Nonequilibrium solvation effects

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

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. 

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],... 

Of course, there is more to a chemical reaction than its rate constant the reaction path or mechanism is also of central interest. Once again, nonequilibrium solvation is crucial in describing this path. In an equilibrium solvation picture, the solvent polarization would remain equilibrated throughout the reaction course, but this assumption is rarely satisfied for an actual reaction path, because of the same considerations noted above for the rate constant. Indeed these nonequilibrium solvation effects can qualitatively change the character of the reaction path as compared with an equilibrium solvation image. Dielectric continuum dynamic descriptions thus have an important role to play here as well. Indeed, we will employ in this contribution the reaction path Hamiltonian formulation previously developed [48,49], which can be used to generate a reaction path which is the analog in solution of the well-known Fukui reaction path in the gas phase [50], The reaction path will be discussed for both reaction topics in this contribution. 

To conclude on the issue of nonequilibrium solvation effects on the radical anion dissociation, while these are not very important for the rate constant itself, for the reasons just given, they are quite significant for the reaction paths as discussed above. 

We have already mentioned in the Introduction (Section 3.7.1) the importance of conical intersections (CIs) in connection with excited electronic state dynamics of a photoexcited chromophore. Briefly, CIs act as photochemical funnels in the passage from the first excited S, state to the ground electronic state S0, allowing often ultrafast transition dynamics for this process. (They can also be involved in transitions between excited electronic states, not discussed here.) While most theoretical studies have focused on CIs for a chromophore in the gas phase (for a representative selection, see refs [16, 83-89], here our focus is on the influence of a condensed phase environment [4-9], In particular, as discussed below, there are important nonequilibrium solvation effects due to the lack of solvent polarization equilibration to the evolving charge distribution of the chromophore. 

We have seen that dynamical solvent effects in the friction can lead to a breakdown of TST. As stressed above, this is also a breakdown in the equilibrium solvation assumption for the transition state and configurations in its neighborhood. In fact, the standard TST view is a special one-dimensional equilibrium perspective, i.e. a mean potential curve for the reacting species is visualized and no friction of any sort is considered. The solvent influence can be felt solely via this potential, hence it is assumed that for each configuration of the reacting species, the solvent is equilibrated. On the contrary, the discussion above about Kramers and Grote-Hynes theories has documented the importance of nonequilibrium solvation effects in a frictional language. 

Where k is the transmission factor, < x >xs is the average of the absolute value of the velocity along the reaction coordinate at the transition state (TS), and P = l/keT ( vhere ke is the Boltzmann constant and T the absolute temperature). The term AG designates the multidimensional activation free energy that expresses the probability that the system vill be in the TS region. The free energy reflects enthalpic and entropic contributions and also includes nonequilibrium solvation effects [4] and, as will be shown below, nuclear quantum mechanical effects. It is also useful to comment here on the common description of the rate constant as... 

Ref. [4], the corresponding rate constants do not show significant dynamical effects. Furthermore, attempts to define dynamical catalytic effect in a different way and to include in such factor nonequilibrium solvation effects [100] have been shown to be very problematic (e.g. Ref. [4]). Similarly, we have shown that the reasonable definition of dynamical effects by the existence of special vibrations that lead coherently to the TS does correspond to the actual simulation in enzyme and solution. 

Berne, Molecular Dynamics Study of an Isomerizing Diatomic in a Lennard-Jones Fluid, J. Chem. Phys., 89, 4833 (1988) b) B. J. Gertner, K. R. Wilson, J. T. Hynes, Nonequilibrium Solvation Effects on Reaction Rates for Model SN2 Reactions in Water,... 

Cramer CJ, Truhlar DG. Solvation thermodynamics and the treatment of equilibrium and nonequilibrium solvation effects by models based on collective solvent coordinates. In Reddy MR, Erion MD, eds. Free Energy Calculations in Rational Drug Design. New York Kluwer/Plenum, 2001 63-95. 

Since the solvent relaxation time is fixed, nonequilibrium solvation effects on k are best studied as a function of i.e., the bare... 

In the last years the theoretical organic chemistry has been increasingly extended beyond the gas phase realm of quantum mechanics to the study of the course of chemical reactions in solution. The success of these methods will indicate the begin of a new period for modeling chemistry in solution. Here, we mainly restrict our attention to a static solvent treatment. The discussion of the limitation of this approach was recently continued.Such studies assume the solvation to be in equilibrium with the chemical system at each point along a HP. This basic hypothesis may first be questioned from possibly different time scales of solvent relaxation and the chemical process and, secondly, from the motion of a (limited number) of solvent molecules which may form an important part of the motion of the whole system along the HP. But apart from dynamical nonequilibrium solvation effects and other limitations in the application of TST to reaction in solvents (see Chap. 1.4), static approaches will give much information on the intermolecular interactions and may represent a suitable ansatz for the estimation and interpretation of solvent effects in many cases. 

A third approach is to incorporate nonequilibrium solvent (NES) effects. In POLYRATE, this is accomplished by replacing the many degrees of freedom of the solvent with a single collective solvent coordinate.Eurther discussion of equilibrium and nonequilibrium solvation effects on liquid-phase reactions is provided elsewhere. 

Reddy and M. D. Erion, Eds., Kluwer Academic/Plenum, New York, 2001, pp. 63-95. Solvation Thermodynamics and the Treatment of Equilibrium and Nonequilibrium Solvation Effects by Models Based on Collective Solvent Coordinates. 

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