Self consistent reaction field model

The interaction of a fixed dipole moment with a polarizable medium is given by eq. (14.61). This, however, is not an SCRF model, as the dipole moment and stabilization are not calculated in a self-consistent way. When the back-polarization of the medium is taken into account, the dipole moment changes, depending on how polarizable the molecule is. Taking only the first-order effect into account, the stabilization is given by eq. (14.62). 

Here a is the molecular polarizability, i.e. the first-order change in the dipole moment with respect to an electric field. In the SCRF model the full polarization is taking into account, i.e. the initial dipole moment generates a polarization of the medium, which changes the dipole moment, which in turn generates a slightly different polarization, etc. 

Once o(rs) is determined the associated potential is added as an extra term to the Hamiltonian operator. 

The potential 0cr from the surface charge is given by the molecular charge distribution (eq. (14.64)), but also enters the Hamiltonian and thus influences the molecular wave function. The procedure is therefore iterative. 

For the case of the Onsager model (spherical cavity, dipole moment only) the term added to the molecular Hamiltonian operator is given by eq. (14.65). 

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Hall, R. J., M. M. Davidson, N. A. Burton, and I. H. Hiller. 1995. Combined Density Functional Self-Consistent Reaction Field Model of Solvation. J. Phys. Chem. 99, 921. 

Chipot C, Rinaldi D, Rivail JL (1992) Intramolecular electron correlation in die self-consistent reaction field model of solvation. A MP2/6-31G ab initio study of the NH3—HC1 complex. Chem Phys Lett 191 287- 292... 

Marenich, A. V. Olson, R. M. Kelly, C. P. Cramer, C. J. Truhlar, D. G. Self-consistent reaction field model for aqueous and nonaqueous solutions based on accurate polarized partial charges, J. Chem. Theor. Comput. 2007, 3, 2011 -2033. 

C. Chipot, D. Rinaldi, and J.-L. Rivail, Chem. Phys. Lett., 191, 287 (1992). Intramolecular Electron Correlation m the Self-Consistent Reaction Field Model of Solvation. A MP2/6-31G Ab Initio Study of the NH,-HC1 Complex. 

Employing a self-consistent reaction field model, Cramer and Truhlar concluded that the hydrophobic effect is always accelerating in aqueous Claisen rearrangements, even if most of the activation stems from polarization contributions to the activation energy [18]. 

To examine this, we make use of the self-consistent reaction field model [29-31] that treats the surrounding polarizable matter as a dielectric continuum. This is, of course, a very simple approach, but it is not possible to actually include enough of the protein and its surroundings to model this effect directly. 

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 absolute solvation Gibbs free energy of a proton can also be calculated using high-level gas phase calculations with a supermolecule-continuum approach, involving a self-consistent reaction field model. 

A many-body perturbation theory (MBPT) approach has been combined with the polarizable continuum model (PCM) of the electrostatic solvation. The first approximation called by authors the perturbation theory at energy level (PTE) consists of the solution of the PCM problem at the Hartree-Fock level to find the solvent reaction potential and the wavefunction for the calculation of the MBPT correction to the energy. In the second approximation, called the perturbation theory at the density matrix level only (PTD), the calculation of the reaction potential and electrostatic free energy is based on the MBPT corrected wavefunction for the isolated molecule. At the next approximation (perturbation theory at the energy and density matrix level, PTED), both the energy and the wave function are solvent reaction field and MBPT corrected. The self-consistent reaction field model has been also applied within the complete active space self-consistent field (CAS SCF) theory and the eomplete aetive space second-order perturbation theory. ... 

Bartkowiak and Misiaszek used the eoupled perturbed Hartree-Fock method and the sum-over-modes formalism to ealeulate the eleetronie and vibrational /i-tensors for 4-nitroaniline, 4-nitro-4 -aminostilbene, 4-amino-4 -nitrobiphenyl and 4-amino-4 -nitrophenylacetylene, all typieal push-pull eonjugated molecules of the kind that have been associated with seeond order optieal non-linearities derived from their large P values. Their ealeulations refer to the gas phase and to chloroform and aqueous solutions, the solvent effects being included through a continuum self-consistent reaction field model. They demonstrate that the solvent effects are much greater for the vibrational hyperpolarizability than for the electronic contribution. 

THE SELF-CONSISTENT REACTION FIELD MODEL FOR MOLECULAR COMPUTATIONS IN SOLUTION... 

In this paper we have developed the main features of a Self-Consistent Reaction Field Model of solvation based on the use of generalized reaction field factors which enable us to relate the perturbation caused by the solvent on the solute to the multipole moments of the solute. 

Rinaldi, D., Bouchy, A., Rivail, J. L., 8c Dillet, V. (2004). A self-consistent reaction field model of solvation using distributed multipoles. I. Energy and energy derivatives. Journal of Chemical... 

To model solvent effects, the Onsager self-consistent reaction field model has also been invoked in a study of the hfcc of the H2NO radical, by Barone. Also here, the model seems to be able to describe accurately the shifts in hyperfine couplings of the system. 

An alternative to using explicit water molecules in modeling solvation phenomena is the use of solvation models. In these models, each solute molecule is assumed to exist in a solvent. The solvent is almost structureless it surrounds the solute, approaching everywhere to within a finite distance, known as the solvent accessible surface. The electric field of the solute induces an electric response in the solvent, on the solvent accessible surface. This respon.se, in turn, modifies the electronic structure of the solute. Because of this, these methods are known as Self-consistent Reaction Field models. 

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