groups, nor torsions with values approaching 0° that could make it a saddle point, so we designate it as a minimum. We believe this intuitive supplementation of the results of this model chemistry is justified, because not including the global minimum could render our reasoning without a good foundation. <float id=tableCompPWat5> <table> <colhead>Conformer <column> <c>1,1,5,5,7,7-TB' <c>1,1,5,5,7,7-TB <colhead>Structure <column> <c><mm entity=fig.tb1PW5>fig.tb1PW5.gif, 0.583KB </mm><mm entity=VR.tb1PW5>tb1PW5.wrl, 15.969KB </mm></c> <c><mm entity=fig.tb2PW5>fig.tb2PW5.gif, 0.601KB </mm><mm entity=VR.tb2PW5>tb2PW5.wrl, 15.815KB </mm></c> <colhead>Energy (kcal/mol) <column> <c>0.00 <c>1.47 <caption>Conformers of <a href="phosphacinium/TableDiMePWat.html">dimethyl dioxazaphosphacinium</a> within 3.0 kcal/mol of global minimum in water. </float> <p>This ring shows conformational homogeneity, with only two conformers within 3.0 kcal/mol above the global minimum (inclusive). <p>Now we can compare our results to those by Dale. <link goesto="j.Dale72">Dale, 1972</> Dale found that 6,6-disubstituted-1,3-dioxocanes prefer BB as the global minimum. The unsubstituted dioxazaphosphacinium ring prefers BB <em>in solution</em>, but in the gas phase it prefers BC. The <em>cis</em>-substituted ring prefers a TB in solution and a BC in the gas phase; the <em>trans</em>-substituted ring has a BB in solution and a TBC in the gas phase; while the dimethyl substituted ring prefers a TB in solution and a TC in the gas phase. Solvation plays heavily in determining the preferred conformation: the unsubstituted ring global minimum in the gas phase (BC) is destabilized in solution by 2.52 kcal/mol. The <em>cis</em>-substituted ring BC in the gas phase is destabilized by 0.19 kcal/mol. In the <em>trans</em>-substituted ring, the gas-phase TBC could not be found in solution. The gas-phase TC found for the dimethyl-substituted ring, shows up 7.51 kcal/mol higher than the global minimum in solution. Dale's finding of a BB as minimum, could be due to a true BB minimum, such as in <em>trans</em>-methyl dimethyldioxazaphosphacinium, or to a pair of rapidly interconverting TBs, which could be the case in the dimethyl substituted ring, although the searches we performed did not find the saddle point for such a transformation. <chapter> <head>Modeling of phosphonates. <section> <head>Modeling of phosphorus species. <p>Many researchers have tried conformational analysis of phosphorus species by computational means, and they have used the full range of computational approaches: molecular mechanics, semiempirical and ab initio. The following sections review the diverse attempts at modeling molecules containing phosphorus (V). This review emphasizes mostly those efforts to <em>develop</em> modeling methods for phosphorus, as opposed to the <em>application</em> of methods already developed. <subsection> <head>Ab initio methods. <p>Ewig and van Wazer calculated phosphinic, phosphonic and phosphoric acids using STO-3G, 3-21G and 4-31G basis sets with <em>d</em> functions added on phosphorus. <link goesto="j.Ewig85">Ewig, 1985</> Later, the same authors studied methyl phosphinate, dimethyl phosphonate and trimethyl phosphate <link goesto="j.VanWazer86">Van Wazer, 1986</> employing STO-3G, 3-21G and 4-31G with <em>d</em> functions on phosphorus. <p>Denmark and Cramer studied <em>P</em>-allylphosphonic diamide the RHF/3-21G(*) level. <link goesto="j.Denmark90">Denmark, 1990</> They found good agreement with data from X-ray for both bond lengths and bond angles, but they point out that inclusion of polarization functions would correct for possible structural artifacts, such as an artificially planar nitrogen attached to the phosphorus. <p>Thatcher and Campbell recommend 3-21+G(*) basis set for modeling of phosphates and phosphonates, based on the need for <em>d</em> orbitals and diffuse functions to describe properly the electronic density. <link goesto="j.Thatcher93">Thatcher, 1993</> <p>Liang <em>et al.</em> used 3-21G*, 6-31G* and 6-31+G* basis sets to calculate geometries of dimethyl phosphate and methylpropyl phosphate anions. <link goesto="j.Liang93">Liang, 1993</> They showed that <term>3-21G*</term> (this basis set includes <em>d</em> orbitals for first and second row atoms) overestimates some bond lengths and the vibrational frequencies agree only qualitatively with those determined by 6-31G* and 6-31+G* basis sets. Their basis set of choice was 6-31G*, given the excellent agreement between its results and those of 6-31+G*, although they did not compare the quality of the charges. <p>Cramer <em>et al.</em> studied phosphorus (V)-substituted methyl anions with full geometry optimization using 3-21G(*). <link goesto="j.Cramer94">Cramer, 1994</> They preferred <term>3-21G(*)</term> (this basis set contains a set of six <em>d</em> orbitals for second row atoms but no <em>d</em> orbitals for first row atoms) because of the computational costs involved in using more extended basis sets, although they stressed the qualitative validity of the hypersurfaces calculated. <p>Landin <em>et al.</em> <link goesto="j.Landin95">Landin, 1986</> studied dimethyl phosphate anion and 2-ammonioethanol at the Hartree-Fock level using 3-21G, and 3-21G(*) basis sets for full geometry optimization, followed by single point calculations with 6-31G* and 6-31+G* basis sets. The most stable conformation had both O-CH<sub>3</sub> in syn-clinal (+sc) orientation. They reported differences in the charges calculated with 6-31G* and 6-31+G* basis sets, with the phosphorus atom suffering the greatest change in the charge when including polarization functions. <subsection> <head>Semiempirical methods. <p>Gorenstein <em>et al.</em> modeled phosphate esters at the CNDO/2 level including <em>d</em> orbitals. The results compared favorably to those of a PCILO calculation, and to an ab initio calculation using a minimal Slater-type orbital basis set without <em>d</em> orbitals. <link goesto="j.Gorenstein76">Gorenstein, 1976</> They compared their calculated bond distances and bond angles against X-ray data and found good agreement. Based on Gorenstein's conclusions, Van der Veken and Herman reported conformational analysis of dimethyl methylphosphonate at the CNDO/2 level including <em>d</em> orbitals. <link goesto="j.vdveken77">van der Veken, 1977</> <p>Koch and Anders compared MP2(full)/6-31+G*//MP2(full)/6-31+G*, MNDO and PM3 calculations on lithiophosphonates. <link goesto="j.Koch95">Koch, 1995</> PM3 reproduced well the energetic ranking of the conformers produced by ab initio, while MNDO failed. The suitability of PM3 to model organolithium species was confirmed, but it underestimated the bond lengths around the phosphorus atom. <p>Landin <em>et al.</em> <link goesto="j.Landin95">Landin, 1995</> found PM3 inadequate to model dimethyl phosphate anion, a result of an underestimation of dipole-dipole interactions which in turn, related to an underestimation of charge separation by the PM3 Hamiltonian. A Fourier analysis of the coefficients for the C-O-P=O torsion indicated that the coefficient associated with the anomeric effect was less important than the one associated with the dipole-dipole interactions, although none could be neglected due to a third coefficient that coupled both effects. <subsection> <head>Molecular mechanics methods. <p>Plyamovatyi <em>et al.</em> modeled dimethyl phosphate anion by a molecular mechanics scheme that emphasized interactions between unshared electron pairs. The results of their suggested molecular mechanics scheme reproduced the global minimum determined experimentally better than an ab initio calculation using the STO-3G basis set. <link goesto="j.Plyamovatyi77a">Plyamovatyi, 1977a</>, <link goesto="j.Plyamovatyi77b">Plyamovatyi, 1977b</>, <link goesto="j.Plyamovatyi90">Plyamovatyi, 1990</>, <link goesto="j.Plyamovatyi93">Plyamovatyi, 1993</> <p>Weiner <em>et al.</em> developed a molecular mechanics force field (AMBER) that could model phosphates. <link goesto="j.Weiner86">Weiner, 1986</> The molecular mechanics parameters were determined by fitting them to experimental geometries. The starting points were experimentally-determined force constants (from IR and Raman) and bond angles (from X-ray). <p>Mikolajczyk <em>et al.</em> studied 2-phosphoryl and 2-thiophosphoryl-1,3-heteroanes by molecular mechanics. <link goesto="j.Mikolajczyk89">Mikolajczyk, 1989</> The potential energy function included nonbonded interactions, torsional energy, angle deformations and lone pair interactions. They concluded that hyperconjugation did not play an important role in determining the conformational stabilities of 2-substituted-1,3-dithianes <p>Fox, Bowen, and Allinger extended their MM3 force field to include alkylphosphines. <link goesto="j.Fox92">Fox, 1992</> As starting points for their parametrization, they used structural parameters from electron diffraction and microwave spectroscopy. The resulting parameters modeled structures, vibrational spectra, moments of inertia and dipole moments fairly accurately. <p>Jin, Benesch, and Weaver developed MM2 parameters for modeling of lipids (MM2(Lipid) force field) by taking structures of phospholipids calculated by AM1. <link goesto="j.Jin94">Jin, 1994</> They observed good agreement between their results and those obtained by Ewig and Van Wazer using ab initio approaches. <link goesto="j.Ewig85">Ewig, 1985</> <link goesto="j.VanWazer86">Van Wazer, 1986</> They showed, however, that AM1 overestimated the barriers to rotation. This overestimation reduced the reliability of their torsional parameters. <section> <head>Development of AMBER* parameters for phosphonates. <p>We suggest three levels of molecular properties that molecular mechanics (MM) should reproduce: <ol><li>Atomic connectivities.</li> <li>Torsion angles.</li> <li>Energetic ranking of conformers.</li> </ol> If we want to believe the result of any computation, we need to ensure that it can reproduce accurately bond lengths and bond angles, otherwise we can discard its results offhand. The accurate reproduction of torsion angles implies a good representation of the intramolecular interactions, such as van der Waals repulsions and electrostatic effects, just to mention the most important. A correct ranking of the conformers means a proper accounting of the relative weights that correspond to the intramolecular forces. From these criteria, we can propose three ways to measure how well MM reproduces molecular properties: <ol><li>Absolute differences in bond lengths and angles between the MM values and the reference values.</li> <li>RMS deviation after least-squares fit of the MM geometry to the reference geometry.</li> <li>Comparison of MM conformational energies against reference energies.