Solvation nonequilibrium

Van der Zwan G and Hynes J T 1983 Nonequilibrium solvation dynamics in solution reaction J. Chem. Phys. 78 4174-85... 

Mavri, J., Berendsen, H.J.C., Van Gunsteren, W.F. Influence of solvent on intramolecular proton transfer in hydrogen malonate. Molecular dynamics study of tunneling by density matrix evolution and nonequilibrium solvation. J. Phys. Chem. 97 (1993) 13469-13476. 

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

Nonequilibrium solvent effects can indeed by significant at the kcal level-maybe even at a greater level, but so far there is no evidence for that when the reaction coordinate involves protonic or heavier motions. Our goal in this section has been to emphasize just how powerful and general the equilibrium model is. In addition, in both the previous section and the present section, we have emphasized the use of models based on collective solvent coordinates for calculating both equilibrium and nonequilibrium solvation properties. 

B. C. Garrett and G. K. Schenter, Nonequilibrium solvation for an aqueous-phase... 

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],... 

The outline of this review is as follows. In Sec.2, we highlight the fundamental equations and structure of the theory Sec.2.1 motivates the choice or the functional form of the solute wave function Sec.2.2 explains the equation for the free energy of the solute plus solvent system in the nonequilibrium solvation regime Sec.2.3 discusses the corresponding Schrodinger... 

Having defined the basic quantities, we can now quote the expression of the free energy in the nonequilibrium solvation regime ... 

Finally, the last two terms in G(2.12) account for the effects of the solvent orientational polarization in the nonequilibrium solvation. The matrix K0 is the inverse of the solvent orientational polarization interaction energy matrix I0 whose elements are defined, analogously to Ienm, by... 

Although in principle one could choose a set of arbitrary values for the solvent coordinates sm, solve the eigenvalue equation (2.23), and compute the free energy (2.12), in practice a preliminary aquaintance with the equilibrium solvation picture for the target reaction system serves as a computationally convenient doorway for the calculations in the nonequilibrium solvation regime. We show this below in the section dedicated to an illustration of the method for a two state case reported in BH-II. 

Hence, we conclude that the nonequilibrium solvation free energy surface for the BuCl Sa/I reaction system in a two VB state framework would be well described as a function of the bond length C-Cl (assuming the geometry of the Bu group is fixed) and of the natural solvent coordinates s3. The natural solvent coordinates Si and s2, on the other hand, would assume their equilibrium value at the given nuclear configuration. Indeed,... 

The theory is capable of describing both the regimes of equilibrium and nonequilibrium solvation for the latter we have developed a framework of natural solvent coordinates which greatly helps the analysis of the reaction system along the ESP, and displays the ability to reduce considerably the burden of the calculation of the free energy surface in the nonequilibrium solvation regime. While much remains to be done in practical implementations for various reactions, the theory should prove to be a very useful and practical description of reactions in solution. 

Kim, H. J. and Hynes, J. T. Equilibrium and nonequilibrium solvation and solute electronic structure, IntJ.Quantum Chem., 24 (1990), 821-833... 

Aguilar, M. A., Olivares del Valle, F. J. and Tomasi, J. Nonequilibrium solvation an ab initio quantum-mechanical method in the continuum cavity model approximation, J.Chem.Phys., 98 (1993), 7375-7384... 

G. van der Zwan and J. T. Hynes, Time-dependent fluorescence solvent shifts, dielectric friction and nonequilibrium solvation in polar solvents, J. Phys. Chem. 89, 418M188 (1985). 

B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798. 

In recent years many attempts have been made to extend the implicit solvent models to the description of time-dependent phenomena. One of these phenomena is nonequilibrium solvation [3] and it can be described effectively in a very simplified way, despite the fact that it actually depends on the details of the full frequency spectrum of the dielectric constant. Typical examples of nonequilibrium solvation are the absorption of light by the solute which produces an excited state which is no longer in equilibrium with the surrounding polarization of the medium [11-13], Another example is intermolecular charge transfer within the solute, also leading to a nonequilibrium polarization [14],... 

