Models solvent reaction field SCRF

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... 

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.

The most common approach to solvation studies using an implicit solvent is to add a self-consistent reaction field (SCRF) term to an ab initio (or semi-empirical) calculation. One of the problems with SCRF methods is the number of different possible approaches. Orozco and Luque28 and Colominas et al27 found that 6-31G ab initio calculations with the polarizable continuum model (PCM) method of Miertius, Scrocco, and Tomasi (referred to in these papers as the MST method)45 gave results in reasonable agreement with the MD-FEP results, but the AM1-AMSOL method differed by a number of kJ/mol, and sometimes gave qualitatively wrong results. 

Self-consistent reaction field (SCRF) models are the most efficient way to include condensed-phase effects into quantum mechanical calculations [8-11]. This is accomplished by using SCRF approach for the electrostatic component. By design, it considers only one physical effect accompanying the insertion of a solute in a solvent, namely, the bulk polarization of the solvent by the mean field of the solute. This approach efficiently takes into account the long range solute-solvent electrostatic interaction and effect of solvent polarization. However, by design, this model cannot describe local solute-solvent interactions. 

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],... 

These approaches date back to the classical papers by Onsager(9) and Kirkwood(lO). A self-consistent reaction field (SCRF) was developed and applied to several solvent effects with reasonable success(8, 11). However, it seems to become clear that these models where the solute and the solvent are represented by separated non-overlapping wave functions are too crude in some cases(12). Studies of solvent effects involving the interaction of the solute with a proton donor solvent (the so-called protic solvents) for instance usually leads to hydrogen bonds and therefore neglecting the overlap of the electron densities between the two subsystem is very difficult to justify. A similar difficulty is obtained for those absorptions where electron is trans-... 

Solvent effects were evaluated by different self consistent reaction field (SCRF) procedures i) the parametrisation AM1-SM4 for cyclohexane and AM1-SM2.1 for water, implemented on the AMSOL-V suite of programs,ii) the ab initio Pisa model (interlocking spheres) implemented in the Gamess (Rev,97) package and, with different options, in the Gaussian 94 package. 

The effect of the solvent is usually modelled either by the use of the Onsager s self consistent reaction field (SCRF) [20] or by the polarizable continuum method (PCM) [21]. With regard to the relative stability of cytosine tautomers in aqueous solution, these methods provided results [14,15] which, in spite of some discrepancies, are in reasonable agreement with experimental data [3]. However, continuum-based methods do not explicitly take into consideration the local solvent-solute interaction which is instead important in the description of the proton transfer mechanism in hydrogen-bonded systems. A reasonable approach to the problem was recently proposed [22,23] in which the molecule of interest and few solvent molecules are treated as a supermolecule acting as solute, while the bulk of the solvent is represented as a polarizable dielectric. 

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... 

Properties of molecules differ considerably in the vacuum and in the presence of solution in the model during the simulation. The effect of solvent is included in the model by numerical representation of the solvent reaction field termed self-consistent reaction field [SCRF] methods [Foresman, 2004]. The polarized continuum model [PCM] is one of such numerical approximations developed by Tomasi [Tomasi and Persico, 1994] and is the most widely used SCRF model to study the effect of solvent in quantum chemical simulations. 

A classical description of the molecule M in Figure 14.9 can be a force field with (partial) atomic charges, while a quantum description involves calculation of the electronic wave function. The latter may be either a semi-empirical model, such as AMI or PM3, or more sophisticated electronic structure methods, i.e. FIF, DFT, MCSCF, MP2, CCSD, etc. When a quantum description of M is employed, the calculated electric moments induce charges in the dielectric medium, which in turn acts back on the molecule, causing the wave function to respond and thereby changing the electric moments, etc. The interaction with the solvent model must thus be calculated by an iterative procedure, leading to various Self-Consistent Reaction Field (SCRF) models. 

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. 

The theory of solvent-effects and some of its applications are overviewed. The generalized selfcon-sistent reaction field (SCRF)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 equations 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 subsystem of interest. The relationship between different approaches used so far to calculate solvent effects and the general SCRF has been established. Recent work using the continuum approach to model the surrounding media is overviewed. Monte Carlo and molecular dynamics studies of solvent effects on molecular properties and chemical reactions together with simulations of solvent effects on protein structure and dynamics are reviewed. 

The QM/MM method has been applied mainly to biological problans such as enzyme reactions and reactions in solution. Hybrid methods are also useful in modeling solvent effects. Some examples are the self-consistent reaction field (SCRF) method (Miertus et al. 1981) and the Our own N-layeied Integrated molecular Orbital molecular Mechanics (ONIOM) method (Svensson et al. 1996). 

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