</li> </ol> <p>As reference values one can take either experimental information (X-ray data) or high level ab initio calculations. In the particular case of the energetic ranking of the conformers, one is usually limited to high level ab initio calculations, given the experimental difficulties involved in determining conformational populations in the gas phase. To see the details of the development process see the <link goesto="paramP">corresponding subsection in Methods</>. <subsection> <head>Calculations on dimethyl methylphosphonate. <p>The following figures show the molecular mechanics curves with the best fit to the ab initio curves. <float id=pc> <mm entity=fig.pc>fig.pc.gif, 3.795KB <caption>Fit of AMBER* phosphonate parameters for P-C bond stretch to 6-31+G* curve. </float> <float id=po> <mm entity=fig.po>fig.po.gif, 3.817KB <caption>Fit of AMBER* phosphonate parameters for P-O bond stretch to 6-31+G* curve. </float> <p>We took the P=O bond length from the ab initio results. The starting point for the fitting of the stretching force constant was the one found for the phosphonate P=O bond. <float id=opo> <mm entity=fig.opo>fig.opo.gif, 3.991KB <caption>Fit of AMBER* phosphonate parameters for O-P-O bond angle to 6-31+G* curve. </float> <float id=cp2o> <mm entity=fig.cp2o>fig.cp2o.gif, 4.142KB <caption>Fit of AMBER* phosphonate parameters for C-P=O bond angle to 6-31+G* curve. </float> <p>Dimethyl methylphosphonate has a total of six bond angles around the phosphorus: C-P=O, O-P-O, 2 O-P=O and 2 C-P-O. We included parameters only for C-P=O and O-P-O because adding parameters for the other bond angles gave rise to erratic behavior in the calculated geometries. Cross-coupling of the bond angle terms may be part of the reason. The simple functions used in AMBER* may not represent adequately such coupling. <float id=hcpo> <mm entity=fig.hcpo>fig.hcpo.gif, 4.349KB <caption>Fit of AMBER* phosphonate parameters for H-C-P=O torsion angle to 6-31+G* curve. </float> <float id=copo> <mm entity=fig.copo>fig.copo.gif, 4.789KB <caption>Fit of AMBER* phosphonate parameters for C-O-P-O torsion angle to 6-31+G* curve. </float> <p>The AMBER* H-C-P=O torsion potential very closely matches the ab initio curve. The C-O-P-O torsion potential from AMBER* has problems reproducing the very flat part of the ab initio ] potential where the C-O bond eclipses the P=O bond. It also introduces an error close to 0.5 kcal/mol in the energy of the minima where the C-O bond is <em>gauche</em> to the singly bonded oxygens. <p>The results in <link goesto="tablePredBLA">the table </> show that our AMBER* parameters reproduce ab initio bond lengths with a maximum deviation of 0.002 Ĺ, and bond angles with a maximum deviation of 1.1°. MM2* has maximum deviations of 0.037Ĺ and 10.9° respectively. MMX shows maximum deviations of 0.062Ĺ and 8.9°, while the maximum errors in UFF predictions amounted to 0.111Ĺ and 6.4° respectively. MM2* and MMX overestimated the P-C bond length, with values greater than 1.83Ĺ. The prediction of UFF was as good as ours (1.799Ĺ vs. 1.797Ĺ). MM2*, MMX and UFF overestimated the P-O bond length, with MM2* getting the closest value (1.605Ĺ) to the ab initio (1.590Ĺ). Our parameters predicted 1.588Ĺ. The smallest error by MM2*, MMX and UFF in the P=O length predictions was 0.02Ĺ. Our modified AMBER* matched the ab initio result within 0.001 Ĺ. In the predictions of the bond angles our modified AMBER* correctly reproduced all the ab initio trends, while MM2 and UFF predict standard tetrahedral angles, with little correlation to the ab initio results. MMX did remarkably well, predicting correctly the trends and most values, although the O-P-O angle resembles more a phosphine-like C-P-C angle. For the full listing of the predicted values for the different bond lengths and angles used in the evaluation, see the <link goesto="TablePredBLA">table of predicted bond lengths and angles</> for dimethyl methylphosphonate. <float id=tablePredBLA> <table> <rowhead> <row> <c>6-31+G* <c>AMBER* ε=1.0 <c>MM2* <c>MMX <c>UFF <rowhead>P-C <row> <c>1.798 <c>1.797 <c>1.835 <c>1.860 <c>1.799 <rowhead>P-O <row> <c>1.590 <c>1.588 <c>1.605 <c>1.622 <c>1.701 <rowhead>P=O <row> <c>1.455 <c>1.455 <c>1.470 <c>1.479 <c>1.510 <rowhead> <row> <c> <c> <c> <c> <c> <rowhead>O-P-O <row> <c>104.8 <c>105.1 <c>107.8 <c>96.7 <c>109.1 <rowhead>O=P-C <row> <c>115.9 <c>116.3 <c>105.8 <c>114.3 <c>109.5 <rowhead>O-P-C <row> <c>104.3 <c>105.2 <c>115.2 <c>109.2 <c>109.1 <rowhead>O=P-O <row> <c>113.3 <c>112.1 <c>106.1 <c>113.1 <c>110.1 <caption>Predicted bond lengths and angles of dimethyl methylphosphonate. </float> <p>The RMS deviations in the least-squares fits do not reveal major differences in the quality of the predictions. Our AMBER* parameters performed <em>marginally better</em> than the other force fields. AMBER* yields RMS values between 0.10 and 0.15, while the other force fields produced values between 0.10 and 0.25, but the difference is probably not significant. See the table of RMS fits of molecular mechanics to ab initio geometries for a full comparison of the RMS values produced by all the force fields. <float id=tableRMSabinit> <table> <colhead> <column> <c>g-,g- <c>g+,g+ <c>g-,g+ <c>g-,a <c>a,g+ <colhead>AMBER* ε=1.0 <column> <c>0.140 <c>0.141 <c>0.135 <c>0.102 <c>0.102 <colhead>MM2* <column> <c>0.187 <c>0.187 <c>0.240 <c>0.192 <c>0.192 <colhead>MMX <column> <c>0.111 <c>0.104 <c>0.250 <c>0.129 <c>0.128 <colhead>UFF <column> <c>0.669 <c>0.169 <c>0.174 <c>0.166 <c>0.160 <caption>RMS fit of molecular mechanics to ab initio geometries. </float> <p>Ab initio reveals only five minima in the conformational hypersurface of dimethyl methylphosphonate. (Our repeated attempts to locate the missing four conformers failed, when all our input structures collapsed to conformers already found.) The table of relative conformational energies shows that AMBER* using constant dielectric closely reproduces the energetic ranking of the minima found by ab initio. The greatest error resides in the energies of the <em>g-</em>, <em>a</em> and <em>a</em>, <em>g+</em> conformers, which AMBER* predicts 0.4 kcal/mol higher than ab initio. AMBER* found two more saddle points than ab initio. We believe this is a manifestation of the less-than-perfect match of our parameters to the ab initio results. <link goesto="f.artifact2">Note.</> <p>The results <link goesto="tableRelEn">tabulated</>, refer to the following conformers: <float id=confs> <mm entity=fig.confs>fig.confs.gif, 4.000KB <caption>Conformers of dimethyl methylphosphonate. </float> <float id=tableRelEn> <table> <rowhead> <row> <c>6-31+G* <c>AMBER* ε=1.0 <c>AMBER*(default) <c>MM2* <c>MMX <c>UFF <rowhead>g-,g- <row> <c>0.00 <c>0.00 <c>0.08 <c>2.01 <c>0.00 <c>0.00 <rowhead>g+,g+ <row> <c>0.00 <c>0.00 <c>0.08 <c>2.01 <c>0.00 <c>0.00 <rowhead>g-,g+ <row> <c>0.14 <c>0.12 <c>n.f.<link goesto="NF">*</> <c>4.07 <c>0.68 <c>0.11 <rowhead>g+,g- <row> <c>n.f.<link goesto="NF">*</> <c>0.16<link goesto="f.saddle">*</> <c>0.00 <c>4.70 <c>0.46 <c>n.f.<link goesto="NF">*</> <rowhead>g-,a <row> <c>2.75 <c>3.17 <c>2.15 <c>0.00 <c>0.39 <c>7.58 <rowhead>a,g+ <row> <c>2.75 <c>3.17 <c>2.15 <c>0.00 <c>0.38 <c>7.58 <rowhead>a,g- <row> <c>n.f.<link goesto="NF">*</> <c>n.f.<link goesto="NF">*</> <c>1.99 <c>2.32 <c>0.64 <c>n.f.<link goesto="NF">*</> <rowhead>g+,a <row> <c>n.f.<link goesto="NF">*</> <c>n.f.<link goesto="NF">*</> <c>1.99 <c>2.32 <c>0.61 <c>n.f.<link goesto="NF">*</> <rowhead>a,a <row> <c>n.f.<link goesto="NF">*</> <c>7.41<link goesto="f.saddle">*</> <c>6.86 <c>3.70 <c>n.f.<link goesto="NF">*</> <c>n.f.<link goesto="NF">*</> <caption>Relative conformational energies (kcal/mol) </float> <footnote id=f.saddle> Saddle point. </footnote> <footnote id=NF> *not found </footnote> <footnote id=f.artifact2> We want to illustrate the importance of dealing properly with the electrostatics: use of the default (distance-dependent) dielectric treatment of electrostatics, completely scrambles the energetic ranking of the conformers, <em>e.g.</em>, the global minima have now a relative energy of 0.08 kcal/mol, the minimum found at 0.14 kcal/mol by ab initio is found at 0.12 kcal/mol by the constant dielectric treatment, while the distance-dependent failed to find it as a stationary point. Two structures that are not part of the hypersurface (a,g- and g+,a) either by ab initio or AMBER* with constant dielectric, were found by the distance-dependent dielectric treatment at 1.99 kcal/mol. A constant dielectric was the proper choice to develop the parameters because the ab initio results were calculated assuming a vacuum, so the dielectric permittivity of the medium stayed constant. In the version of AMBER included in MacroModel, <link goesto="j.Weiner86">Weiner, 1986</> the parameters fit <em>experimental</em> values so the authors found that a distance-dependent dielectric gave a better fit because of its emulation of polarization effects. </footnote> <p>MM2* found degenerate pairs, but its energetic ranking differs from that by ab initio. MM2* finds <em>g-,a</em> and <em>a,g+</em> as global minima. MMX found the same global minima as ab initio and nearly degenerate pairs of conformers, but the conformational energies span a narrow range. The hypersurface is, thus, very flat. The hypersurface contains two minima not found by ab initio. UFF found the same global minima as ab initio and the energetic ranking is qualitatively the same, but the conformational energies are much higher than the ab initio predictions. We looked repeatedly for the <em>g+,g-</em> conformer without success. <float id=profiles> <mm entity=fig.profiles>fig.profile.gif, 4.658KB <caption>Comparison of molecular mechanics C-O-P=O torsion profiles vs. ab initio. </float> <p>Our computational results agree with the experimental work by Katolichenko <em>et al.</em> <link goesto="j.Katolichenko73">Katolichenko, 1973</> who used IR spectroscopy and measurements of dipole moments, and detected two major conformers: gauche-trans (<em>a,g-</em> and <em>g+,a</em> by our notation) and gauche-gauche (<em>g+,g+</em>, <em>g-,g+</em>, <em>g+,g-</em>, and <em>g-,g+</em>). They deduced the presence of the gauche-trans by elimination of other conformers due to dipole moment considerations. The difference in energy found between the gauche-trans and the gauche-gauche was less than 0.5 kcal/mol. <subsection> <head>Comparison vs. crystal structures. <p>After developing the parameters, we tested them against our molecule of interest and several crystal structures to see how well could they reproduce results in the condensed phase. The structures were retrieved from the Cambridge Crystallographic Data File (CCDF) <link goesto="j.Allen77">Allen, 1977</> and their codenames are: <a href="methylphosp/zaysib.wrl">ZAYSIB (zaysib.wrl, 13.587KB)</a>, <link goesto="j.Kumaravel95">Kumaravel, 1995</> <a href="methylphosp/cegxuh.wrl">CEGXUH (cegxuh.wrl, 15.784KB)</a>, <link goesto="j.Day84">Day, 1984</> <a href="methylphosp/felsoe.wrl">FELSOE (felsoe.wrl, 23.386KB)</a>, <link goesto="j.Nastopoulos87">Nastopoulos, 1987</> <a href="methylphosp/duksor.wrl">DUKSOR (duksor.wrl, 15.993KB)</a> and <link goesto="j.Bentrude86">Bentrude, 1986</> <a href="methylphosp/dumlec.wrl">DUMLEC (dumlec.wrl, 26.911KB)</a>. <link goesto="j.Dyrbusch86">Dyrbusch, 1986</> We looked for structural variety, always accounting for the limitations of our parameters: <ul> <li>No P-C(<em>sp<sup>2</sup></em>) fragments.</li> <li>No P-C(<em>sp</em>) fragments.</li> <li>No P-O-C(<em>sp</em>).</li> <li>No charges on the oxygens.