Nonelectrostatic terms

The evaluation of the nonelectrostatic term is usually empirical and multifarious. Based on a skillful argument, however, Volkov and coworkers [9,11,12] proposed that the nonelectrostatic term of the ion transfer energy, AGfr Cne), should be expressed by a semiempirical equation called the Uhlig equation [13], which is given by... 

In this expression, the dipole dipole interactions are included in the electrostatic term rather than in the van der Waals interactions as in Eq. (9.43). Of the four contributions, the electrostatic energy can be derived directly from the charge distribution. As discussed in section 9.2, information on the nonelectrostatic terms can be deduced indirectly from the charge density. The polarizability a, which occurs in the expressions for the Debye and dispersion terms of Eqs. (9.41) and (9.42), can be expressed as a functional of the density (Matsuzawa and Dixon 1994), and also obtained from the quadrupole moments of the experimental charge density distribution (see section 12.3.2). However, most frequently, empirical atom-atom pair potential functions like Eqs. (9.45) and (9.46) are used in the calculation of the nonelectrostatic contributions to the intermolecular interactions. 

This very empirically parameterized equation for nonelectrostatic terms is a characteristic of the SMx series (solvent model 1,2,..., now up to SM8) of Cramer and Truhlar [22]. 

The formulation of the method we have sketched, thus far applied with some approximations, may in principle also be applied to nonpolar solvents. However, there are practical difficulties to overcome. The mode analysis in nonpolar solvents is less developed and experimental data on the dielectric spectra are scarcer. The solution of using computed values of s(m) for the whole spectmm is expensive and computationally delicate. The best way is perhaps to develop for apolar solvents a variant of the reduction of Q(r, r, t) that we have introduced for polar solvents, which takes into account that in nonpolar solvents the interaction is dominated by nonelectrostatic terms. The reformulation of the theory has not yet been attempted, at least by our group, but in recent versions of the continuum ab initio solvation methods there are the elements to develop and test this new implementation. 

To characterize the intermolecular interactions it is necessary to take into account the nonelectrostatic terms. There are different approaches to the modelling of repulsion and dispersion interactions. Recently, Amovilli and Mennucci have described an approach where repulsion and dispersion terms are computed self-consistently as part of the reaction field operator [29],... 

The nonelectrostatic terms include van der Waals, polarization, repulsive, and zero-point energies. The van der Waals energy has been calculated in several ways with results ranging from 5 to 15 kcal./mole. Examples of these results are indicated in Table I. In the first two entries polarizabilities were taken from Bottcher (3), and the nitrate group was treated as a single entity with an ionization potential of 99 kcal./mole for the London equation (23) and an effective electron number of 24 for the Slater-Kirkwood equation (23). A simple CsCl type of lattice was assumed. 

By combining all the electrostatic and nonelectrostatic terms we obtain the generalized Fock equation ... 

Electrostatic BE methods can be supported by nonelectrostatic terms, such as dispersion and exchange, in different ways, and their basic theory can be extended to treat both classical and quantum mechanical solutes in addition, many features, including analytical gradients with respect to various parameters, have been added to the original models so as to... 

Plyasunov developed an equation for V° (Plyasunov, 1993) based on the concept of total equUibrimn constant (Marshall, 1970) and a nonelectrostatic term similar to that of the HFK model ... 

The values of W can be either positive or negative. If the reagents do not have a specific adsorbability, we get W = zeil i for electrode reactions, where z is the charge of the corresponding ion. In the case of a specific adsorption, W also includes a nonelectrostatic term. A well-known conclusion follows from (3.18) i/ i-effect... 

Fig. 7.4, curve 4). By analogy with this behavior, it has been proposed as a way of accounting for nonelectrostatic interaction forces between ions, to supplement Eq. (7.43) with an additional term b c or bl ... 

In addition to the nonelectrostatic adsorptive force, there is an image force between a dipole and a metal, which will be present whenever charged or dipolar particles in a medium of one dielectric constant are near a region of another dielectric constant. If the metal is treated as an ideal conductor, the image-force contribution to the energy of a dipole in the electrolyte is proportional to p2j z3, where z is the distance of the dipole from the plane boundary of the metal (considered ideal, with no surface structure), and to 1 + cos2 0. This ideal term is, of course, the same for all metals. If... 

The nonelectrostatic components of the free energy such as the energy of cavity formation AGcav or components that take into account atomistic details of the medium (interactions between atoms inside the cavity and those in the medium) are calculated using empirical approximations (see Reference 164 for review or 165 for recent developments). These terms are do not affect the SCF procedure since their dependence on electron density p is usually neglected. 

In the previous section, various methods employed to calculate the electrostatic contributions to the free energy of solvation have been presented. However, it is important to provide some ideas about the calculation of nonelectrostatic contributions. These factors are essential for solutes, which are neither charged nor polar. The cavity and van der Waals terms can be combined and represented as [5]... 

The Debye-Hiickel term, which is the dominant term in the expression for the activity coefficients in dilute solution, accounts for electrostatic, nonspecific long-range interactions. At higher concentrations, short-range, nonelectrostatic interactions have to be taken into account. This is usually done by adding ionic strength dependent terms to the Debye-Hiickel expression. This method was first outlined by Bronsted [5,6], and elaborated... 

Among the alternative definitions of the dispersion-repulsion energy, we mention the quantum mechanical approach presented in ref. [12], which has the merit of including this part of the nonelectrostatic contribution in the molecular Hamiltonian (like the electrostatic term), so that the solvent affects not only the free energy but also the electronic distribution. In this approach, however, the dispersion part is highly expensive except for very small systems, and it is not routinely used in any computational package the analytical derivatives of quantum mechanical /disp rep can be derived but they have not been implemented until now. 

To determine the coupling work between solute and solvent, it is convenient to decompose AGsol into separate, more manageable terms, which typically involve the separation between electrostatic and nonelectrostatic contributions. The former accounts for the work required to assemble the charge distribution of the solute in solution, while the latter is typically used to account for dispersion and repulsion interactions between solute and solvent molecules, as well as for cavitation, i.e. the work required to create the cavity that accommodates the solute. 

But consistent with the overall theme of this chapter, we need to ask ourselves whether we really have to conclude that the mechanism of vibrational energy relaxation is fundamentally electrostatic just because we find the overall relaxation rate to be sensitive to Coulombic forces. Let us attempt to get at this question through another mechanistic analysis of the INM vibrational influence spectrum, this time looking at the respective contributions of the electrostatic part of the solvent force on our vibrating bond, the nonelectrostatic part (in most simulations, the Lennard-Jones forces), and whatever cross terms there may be. 

Due to the symmetry of the present ion-dipole model, the WOZ equation decouples into electrostatic and nonelectrostatic parts. The nonelectrostatic part has the form of WOZ equation for the two-component dimerizing-nondimerizing mixture [67], Using the Wertheim-Baxter factorization technique, the solution of WOZ equation for the electrostatic part was performed in terms of energy parameters [68, 69],... 

After the experimental demonstration of TSS by HBs, it has been proposed by several workers that HBs stabilize TSs in a special nonelectrostatic way, which was termed low-barrier hydrogen bond (LBHB).107 109 The LBHB proposal has suggested that catalytic HBs involve a flat minimum rather than a double minimum. Unfortunately, this suggestion (which is sometimes true) does not allow one to distinguish the LBHB proposal from the previous proposal of ionic HBs (and thus, does not provide a testable definition). 

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