Kirkwood model, solvation

Kinetic balance, of basis sets, 214 Kirkwood model, solvation, 395 Kirkwood-Westheimer model, solvation, 395... 

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 ... 

Continuum models have a long and honorable tradition in solvation modeling they ultimately have their roots in the classical formulas of Mossotti (1850), Clausius (1879), Lorentz (1880), and Lorenz (1881), based on the polarization fields in condensed media [32, 57], Chemical thermodynamics is based on free energies [58], and the modem theory of free energies in solution is traceable to Bom s derivation (1920) of the electrostatic free energy of insertion of a monatomic ion in a continuum dielectric [59], and Kirkwood and Onsager s... 

Quantitative models of solute-solvent systems are often divided into two broad classes, depending upon whether the solvent is treated as being composed of discrete molecules or as a continuum. Molecular dynamics and Monte Carlo simulations are examples of the former 8"11 the interaction of a solute molecule with each of hundreds or sometimes even thousands of solvent molecules is explicitly taken into account, over a lengthy series of steps. This clearly puts a considerable demand upon computer resources. The different continuum models,11"16 which have evolved from the work of Bom,17 Bell,18 Kirkwood,19 and Onsager20 in the pre-computer era, view the solvent as a continuous, polarizable isotropic medium in which the solute molecule is contained within a cavity. The division into discrete and continuum models is of course not a rigorous one there are many variants that combine elements of both. For example, the solute molecule might be surrounded by a first solvation shell with the constituents of which it interacts explicitly, while beyond this is the continuum solvent.16... 

Models to describe frequency shifts have mostly been based on continuum solvation models (see Rao et al. [13] for a brief review). The most important steps were made in the studies of West and Edwards [14], Bauer and Magat [15], Kirkwood [16], Buckingham [17,18], Pullin [19] and Linder [20], all based on the Onsager model [21], which describes the solvated solute as a polarizable point dipole in a spherical cavity immersed in a continuum, infinite, homogeneous and isotropic dielectric medium. In particular, in the study of Bauer and Magat [15] the solvent-induced shift in frequency Av is given as ... 

Continuum solvation models have a quite long history which goes back to the first versions by Onsager (1936) and Kirkwood (1934), however only recently (starting since the 90s) they have become one of the most used computational techniques in the field of molecular modelling. This has been made possible by two factors which will be presented and discussed in the book, namely the increase in the realism of the model on the one hand, and the coupling with quantum-mechanical approaches on the other. The greater realism has also meant an important evolution in the mathematical formalism and in the computational implementation of the continuum models while the QM reformulation of such models has allowed the study of chemical and physical... 

Solvent continuum models are now routinely used in quantum mechanical (QM) studies to calculate solvation effects on molecular properties and reactivity. In these models, the solvent is represented by a dielectric continuum that in the presence of electronic and nuclear charges of the solute polarizes, creating an electrostatic potential, the so-called reaction field . The concept goes back to classical electrostatic schemes by Martin [1], Bell [2] and Onsager [3] who made fundamental contributions to the theory of solutions. Scholte [4] and Kirkwood [5] introduced the use of multipole moment distributions. The first implementation in QM calculations was reported in a pioneer work by Rivail and Rinaldi [6,7], Other fundamental investigations were carried out by Tapia and Goscinski [8], Hilton-McCreery et al. [9] and Miertus et al. [10], Many improvements have been made since then (for a review,... 

The exciplex or CIP is treated as a dipole of radius q and dipole moment p. The last term in Eq. (15) describes the energy of this dipole, based on the Kirkwood-Onsager model (assuming formation of a spherical complex) [14]. Thus, an exciplex or CIP is stabilized by Coulombic interactions and by solvation. The solvation energy is expected to be favored by increasing solvent polarity and a large dipole... 

Simple electrostatic models can be used to interpret the activity coefficients of polar molecules in terms of just three parameters a radius, the dipole moment of the solute, and the dielectric constant of the solvent. The continuum model of the solvent can be used to deduce a value for the free energy of solvation of a spherical molecule of radius r containing a point dipole at its center. The value obtained by Kirkwood from electrostatic theory is... 

Applications of the Born—Kirkwood-Onsager model at the ab initio level include investigations of solvation effects on sulfamic acid and its zwitterion,23i an examination of the infrared spectra of formamide and formamidic acid,222 and a number of studies focusing on heterocyclic tautomeric equilibria.222,232,233 a more detailed comparison of some of the heterocyclic results is given later. The gas phase dipole moment depends on basis set, and systematic studies of this dependence are available. Furthermore, the effects of basis set choice and level of correlation analysis have been explored in solvation studies as well,222,233 but studies to permit identification of particular trends in their impact on the solvation portion of the calculation are as yet insufficient. 

The aqueous solvation free energies of the four tautomers available to the 5-(2H)-isoxazolone system have also been studied using a variety of continuum models (Table 7). Hillier and co-workers - " have provided data at the ab initio level using the Born-Kirkwood-Onsager model, the classical multipolar expansion model (up to I = 7), and an ab initio polarized continuum model. We examined the same BKO model with a different cavity radius and the AMl-SMl and AMl-SMla o- models, and Wang and Ford have performed calculations with the AMl-PCM model. 

In the case of a single test particle B in a fluid of molecules M, the effective one-dimensional potential f (R) is — fcrln[R gBM(f )]. where 0bm( ) is th radial distribution function of the solvent molecules around the test particle. In this chapter it will be assumed that 0bm( )> equilibrium property, is a known quantity and the aim is to develop a theory of diffusion of B in which the only input is bm( )> particle masses, temp>erature, and solvent density Pm- The friction of the particles M and B will be taken to be frequency indep>endent, and this should restrict the model to the case where > Wm, although the results will be tested in Section III B for self-diffusion. Instead of using a temporal cutoff of the force correlation function as did Kirkwood, a spatial cutoff of the forces arising from pair interactions will be invoked at the transition state Rj of i (R). While this is a natural choice because the mean effective force is zero at Rj, it will preclude contributions from beyond the first solvation shell. For a stationary stochastic process Eq. (3.1) can then be... 

The traditional treatment regarding medium effects is the dielectric continuum model in the Kirkwood-Onsager theory [76]. This simple model assumes that the solvation energy arises from the electrostatic interaction between the solutes and... 

The quantum Onsager model, which has also been termed the Self-Consistent Reaction Field (SCRF) method, is the simplest of the continuum models used in solvation studies. In this model, which dates from the work of Kirkwood[44] and Onsager[45] in the 1930s, the solvent is represented by a continuous rmifonn dielectric with a static dielectric constant, e, surrounding a solute in a spherical cavity[46] - [48]. 

We have discussed some formal developments around the fluctuation theory of mixtures from Kirkwood and Buff, with special emphasis on the behavior of dilute species in highly compressible media. These formal results were then used to interpret a few specific solvation phenomena, to provide support to the selection of macroscopic quantities for the successful regression of experimental data, and to facilitate the development of truly molecular-based modeling of these challenging systems. 

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