</li> </ul> We chose only one structure from several reported by Nastopoulos <link goesto="j.Nastopoulos87">Nastopoulos, 1987</> because including several molecules of the same structural type could bias the evaluation by giving a greater relative weight to a particular kind of functionality. <float id=zaysib> <mm entity=fig.phosp>fig.phosp.gif, 0.591KB </mm> <caption>First crystal structure used for comparison (ZAYSIB). </float> <float id=crystals> <mm entity=fig.crystals>fig.crystals.gif, 4.624KB</mm> <caption>Additional crystal structures used in the comparison. </float> <p>The <link goesto="tableMMXray">table of molecular mechanics vs. X-ray</> displays the results of the tests against crystal structures. <float id=tableMMXray> <table> <colhead> <column> <c>P-C <c>P-O <c>P=O <c>O-P-O <c>O=P-C <c>O-P-C <c>O=P-O <colhead>X-ray <column> <c>1.797 <c>1.574 <c>1.461 <c>104.2 <c>114.8 <c>106.2 <c>112.7 <colhead>6-31+G* <column> <c>1.798 <c>1.590 <c>1.455 <c>104.8 <c>115.9 <c>104.3 <c>113.3 <colhead>AMBER* ε=1.0 <column> <c>1.798 <c>1.592 <c>1.455 <c>103.7 <c>117.9 <c>106.5 <c>110.6 <colhead>MM2* <column> <c>1.833 <c>1.592 <c>1.466 <c>100.3 <c>108.5 <c>114.4 <c>109.4 <colhead>MMX <column> <c>1.869 <c>1.620 <c>1.479 <c>98.7 <c>114.3 <c>108.7 <c>112.6 <colhead>UFF <column> <c>1.830 <c>1.707 <c>1.512 <c>109.6 <c>109.5 <c>110.1 <c>108.7 <caption>Comparison of Molecular Mechanics results vs. X-ray. </float> <p>We observe the same trends as from the comparison against ab initio. Ab initio does show some discrepancies with the crystal structures. Two of the most intriguing are the longer P-O bond predicted by ab initio (1.590Ĺ ab initio vs. 1.574Ĺ X-ray), and the shorter P=O bond (1.455Ĺ ab initio vs. 1.461Ĺ X-ray). We can only suggest a few reasons for these differences: a) correlation effects not included in the calculations, b) crystal packing forces affecting the experimental values or c) a combination of a) and b). Regarding the inclusion of correlation, calculations by Koch and Anders <link goesto="j.Koch95">Koch, 1995</> on methylphosphonic acid at the HF/6-31+G* and MP2/6-31+G* levels show that electronic correlation <em>increases</em> both bond lengths: P=O (1.460Ĺ by HF to 1.494Ĺ by MP2) and P-O (1.596Ĺ by HF to 1.629Ĺ by MP2) so we find it difficult to justify the differences on these grounds. <link goesto="f.artifact3">Note.</> <footnote id=f.artifact3> MP2 is known to overestimate corrections in bond lengths when the basis set used is too small <link goesto="b.Szabo96">Szabo, 1996</> and the effect is more pronounced on multiply bonded species. One could expect, then, to see a greater increase in the P=O length than in the P-O length. The P=O bond increases 0.034Ĺ, while the P-O increases 0.033Ĺ. Most likely, only a calculation using a larger basis set (and probably more terms in the Mřller-Plesset expansion) can settle the issue of the appropriateness of the basis set used. </footnote> Crystal packing forces become unlikely candidates after realizing that all the molecules used for testing crystallize in different systems. AMBER* reproduces fairly closely the deficiencies shown by HF/6-31+G* in the predicted bond lengths (maximum deviation of 0.018Ĺ) and in the bond angles (maximum deviation of 3.1°). MM2* overestimates the P-C and P-O bond lengths by 0.035Ĺ at the most, while the greatest deviation from the experimental bond angles amounts to 8°. MMX fits well the angles, but it overestimates P-C and P-O lengths by as much as 0.07Ĺ. UFF has the greatest errors in bond lengths (maximum deviation of 0.13Ĺ) and has little predictive value for the angles, as they cluster around 109.5°. <float id=tableRMSheavy> <table> <colhead> <column> <c><em>Gas phase</em> <c>AMBER* <c>MM2* <c>MMX <c><em>Water</em> <c>AMBER* <c>MM2* <c>MMX <colhead>ZAYSIB <column> <c> <c>0.603 <c>0.167 <c>0.086 <c> <c>0.086 <c>0.160 <c>0.084 <colhead>CEGXUH <column> <c> <c>0.241 <c>0.416 <c>0.013 <c> <c>0.474 <c>0.417 <c>0.013 <colhead>FELSOE <column> <c> <c>0.602 <c>0.602 <c>0.034 <c> <c>0.476 <c>0.557 <c>0.032 <colhead>DUKSOR <column> <c> <c>0.862 <c>0.631 <c>0.713 <c> <c>0.656 <c>0.575 <c>0.681 <colhead>DUMLEC <column> <c> <c>0.445 <c>0.446 <c>0.056 <c> <c>0.502 <c>0.433 <c>0.284 <caption>RMS values of MM vs. X-ray including all heavy atoms. </float> <p>The RMS values including all heavy atoms show that MMX yields best fits both in the gas phase and in water. AMBER* produces a low RMS value only for ZAYSIB in water, but we note that some torsion angles far from the phosphonate group change after minimization. MM2* yields RMS values close to those by AMBER*. Differences in torsion angles dominate RMS values, so changes in torsion angles not controlled by our parameters can give a wrong idea of the quality of the fit. <float id=tableRMSphosph> <table> <colhead> <column> <c><em>Gas phase</em> <c>AMBER* <c>MM2* <c>MMX <c><em>Water</em> <c>AMBER* <c>MM2* <c>MMX <colhead>ZAYSIB <column> <c> <c>0.445 <c>0.170 <c>0.097 <c> <c>0.078 <c>0.159 <c>0.087 <colhead>CEGXUH <column> <c> <c>0.240 <c>0.287 <c>0.262 <c> <c>0.281 <c>0.294 <c>0.011 <colhead>FELSOE <column> <c> <c>0.176 <c>0.182 <c>0.150 <c> <c>0.157 <c>0.186 <c>0.013 <colhead>DUKSOR <column> <c> <c>0.039 <c>0.094 <c>0.058 <c> <c>0.046 <c>0.099 <c>0.055 <colhead>DUMLEC <column> <c> <c>0.347 <c>0.286 <c>0.213 <c> <c>0.280 <c>0.280 <c>0.251 <caption>RMS values of MM vs. X-ray including phosphonate heavy atoms only. </float> <p>If we include only the phosphonate atoms, we observe a much improved fit in the AMBER* results for water. MM2* has values slightly higher than those by AMBER* both in the gas phase and water. MMX consistently yields very low RMS values in the gas phase and water. <p>The low RMS values obtained by MMX are misleading because MMX provides a very flat hypersurface, as evidenced in the <link goesto="tableRelEn">table</> and in the <link goesto="profiles">profiles</>. This means that the starting geometry changes very little. <chapter> <head>Methods. <section> <head>General methods and software. <subsection> <head>Molecular mechanics. <p>We employed the package MacroModel v.5.0 for Silicon Graphics workstations. All the conformational searches used the AMBER* force field and MonteCarlo sampling routine with Normal setup and Full Matrix Newton Raphson (FMNR) minimization with line search disabled. All the stationary points obtained were characterized as minima or saddle points by using the MTEST utility (calculation of vibrational frequencies) available in MacroModel. All the saddle points showed only one imaginary frequency and the minima had only real frequencies. <p>FMNR with line search disabled requires substantial storage resources and accumulates many structures with high gradients which render them meaningless chemically; however, the author opted for this algorithm due to its extreme speed (even when including solvent effects) and because of the <em>good ability of the algorithm to find saddle points</em>. Polak-Ribiere Conjugate Gradient (PRCG) and Oren-Spedicato Variable Metric (OSVM) are not likely to converge to saddle points. TCNG can converge to saddle points, but its speed makes it less convenient than FMNR, while Steepest Descent (SD) is a mediocre gradient minimizer. SD requires a postprocessing step of the structures it generates by some algorithm able to reduce the gradients under acceptable cutoffs. For a better discussion of the relative merits of the different minimization algorithms available in MacroModel, see the MacroModel Manual. The spurious structures are easily filtered out by cutting and pasting only the structures with gradients <0.05. <p>The AMBER* calculations in water used the GB/SA solvent model. In all cases we calculated the vibrational frequencies of the conformations to characterize them as minima or as saddle points. The morpholinium rings and the cyclohexanes used the default distance-dependent dielectric. <p>When using PCMODEL <link goesto="c.Pcmodel">v.4.0</> we used all the default settings. When including the effect of water the dielectric constant was set to 78.3. PCMODEL uses the MMX force field. We also used PCMODEL as a front end for MOPAC 6.0 and MOPAC93. <link goesto="b.Gajewski90">Gajewski, 1991</> </subsection> <subsection> <head>Semiempirical calculations. <p>We used MOPAC 6.0 <link goesto="c.Jstewart90">Stewart, 1990</> and MOPAC93 for the semiempirical calculations. We chose AM1 as the Hamiltonian in all cases. The solvent model COSMO <link goesto="j.Klamt93">Klamt, 1993</> employed a dielectric constant of 78.3. All the structures were minimized (sometimes requiring an Intrinsic Reaction Coordinate calculation) until a vibrational analysis showed absence of imaginary frequencies. The optimizations in the gas phase used the Broyden-Fletcher-Golfarb-Shannon (BFGS) minimization routine, reducing all the gradient norms under 0.01. The minimizations in solution benefitted from using Eigenvector Following (EF), to lower all the gradient norms under 0.3. <subsection> <head>Ab initio calculations. <p>All the ab initio computations were done using Gaussian94 <link goesto="c.Gaussian94">Gaussian, Inc.</> In those cases where the structure corresponded to a stationary point, the vibrational frequencies were calculated to confirm the absence of imaginary frequencies, for the minima, or the presence of just one imaginary frequency, for the saddle points. We chose single points for the carnitine calculations after finding out that full optimization including solvent effects was prohibitively expensive, and only a supercomputer could tackle such calculations. <section> <head>Acetylcarnitine calculations. <subsection> <head>Conformational search strategy by molecular mechanics. <p>We performed a grid search with the following guidelines: <ol> <li>We allowed three initial values, 60°, -60° and 180° (<em>g+</em>, <em>g-</em> and <em>a</em> respectively) for the following torsions: N-CH<sub>2</sub>-CH-OH(Ac), CH<sub>2</sub>-CH-CH<sub>2</sub>COO<sup>-</sup>, and CH<sub>2</sub>-CH-O-H(Ac)</li> <li>We used initial values of 0° and 180° (<em>s</em> and <em>a</em> conformations) for the CH-O-C(O)-CH<sub>3</sub>torsion angle.</li> <li>We used initial values of 90° and 180° for the CH-CH<sub>2</sub>-C(O)-O<sup>-</sup> torsion angle</li> <li>No initial values were given to torsions containing symmetric tops, like those for methyl groups and (CH<sub>3</sub>)<sub>3</sub>N<sup>+</sup>-CH<sub>2</sub>, but they were left free for optimization.</li> </ol> <p>The previous conditions yielded 108 conformers for acetylcarnitine, 54 for carnitine, 27 for acetylcholine and 9 for choline. All input geometries were fully optimized in the gas phase (AM1) and with solvent (AM1/COSMO). We also calculated water and acetic acid. <subsection> <head>Conformational populations. <p>Boltzmann factors (F) were calculated by the following formula:<br> F(c)=exp(-δH<sub>f</sub>/RT)/σi(exp(-δH<sub>f</sub>/RT)) <br>where: <dl> <dt>F(c) <dd>Boltzmann factor corresponding to conformer c <dt>δH<sub>f</sub> <dd>Heat of formation, <dt>R <dd>Gas constant <dt>T <dd>Temperature. </dl> <p>Heats of formation that included the contributions of individual conformers were calculated with the following equation:<br> δH<sub><em>ftot</em></sub> = σi (F(c))(δH<em>f</em>(c<sub>i</sub>)) <br>where: <dl> <dt>δH<sub><em>ftot</em></sub> <dd>Heat of formation over all conformers <dt>F(c<sub>i</sub>) <dd>Boltzmann factor for conformer i <dt>δH<em>f</em>(c<sub>i</sub>) <dd>Heat of formation for conformer i </dl> <subsection> <head>Semiempirical calculations on carnitines, cholines and propanoates. <p>The first route card we tried was: <br><br><tt> AM1 NOXYZ NOINTER PRECISE </tt><br><br> but the most effective route card used for the carnitines in the gas phase was: <br><br><tt> AM1 NOINTER T=3600.00 EF LET DDMIN=0.0 </tt><br><br> The cholines required a different route card: <br><br><tt> AM1 CHARGE=+1 GNORM=0.01 GEO-OK EF LET DDMIN=0.0 NOINTER T=3600.00 </tt><br><br> The acetoxypropanoates used: <br><br><tt> AM1 CHARGE=-1 GEO-OK GNORM=0.5 NOXYZ NOINTER NOLOG T=3600.00 XYZ </tt><br><br> The hydroxypropanoates used: <br><br><tt> AM1 CHARGE=-1 GNORM=0.5 T=3600.00 GEO-OK NOXYZ NOINTER NOLOG </tt><br><br> <p>The inclusion of solvent required the following route card for carnitines: <br><br><tt> AM1 NOINTER T=3600.00 EPS=78.3 PRECISE EF LET DDMIN=0.0 </tt><br><br> while the carnitines needed more care with the gradient norm: <br><br><tt> AM1 T=3600.00 EF LET DDMIN=0.0 EPS=78.3 GNORM=0.01 NOINTER PRECISE </tt><br><br> The acetylcholines used: <br><br><tt> AM1 CHARGE=+1 GNORM=0.01 GEO-OK EF LET DDMIN=0.0 EPS=78.3 NOINTER T=3600.00 </tt><br><br> and the cholines: <br><br><tt> AM1 CHARGE=+1 GNORM=0.01 GEO-OK EPS=78.3 EF LET DDMIN=0.0 NOINTER T=3600.00 </tt><br><br> The propanoates used: <br><br><tt> AM1 CHARGE=-1 EPS=78.3 GNORM=0.5 NOXYZ NOINTER NOLOG T=3600.00 </tt><br><br> The hydroxypropanoates used: <br><br><tt> AM1 CHARGE=-1 EPS=78.3 T=3600.00 GNORM=0.5 NOXYZ NOINTER NOLOG </tt><br><br> <p>To simplify, a general route card would be: <br><br><strong><tt> AM1 CHARGE=(charge) EPS=78.3 EF LET DDMIN=0.0 T=(time) PRECISE + GNORM=X.XXXX GEO-OK NOXYZ NOINTER NOLOG XYZ </tt></strong><br><br> <dl> <dt>AM1 CHARGE=(charge) EPS=78.3 </dt> <dd>Specify Hamiltonian, charge on the system and solvent dielectric constant.