Reaction field function

The application of eight different reaction-field models to the solvent-induced shift of the carbonyl IR absorption band of 2-butanone, determined in 27 non-HBD solvents, has shown that in this group of solvents the dipolarity and polarizability are the dominating solvent properties responsible for the observed band shift (Avc o = —16 cm for -hexane —> sulfolane) [499]. Among the various reaction-field functions tested, a two-parameter equation with the Kirkwood-Bauer-Magat function /(fir) and the cross function f si,n ) was the most successful one. 

C2H6, N2O and NH3 as a function of density, and have been analyzed using the Onsager reaction field function(15L i.e. L(n2)=(n2-l)/(2n2 +1) as shown in Figure 5. In order to explain the plot of n versus the reaction field, two straight lines were... 

HB interactions, is claimed to lie in different responses to solvent polarizability effects. Likewise, in the relationship between the Ji scale and the reaction field functions of the refractive index (whose square is called the optical dielectric constant e ) and the dielectric constant, the aromatic and the halogenated solvents were found to constitute special cases." This feature is also reflected by die polarizability correction term in eq. [13.1.2] below. For the select solvents, the various polarity scales are more or less equivalent. A recent account of the various scales has been given by Marcus, and in particular of by Laurence et al., and of Ey by Reichardt. ... 

The same idea was actually exploited by Neumann in several papers on dielectric properties [52, 69, 70]. Using a tin-foil reaction field the relation between the (frequency-dependent) relative dielectric constant e(tj) and the autocorrelation function of the total dipole moment M t] becomes particularly simple ... 

IS added to the short-range molecule-molecule interaction. Problems with the reaction ethod may arise from discontinuities in the energy and/or force when the number of les j rvithin the cavity of the molecule i changes. These problems can be avoided by dng a switching function for molecules that are near the reaction field boundary. 

J Li, MR Nelson, CY Peng, D Bashford, L Noodleman. Incorporating protein environments in density functional theory A self-consistent reaction field calculation of redox potentials of [2Ee2S] clusters in feiTedoxm and phthalate dioxygenase reductase. J Phys Chem A 102 6311-6324, 1998. 

We recently proposed a new method referred to as RISM-SCF/MCSCF based on the ab initio electronic structure theory and the integral equation theory of molecular liquids (RISM). Ten-no et al. [12,13] proposed the original RISM-SCF method in 1993. The basic idea of the method is to replace the reaction field in the continuum models with a microscopic expression in terms of the site-site radial distribution functions between solute and solvent, which can be calculated from the RISM theory. Exploiting the microscopic reaction field, the Fock operator of a molecule in solution can be expressed by... 

Control of catalytic functions using reaction fields... 

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... 

To calculate free energies of solvation for several organic molecules, Fortunelli and Tomasi applied the boundary element method for the reaction field in DFT/SCRF framework173. The authors demonstrated that the DFT/SCRF results obtained with the B88 exchange functional and with either the P86 or the LYP correlation functional are significantly closer to the experimental ones than the ones steming from the HF/SCRF calculations. The authors used the same cavity parameters for the HF/SCRF and DFT/SCRF calculations, which makes it possible to attribute the apparent superiority of the DFT/SCRF results to the density functional component of the model. The boundary element method appeared to be very efficient computationally. The DFT/SCRF calculations required only a few percent more CPU time than the corresponding gas-phase SCF calculations. 

Rashin, A.A., M.A. Bukatin, J. Andzelm, and T. Hagler. 1994. Incorporation of reaction field effects into density functional calculations for molecules of arbitrary shape. Biophys. Chem. 51, 375. 

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. 

Theoretical considerations leading to a density functional theory (DFT) formulation of the reaction field (RF) approach to solvent effects are discussed. The first model is based upon isolelectronic processes that take place at the nucleus of the host system. The energy variations are derived from the nuclear transition state (ZTS) model. The solvation energy is expressed in terms of the electrostatic potential at the nucleus of a pseudo atom having a fractional nuclear charge. This procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy, since all integrations involved are performed over [O.ooJ The quality of the approximations made are discussed within the frame of the Kohn-Sham formulation of density functional theory. 

In chapter 2, Profs. Contreras, Perez and Aizman present the density functional (DF) theory in the framework of the reaction field (RF) approach to solvent effects. In spite of the fact that the electrostatic potentials for cations and anions display quite a different functional dependence with the radial variable, they show that it is possible in both cases to build up an unified procedure consistent with the Bom model of ion solvation. The proposed procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy. Especially interesting is the introduction of local indices in the solvation energy expression, the effect of the polarizable medium is directly expressed in terms of the natural reactivity indices of DF theory. The paper provides the theoretical basis for the treatment of chemical reactivity in solution. 

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