Generalized Self-Consistent Reaction Field Theory

2 Generalized Self-Consistent Reaction Field Theory 

The concept of reaction field, originally formulated by Onsager [194], has been proved to be fruitful in the quantum chemical treatment of polar subsystems (solutes) embedded in polarizable environment (solvent) [195]. Simple cavity models, where the solvent is represented by a continuous dielectric medium and the solute is sitting in a cavity inside this dielectric, has numerous application in the framework of semiempirical [196-200] and ab initio [201-205] methods. The utility of this concept in the modelisation of biochemical processes was pointed out by Tapia and his coworkers [206]. 

The obvious limitations of the continuum representation of the solvent necessitated the development of microscopic models of the surroundings. Whereas for liquid phases this task is not trivial at all, for structurally well-characterized environments, like proteins [190, 207] or crystals [208] it is possible to calculate the reaction field from the polarizability distribution [209]. Assuming the existence of strongly bound solvent 

The above-mentioned works were based on simplified representations of the solvent charge- and polarizability-distribution, and use dipolar approximation to solute-solvent interactions. A generalized version of this microscopical reaction field theory was recently proposed by Tapia [211]. In the following we present the generalized reaction field model from a slightly different aspect. We show that one can obtain the relevant equations from the coupled set of group function equations for the solute and solvent subsystems [212]. 

Similarly to the case of the mutually consistent field (MCF) or interaction field modified Hamiltonian (IFMH) approaches we start from the group function equations for the solute (S) and solvent (B) subsystems (c.f. Sect. 3). 

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Tapia, O., Colonna, F. and Angyan, J. G. Generalized self-consistent reaction field theory in multicenter-multipole ab initio LCGO framework. I. Electronic properties of the water molecule in a Monte Carlo sample of liquid water molecules studied with standard basis sets, J.ChimPhys., (1990), 875-903... 

O. Tapia, F. Colonna, and J. G. Angyan, ]. Chim. Phys., 87, 875 (1990). Generalized Self-Consistent Reaction Field Theory in a Multicenter-Multipole Ab Initio LCGO Framework. I. Electronic Properties of the Water Molecule in a Monte Carlo Sample of Liquid Water Molecules Studied with Standard Basis Sets. 

O. Tapia, /. Mol. Struct. (THEOCHEM), 226, 59 (1991). On the Theory of Solvent-Effect Representation. I. A Generalized Self-Consistent Reaction Field Theory. 

The theory of solvent-effects and some of its applications have been overviewed. The generalized self-consistent reaction field theory has been used to give a unified approach to quantum chemical calculations of subsystems embedded in a given milieu. The statistical mechanical theory of projected equation of motion has been briefly described. This theory underlies applications of molecular dynamics simulations to the study of solvent and thermal bath effects on carefully defined subsystems of interest. The relationship between different approaches used so far to calculate solvent effects and the general approach advocated by this reviewer has been established. Applications to molecular properties in a time independent framework have been presented. 

Equations (1)- (4) have been generalized to molecules [2,3,10-13], in the context of the self consistent reaction field (SCRF) theory [14],... 

Among the few determinations of of molecular crystals, the CPHF/ INDO smdy of Yamada et al. [25] is unique because, on the one hand, it concerns an open-shell molecule, the p-nitrophenyl-nitronyl-nitroxide radical (p-NPNN) and, on the other hand, it combines in a hybrid way the oriented gas model and the supermolecule approach. Another smdy is due to Luo et al. [26], who calculated the third-order nonlinear susceptibility of amorphous thinmultilayered films of fullerenes by combining the self-consistent reaction field (SCRF) theory with cavity field factors. The amorphous namre of the system justifies the choice of the SCRF method, the removal of the sums in Eq. (3), and the use of the average second hyperpolarizability. They emphasized the differences between the Lorentz Lorenz local field factors and the more general Onsager Bbttcher ones. For Ceo the results differ by 25% but are in similar... 

While this result confirmed the feasibility of the general approach, it did not precipitate wider exploration of dielectric medium effects. Recently, however, Wiberg et al. have incorporated the Onsager self-consistent reaction-field model into ab initio MO theory in an implementation which provides analytical gradients and second derivatives. The model considers just the dipole of the solute molecules and a spherical cavity whose radius is chosen for a given solute molecule from the molecular volume estimated at the 0.001 eB electron-density contour (B is the Bohr radius), plus an empirical constant 0.5 A to account for the nearest approach of solvent molecules [164]. Cieplak and Wiberg have used this model to probe solvent effects on the transition states for nucleophilic additions to substituted acetaldehydes [165]. For each... 

Quantum mechanical formulation. By incorporating the essential elements of reaction field theory in conventional quantum mechanical approaches of molecular electronic structure theories, such as the Hartree-Fock self-consistent field (SCF) or density functional methods, the effects of solvation on the properties of molecules can be conveniently studied. The resulting techniques, generally referred to as self-consistent reaction field (SCRF) methods, consider the classical reaction field as a perturbation to the molecular Hamiltonian and write the latter simply as... 

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],... 

Purely quantum studies of the fully coupled anharmonic (and sometimes nonrigid) rovibrational state densities have also been obtained with a variety of methods. The simplest to implement are spectroscopic perturbation theory based studies [121, 122, 124]. Related semiclassical perturbation treatments have been described by Miller and coworkers [172-174]. Vibrational self-consistent field (SCF) plus configuration interaction (Cl) calculations [175, 176] provide another useful alternative, for which interesting illustrative results have been presented by Christoffel and Bowman for the H + CO2 reaction [123] and by Isaacson for the H2 + OH reaction [121]. The MULTIMODE code provides a general procedure for implementing such SCF-CI calculations [177]. Numerous studies of the state densities for triatomic molecules have also been presented. 

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