</dd> <dt>EF LET DDMIN=0.0 T=(time)</dt> <dd>Minimization options: eigenvector following, let the heat of formation increase, take the smallest possible step for the trust radius. Specify a time long enough to complete the optimization.</dd> <dt>PRECISE</dt> <dd>(optional) Tighten up criteria in case the final gradients are >2.0. Adjust (time) appropriately. Sometimes (not always) MOPAC prints out a message to indicate this keyword is needed.</dd> <dt>GNORM=X.XXXX</dt> <dd>(optional) Tighten up the gradient norm criterion to finish the minimization to <X.XXXX (0.01 < X.XXXX < 2.0). Use this keyword in case PRECISE is unable to reduce the gradients <2.0.</dd> <dt>GEO-OK</dt> <dd>(optional) Some distorted input geometries may require this keyword. MOPAC prints out a message whenever this keyword is needed.</dd> <dt>NOXYZ NOINTER NOLOG</dt> <dd>(preferred) Keywords to reduce the size of the output files: do not print cartesian coordinates, do not print interatomic distances, suppress log trail if possible.</dd> <dt>XYZ</dt> <dd>(optional) Last resort for difficult minimization cases: perform optimization in cartesian coordinates.</dd> </dl> <subsection> <head>Ab initio calculations on carnitines, cholines and propanoates. <p><target id=abinitio>In gas phase, the output geometries after full optimization by AM1 were used as input for Gaussian94. We used the following route card</target>: <br><br><tt> #rhf 6-31G* opt freq scf=direct maxdisk=10000000 geom=(nodistance, noangle) </tt><br><br> for the carnitines and the cholines. For the propanoates we used: <br><br><tt> #rhf 6-31+G opt freq scf=direct maxdisk=10000000 geom=(nodistance, noangle) </tt><br><br> notice that the only difference resides in the choice of basis set. The MP2 calculations had the following route cards: <br><br><tt> #rhf mp2 6-31g* scf=direct maxdisk=10000000 geom=(nodistance, noangle) </tt><br><br> for the carnitines and the cholines, and <br><br><tt> #rhf mp2 6-31+g scf=direct maxdisk=10000000 geom=(nodistance, noangle) </tt><br><br> for the propanoates. <p>In solvent, the output geometries after full optimization by AM1/COSMO (ε=78.3) were used as input for single point calculations including the Tomasi solvent model. The route card was: <br><br><tt> #rhf 6-31G* scrf=Tomasi scf=direct maxdisk=10000000 geom=(noangle, nodistance) </tt><br><br> for the carnitines and the cholines. The propanoates used: <br><br><tt> #rhf 6-31+G scrf=Tomasi scf=direct maxdisk=10000000 geom=(noangle, nodistance) </tt><br><br> Again, the only difference resides in the choice of basis set. The acetylcarnitines used <tt>78.3 100</tt>, the carnitines used <tt>78.3 200</tt>, the acetylcholines used <tt>78.5 128</tt>, the cholines used <tt>78.3 200</tt>, the acetoxypropanoates and hydroxypropanoates used <tt>78.3 128</tt>. The value <tt>78.5</tt> for the acetylcholines was the product of attempts at eliminating oscillatory behavior of the wavefunction. The choice of the number of points per sphere was governed by the possibility to achieve convergence in the wavefunction. In every case we started with the default value of <q>200</q> and reduced the number of points until the program could achieve self-consistency. According to the Gaussian94 manual, the number of points per sphere has to be a number in the series #points = 2(n<sup>2</sup>) where <q>n</q> is a positive integer. <section> <head>Conformational search in six-membered rings. <p>An average of 15,000 structures were generated for each compound to achieve convergence. The criterion for convergence was that one 2,000-structure run failed to generate any new conformers after examination of a minimum of 10,000 structures. The energy window was 35.8 kcal/mol above the global minimum (150 kJ/mol). The default distance-dependent dielectric constant was used for the calculations in the gas phase. <section> <head>Conformational search and analyses in eight-membered rings. <p>For the eight-membered rings, an average of 130,000 structures for each compound were generated and minimized until convergence was achieved. The criterion for convergence was that one 15,000-structure run failed to produce any new conformers after examination of a minimum of 100,000 structures. All the calculations in the gas phase were done specifying constant dielectric treatment of the electrostatics, instead of the default distance-dependent dielectrics. <p>The conformations were named by comparing the structures to perspective drawings of cyclooctane conformers. In difficult cases (distorted structures), recourse to Weiler plots usually afforded a fast identification of the conformer. <section> <head>AMBER* parametrization of phosphonates. <p><target id=paramP>We followed the procedure described by Hopfinger and Pearlstein</target>. <link goesto="j.Hopfinger84">Hopfinger, 1984</> All the points for the parametrization of dimethylmethylphosphonate were calculated at the RHF/6-31+G* level of theory. 6-31G* can easily match the 6-31+G* geometries, the reason for the choice of 6-31+G* was our desire to generate high-quality charges for the inclusion of solvation effects. Landin <em>et al.</em> <link goesto="j.Landin95">Landin, 1995</> found appreciable differences in the charges calculated by 6-31G* and 6-31+G* in their calculations. We calculated seven points, taken at 0.1 Ĺ steps, for each of the P-C, and P-O bonds stretchings. For the C-P=O, and O-P-O bond angles, we calculated 15 points with 1° separation. The H-C-P=O and C-O-P-O torsions each required 36 points, at 10° steps, to parametrize the full rotation. We used the optimized values of the bond lengths and angles as first guesses for the parameters. The parameters were then adjusted by trial and error, judging "by eye" the best fit to the ab initio curves. <p>In the evaluation of the RMS fits, we used the least-squares fit utility provided in each MM program. Only heavy atoms were included in the fitting. We used the program Babel v.1.1 <link goesto="c.Babel">Babel, v.1.1</> for the translation of structures between the different file formats required by each program. <p>Cerius<sup>2</sup> v.2.0, which employs the Universal Force Field (UFF) <link goesto="j.Castonguay92">Castonguay, 1992</> <link goesto="j.Rappe92">Rappé, 1992</> <link goesto="j.Rappe93">Rappé, 1993</> was used only for comparison purposes in the calculations on dimethyl methylphosphonate. We set the phosphorus atom type to P_3+5, disabled "Automatic Atom Typing". Enabled "Update Charges" by the QEq charge equilibration scheme <link goesto="j.Rappe91">Rappé, 1991</> every 50 iterations. Selected "Grid Search" varying both C-O-P=O torsions from -150° to 130° with 30° steps, minimizing each conformer. We disabled restraining of the torsions and kept unique conformers within 100.00 kcal/mol above the current minimum. <section> <head>Least-squares fit of phosphonate rings to tetrahedral intermediate.<target id=LSFit></target> <p>First, we fit only the N-C-C-O atom pairs, to determine the atoms that corresponded best to the <em>oxo</em> on the phosphorus, and the corresponding methyl groups on the quaternary nitrogens. After that, we repeated the least-squares fitting including all the atoms pairs described in the <link goesto="FitTI">figure</>. <section> <head>Hardware. <p>PCMODEL v.4.0, MacroModel v.5.0, Cerius<sup>2</sup> v.2.0, MOPAC 6.0 and MOPAC93 ran on a Silicon Graphics Indigo<sup>2</sup> Extreme with 96 MB of RAM, R4400 CPU and R4010 FPU, under IRIX 5.3. Gaussian94 (serial version) ran on an IBM SP2 equipped with 14 nodes, 128 MB/node of RAM and 2 GB/node of scratch space, running under AIX 3.2/4.0 and LoadLeveler as a batch process controller. </chapter> <chapter> <head>Conclusions. <section> <head>Summary <p>One goal of our research is determine what are the conformations and configurations of the tetrahedral intermediates in carnitine acyl transfers. So far, the approach has been experimental, by designing conformationally constrained analogues of the tetrahedral intermediates. To make the approach cost-effective, we need reliable modeling methods to guide the choice of the next generation of inhibitors. The modeling methods developed in this dissertation fulfill that need for the most part. <p>This dissertation addressed two additional questions: <ul> <li>Why does acetylcarnitine have such a high free energy of hydrolysis?</li> <li>What are the conformations of our heterocyclic moieties that could best fit the tetrahedral intermediate for acetylcarnitine-CoA exchange?</li> </ul> Acetylcarnitine reaches its high energy of hydrolysis by drawing from the solvation energy. The coupling between solvation energy, dipole moment and conformational change, supplies the necessary energy from the solvation term to yield a free energy of hydrolysis that compares to that of AcCoA. The high-energy status of acylcarnitine makes possible an exchange equilibrium with CoA (K<sub>eq</sub> = 0.6), that minimizes the energy consumed by processes other than the transport through the cell membrane. <p>From the preliminary results for the modeling of the tetrahedral intermediate, <link goesto="tableTIWat1">shown in the table in chapter 3,</> we see the RMS fits of the dioxazaphosphacinium rings to the intermediate. The most promising candidates are both boat-boat conformers that correspond to the <em>R,S</em> diastereomer of the tetrahedral intermediate. The <em>cis</em>-substituted ring and the dimethyl-substituted ring yield the closest fit to the <em>R,S</em> tetrahedral intermediate. These fits should be considered as one parameter in a quantitative structure-activity relationship for the inhibitory potency of the inhibitors already developed by our group. This will help in the prediction of the next generation of inhibitors. The morpholinium rings should receive a similar treatment. <p><ul> <li>Upon hydrolysis, the zwitterion of acetylcarnitine keeps a nearly constant dipole moment thanks to the influence of conformational flexibility on the positioning of the charged centers. This keeps the solvation energy nearly constant, leaving more chemical energy available to be released.</li> <li>Conformational change can act as a mechanism for the storage of chemical energy.</li> <li>In morpholinium rings, the conformational preference in aqueous media obeys more the increased steric interactions due to the shorter C-N and C-O bonds than the differences in dipole moment.</li> <li><em>Gem</em> substitution in morpholinium rings can help control the relative stabilities of the chair and the twist-boat. </li> <li>Addition of substituents in a 1,1,3,3-di<em>gem</em> pattern on dioxazaphosphacinium rings can favor a twist-boat global minimum over a boat-chair conformation.</li> <li>Differences in polarity in dioxazaphosphacinium rings override steric effects, when methyl groups are involved, in determining the preferred conformation in aqueous solution.