Generalized self-consistent reaction field

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. 

This energy expression can be used to build up the respective variational functional to get the molecular orbitals [above]. A crucial step in the general self-consistent reaction field procedure is the estimation of the solvent charge density needed to obtain the response function G(r,r ) and the reaction potential. The use of Monte Carlo or molecular dynamics simulations of the system consisting the solute and surrounding solvent molecules has been proposed to find the respective solvent static and polarization densities. 

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. 

Finally, we note that we have mostly limited attention so far to the self-consistent reaction field limit of dynamical solvent polarization, which is the only one that has been generally implemented (see next Section). Nevertheless, there are problems where the solute-solvent dynamical correlation must be considered, and we will address that topic in Section 5. 

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

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],... 

The details on the operators introduced in the two schemes will be given below, here we only want to add that the addition of Henv to the solute Hamiltonian automatically leads to a modification of the solute wavefunction which has now to be determined by solving the effective Eq. (1-1). This can be done using exactly the same methods used for isolated molecules here in particular we shall mainly focus on the standard self-consistent field (SCF) approach (either in its Hartree-Fock or DFT formulation). Due to the presence of Hem the modified SCF scheme is generally known as self-consistent reaction field (SCRF). Historically the term SCRF has been coined for the QM/continuum approach but here, due the parallelism between the two schemes which will be made clear in the following sections, it will be used indistinctly for both. 

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... 

Karelson et al. [124] had also carried out a comparative analysis of the molecular descriptors calculated for the isolated molecules (gas phase) and for the molecules embedded into a dielectric continuum corresponding to aqueous solution. The self-consistent reaction field method [125] was used for the latter calculations. The results indicated that, in general, the quantum-chemically derived descriptors are rather insensitive towards the change in the environment surrounding the molecule. However, the most influenced are the polarizability and several other MO-related descrip-... 

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... 

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. 

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... 

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