Self-consistent reaction field cavities

One femily of models for systems in non-aqueous solution are referred to as Self-Consistent Reaction Field (SCRF) methods. These methods all model the solvent as a continuum of uniform dielectric constant e the reaction field. The solute is placed into a cavity within the solvent. SCRF approachs differ in how they define the cavity and the reaction field. Several are illustrated below. 

The Self-Consistent Reaction Field (SCRF) model considers the solvent as a uniform polarizable medium with a dielectric constant of s, with the solute M placed in a suitable shaped hole in the medium. Creation of a cavity in the medium costs energy, i.e. this is a destabilization, while dispersion interactions between the solvent and solute add a stabilization (this is roughly the van der Waals energy between solvent and solute). The electric charge distribution of M will furthermore polarize the medium (induce charge moments), which in turn acts back on the molecule, thereby producing an electrostatic stabilization. The solvation (free) energy may thus be written as... 

Conceptually, the self-consistent reaction field (SCRF) model is the simplest method for inclusion of environment implicitly in the semi-empirical Hamiltonian24, and has been the subject of several detailed reviews24,25,66. In SCRF calculations, the QM system of interest (solute) is placed into a cavity within a polarizable medium of dielectric constant e (Fig. 2.2). For ease of computation, the cavity is assumed to be spherical and have a radius ro, although expressions similar to those outlined below have been developed for ellipsoidal cavities67. Using ideas from classical electrostatics, we can show that the interaction potential can be expressed as a function of the charge and multipole moments of the solute. For ease... 

Fig. 2.2 Self-Consistent Reaction Field (SCRF) model for the inclusion of solvent effects in semi-empirical calculations. The solvent is represented as an isotropic, polarizable continuum of macroscopic dielectric e. The solute occupies a spherical cavity of radius ru, and has a dipole moment of p,o. The molecular dipole induces an opposing dipole in the solvent medium, the magnitude of which is dependent on e.

Organometallic systems such as porphyrines have been investigated because of the possibility to fine tune their response by functionalization[105-107]. Systems of increased the dimensionality have been of particular interest [108-111], Concomitant to the large effort to establish useful structure-to-properties relationships, considerable effort has now been put to investigate the environmental effects on TPA[112-114], For example, the solvent effect has been studied for a small linear push-pull chromophore using a self-consistent reaction field (homogeneous solvation) method employing a spherical cavity and an internal force field (IFF) method[l 12] in another study the polarizable continuum model has been employed to calculate the relevant quantities to obtain the TPA cross-section in the limit of a two-state model[113] Woo et al. made a critical study of experimental comparison of TPA cross-sections in different solvents[114]. 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

Keywords Solvent Effects, Self-consistent Reaction Field, Continuum, Cavity, Polarizable Contin-... 

G. P, Ford and B. Wang, J. Comput. Chem., 13, 229 (1992). The Optimized Ellipsoidal Cavity and Its Application to the Self-Consistent Reaction Field Calculation of Hydration Energies of Cations and Neutral Molecules. 

Self-consistent reaction-field (SCRF) theories are obtained by introducing solute-solvent interactions into the Hamiltonian. (Cf. Tapia, 1982.) Based on Cl wave functions and on reasonable approximation for the cavity radius... 

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... 

The study of solvatochromic shifts is of great importance and has received enormous theoretical attention in recent years. Progress has been achieved in the use of the self-consistent reaction field and cavity models. These advances have also shown several limitations. It is thus of great interest to have alternative procedures to calculate solvent effects. In this respect the use of Monte Carlo/Molecular Dynamics simulations has been growing. In this paper we suggest a procedure to allow a full quantum mechanical calculation of the solute-solvent system. The basic idea is to treat the solute, the solvent and its interaction by quantum mechanics. First a Monte Carlo simulation is performed to characterize the liquid structure. These structures are then used in the quantum mechanical calculation. As a liquid has not one but a great number of structures equally possible within a... 

A short overview of the quantum chemical and statistical physical methods of modelling the solvent effects in condensed disordered media is presented. In particular, the methods for the calculation of the electrostatic, dispersion and cavity formation contributions to the solvation energy of electroneutral solutes are considered. The calculated solvation free energies, proceeding from different geometrical shapes for the solute cavity are compared with the experimental data. The self-consistent reaction field theory has been used for a correct prediction of the tautomeric equilibrium constant of acetylacetone in different dielectric media,. Finally, solvent effects on the molecular geometry and charge distribution in condensed media are discussed. 

Recently, a new category of methods, the cavity model, has been proposed to account for the solvent effect. Molecules or supermolecules are embedded in a cavity surrounded by a dielectric continuum, the solvent being represented by its static dielectric constant. The molecules (supermolecules) polarize the continuum. As a consequence this creates an electrostatic potential in the cavity. This reaction potential interacts with the molecules (supermolecules). This effect can be taken into account through an interaction operator. The usual SCF scheme is modified into a SCRF (self consistent reaction field) scheme, and similar modifications can be implemented beyond the SCF level. Several studies based on this category of methods have been published on protonated hydrates. They account for the solvent effect on the filling of the first solvation shell (53, 69), the charges (69, 76) and the energy barrier to proton transfer (53, 76). 

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... 

The quantum Onsager model, which has also been termed the Self-Consistent Reaction Field (SCRF) method, is the simplest of the continuum models used in solvation studies. In this model, which dates from the work of Kirkwood[44] and Onsager[45] in the 1930s, the solvent is represented by a continuous rmifonn dielectric with a static dielectric constant, e, surrounding a solute in a spherical cavity[46] - [48]. 

In the usual quantum-mechanical implementation of the continuum solvation model, the electronic wave function and electronic probability density of the solute molecule M are allowed to change on going firom the gas phase to the solution phase, so as to achieve self-consistency between the M charge distribution and the solvent s reaction field. Any treatment in which such self-consistency is achieved is called a self-consistent reaction-field (SCRF) model. Many versions of SCRF models exist. These differ in how they choose the size and shape of the cavity that contains the solute molecule M and in how they calculate t nf... 

Reaction field methods model solutions by placing the solute in a cavity of a polarizable medium. The electrostatic potential due to the solute molecule polarizes the surrounding medium which in turn changes the charge distribution of the solute. Hence, the electrostatic interaction has to be evaluated self-consistently (self-consistent reaction field, SCRF). A term for creating the cavity (calculated from the surface of the cavity) has a be added to the solvation energy. Explicit treatment of solvent molecules can be combined with a reaction field method. 

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