</li> <li>We have developed parameters for accurate modeling of neutral dialkyl alkylphosphonates by molecular mechanics (AMBER*). We used three measures of the goodness of fit when testing against ab initio results and crystal structures, and found our parameters more reliable than other commonly used force fields (MM2*, MMX and UFF)</li> </ul> <section> <head>Future work. <p>Based on the results obtained from the acetylcarnitine hydrolysis, the aqueous modeling of the heterocycles including a methylenecarboxylate should pay attention to the influence of the dipole moments. In the dioxazaphosphacinium rings, there will be two sources of polarity: the dipoles due to the C-O-P=O torsions, and the dipole due to the zwitterion. How will the conformational preference of the rings be affected by the presence of the zwitterion?. Answering such question will require careful attention to the charge set used in the calculation. It may be desirable to determine a new charge set for the methylenecarboxylate-substituted ring, at the HF/6-31+G* level of theory using the CHelpG scheme, to ensure that the charge set found in this dissertation is still applicable (see the file <a href="methylphosp/Abinitio/BondPC.txt">BondPC.txt</a> for the output from the CHelpG calculation). After all, changing from a cation to a neutral species will likely affect the charge distribution in the molecule. In addition, unless newer versions of MacroModel provide utilities for the calculation of the dipole moment, it will be necessary to supplement the MacroModel results with some other modeling package. Single-point calculations on the AMBER*-optimized geometries, using the AM1 Hamiltonian in MOPAC93, would provide an appropriate starting point. <p> <ul> <li>Improved modeling of the transition structure for the acetyl exchange between acetylcarnitine and CoA by: <ol> <li>Modeling by semiempirical (or ab initio) methods, including a solvent model.</li> <li>Determination of molecular mechanics parameters specific to the sulfur found in the molecule (from ab initio).</li> <li>Molecular mechanics modeling including longer chains in place of the acetyl group.</li> </ol> </li> <li>Modeling of the morpholinium rings including a methylenecarboxylate, both in the gas phase and solution.</li> <li>Modeling of the phosphonate rings including a methylenecarboxylate, both in the gas phase and solution.</li> </ul> </chapter> </body> <!-- Back matter --> <back> <bibliography> <citation id=b.Alder88 worktype=book published=published> <workauthor>Alder, R. W.; <workauthor>White, J. 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Res. <pubdate>1972, <volume>5, <pages>102-111 </citation> <citation id=j.Wolfenden69 worktype=journal published=published> <workauthor>Wolfenden, R. <worktitle>Nature <pubdate>1969, <volume>223, <pages>704-705 </citation> <citation id=j.Wolfenden88 worktype=journal published=published> <workauthor>Wolfenden, R.; <workauthor>Liang, Y.-L. <worktitle>J. Biol. Chem. <pubdate>1988, <volume>263, <pages>8022-8026 </citation> <citation id=j.Wolfenden89 worktype=journal published=published> <workauthor>Wolfenden, R.; <workauthor>Liang, Y.-L. <worktitle>Bioorg. Chem. <pubdate>1989, <volume>17, <pages>486-489 </citation> <appendix> <head>Naming and numbering scheme for cyclooctane conformers. <section> <head>Boat-chair family. <p><target id=rules1>We have tried to keep the scheme simple and, primarily, to make it easy to draw a particular conformer from the name.</target> BC has a C<sub><em>s</em></sub> point group. In general, as soon as substituents are introduced in the ring, the point group becomes C<sub><em>1</em></sub> unless the substituents happen to lie in the carbons split by the mirror plane that defines C<sub><em>s</em></sub> symmetry. Thus, in the general case, we can distinguish two enantiomeric BC conformers, one \ <q>left-oriented</q> and one <q>right-oriented</q> <float id=chiralBCs> <mm entity="fig.chiralBCs">fig.chiralBCs.gif, 1.640KB <caption><q>Left-oriented</q> and <q>right-oriented</q> BCs </float> We denote the <q>left-oriented</q> version by BC, while the <q>right-oriented</q> is BC'. The numbers on the carbons follow a specular relationship to the numbers in the conformational enantiomer. <p>To name a particular conformer, we keep the numbering fixed. We do follow the chemical convention of always trying to assign the lowest possible numbers, within the constraint that the positions of fixed number positions. Thus, if the substitution pattern allows it, the choice between BC and BC' depends on which one yields the lowest numbers. We define completely the position of a substituent by choosing the appropriate letter among the following: <dl> <dt><em>e</em></dt> <dd>equatorial</dd> <dt><em>a</em></dt> <dd>axial</dd> <dt><em>b</em></dt> <dd>bowsprit</dd> <dt><em>f</em></dt> <dd>flagpole</dd> <dt><em>i</em></dt> <dd>isoclinal</dd> </dl> according to the following scheme (we have left some of the positions unlabeled for the sake of clarity in the drawing): <float id=BCtags> <mm entity="fig.BCtags">fig.BCtags.gif, 0.939KB <caption>Labels for the orientations of substituents in BC </float> <p>The point group of TBC is C<sub>2</sub>. This is a disymmetric group and allows for chiral shapes. We can therefore distinguish two conformers, one <q>twisted to the right</q> and one <q>twisted to the left</q>. We designate the one <q>twisted to the left</q> as TBC, and the <q>twisted to the right</q> as TBC'. See the scheme: <float id=chiralTBCs> <mm entity="fig.chiralTBCs">fig.chiralTBCs.gif, 1.689KB <caption><q>Left-oriented</q> and <q>right-oriented</q> TBCs </float> The labels for the orientation are as follows: <float id=TBCtags> <mm entity="fig.TBCtags">fig.TBCtags.gif, 1.257KB <caption>Labels for the orientations of substituents in TBC </float> <section> <head>Chair-chair family. <p>The CC has a C<sub>2<em>v</em></sub> point group. Its shape is slightly elliptical (when seen from the z axis). It has four sets of <term>isochronous</term> carbons (same NMR signal by symmetry). C<sub>2<em>v</em></sub> is not a chiral point group so we only have: <float id=CCtags> <mm entity="fig.CCtags">fig.CCtags.gif, 0.846KB <caption>CC numbering and labeling scheme. </float> The numbering starts on one carbon along the major axis of the ellipse. <p>The Crown is a very high-symmetry conformer, with a D<sub>4<em>d</em></sub> point group. All the carbons are undistinguishable by symmetry operations so the choice of any particular carbon to start the numbering is immaterial. The Crown is actually a special case of the CC , but we give the numbering and labels for substituents for the sake of completeness. The introduction of substituents is bound to perturb the high symmetry of the molecule, rendering it as a CC. We do not have any examples of crowns in our results, and we do not find any crown conformers among substituted cyclooctanes, although some authors have referred to CCs as crowns in the past. <float id=crowntags> <mm entity="fig.crowntags">fig.crowntags.gif, 0.941KB <caption>Crown. </float> <p>The TCC has a D<sub>2</sub> point group. This is a disymmetric group, so we find two enantiomers. The numbering and the names follow this scheme: <float id=TCCtags> <mm entity="fig.TCCtags">fig.TCCtags.gif, 1.751KB <caption>TCC numbering and labeling scheme. </float> <p>The TC has a C<sub>2<em>h</em></sub> point group. The numbering and the names follow this scheme: <float id=TCtags> <mm entity="fig.TCtags">fig.TCtags.gif, 1.593KB <caption>TC numbering and labeling scheme. </float> <p>The C has a C<sub>2<em>h</em></sub> point group. The numbering and labeling are as follows: <float id=Ctags> <mm entity="fig.Ctags">fig.Ctags.gif, 0.971KB <caption>C numbering and labeling scheme. </float> <section> <head>Boat-boat family. <p>Boat. <float id=Btags> <mm entity="fig.Btags">fig.Btags.gif, 0.944KB <caption>B numbering and labeling scheme. </float> Boat-boat. <float id=BBtags> <mm entity="fig.BBtags">fig.BBtags.gif, 0.997KB <caption>BB numbering and labeling scheme. </float> Twist-boat. <float id=TBtags> <mm entity="fig.TBtags">fig.TBtags.gif, 1.700KB <caption>TB numbering and labeling scheme. </float> </appendix> <appendix> <head>Rules for naming hetero-substituted cyclooctanes. <p><target id=rules2></target> <ul> <li>Keep the numberings assigned to the conformations of cyclooctane fixed.</li> <li>Keep the orientation descriptors, such as equatorial and axial, assigned to the conformations of cyclooctane fixed.</li> <li>Find out the numbers that correspond to the heteroatoms <em>within</em> the ring.</li> <li>In case there is more than one way to read the numbers that correspond to the heteroatoms, <em>e. g.</em> 2<em>P</em>-6<em>N</em> in BC vs. 4<em>N</em>-8<em>P</em> in BC', choose the locant set that assigns the lowest numbers.</li> <li>If the numbers are the same and they just switch positions, <em>e. g.</em>, 1<em>N</em>-5<em>P</em> in TBC vs. 1<em>P</em>-5<em>N</em> in TBC', the atom with the highest priority by Cahn-Ingold-Prelog rules gets the lowest number.</li> <li>If it is not clear which locant set assigns the lowest numbers <em>e.g.</em>, 1,4,5,6 or 1,2,7,8 then the locant set that assigns the lowest number to the highest priority atom (CIP rules) is chosen. In the previous locant sets, if the highest priority atom can be either 2 or 4, then the locant set 1,2,7,8 should be chosen, despite the 7,8 being higher than 5 and 6.</li> <li>Read the numbers that correspond to the substituents <em>on</em> the ring.</li> <li>List the substituents on the ring preceded by the numbers and an appropriate prefix to indicate the number of times the substituent appears.</li> <li>Attach to the numbers the abbreviation of the appropriate orientational descriptor.</li> <li>For substituents on isoclinal positions, specify the <em>R</em> or <em>S</em> configuration of the atom.</li> </ul> <p>By the previous rules the name for the following conformer: <float id=example> <mm entity=fig.example>fig.example.gif, 0.827KB <caption>Example conformer. </float> is 1,1,5<em>e</em>,8,8-pentamethyl-5<em>a</em>-oxo-1<em>N</em>-4,6-di<em>O</em>-5<em>P</em>-TBC. </appendix> <appendix> <head>Software standards used. <p>This document is encoded in Electronic Theses and Dissertations Markup Language (ETDML) using etd.dtd v.1.1. Non-ASCII characters are encoded in Unicode v.2.0. All the figures are GIF87a (Data type: unsigned char, Dimension order: interleaved, Color model: color index, Coordinate space: upper-left, Minimum: 0, Maximum: 255). The virtual reality models (*.wrl files) are encoded in VRML 1.0. <p>The SGML parser used to check this document was "nsgmls" included as part of the package SP v.1.0.1 by James Clark. The word processor was "jot", a utility provided in IRIX 5.3. ISIS/Draw v.1.2 was used for all the chemical drawings. The figures were generated either by using the <q>snapshot</q> utility provided in IRIX 5.3 to make a *.rgb image file, which was later converted to GIF87a by <q>movieconvert</q>, another image processing utility provided in IRIX 5.3; or by saving the image as a Microsoft *.bmp file, which was later converted to GIF87a by LView for Windows v.3.1. The *.wrl files were generated by saving the molecule in PDB format from MacroModel, and then translating with the program pdb2vrml using the "-stick" flag. All the conversions between chemical file formats were done using Babel v.1.1. <p>Mention of a given program or brand name does not imply endorsement by Virginia Polytechnic Institute and State University or any of its departments. </appendix> <appendix> <head>Chemical files included. <p>For each VRML model I have included the corresponding file in PDB format (found in the PDB directory). I have also included all the consolidated output files from the conformational searches in macromodel format. </appendix> <appendix> <head>README: Notes on the creation of a dissertation in ETD-ML. <section> <head>ETD-ML source encoding. <p>This the first ETD-ML ETD ever to be submitted. As a hint for future ETD-ML authors, we have made the encoding for this ETD available