John D. Roberts
Assistant: Victoria Brennan
In our research, we try to evaluate steric, electrostatic, hydrogen-bonding and solvent effects on conformational equilibria. Studies of conformations are most easily carried out with the aid of nuclear magnetic resonance (NMR) spectroscopy and this, using the resonances of 1H, 13C, 15N or 31P as needed, is the instrumentation of our choice. You might well think that such research is not very sophisticated relative to the present state of knowledge of chemistry and wonder why anyone would find it very interesting. Read on and we will tell you why we do it and how we find it interesting.
Many problems in physical organic chemistry can only be said to be solved in principle, because while we now understand the general nature of many factors that influence various outcomes, accurate predictions of any one particular outcome, may be difficult. Why? Because, if the factors operate in different directions, it is only when one dominates, that we can be reasonably sure of even qualitative prediction of a given outcome. An outstanding figure in physical organic chemistry, the late Paul D. Bartlett of Harvard University, advised workers in the field to search for problems where differences between outcomes are expected to be a factor of 106. With differences of this magnitude, the odds of having a predominance of one, clearly recognizable and physically understandable, factor is very favorable.
In his early career, Bartlett followed his own admonition, when he demonstrated that a tertiary cationic carbon is most likely to be stable if the bonds connected to it can lie in one plane. He did this by synthesizing a bicyclic bridgehead chloride, where the cationic carbon could not become planar, except with very substantial distortion of normal bond angles. This tertiary chloride turned out to be less than 1/106 as reactive as tert-butyl chloride. (1)
Now, it turns out that a factor of 106 in an equilibrium constant or in ease of formation of a transition state at room temperature corresponds to a free-energy (or free-energy of activation) difference of 8.2 kcal. Such an energy difference is substantial, but one should not believe that once you have achieved a 106or more equilibrium or rate factor, you have also necessarily achieved understanding. Cogent examples are supplied by enzyme-catalyzed reactions, where rate factors of more than 106are observed between catalyzed and uncatalyzed rates with the enzyme displaying both extraordinary stereo- and regiospecificity. Precise understandings of the factors that allow such large rate differences are still unclear, although much progress is being made. What is clear for an enzyme-catalyzed reaction is that there are multiple interactions that contribute to both the enthalpies and entropies of the various stages of the overall process. One might well hope that the importance and nature of those interactions could be defined and understood by the study of model compounds.
The factors that enter into enzyme-induced catalysis must include, although not necessarily be limited to, enthalpy and entropy changes arising from hydrogen bonding, electrostatic interactions, steric hindrance, changes in solvation, quantum-mechanical effects and van der Waals' interactions. Tending to nullify a balance of favorable enthalpy changes for formation of enzyme-substrate complexes, will be entropic factors associated with diminished translational and rotational freedom, along with changes in the vibrational degrees of freedom associated with substrate-protein binding, as well as with hydrogen bonding to water.
In our research, we try to understand some of the factors that we expect to be important in enzyme-substrate binding using very simple model compounds. Particular emphasis has been placed on trying to evaluate steric, electrostatic, solvent and hydrogen-bonding effects on conformational equilibria. Studies of this kind are most easily carried out with the aid of nuclear magnetic resonance (NMR) spectroscopy and this is the instrumentation of our choice. (2)
If one considers the conformational equilibria of substances as simple as 1,2-disubstituted ethanes, X-CH2-CH2-Y, it would seem obvious that evidence as to the interactions between various kinds of groups could be gained by determining the equilibrium preferences for gauche/trans conformations as a function of the nature of X and Y. Presumably, a well-informed organic chemist should be able to predict, with reasonable accuracy, the balance of some of the factors that should determine the equilibrium preferences. Thus, if X and Y were both tert-butyl groups, steric hindrance would be particularly large in the gauche conformations and the trans conformation should and does predominate. With other combinations of groups, the factors can operate in different directions to influence the position of equilibrium. With the halogens, for example, we might expect steric hindrance with the large halogens and dipole-dipole electrostatic interactions to favor trans, while van der Waals' attractive forces and quantum-mechanical effects with smaller halogens would favor gauche. Because the balance between the effects depends on the particular pair of halogens involved, the most we may be able to do is to simply rationalize that one influence or group of influences is the more important in contributing to the overall result.
When we throw in the possibility of intramolecular hydrogen-bonding with X and Y as OH, NH2, -CO2H and so on groups, we anticipate that gauche conformations should be favored, although in some solvents, there can be competing solvent effects. In dilute solution in a nonprotic solvent such as CCl4, intramolecular hydrogen bonding should be very favorable. In dimethyl sulfoxide, (CH3)2S=O, the oxygen is a good hydrogen-bond acceptor and could divert OH and other hydrogen-bonding groups from intramolecular to intermolecular hydrogen bonding. Water as solvent is both a hydrogen-bond acceptor and donor and could be expected to divert OH and like groups from intramolecular to intermolecular hydrogen bonding. Whatever the result, we see it is capable of being rationalized, if not predictable.
