Equilibrium solvation effects

The treatment of equilibrium solvation effects in condensed-phase kmetics on the basis of TST has a long history and the literature on this topic is extensive. As the basic ideas can be found m most physical chemistry textbooks and excellent reviews and monographs on more advanced aspects are available (see, for example, the recent review article by Tnihlar et al [6] and references therein), the following presentation will be brief and far from providing a complete picture. 

Onsager s reaction field model in its original fonn offers a description of major aspects of equilibrium solvation effects on reaction rates in solution that includes the basic physical ideas, but the inlierent simplifications seriously limit its practical use for quantitative predictions. It smce has been extended along several lines, some of which are briefly sunnnarized in the next section. 

With Monte Carlo methods, the adoption of the Metropolis sampling scheme intrinsically assumes equilibrium Boltzmann statistics, so special modifications are required to extend MC methods to non-equilibrium solvation as well. Fortunately, for a wide variety of processes, ignoring non-equilibrium solvation effects seems to introduce errors no larger than those already inherent from other approximations in the model, and thus both implicit and explicit models remain useful tools for studying chemical reactivity. 

Discrete and continuum models for the solvent involvement have been employed to steady equilibrium and non-equilibrium solvation effects on bromination of ethylene. Two mechanisms were identified that lead to transition states of different symmetry. One mechanism operates in the gas phase and non-polar solvents. The second one, that leads to the typical C2V transition state, holds in medium-to-very polar solvents. In water, the solvent molecules participate actively and non-equilibration solvations effects proved to be substantial and larger than those previously reported for the >SN2 reaction.23... 

Attempts to imply that dynamical effects are associated with the so-called nonequilibrium solvation effects125 have been shown to be very problematic (see Ref. 4). Furthermore, it has been clearly demonstrated that the difference between the non-equilibrium solvation effects in enzyme and solution is an integral part of the difference between the corresponding activation barriers.4... 

However, the two cases differ both with respect to the relaxation of the molecular orbitals (MO) of the Hartree-Fock reference state of the solute, and with respect to the presence of non-equilibrium solvation effects. 

Figure 1 Illustration of equilibrium solvation effects on reaction free energies as a function of the reaction coordinate s (a) for a. symmetric reaction with no variational effects and (b) for a nonsymmetric reaction in which the solvation causes the maximum of the free energy of activation profile to shift. The long-dashed curves are the gas-phase free energy of activation profile, solid cui ves are the liquid-phase free energy of activation profile, and the short-dashed curves are the solvation free energy of the solute, called AG in the text and AGsoiv in the figure. Free energies depicted in the figures are discussed in the text...

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

A theoretical ab initio study of the gas-phase basicities of methyldiazoles (90JA1303) included a discussion of the 4(5)-methylimidazole tautomer-ism. The RHF/4-31G calculations led to the conclusion that the 4-methyl tautomeric form 14a (R = Me, R = R = H) is 5.2 kJ moP more stable than its 5-methyl counterpart 14b. It was emphasized that this result is to be considered as basic-set dependent. However, a recent theoretical study [94JST(T)45] showed that, starting from the RHF/6-31G level, all the more accurate approximations indicate a higher intrinsic stability for the 4-methyl tautomer. At the MP2/6-31G level, the total energy of the 4-methyl tautomer is 0.7 kJ mol lower than that of the 5-methyl tautomer. Inclusion of solvation effects can, thus, strongly affect the position of the tautomeric equilibrium 14a 14b. Recently, a systematic theoretical study... 

Solvation Thermodynamics and the Treatment of Equilibrium and Nonequilibrium Solvation Effects by Models Based on Collective Solvent Coordinates... 

There are two major approaches to including nonequilibrium effects in reaction rate calculations. The first approach treats the inability of the solvent to maintain its equilibrium solvation as the system moves along the reaction coordinate as a frictional drag on the reacting solute system.97, 100 The second approach adds one or more collective solvent coordinate to the nuclear coordinates of the solute.101 107 When these solvent coordinates are... 

A tautomeric equilibrium is a unimolecular equilibrium in which the various contributors differ based upon bond connectivity. In the special case of a protomeric tautomeric equilibrium, they differ only in how many protons are attached to each heavy atom. In-text figures throughout this section illustrate molecules for which multiple tautomers exist. When the molecules of interest are heterocycles, different tautomers may exhibit very large differences in electronic properties [266], In particular, they may span a wide range of polarities. That being the case, tautomeric equilibria can be quite sensitive to solvation effects, and they have thus proven to be attractive testing grounds for continuum solvation models. 

The comparisons made by Parchment et al. [271] illustrate the importance of combining electronic polarization effects with corrections for specific solvation effects. The latter are accounted for parametrically by the explicit simulation, but that procedure cannot explicitly account for the greater polarizability of tautomer 8. The various SCRF models do indicate 8 to be more polarizable than any of the other tautomers, but polarization alone is not sufficient to shift the equilibrium to that experimentally observed. Were these two effects to be combined in a single theoretical model, a more accurate prediction of the experimental equilibrium would be expected. 

In addition to heterocycles, other molecular systems have attracted theoretical attention with respect to prediction of tautomeric equilibria and solvation effects thereon. The most commonly studied example in this class is the equilibrium between formamide and formamidic acid, discussed in the next section. In addition, some continuum modeling of solvation effects on keto/enol equilibria have appeared these are presented in section 4.2.2.2. We note that the equilibrium... 

Even at this level of dynamical theory, one is not restricted to considering equilibrium solvation of the gas-phase saddle point or of configurations along the gas-phase reaction path [109, 338-344], and to the extent that the solvent is allowed to affect the choice of the reaction path itself, dynamic (i.e., nonequilibrium) solvation effects begin to appear in the theory. 

One should take careful note of the fact that in the nonadiabatic solvation, or frozen solvent" limit, it is the absence of solvation dynamics that is important. But is just this lack that is responsible for the deviation from equilibrium solvation, which instead assumes the dynamics are effective in always maintaining equilibrium. 

In this contribution, we describe and illustrate the latest generalizations and developments[1]-[3] of a theory of recent formulation[4]-[6] for the study of chemical reactions in solution. This theory combines the powerful interpretive framework of Valence Bond (VB) theory [7] — so well known to chemists — with a dielectric continuum description of the solvent. The latter includes the quantization of the solvent electronic polarization[5, 6] and also accounts for nonequilibrium solvation effects. Compared to earlier, related efforts[4]-[6], [8]-[10], the theory [l]-[3] includes the boundary conditions on the solute cavity in a fashion related to that of Tomasi[ll] for equilibrium problems, and can be applied to reaction systems which require more than two VB states for their description, namely bimolecular Sjy2 reactions ],[8](b),[12],[13] X + RY XR + Y, acid ionizations[8](a),[14] HA +B —> A + HB+, and Menschutkin reactions[7](b), among other reactions. Compared to the various reaction field theories in use[ll],[15]-[21] (some of which are discussed in the present volume), the theory is distinguished by its quantization of the solvent electronic polarization (which in general leads to deviations from a Self-consistent limiting behavior), the inclusion of nonequilibrium solvation — so important for chemical reactions, and the VB perspective. Further historical perspective and discussion of connections to other work may be found in Ref.[l],... 

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