in its source format. <ul> <li><mm entity="source">ETD-ML source</mm> </ul> <p> The whole document is structured, with left-indentation corresponding to the logical subdivisions: <pre> No spaces for a chapter, 4 spaces for a section, 8 spaces (tab) for a subsection, 12 spaces (tab + 4) for a block and 16 spaces (2 tabs) for a subblock. </pre> <p> Links, floating matter, footnotes and tables are not indented. That is to allow an easier construction of a list of tables and list of figures by a reformatter (so far, I am the "reformatter" for those lists, I use the UNIX command "grep" and pipe the output to a file, so I have to keep all the text of the captions in the same line). <p> Greek letters are symbolyzed by their "{name}" to allow them to show up in the HTML version (there is no provision for greek characters in HTML 2.0). The "{name}" should be substituted by the Unicode number. Note: micro and mu are expressed by the same greek letter, but micro is a prefix in the SI system, while mu may have many other meanings. I considered them as separate entities to allow for a "smart" reformatter or search engine that could take that into account. <p> The entities chemname, casnum and chemform are included only to help in the search of chemical names, Chemical Abstracts Registry Numbers and chemical formulas, respectively. <section> <head>Virtual Reality Modeling Language (VRML). <p> The three dimensional figures are VRML 1.0 models. The way to incorporate them into a formatted document depends on the technology available and the effect desired by the formatter. VRML figures can be shown as hyperlinks (in HTML) by means of an anchored reference, such as: <pre> <![CDATA[ <a href="carnitine/fig.RSWat.gif">(caption text)</a> ]]> </pre> <p> This is what I did in the HTML version of my dissertation, because of the computational overhead involved in loading and displaying literally hundreds of little VRML viewers in the same page. Anyway, the VRML models are still encoded as: <pre> <![CDATA[ <mm entity=VR.name>(caption text)</mm> ]]> </pre> so the reformatter has to make the decision about displaying them as an anchored reference or as an embedded VRML viewer window, e.g., a smart reformatter could choose to display some of the 3D models as anchored references and embed the others. <p> The virtual reality viewer can also be embedded in a HTML homepage by means of the following code: <pre> <![CDATA[ <embed border=0 type="x-world/x-vrml" src="file.wrl" align=abscenter width=300 height=300> (caption text) </embed> ]]> </pre> <p> It is strongly recommended that the "type" parameter be present. This helps the browser correctly handle the rendering of the image. In the future, it may be necessary to change the x-world/x-vrml type to the definitive MIME type declaration (probably "world/vrml"). So far, "x-world/x-vrml" is an experimental MIME type (thus the "x-" prefix), although it is recognized by most browsers. <p> These VRML files were succesfully viewed using CosmoPlayer and Live3D. PDB files can be converted to VRML using the script pdb2vrml, available from: <ul> <li><a href="http://www.pc.chemie.th-darmstadt.de/vrml/pdb2vrml.html">http://www.pc.chemie.th-darmstadt.de/vrml/pdb2vrml.html</a> </ul> <section> <head>Chemical Markup Language (CML). <p> Markup coding of chemical information is still in its infancy. There is a beginning in CML v.1.0 (Chemical Markup Language). You can find all there is to know about CML at (as of June, 1997): <ul> <li><a href="http://www.venus.co.uk/omf/cml-1.0/intro.html">http://www.venus.co.uk/omf/cml-1.0/intro.html</a> </ul> <p> If the URL doesn't work, a Web search specifying "Chemical Markup Language" or "Open Molecule Foundation" should yield some relevant hits. <p> Attempting a "merge" of CML coding into ETD-ML coding was beyond the resources (mostly time) available to this writer, although it is clearly the best way to go. Future customizations of the ETD-ML for chemistry should allow for elements encoded in CML. Anyway, since so far there is no accepted standard format for encoding molecular structures I decided to store the structures as VRML models and in PDB format. The PDB format files are not referred to *at any point* in the text of the dissertation, they are kept only because they are the actual results obtained from the modeling and, therefore, contain more chemical information than VRML files. PDB is not even a de facto standard, but it is widely used and it is better than XYZ coordinates because it preserves the connectivities between the atoms (XYZ readers have to make educated guesses about how atoms are connected and about the bond orders). <section> <head>Babel, PDB, Chime. <p> It is possible to use Babel, together with the PDB files and a Netscape plug-in called Chime (available without cost from MDL, Inc.), to yield a fancier rendering of the molecules. Use Babel to transform the PDB files to MDL's MOL format and embed the images in a HTML page using the following code: <pre> <![CDATA[ <embed border=0 type="chemical/x-mdl-molfile" src="file.mol" align=abscenter width=150 height=150> (caption text) </embed> ]]> </pre> <p> This will result in a figure containing a 2D projection of the 3D structure. Clicking on the right button of the mouse will bring up the option of 3D rendering. It also allows for real-time rotation, rendering as wires, ball and stick, sticks, VDW spheres and others. I have included the MDL molfiles. They have the extension ".mol". Chime can be downloaded from: <ul> <li><a href="http://www.mdli.com/chemscape/chime/chime.html">http://www.mdli.com/chemscape/chime/chime.html</a> </ul> <p> Chime can identify and render many other chemical types, such as: PDB, XYZ, MOPAC and Gaussian input, MDL's molfile and rxnfile, and EMBL nucleotide format. Only the MDL molfile format will yield the switchable 2D<->3D view.<link goesto="fchime">Note.</> <footnote id=fchime>NOTE: The SGI version of Chime will not work reading molfiles in a local filesystem, only through a network.</footnote> <p> BTW, Babel can be downloaded from the software archives of the Computational Chemistry Mailing List at: <ul> <li><a href="ftp://ccl.osc.edu/pub/chemistry/software/">ftp://ccl.osc.edu/pub/chemistry/software/</a> </ul> looking under the appropriate operating system. <section> <head>Reformatting the molecules. <p> If a reformatter decides to use XYZ files to visualize the molecules (after converting the PDB files to XYZ format), there is a Java applet developed by Sun Microsystems named XYZApp.class (downloadable from http://java.sun.com) that can do the job, although the rendering is somewhat primitive. <p> A minimum code to embed XYZApp.class in a HTML document is: <pre> <![CDATA[ <applet code=XYZApp.class width=300 height=300> <param name=model value=file.xyz> </applet> ]]> </pre> <p> It is necessary to have Matrix3D.class to be able to run XYZApp.class. <section> <head>Footnotes. <p> All the footnotes are referred to as "Note."s. It would be desirable to have a reformatter that used more standard designations: superscript arabic numbers (Journal of American Chemical Society-style), or a standard sequence of characters (such as the ones specified in the journals "Science" or the "Proceedings of the National Academy of Sciences of the USA") <section> <head>Notes on MOL notation substitution. <p> The following table contains only GIF images and VRML models. Substituting the extension "mol" instead of the "wrl" will access the MDL molfiles, displayable with Chime. It will also be necessary to move the *.mol files out of the MOL directory.In that case, the GIF images will be unnecessary, because molfiles in Chime yield both 2D and 3d views. This is likely to require human intervention, because a reformating script would have to be *really* smart to accomodate all these changes. The caption is all in one line to make it easier to use a utility like "grep" when gathering a "List of Tables." <link goesto="tableComp0O">See table.</link> <section> <head>README.TXT: Files in this ETD. <p> <pre> Rosas.tar.gz can be gunzipped to yield a tarred file that contains all the files of my dissertation. When untarred, the whole thing takes about 6.5MB. The following is a list of all the files included (total of 457, not including directories): The version of gzip was 1.2.4. dissertation: total 1166 -rw-r--r-- 1 rosas user 320242 Jul 3 17:30 diss.etd -rw-r--r-- 1 rosas user 243 Jun 17 13:16 README.TXT drwxr-xr-x 4 rosas user 1024 Jun 17 11:17 carnitine drwxr-xr-x 3 rosas user 512 Jun 17 11:09 cyclohexane drwxr-xr-x 5 rosas user 3072 Jun 17 11:04 cyclooctane -rw-r--r-- 1 rosas user 13594 Mar 11 03:09 etd.dtd drwxr-xr-x 4 rosas user 512 Jun 17 11:31 methylphosp drwxr-xr-x 3 rosas user 512 Jun 17 11:10 morpholinium drwxr-xr-x 5 rosas user 3072 Jun 17 11:21 phosphacinium drwxr-xr-x 2 rosas user 1024 Jun 17 11:26 reviews dissertation/carnitine: total 247 drwxr-xr-x 2 rosas user 512 Jun 17 11:17 MOL drwxr-xr-x 2 rosas user 512 Jun 17 11:17 PDB -rw-r--r-- 1 rosas user 16959 May 17 11:46 RRGas.wrl -rw-r--r-- 1 rosas user 17048 May 17 11:47 RRWat.wrl -rw-r--r-- 1 rosas user 17017 May 17 11:48 RSGas.wrl -rw-r--r-- 1 rosas user 16938 May 17 11:51 RSWat.wrl -rw-r--r-- 1 rosas user 1967 May 1 12:32 TableAcCarnAM1Gas.html -rw-r--r-- 1 rosas user 4961 May 1 12:33 TableAcCarnAM1Wat.html -rw-r--r-- 1 rosas user 1781 May 1 12:33 TableAcCholAM1Gas.html -rw-r--r-- 1 rosas user 2935 May 1 12:34 TableAcCholAM1Wat.html -rw-r--r-- 1 rosas user 1949 May 1 12:34 TableCarnAM1Gas.html -rw-r--r-- 1 rosas user 3251 May 1 12:34 TableCarnAM1Wat.html -rw-r--r-- 1 rosas user 1203 May 1 12:34 TableCholAM1Gas.html -rw-r--r-- 1 rosas user 1172 May 1 12:35 TableCholAM1Wat.html -rw-r--r-- 1 rosas user 4805 May 1 12:36 TableOAcPrAM1Gas.html -rw-r--r-- 1 rosas user 3950 May 1 12:36 TableOAcPrAM1Wat.html -rw-r--r-- 1 rosas user 3356 May 1 12:37 TableOHPrAM1Gas.html -rw-r--r-- 1 rosas user 2896 May 1 12:37 TableOHPrAM1Wat.html -rw-r--r-- 1 rosas user 801 May 17 11:29 fig.RRWat.gif -rw-r--r-- 1 rosas user 807 May 17 11:36 fig.RSWat.gif -rw-r--r-- 1 rosas user 608 Feb 8 23:41 fig.extended.gif -rw-r--r-- 1 rosas user 1511 May 18 12:47 fig.fitTI.gif -rw-r--r-- 1 rosas user 510 May 22 14:17 fig.folded.gif -rw-r--r-- 1 rosas user 4852 Apr 1 00:25 fig.highlight.gif -rw-r--r-- 1 rosas user 2491 Apr 1 12:51 fig.hydrolysis1.gif -rw-r--r-- 1 rosas user 4823 Apr 3 18:56 fig.solvation.gif -rw-r--r-- 1 rosas user 731 May 5 21:15 fig.torsions.gif dissertation/carnitine/MOL: total 24 -rw-r--r-- 1 rosas user 2679 May 27 13:56 RRGas.mol -rw-r--r-- 1 rosas user 2679 May 27 13:56 RRWat.mol -rw-r--r-- 1 rosas user 2679 May 27 13:56 RSGas.mol -rw-r--r-- 1 rosas user 2679 May 27 13:56 RSWat.mol dissertation/carnitine/PDB: total 40 -rw-r--r-- 1 rosas user 4620 May 17 11:41 RRGas.pdb -rw-r--r-- 1 rosas user 4620 May 17 11:41 RRWat.pdb -rw-r--r-- 1 rosas user 4620 May 17 11:41 RSGas.pdb -rw-r--r-- 1 rosas user 4620 May 17 11:42 RSWat.pdb dissertation/cyclohexane: total 68 drwxr-xr-x 2 rosas user 512 Jun 17 11:10 MOD -rw-r--r-- 1 rosas user 1545 Jan 30 14:16 TableCyclohGas.html -rw-r--r-- 1 rosas user 3660 May 1 13:49 TableDiMeCyclohGas.html -rw-r--r-- 1 rosas user 15426 May 1 14:11 TableEtTriMeCyclohGas.html -rw-r--r-- 1 rosas user 3913 May 1 14:03 TableTetraMeCyclohGas.html -rw-r--r-- 1 rosas user 4378 May 1 14:02 TableTriMeCyclohGas.html -rw-r--r-- 1 rosas user 3085 Mar 8 23:56 fig.hexConfs.gif dissertation/cyclohexane/MOD: total 813 -rw-r--r-- 1 rosas user 9431 Jun 17 11:09 CyclohexGas.out -rw-r--r-- 1 rosas user 37811 Jun 17 11:09 DiMeCyclohexGas.out -rw-r--r-- 1 rosas user 51129 Jun 17 11:09 TetMeCyclohexGas.out -rw-r--r-- 1 rosas user 70920 Jun 17 11:09 TriMeCyclohexGas.out -rw-r--r-- 1 rosas user 246240 