This model accounts only partially for the specific structure of liquid water, and to refine it, calculations within supermolecular and semicontinuum models were also performed. In these cases, the properties were computed for a cluster of five water molecules, simulating the inclusion of a first solvation shell. In the semicontinuum model, the cluster was immersed in the dielectric continuum. Because of the (prohibitive for the times) size of the cluster, it was possible to obtain only an uncorrelated result. On the other hand, a nonequilibrium solvation model was used in computing the orientational contribution of Equation (2.218). Finally, to determine mC(o>, T), an extensive property, a differential shell method was employed. 

Nonequilibrium solvation model for the electric dipole polarizability. b Result corrected for local field effects. c Ref.[27], mean value for T between 283.1 5 and 293.1 5 K. 

We model the nonequilibrium solvation for a molecular state using the following interaction operator between the outer dielectric medium and the molecular system[2]... 

O. Christiansen and K. V. Mikkelsen, Coupled cluster response theory for solvated molecules in equilibrium and nonequilibrium solvation, J. Chem. Phys., 110 (1999) 8348. 

A new issue arises when one makes a solute-solvent separation. If the solvent enters the theory only in that V(R) is replaced by TT(R), the treatment is called equilibrium solvation. In such a treatment only the coordinates in the set R can enter into the definition of the transition state. This limits the quality of the dynamical bottleneck that one can define depending on the system, this limitation may cause small quantitative errors or larger more qualitative ones, even possibly missing the most essential part of a reaction coordinate (in a solvent-driven reaction). Going beyond the equilibrium solvation approximation is called nonequilibrium solvation or solvent friction [4,26-28], This is discussed further in Section 3.3.2. 

The most useful theoretical framework for studying chemical reactions in solution is transition state theory. Building on the material presented in the introduction, we will begin by presenting a general theory called the equilibrium solvation path (ESP) theory of reactions in a liquid. We then present an approximation to ESP theory called separable equilibrium solvation (SES). Finally we present a more complete theory, still based on an implicit treatment of solvent, called nonequilibrium solvation (NES). All three... 

The SES, ESP, and NES methods are particularly well suited for use with continuum solvation models, but NES is not the only way to include nonequilibrium solvation. A method that has been very useful for enzyme kinetics with explicit solvent representations is ensemble-averaged variational transition state theory [26,27,87] (EA-VTST). In this method one divides the system into a primary subsystem and a secondary one. For an ensemble of configurations of the secondary subsystem, one calculates the MEP of the primary subsystem. Thus the reaction coordinate determined by the MEP depends on the coordinates of the secondary subsystem, and in this way the secondary subsystem participates in the reaction coordinate. 

Other methods of including nonequilibrium solvation are reviewed elsewhere [86], and the reader is also referred to selected relevant and more recent original papers [66,88-100], Particularly relevant to the present volume are methods that introduce extra degrees of freedom by using the solvent reaction field not only at the current value of R but also at nearby values [65,66], Many of the approaches introduce finite-time effects and additional degrees of solvent freedom by introducing different time scales for electronic and atomic polarization [88-97,99,100],... 

A significant recent advance in continuum SD has been achieved by combining the solvation response expressions in terms of the solvent s(cu) with quantum mechanical (QM) electronic structure methodology for solvated species. Specifically, the polarizable continuum model (PCM) [51], which was originally developed to predict the electronic structure of solutes in polar media, has been extended to nonequilibrium solvation [52]. A review by Mennucci [8] describes this extension of PCM and its application to the evaluation of S(t). The readers are referred to that article for the outline of the overall approach and for the details of the methods used. 

R. Cammi and J. Tomasi, Nonequilibrium solvation theory for the polarizable continuum model - a new formulation at the SCF level with application to the case of the frequency-dependent linear electric-response function, Int. J. Quantum Chem., (1995) 465-74 B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798-807 R. Cammi, L. Frediani, B. Mennucci, J. Tomasi, K. Ruud and K. V. Mikkelsen, A second-order, quadratically... 

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