Solvation models reaction field

Similar calculated changes in carbonyl frequencies have been observed by Wong et al. [98] using their Onsager model reaction field techniques. For formaldehyde, their calculated shifts in frequencies are similar across a wide variety of extended basis sets at the 6-31 G level, but are much smaller at the 3-21G and STO-3G level. The shifts in carbonyl frequency are an important test for the computational methods since this is the most sensitive probe for the effects of solvation [134,135. ... 

The factors fU i" (J, 1), called the reaction-field factors, appear to be dependent on the dielectric constant of the solvent, and on the shape of the cavity only. They can be determined fully analytically in the cases of a single center expansion and of a cavity with a regular shape, such as a sphere, a spheroid or an ellipsoid. The case of the sphere is particularly simple and corresponds to the well-known Kirkwood model of solvation the reaction-field factors are scalar quantities which depend on I and on the radius a of the sphere ... 

Onsager s reaction field model in its original fonn offers a description of major aspects of equilibrium solvation effects on reaction rates in solution that includes the basic physical ideas, but the inlierent simplifications seriously limit its practical use for quantitative predictions. It smce has been extended along several lines, some of which are briefly sunnnarized in the next section. 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

Solvent effects on chemical equilibria and reactions have been an important issue in physical organic chemistry. Several empirical relationships have been proposed to characterize systematically the various types of properties in protic and aprotic solvents. One of the simplest models is the continuum reaction field characterized by the dielectric constant, e, of the solvent, which is still widely used. Taft and coworkers [30] presented more sophisticated solvent parameters that can take solute-solvent hydrogen bonding and polarity into account. Although this parameter has been successfully applied to rationalize experimentally observed solvent effects, it seems still far from satisfactory to interpret solvent effects on the basis of microscopic infomation of the solute-solvent interaction and solvation free energy. 

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... 

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. 

Marten, B., K. Kim, C. Cortis, R. A. Friesner, R. B. Murphy, M. N. Ringnalda, D. Sitkoff, and B. Honig. 1996. New Model for Calculation of Solvation Free Energies Correction to Self-consistent Reaction Field Continuum Dielectric Theory for Short-Range Hydrogen-Bonding Effects. J. Phys. Chem. 100, 11775. 

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. 

Diastereoselectivity of the reactions of the cation 26 and the anion 29 derived from 25 (R2 = Me) was modeled by self-consistent reaction field solvation models obtained from ab initio SCF-MO calculations. The experimentally found cis/trans ratios confirmed the model (Scheme 1) <2002JOC2013>. 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

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. 

Abstract This chapter reviews the theoretical background for continuum models of solvation, recent advances in their implementation, and illustrative examples of their use. Continuum models are the most efficient way to include condensed-phase effects into quantum mechanical calculations, and this is typically accomplished by the using self-consistent reaction field (SCRF) approach for the electrostatic component. This approach does not automatically include the non-electrostatic component of solvation, and we review various approaches for including that aspect. The performance of various models is compared for a number of applications, with emphasis on heterocyclic tautomeric equilibria because they have been the subject of the widest variety of studies. For nonequilibrium applications, e.g., dynamics and spectroscopy, one must consider the various time scales of the solvation process and the dynamical process under consideration, and the final section of the review discusses these issues. 

As discussed in Section 2, one key assumption of reaction field models is that the polarization field of the solvent is fully equilibrated with the solute. Such a situation is most likely to occur when the solute is a long-lived, stable molecular structure, e g., the electronic ground state for some local minimum on a Bom-Oppenheimer potential energy surface. As a result, continuum solvation models... 

Two tautomeric equilibria have been considered for substituted imidazoles, that between 2-imidazolone 3 and its 2-hydroxyimidazole tautomer 4 [268] and also that between the 1H and 3H tautomers of 4-nitroimidazole, 6 and 5, respectively [269, 270], Karelson et al. used the D02 model with a spherical cavity of 2.5 A radius and found 2-imidazolone to be better solvated than its tautomer by 7.7 kcal/mol at the AMI level. [The asterisk in D02 indicates that the reaction field... 

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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