Jun 17 11:09 TriMeEtCyclohexGas.out dissertation/cyclooctane: total 1331 drwxr-xr-x 2 rosas user 512 Jun 17 11:04 MOD drwxr-xr-x 2 rosas user 512 Jun 17 10:02 MOL drwxr-xr-x 2 rosas user 1024 Jun 17 10:02 PDB -rw-r--r-- 1 rosas user 10455 May 1 14:28 Table4MeCyclooctGas.html -rw-r--r-- 1 rosas user 27249 May 1 14:28 Table5MeCyclooctGas.html -rw-r--r-- 1 rosas user 19927 May 15 11:11 Table6MeCyclooctGas.html -rw-r--r-- 1 rosas 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-rw-r--r-- 1 rosas user 939 Mar 12 02:34 fig.BCtags.gif -rw-r--r-- 1 rosas user 944 Mar 12 13:59 fig.Btags.gif -rw-r--r-- 1 rosas user 846 Mar 12 12:30 fig.CCtags.gif -rw-r--r-- 1 rosas user 971 Mar 12 13:48 fig.Ctags.gif -rw-r--r-- 1 rosas user 1257 Mar 12 11:37 fig.TBCtags.gif -rw-r--r-- 1 rosas user 1700 Mar 12 16:24 fig.TBtags.gif -rw-r--r-- 1 rosas user 1751 Mar 12 12:46 fig.TCCtags.gif -rw-r--r-- 1 rosas user 1593 Jun 13 15:25 fig.TCtags.gif -rw-r--r-- 1 rosas user 430 May 14 21:50 fig.bb14O.gif -rw-r--r-- 1 rosas user 435 May 14 21:49 fig.bb24O.gif -rw-r--r-- 1 rosas user 489 May 15 11:04 fig.bb5O.gif -rw-r--r-- 1 rosas user 449 May 15 14:18 fig.bb6O.gif -rw-r--r-- 1 rosas user 249 May 14 20:01 fig.bc0O.gif -rw-r--r-- 1 rosas user 301 May 14 21:23 fig.bc14O.gif -rw-r--r-- 1 rosas user 364 May 14 22:15 fig.bc15O.gif -rw-r--r-- 1 rosas user 439 May 15 14:21 fig.bc16O.gif -rw-r--r-- 1 rosas user 301 May 14 21:20 fig.bc24O.gif -rw-r--r-- 1 rosas user 365 May 14 22:37 fig.bc25O.gif -rw-r--r-- 1 rosas user 441 May 15 14:20 fig.bc26O.gif -rw-r--r-- 1 rosas user 402 May 14 23:20 fig.bc35O.gif -rw-r--r-- 1 rosas user 405 May 14 23:24 fig.bc45O.gif -rw-r--r-- 1 rosas user 434 May 15 10:58 fig.bc55O.gif -rw-r--r-- 1 rosas user 435 May 15 11:01 fig.bc65O.gif -rw-r--r-- 1 rosas user 324 May 14 21:54 fig.cc4O.gif -rw-r--r-- 1 rosas user 334 May 14 22:52 fig.cc5O.gif -rw-r--r-- 1 rosas user 1640 Mar 12 02:09 fig.chiralBCs.gif -rw-r--r-- 1 rosas user 1689 Mar 12 02:47 fig.chiralTBCs.gif -rw-r--r-- 1 rosas user 941 Mar 12 12:16 fig.crowntags.gif -rw-r--r-- 1 rosas user 823 May 14 16:07 fig.hmx.gif -rw-r--r-- 1 rosas user 435 May 14 21:32 fig.tb14O.gif -rw-r--r-- 1 rosas user 435 May 14 22:58 fig.tb15O.gif -rw-r--r-- 1 rosas user 511 May 15 11:18 fig.tb16O.gif -rw-r--r-- 1 rosas user 427 May 14 21:34 fig.tb24O.gif -rw-r--r-- 1 rosas user 459 May 14 23:04 fig.tb25O.gif -rw-r--r-- 1 rosas user 515 May 15 11:21 fig.tb26O.gif -rw-r--r-- 1 rosas user 481 May 14 23:07 fig.tb35O.gif -rw-r--r-- 1 rosas user 489 May 14 23:17 fig.tb45O.gif -rw-r--r-- 1 rosas user 307 May 14 20:42 fig.tbc-10O.gif -rw-r--r-- 1 rosas user 311 May 14 20:29 fig.tbc10O.gif -rw-r--r-- 1 rosas user 377 May 14 21:57 fig.tbc14O.gif -rw-r--r-- 1 rosas user 394 May 15 10:38 fig.tbc15O.gif -rw-r--r-- 1 rosas user 379 May 14 21:59 fig.tbc24O.gif -rw-r--r-- 1 rosas user 389 May 15 10:41 fig.tbc25O.gif -rw-r--r-- 1 rosas user 396 May 15 10:49 fig.tbc35O.gif -rw-r--r-- 1 rosas user 392 May 15 10:51 fig.tbc45O.gif -rw-r--r-- 1 rosas user 280 May 14 20:19 fig.tcc-10O.gif -rw-r--r-- 1 rosas user 257 May 14 20:03 fig.tcc10O.gif -rw-r--r-- 1 rosas user 365 May 14 21:27 fig.tcc14O.gif -rw-r--r-- 1 rosas user 381 May 14 22:44 fig.tcc15O.gif -rw-r--r-- 1 rosas user 357 May 14 21:28 fig.tcc24O.gif -rw-r--r-- 1 rosas user 405 May 14 22:48 fig.tcc25O.gif -rw-r--r-- 1 rosas user 14069 May 15 15:25 tb14O.wrl -rw-r--r-- 1 rosas user 15190 May 16 15:33 tb15O.wrl -rw-r--r-- 1 rosas user 16172 May 16 22:26 tb16O.wrl -rw-r--r-- 1 rosas user 14143 May 15 15:28 tb24O.wrl -rw-r--r-- 1 rosas user 15177 May 16 15:34 tb25O.wrl -rw-r--r-- 1 rosas user 16226 May 16 22:27 tb26O.wrl -rw-r--r-- 1 rosas user 15126 May 16 15:35 tb35O.wrl -rw-r--r-- 1 rosas user 15168 May 16 15:36 tb45O.wrl -rw-r--r-- 1 rosas user 9649 May 15 14:02 tbc1.wrl -rw-r--r-- 1 rosas user 14084 May 15 15:37 tbc14O.wrl -rw-r--r-- 1 rosas user 15276 May 16 15:40 tbc15O.wrl -rw-r--r-- 1 rosas user 9654 May 15 14:04 tbc2.wrl -rw-r--r-- 1 rosas user 14084 May 15 15:38 tbc24O.wrl -rw-r--r-- 1 rosas user 15220 May 16 15:41 tbc25O.wrl -rw-r--r-- 1 rosas user 9667 May 15 14:04 tbc3.wrl -rw-r--r-- 1 rosas user 15116 May 16 15:45 tbc35O.wrl -rw-r--r-- 1 rosas user 9667 May 15 14:05 tbc4.wrl -rw-r--r-- 1 rosas user 15141 May 16 15:46 tbc45O.wrl -rw-r--r-- 1 rosas user 9651 May 15 14:05 tcc1.wrl -rw-r--r-- 1 rosas user 14027 May 15 15:23 tcc14O.wrl -rw-r--r-- 1 rosas user 15302 May 16 15:29 tcc15O.wrl -rw-r--r-- 1 rosas user 14082 May 15 15:24 tcc24O.wrl -rw-r--r-- 1 rosas user 15238 May 16 15:31 tcc25O.wrl dissertation/cyclooctane/MOD: total 1177 -rw-r--r-- 1 rosas user 56619 Jun 17 11:03 CycloocTotGas.out -rw-r--r-- 1 rosas user 190512 Jun 17 11:03 HexMeCycloocTotGas.out -rw-r--r-- 1 rosas user 171493 Jun 17 11:03 PentMeCycloocTotGas.out -rw-r--r-- 1 rosas user 183139 Jun 17 11:03 TetMeCycloocTotGas.out dissertation/cyclooctane/MOL: total 138 -rw-r--r-- 1 rosas user 2697 May 27 13:56 bb5O.mol -rw-r--r-- 1 rosas user 2901 May 27 13:56 bb6O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 bc15O.mol -rw-r--r-- 1 rosas user 2902 May 27 13:56 bc16O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 bc25O.mol -rw-r--r-- 1 rosas user 2902 May 27 13:56 bc26O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 bc35O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 bc45O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 bc55O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 bc65O.mol -rw-r--r-- 1 rosas user 2697 May 27 13:56 cc5O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 tb15O.mol -rw-r--r-- 1 rosas user 2902 May 27 13:56 tb16O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 tb25O.mol -rw-r--r-- 1 rosas user 2902 May 27 13:56 tb26O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 tb35O.mol -rw-r--r-- 1 rosas user 2698 May 27 13:56 tb45O.mol -rw-r--r-- 1 rosas user 2699 May 27 13:56 tbc15O.mol -rw-r--r-- 1 rosas user 2699 May 27 13:56 tbc25O.mol -rw-r--r-- 1 rosas user 2699 May 27 13:56 tbc35O.mol -rw-r--r-- 1 rosas user 2699 May 27 13:56 tbc45O.mol -rw-r--r-- 1 rosas user 2699 May 27 13:56 tcc15O.mol -rw-r--r-- 1 rosas user 2699 May 27 13:56 tcc25O.mol dissertation/cyclooctane/PDB: total 347 -rw-r--r-- 1 rosas user 2899 May 15 11:28 BC.pdb -rw-r--r-- 1 rosas user 2899 May 15 11:32 TBC1.pdb -rw-r--r-- 1 rosas user 2899 May 15 11:31 TBC2.pdb -rw-r--r-- 1 rosas user 2899 May 15 11:34 TBC3.pdb -rw-r--r-- 1 rosas user 2899 May 15 11:35 TBC4.pdb -rw-r--r-- 1 rosas user 2899 May 15 11:27 TCC1.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:56 bb140.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:57 bb240.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:04 bb5O.pdb -rw-r--r-- 1 rosas user 4865 May 16 21:49 bb6O.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:52 bc140.pdb -rw-r--r-- 1 rosas user 4550 May 16 14:57 bc15O.pdb -rw-r--r-- 1 rosas user 4865 May 16 21:49 bc16O.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:52 bc240.pdb -rw-r--r-- 1 rosas user 4550 May 16 14:57 bc25O.pdb -rw-r--r-- 1 rosas user 4865 May 16 21:50 bc26O.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:01 bc35O.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:01 bc45O.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:04 bc55O.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:04 bc65O.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:57 cc40.pdb -rw-r--r-- 1 rosas user 4550 May 16 14:58 cc5O.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:55 tb140.pdb -rw-r--r-- 1 rosas user 4550 May 16 14:59 tb15O.pdb -rw-r--r-- 1 rosas user 4865 May 16 21:47 tb16O.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:55 tb240.pdb -rw-r--r-- 1 rosas user 4550 May 16 14:58 tb25O.pdb -rw-r--r-- 1 rosas user 4865 May 16 21:48 tb26O.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:00 tb35O.pdb -rw-r--r-- 1 rosas user 4550 May 16 14:59 tb45O.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:57 tbc140.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:02 tbc15O.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:58 tbc240.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:02 tbc25O.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:05 tbc35O.pdb -rw-r--r-- 1 rosas user 4550 May 16 15:05 tbc45O.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:53 tcc140.pdb -rw-r--r-- 1 rosas user 4550 May 16 14:57 tcc15O.pdb -rw-r--r-- 1 rosas user 4197 May 15 14:55 tcc240.pdb -rw-r--r-- 1 rosas user 4550 May 16 14:58 tcc25O.pdb dissertation/methylphosp: total 271 drwxr-xr-x 2 rosas user 512 Jun 17 11:15 Abinitio drwxr-xr-x 2 rosas user 512 Jun 17 11:31 PDB -rw-r--r-- 1 rosas user 15784 Mar 15 02:53 cegxuh.wrl -rw-r--r-- 1 rosas user 15993 Mar 15 02:53 duksor.wrl -rw-r--r-- 1 rosas user 26911 Mar 15 02:54 dumlec.wrl -rw-r--r-- 1 rosas user 23386 Mar 15 02:54 felsoe.wrl -rw-r--r-- 1 rosas user 4000 May 19 10:18 fig.confs.gif -rw-r--r-- 1 rosas user 4789 May 13 14:31 fig.copo.gif -rw-r--r-- 1 rosas user 4142 May 13 14:31 fig.cp2o.gif -rw-r--r-- 1 rosas user 4624 May 13 16:04 fig.crystals.gif -rw-r--r-- 1 rosas user 4349 May 13 14:31 fig.hcpo.gif -rw-r--r-- 1 rosas user 3991 May 13 14:31 fig.opo.gif -rw-r--r-- 1 rosas user 3795 May 13 14:31 fig.pc.gif -rw-r--r-- 1 rosas user 3817 May 13 14:31 fig.po.gif -rw-r--r-- 1 rosas user 4658 Jun 12 15:27 fig.profiles.gif -rw-r--r-- 1 rosas user 13587 Mar 15 02:54 zaysib.wrl dissertation/methylphosp/Abinitio: total 303 -rw-r--r-- 1 rosas user 17096 Jun 17 11:14 AngleCP2O.txt -rw-r--r-- 1 rosas user 19003 Jun 17 11:14 AngleOPO.txt -rw-r--r-- 1 rosas user 12499 Jun 17 11:14 BondPC.txt -rw-r--r-- 1 rosas user 9487 Jun 17 11:14 BondPO.txt -rw-r--r-- 1 rosas user 1958 Jun 17 11:14 CP1O2angle.txt -rw-r--r-- 1 rosas user 10562 Jun 17 11:14 CP1Oangle.txt -rw-r--r-- 1 rosas user 59929 Jun 17 11:14 TorCOPO.txt -rw-r--r-- 1 rosas user 21441 Jun 17 11:14 TorHCPO.txt -rw-r--r-- 1 rosas user 1014 Jun 17 11:14 diMephopGM.txt dissertation/methylphosp/PDB: total 54 -rw-r--r-- 1 rosas user 4491 Mar 15 02:48 cegxuh.pdb -rw-r--r-- 1 rosas user 4308 Mar 15 02:48 duksor.pdb -rw-r--r-- 1 rosas user 7539 Mar 15 02:49 dumlec.pdb -rw-r--r-- 1 rosas user 6677 Mar 15 02:49 felsoe.pdb -rw-r--r-- 1 rosas user 3508 Mar 15 02:47 zaysib.pdb dissertation/morpholinium: total 113 drwxr-xr-x 2 rosas user 512 Jun 17 11:12 MOD -rw-r--r-- 1 rosas user 3762 May 1 14:18 TableDiMeMorpholGas.html -rw-r--r-- 1 rosas user 3635 May 1 14:20 TableDiMeMorpholWat.html -rw-r--r-- 1 rosas user 13510 May 11 17:36 TableMeOHMorpholGas.html -rw-r--r-- 1 rosas user 13489 May 1 14:24 TableMeOHMorpholWat.html -rw-r--r-- 1 rosas user 3031 May 1 13:46 TableMorpholGas.html -rw-r--r-- 1 rosas user 3655 May 1 14:13 TableMorpholWat.html -rw-r--r-- 1 rosas user 4232 May 1 14:22 TableSMeMorpholGas.html -rw-r--r-- 1 rosas user 4452 May 1 14:23 TableSMeMorpholWat.html -rw-r--r-- 1 rosas user 607 Apr 3 12:04 fig.MeOHtags.gif -rw-r--r-- 1 rosas user 497 Apr 3 11:42 fig.Morphtags.gif -rw-r--r-- 1 rosas user 539 Apr 3 11:47 fig.StriMetags.gif -rw-r--r-- 1 rosas user 440 Mar 4 16:34 fig.morph.gif -rw-r--r-- 1 rosas user 583 May 19 12:25 fig.savle97.gif -rw-r--r-- 1 rosas user 527 Apr 3 11:57 fig.tetraMetags.gif dissertation/morpholinium/MOD: total 1830 -rw-r--r-- 1 rosas user 58800 Jun 17 11:11 DiMeMorphGas.out -rw-r--r-- 1 rosas user 76314 Jun 17 11:11 DiMeMorphWat.out -rw-r--r-- 1 rosas user 384203 Jun 17 11:11 MeOHMorphGas.out -rw-r--r-- 1 rosas user 224436 Jun 17 11:11 MeOHMorphWat.out -rw-r--r-- 1 rosas user 34813 Jun 17 11:11 MorphGas.out -rw-r--r-- 1 rosas user 43515 Jun 17 11:11 MorphWat.out -rw-r--r-- 1 rosas user 55895 Jun 17 11:11 SMeMorphGas.out -rw-r--r-- 1 rosas user 57159 Jun 17 11:11 SMeMorphWat.out dissertation/phosphacinium: total 1575 drwxr-xr-x 2 rosas user 512 Jun 17 11:07 MOD drwxr-xr-x 