Generalized Kirkwood model

The spherical cavity, dipole only, SCRF model is known as the OnMger model.The Kirkwood model s refers to a general multipole expansion, if the cavity is ellipsoidal the Kirkwood—Westheimer model arise." A fixed dipole moment of yr in the Onsager model gives rise to an energy stabilization. 

Phillies, G. D. J., Low-shear viscosity of nondilute polymer solutions from a generalized Kirkwood-Riseman model, J. Chem. Phys., 116, 5857-5866 (2002b). 

The Kirkwood model refers to a general multipole expansion in a spherical cavity, while the Kirkwood-Westheimer model arises for an ellipsoidal cavity. ... 

The cavity size in the Bom/Onsager/Kirkwood models strongly influences the calculated stabilization. Unfortunately, there is no consensus on how to choose the cavity radius. In some cases, the molecular volume is calculated from the experimental density of the solvent and the cavity radius is defined by equating the cavity volume to the molecular volume. Alternatively, the cavity size may be derived from the (experimental) dielectric constant and the calculated dipole moment and polarizability. In any case, the underlying assumption of these models is that the molecule is roughly spherical or ellipsoidal, which is only generally true for small compact molecules. 

There were several attempts to generalize the Debye function like the Cole/Cole formula (Cole and Cole 1941) (symmetric broadened relaxation function), the Cole/Davidson equation (Davidson and Cole 1950, 1951), or the Fuoss/Kirkwood model (asymmetric broadened relaxation function) (Fuoss and Kirkwood 1941). The most general formula is the model function of Havriliak and Negami (HN function) (Havriliak and Negami 1966,1967 Havriliak 1997) which reads... 

It is straightforward to generalize Kirkwood s multipole model by the inclusion of polarization effects using the dipole, quadrupole, etc., polarizabilities and hyperpolarizabilities and employing an iterative technique for the self-consistent calculation of the reaction field. ... 

The Quasi-Chemical Approximation. The mean-field approximation ignores all correlation in the occupation of neighboring sites. This is incorrect when there is a strong interaction between adsorbates at such sites. The simplest way to include some correlation is to work with probabilities of occupations of two sites (XY) instead of one site (X). Approximations that do this are generally called pair approximations (not to be confused with pair interactions). There are more possibilities to reduce multi-site probabilities as in eqn. (8) to 2-site probabilities than to 1-site probabilities. This leads to different types of pair approximations. The best-known approximation that is used for Ising models is the Kirkwood approximation, which uses for example ... 

The kinetic equations [1-3, 12] were rewritten in [15] for a special choice of the recombination law cr(r), adequate to the NAN model, and solved numerically for d— 1. The general conclusion was drawn that the Kirkwood approximation is quite correct but leads to the error of the order of 10% for the critical exponent a in the asymptotic decay law n(R) oc R a. This quantity (10%) was suggested to be used as a measure of the accuracy of the Kirkwood approximation in the kinetics of the bimolecular reaction A + B -> 0. 

Reaction Fields from Higher Order Multipolar Expansions Generalizations of the Born—Kirkwood—Onsager model have appeared which extend the multipole series to arbitrarily high order.20,62,144,234-236 ybis approach yields... 

Equation (144a) states that molar refraction is a constant, independent of structure and of the thermodynamic state of the medium. Numerous studies have shown this to be closely correct, at certain special conditions, in a first approximation, since in general Rm is a function of tepiperature and density, or pressure in the case of real gases. The non-constancy of has been explained theoretically by Yvon as well as by Mazur and Mandel.3 We shall deal here only with deviations from constancy in Rm due to Kirkwood-Yvon translational statistical fluctuations, omitting for simplidty the fact that molecular interactions perturb the intrinsic polarizabilities in accordance with the Jansen-Mazm model. For a molecule immersed in a statistically inhomogeneous medium, this in place of (145) leads to ... 

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