One aid to rationalization is that, in general, non-steric interactions between X and Y are not usually expected, or found, to be large. For example, a substantial number of well-informed organic chemists asked to predict the gauche/trans ratio for the butanedioate dianion, -O2C-CH2-CH2-CO2-, in water. If there were no structural preferences operating for one or the other, simple statistics would mandate a 2/1 gauche to trans ratio. The usual prediction is a gauche/trans ratio of about 1/5, which is a factor of ten and corresponds to a free-energy difference of 1.4 kcal, easily ascribable to repulsions between the negatively charged carboxylate groups. Thus, informed opinion, does not contemplate either, a large electrostatic effect, because water has a substantial dielectric constant of 80, or steric hindrance associated with a substantial bulking of the carboxylate groups by solvation interactions with water, both of which would favor the trans conformation. This informed conservatism in assessing conformational influences seems well justified by the finding that the experimental gauche/trans ratio of about 1/1 in water is only a factor of two different from statistical equilibrium. (3)
The conformational preferences in water of butanedioic acid, HO2C-CH2-CH2-CO2-H and of the hydrogen butanedioate, HO2C-CH2-CH2-CO2- has been of particular and disputed interest over the years, (3,4) because of the possibility of intramolecular hydrogen bonding in its gauche conformation. (5) The energy of such a hydrogen bond involving two acidic hydrogens or one acidic hydrogen as donor and an anionic oxygen as acceptor would conservatively be estimated as perhaps 5 kcal and, if all of that were exercised as conformational preference, the gauche forms should be favored by a factor of 4500. The experimental finding in water that the rather slight gauche preference of the diacid in water surely arises from other influences, (3,4) while with the monoanion, there is essentially NO conformational preference at all, provides a measure of intellectual challenge - to wit, how to account for a zero-sum game, the situation Bartlett suggested should be avoided, at least if you want to become famous. (1, 3)
Of course, the lack of conformational preference for HO2C-CH2-CH2-CO2- could be an isolated fluke with little general interest. But this does not seem to be the case. Thus, the different ionization states of beta-alanine, +NH3-CH2-CH2-CO2H, +NH3-CH2-CH2-CO2-, and NH2-CH2-CH2-CO2- are found at low, intermediate or high pH values to show very little conformational preference, the gauche/trans ratios being nearly the statistical values of 2/1 for each. (6)
Much of our current research is devoted to experimental and quantum-mechanical approaches to trying to understand the inadequacies of our understanding of these problems by investigating what happens with changes in solvent, salts, temperature and counterion. In effect, we try to see what can possibly be done to convert our observed net minuscule influences on conformational equilibria to large enough net effects, comparable to 106that would make Bartlett proud. Indeed, in several cases, we appear to have been outstandingly successful. Thus, the vicinal H-H coupling constants obtained from the proton NMR spectra of 13C-labeled butanedioate monoanion, HO2C-CH2-CH2-CO2-, and dianion, -O2C-CH2-CH2-CO2- as the tetrabutylammonium salts in tetrahydrofuran and dimethyl sulfoxide solutions indicate that the monoanion is 100% gauche, as expected for strong internal hydrogen bonding. In contrast, the dianion, which certainly in a low dielectric solvent, should also be expected have a very substantial contribution of the trans conformation with the negative carboxylate groups as far apart as possible, actually has an unexpected, hardly negligible, proportion of gauche. (7) To a degree, this latter finding would appear to fly in the face of simple electrostatic theory and, indeed, calculations for the dianion in the vapor phase indicate that the trans conformation should be favored by some 20 kcal. (7) However, the Born charging equation (8) describing the stabilization of an ion in a dielectric medium, even one with as low a dielectric constant as that of tetrahydrofuran (7.5), suggests the opposite might be true and, to make matters still more interesting, quantum calculations support that possibility. Furthermore, the quantum calculations suggest that the dihedral angle between the carboxylate groups should be about 40  rat rather than the usually expected 60º for simple gauche conformers. (7)
Further experimentation is in progress to determine the generality of this behavior of dianions and to measure the dihedral angles of the conformers in solution..
(1) "Paul D. Bartlett (August 14, 1907-October 11, 1997). Some reflections on his impact on physical organic chemistry," J. D. Roberts, The Chemical Intelligencer, p. 34-39, April, 1998.
(2) "Organic Chemistry, Applications," D. M. Grant and R. K. Harris, Eds., Encyclopedia of NMR, John Wiley & Sons, New York, 1996, pp. 3386-3400.
(3) "Conformational Changes of Butanedioic Acid as a Function of pH as Determined from Changes in Vicinal Proton-Proton Coupling Constants," E. Lit, F. Mallon, H. Tsai and J.D. Roberts, J. Am. Chem. Soc., 115, 9563 (1993).
(4). "The Conformations of 1,4-Butanedioic Acid as a Function of Solvent Polarity in a Series of Alcohols as Determined by NMR Spectroscopy." L. N. Williams, K. A. Petterson, and J.D. Roberts. J. Phys. Chem. A 106, 7491-7493 (2002).
(5) "Conformational Complexity of Succinic Acid and its Monoanion in the Gas Phase and in Solution: Ab Initio Calculations and Monte Carlo Simulations," J. Am. Chem. Soc., 120, 9672-9679 (1998). D. J. Price, W. L. Jorgensen and J. D. Roberts.
(6) "Conformational Equilibria of beta-Alanine and Related Compounds as Studied by NMR Spectroscopy," J. Am. Chem. Soc., 120, 7537-7543 (1998). F. Gregoire, S. H. Wei, E. W. Streed, K. A. Brameld, D. Fort, L. J. Hanely, J. D. Walls and W. A. Goddard III, and J. D. Roberts
(7) "An NMR and Quantum-Mechanical Investigation of Tetrahydrofuran Solvent Effects on the Conformational Equilibria of 1,4-Butanedioic Acid and its Salts," J. Am, Chem, Soc., 124, 4481-4486 (2002) D. R. Kent IV, K. A. Petterson, F. Gregoire, E. Snyder-Frey, L. J. Hanely, R. P. Muller, W. A. Goddard III, and . D. Roberts.
(8) "Volumen und Hydrationswarme der Ionen," Z. Phyzik, 1, 45-48 (1920), M. Born