2 rosas user 512 Jun 17 10:00 MOL drwxr-xr-x 2 rosas user 1024 Jun 17 10:00 PDB -rw-r--r-- 1 rosas user 21169 May 1 14:35 TableCisMedioxPGas.html -rw-r--r-- 1 rosas user 22816 May 1 14:35 TableCisMedioxPWat.html -rw-r--r-- 1 rosas user 28178 May 1 14:36 TableDiMePGas.html -rw-r--r-- 1 rosas user 41551 Jun 17 10:52 TableDiMePWat.html -rw-r--r-- 1 rosas user 20393 May 10 11:24 TableDioxPGas.html -rw-r--r-- 1 rosas user 30599 May 8 20:27 TableDioxPWat.html -rw-r--r-- 1 rosas user 29038 May 1 14:40 TableTransMedioxPGas.html -rw-r--r-- 1 rosas user 37001 Jun 17 11:00 TableTransMedioxPWat.html -rw-r--r-- 1 rosas user 13903 May 16 20:25 bb1PW2.wrl -rw-r--r-- 1 rosas user 14854 Jun 13 10:44 bb1PW4.wrl -rw-r--r-- 1 rosas user 13751 May 16 20:27 bb2PW2.wrl -rw-r--r-- 1 rosas user 14818 May 16 21:40 bb2PW4.wrl -rw-r--r-- 1 rosas user 14764 May 16 21:38 bbPW3.wrl -rw-r--r-- 1 rosas user 13665 May 26 11:18 bc1P2.wrl -rw-r--r-- 1 rosas user 15785 Jun 13 10:45 bc1P5.wrl -rw-r--r-- 1 rosas user 13695 May 16 20:28 bc1PW2.wrl -rw-r--r-- 1 rosas user 14847 May 16 21:36 bc1PW3.wrl -rw-r--r-- 1 rosas user 14860 May 16 21:37 bc1PW4.wrl -rw-r--r-- 1 rosas user 13653 May 16 22:40 bc2P2.wrl -rw-r--r-- 1 rosas user 15785 Jun 16 15:47 bc2P5.wrl -rw-r--r-- 1 rosas user 13702 May 16 20:32 bc2PW2.wrl -rw-r--r-- 1 rosas user 14796 May 16 21:36 bc2PW3.wrl -rw-r--r-- 1 rosas user 14924 May 16 21:37 bc2PW4.wrl -rw-r--r-- 1 rosas user 14873 May 16 22:55 bcP3.wrl -rw-r--r-- 1 rosas user 14860 Jun 13 10:47 bcP4.wrl -rw-r--r-- 1 rosas user 489 May 16 10:42 fig.bb1PW2.gif -rw-r--r-- 1 rosas user 527 May 16 11:34 fig.bb1PW4.gif -rw-r--r-- 1 rosas user 457 May 16 10:42 fig.bb2PW2.gif -rw-r--r-- 1 rosas user 519 May 16 11:29 fig.bb2PW4.gif -rw-r--r-- 1 rosas user 524 May 16 11:21 fig.bbPW3.gif -rw-r--r-- 1 rosas user 451 May 15 16:02 fig.bc1P2.gif -rw-r--r-- 1 rosas user 530 May 16 14:38 fig.bc1P5.gif -rw-r--r-- 1 rosas user 446 May 16 10:45 fig.bc1PW2.gif -rw-r--r-- 1 rosas user 477 May 16 11:15 fig.bc1PW3.gif -rw-r--r-- 1 rosas user 487 May 16 11:39 fig.bc1PW4.gif -rw-r--r-- 1 rosas user 434 May 15 16:05 fig.bc2P2.gif -rw-r--r-- 1 rosas user 521 May 16 14:37 fig.bc2P5.gif -rw-r--r-- 1 rosas user 437 May 16 10:47 fig.bc2PW2.gif -rw-r--r-- 1 rosas user 482 May 16 11:14 fig.bc2PW3.gif -rw-r--r-- 1 rosas user 481 May 16 11:44 fig.bc2PW4.gif -rw-r--r-- 1 rosas user 525 May 16 13:58 fig.bcP3.gif -rw-r--r-- 1 rosas user 517 May 16 14:06 fig.bcP4.gif -rw-r--r-- 1 rosas user 695 Mar 25 01:16 fig.cis.gif -rw-r--r-- 1 rosas user 728 Mar 25 01:25 fig.diMeP.gif -rw-r--r-- 1 rosas user 827 Apr 3 14:05 fig.example.gif -rw-r--r-- 1 rosas user 591 Feb 8 23:03 fig.phosp.gif -rw-r--r-- 1 rosas user 670 Mar 18 22:59 fig.phospTab.gif -rw-r--r-- 1 rosas user 522 May 16 13:39 fig.tb1P2.gif -rw-r--r-- 1 rosas user 497 May 16 14:11 fig.tb1P4.gif -rw-r--r-- 1 rosas user 570 May 16 14:44 fig.tb1P5.gif -rw-r--r-- 1 rosas user 583 May 16 13:21 fig.tb1PW5.gif -rw-r--r-- 1 rosas user 516 May 16 13:37 fig.tb2P2.gif -rw-r--r-- 1 rosas user 536 May 16 14:28 fig.tb2P4.gif -rw-r--r-- 1 rosas user 552 May 16 14:48 fig.tb2P5.gif -rw-r--r-- 1 rosas user 601 May 16 13:24 fig.tb2PW5.gif -rw-r--r-- 1 rosas user 555 May 16 11:07 fig.tbPW3.gif -rw-r--r-- 1 rosas user 461 May 15 16:13 fig.tbc1P2.gif -rw-r--r-- 1 rosas user 509 May 16 14:02 fig.tbc1P4.gif -rw-r--r-- 1 rosas user 460 May 15 16:11 fig.tbc2P2.gif -rw-r--r-- 1 rosas user 519 May 16 14:17 fig.tbc2P4.gif -rw-r--r-- 1 rosas user 534 May 16 14:51 fig.tbcP5.gif -rw-r--r-- 1 rosas user 497 May 16 14:08 fig.tc1P4.gif -rw-r--r-- 1 rosas user 511 May 16 14:20 fig.tc2P4.gif -rw-r--r-- 1 rosas user 477 May 16 13:46 fig.tcP2.gif -rw-r--r-- 1 rosas user 504 May 16 13:51 fig.tcP3.gif -rw-r--r-- 1 rosas user 529 May 16 14:31 fig.tcP5.gif -rw-r--r-- 1 rosas user 730 Mar 25 01:12 fig.trans.gif -rw-r--r-- 1 rosas user 13780 May 16 22:50 tb1P2.wrl -rw-r--r-- 1 rosas user 14814 Jun 13 10:47 tb1P4.wrl -rw-r--r-- 1 rosas user 15871 Jun 13 10:49 tb1P5.wrl -rw-r--r-- 1 rosas user 15969 May 16 21:42 tb1PW5.wrl -rw-r--r-- 1 rosas user 13732 May 16 22:53 tb2P2.wrl -rw-r--r-- 1 rosas user 14881 Jun 13 10:50 tb2P4.wrl -rw-r--r-- 1 rosas user 15844 Jun 13 10:50 tb2P5.wrl -rw-r--r-- 1 rosas user 15815 May 16 21:43 tb2PW5.wrl -rw-r--r-- 1 rosas user 14900 May 16 21:36 tbPW3.wrl -rw-r--r-- 1 rosas user 13678 May 16 22:42 tbc1P2.wrl -rw-r--r-- 1 rosas user 14853 May 16 23:00 tbc1P4.wrl -rw-r--r-- 1 rosas user 13697 May 16 22:41 tbc2P2.wrl -rw-r--r-- 1 rosas user 14857 Jun 13 10:52 tbc2P4.wrl -rw-r--r-- 1 rosas user 15826 Jun 13 10:53 tbcP5.wrl -rw-r--r-- 1 rosas user 14841 Jun 13 10:54 tc1P4.wrl -rw-r--r-- 1 rosas user 14813 Jun 13 10:57 tc2P4.wrl -rw-r--r-- 1 rosas user 13635 May 16 22:54 tcP2.wrl -rw-r--r-- 1 rosas user 14910 May 16 22:57 tcP3.wrl -rw-r--r-- 1 rosas user 15871 Jun 13 10:56 tcP5.wrl dissertation/phosphacinium/MOD: total 2564 -rw-r--r-- 1 rosas user 117723 Jun 17 11:05 CisMeDioxTotGas.out -rw-r--r-- 1 rosas user 127314 Jun 17 11:06 CisMedioxTotWat.out -rw-r--r-- 1 rosas user 157966 Jun 17 11:05 DiMeTotGas.out -rw-r--r-- 1 rosas user 234647 Jun 17 11:06 DiMetotalWat.out -rw-r--r-- 1 rosas user 120205 Jun 17 11:05 DioxTotGas.out -rw-r--r-- 1 rosas user 208927 Jun 17 11:06 DioxTotWat.out -rw-r--r-- 1 rosas user 173618 Jun 17 11:05 TransMeDioxTotGas.out -rw-r--r-- 1 rosas user 170490 Jun 17 11:06 TransMeDioxTotWat.out dissertation/phosphacinium/MOL: total 139 -rw-r--r-- 1 rosas user 2019 May 27 13:56 bb1PW2.mol -rw-r--r-- 1 rosas user 2223 May 27 13:56 bb1PW4.mol -rw-r--r-- 1 rosas user 2019 May 27 13:56 bb2PW2.mol -rw-r--r-- 1 rosas user 2223 May 27 13:56 bb2PW4.mol -rw-r--r-- 1 rosas user 2222 May 27 13:56 bbPW3.mol -rw-r--r-- 1 rosas user 2018 May 27 13:56 bc1P2.mol -rw-r--r-- 1 rosas user 2019 May 27 13:56 bc1PW2.mol -rw-r--r-- 1 rosas user 2223 May 27 13:56 bc1PW3.mol -rw-r--r-- 1 rosas user 2223 May 27 13:56 bc1PW4.mol -rw-r--r-- 1 rosas user 2018 May 27 13:56 bc2P2.mol -rw-r--r-- 1 rosas user 2019 May 27 13:56 bc2PW2.mol -rw-r--r-- 1 rosas user 2223 May 27 13:56 bc2PW3.mol -rw-r--r-- 1 rosas user 2223 May 27 13:56 bc2PW4.mol -rw-r--r-- 1 rosas user 2221 May 27 13:56 bcP3.mol -rw-r--r-- 1 rosas user 2221 May 27 13:56 bcP4.mol -rw-r--r-- 1 rosas user 2018 May 27 13:56 tb1P2.mol -rw-r--r-- 1 rosas user 2222 May 27 13:56 tb1P4.mol -rw-r--r-- 1 rosas user 2427 May 27 13:56 tb1PW5.mol -rw-r--r-- 1 rosas user 2018 May 27 13:56 tb2P2.mol -rw-r--r-- 1 rosas user 2222 May 27 13:56 tb2P4.mol -rw-r--r-- 1 rosas user 2427 May 27 13:56 tb2PW5.mol -rw-r--r-- 1 rosas user 2222 May 27 13:56 tbPW3.mol -rw-r--r-- 1 rosas user 2019 May 27 13:56 tbc1P2.mol -rw-r--r-- 1 rosas user 2019 May 27 13:56 tbc2P2.mol -rw-r--r-- 1 rosas user 2223 May 27 13:56 tbc2P4.mol -rw-r--r-- 1 rosas user 2222 May 27 13:56 tbcP4.mol -rw-r--r-- 1 rosas user 2222 May 27 13:56 tc1P4.mol -rw-r--r-- 1 rosas user 2222 May 27 13:56 tc2P4.mol -rw-r--r-- 1 rosas user 2017 May 27 13:56 tcP2.mol -rw-r--r-- 1 rosas user 2221 May 27 13:56 tcP3.mol dissertation/phosphacinium/PDB: total 285 -rw-r--r-- 1 rosas user 3508 May 16 15:56 bb1PW2.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:17 bb1PW4.pdb -rw-r--r-- 1 rosas user 3508 May 16 15:57 bb2PW2.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:18 bb2PW4.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:16 bbPW3.pdb -rw-r--r-- 1 rosas user 3508 May 16 21:51 bc1P2.pdb -rw-r--r-- 1 rosas user 4138 Jun 12 15:32 bc1P5.pdb -rw-r--r-- 1 rosas user 3508 May 16 15:58 bc1PW2.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:15 bc1PW3.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:18 bc1PW4.pdb -rw-r--r-- 1 rosas user 3508 May 16 21:51 bc2P2.pdb -rw-r--r-- 1 rosas user 4138 Jun 12 15:32 bc2P5.pdb -rw-r--r-- 1 rosas user 3508 May 16 15:58 bc2PW2.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:16 bc2PW3.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:19 bc2PW4.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:56 bcP3.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:58 bcP4.pdb -rw-r--r-- 1 rosas user 3508 May 16 21:54 tb1P2.pdb -rw-r--r-- 1 rosas user 3823 May 16 22:03 tb1P4.pdb -rw-r--r-- 1 rosas user 4138 Jun 12 15:32 tb1P5.pdb -rw-r--r-- 1 rosas user 4138 May 16 21:20 tb1PW5.pdb -rw-r--r-- 1 rosas user 3508 May 16 21:53 tb2P2.pdb -rw-r--r-- 1 rosas user 3823 May 16 22:05 tb2P4.pdb -rw-r--r-- 1 rosas user 4138 Jun 12 15:32 tb2P5.pdb -rw-r--r-- 1 rosas user 4138 May 16 21:20 tb2PW5.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:15 tbPW3.pdb -rw-r--r-- 1 rosas user 3508 May 16 21:52 tbc1P2.pdb -rw-r--r-- 1 rosas user 3508 May 16 21:52 tbc2P2.pdb -rw-r--r-- 1 rosas user 3823 May 16 22:03 tbc2P4.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:57 tbcP4.pdb -rw-r--r-- 1 rosas user 4138 Jun 12 15:33 tbcP5.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:59 tc1P4.pdb -rw-r--r-- 1 rosas user 4138 Jun 12 15:31 tc1P5.pdb -rw-r--r-- 1 rosas user 3823 May 16 22:04 tc2P4.pdb -rw-r--r-- 1 rosas user 3508 May 16 21:55 tcP2.pdb -rw-r--r-- 1 rosas user 3823 May 16 21:56 tcP3.pdb dissertation/reviews: total 105 -rw-r--r-- 1 rosas user 573 Feb 21 00:20 fig.2266dioxo.gif -rw-r--r-- 1 rosas user 516 Feb 21 00:20 fig.22dioxo.gif -rw-r--r-- 1 rosas user 530 Feb 21 00:20 fig.66dioxo.gif -rw-r--r-- 1 rosas user 740 Mar 15 01:07 fig.HAC.gif -rw-r--r-- 1 rosas user 595 Feb 26 01:18 fig.aminocarn.gif -rw-r--r-- 1 rosas user 842 Feb 26 01:56 fig.anderson951.gif -rw-r--r-- 1 rosas user 980 May 14 10:02 fig.anderson952.gif -rw-r--r-- 1 rosas user 1774 Mar 4 15:45 fig.anomeric.gif -rw-r--r-- 1 rosas user 2302 Feb 10 16:10 fig.b.gif -rw-r--r-- 1 rosas user 2486 Feb 10 16:09 fig.bb.gif -rw-r--r-- 1 rosas user 2304 Feb 10 16:09 fig.bc.gif -rw-r--r-- 1 rosas user 2416 Feb 10 16:10 fig.c.gif -rw-r--r-- 1 rosas user 2539 Feb 10 16:10 fig.cc.gif -rw-r--r-- 1 rosas user 3852 Mar 3 14:56 fig.crown.gif -rw-r--r-- 1 rosas user 411 May 14 11:36 fig.dioxo.gif -rw-r--r-- 1 rosas user 2362 Feb 23 00:42 fig.fritz63.gif -rw-r--r-- 1 rosas user 1231 May 22 14:09 fig.gandour93.gif -rw-r--r-- 1 rosas user 2714 Apr 15 11:30 fig.hydrolysis2.gif -rw-r--r-- 1 rosas user 743 May 14 10:00 fig.kumaravel94.gif -rw-r--r-- 1 rosas user 414 May 14 11:35 fig.oxo.gif -rw-r--r-- 1 rosas user 581 Feb 26 01:21 fig.saeed93.gif -rw-r--r-- 1 rosas user 585 Mar 4 16:39 fig.saeed94.gif -rw-r--r-- 1 rosas user 1157 Apr 15 10:24 fig.sun95.gif -rw-r--r-- 1 rosas user 2426 Feb 10 16:11 fig.tb.gif -rw-r--r-- 1 rosas user 2601 Feb 10 16:20 fig.tbc-1.gif -rw-r--r-- 1 rosas user 2639 Feb 10 16:10 fig.tbc1.gif -rw-r--r-- 1 rosas user 2500 Feb 10 16:11 fig.tc.gif -rw-r--r-- 1 rosas user 2446 Feb 10 16:11 fig.tcc.gif -rw-r--r-- 1 rosas user 432 May 14 11:34 fig.tetraoxo.gif -rw-r--r-- 1 rosas user 420 May 14 11:36 fig.trioxo.gif </pre> <vita> <p>Víctor was born in Monterrey, México, on February 24<sup>th</sup>, 1969. Due to his father's job, the family alternated residence between Monterrey and México City, to finally settle down in Monterrey. There Víctor pursued his B.S. in Industrial Chemistry at UANL and, after graduation, held his first job as a Quality Control chemist. Having decided that his chemical skills required (substantial) polishing, he joined the PhD program at Louisiana State University in Baton Rouge, LA. At LSU he joined Professor Gandour's research group, while thoroughly enjoying the Cajun and Creole heritage of the land (Mardi Gras included). Little he suspected that he would later be transferring to Virginia Tech, following his advisor. While at Virginia Tech, he decided that computers were fun and chemistry was fun so putting them together would be fun<sup>2</sup>. Thus he turned his interests to Computational Chemistry, to finally get his Ph.D. as a Computational Bioorganic Chemist. </vita> </back>