Onsager-Kirkwood approximation

The method of calculating of complex mixtures using the above equation would theoretically be correct only if the mixture behaves like an ideal solution. Since, most solvent mixtures may exhibit a high degree of intermolecular association af such system would lead to a deviation from the experimental data. The simpliLed Onsager-Kirkwood equation provides only a good approximate dielectric constant for mixed solvent systems. 

The charge distribution of the molecule can be represented either as atom-centred partial charges or as a multipole expansion. For a neutral molecule, the lowest order approximation considers only the dipole moment. This may be a quite poor approximation, and fails completely for symmetric molecules that do not have a dipole moment. For obtaining converged results, it is often necessarily to extend the expansion up to order six or more, i.e. including dipole, quadrupole, octupole, etc., moments. Furthermore, only for small and symmetric molecules can the approximation of a spherical or ellipsoidal cavity be considered realistic. The use of the Bom/ Onsager/Kirkwood models should therefore only be considered as a rough estimate of the solvent effects, and quantitative results can rarely be obtained. 

SASA), a concept introduced by Lee and Richards [9], and the electrostatic free energy contribution on the basis of the Poisson-Boltzmann (PB) equation of macroscopic electrostatics, an idea that goes back to Born [10], Debye and Htickel [11], Kirkwood [12], and Onsager [13]. The combination of these two approximations forms the SASA/PB implicit solvent model. In the next section we analyze the microscopic significance of the nonpolar and electrostatic free energy contributions and describe the SASA/PB implicit solvent model. 

From a computational view point, chemical reactions in solution present a yet not solved challenge. On one hand, some of the solvent effects can be approximated as if the solute molecule would be in a continuum with a given dielectric characterization of the liquid, and this view point has been pioneered by Bom [1], later by Kirkwood [2] and Onsager [3] and even later by many computational quantum chemists [4-9], On the other hand, the continuum model fails totally when one is interested in the specific... 

The nature of approximations involved in the derivation of the LPBE remains obscure (2), and after the analyses of Fowler (12), Onsager (13), and Kirkwood (14), it appears that no more can be learned about them from a statistical-mechanical argument. Following the early pronouncement of Guggenheim and Fowler (15), supported by other analysis (4), we consider the LPBE the only logical choice for a model in which the ions obey the laws of electrostatics. 

Born—Kirkwood—Onsager Reaction Field The theory underlying the implementation of the BKO model at the semiempirical level is no different from that presented in Equations [22] and [23], although the approximations inherent to various levels of semiempirical theory make certain technicalities of the... 

The Quantum-Onsager SCRF Method. In the dipole-in-a-sphere (or quantum-Onsager or Born-Kirkwood-Onsager) SCRF method, the molecular cavity is a sphere of radius a and the interaction between the molecular charge distribution and the reaction field is calculated by approximating the molecular charge distribution as an electric dipole located at the cavity center with electric dipole moment fi. In 1936, Onsager showed that the electric field in the cavity (the reaction field) produced by the polarization of the solvent by fi is (in atomic units)... 

In relation to general interactions, the solvent is assumed to be a dielectric continuum. The earliest models for this type of interaction were developed by Kirkwood and Onsager, and were later modified with corrections for the effect of electrostatic saturation. " The intrinsic difficulty of these models in accurately determining the dimensions of the cybotactic region (viz. the solvent region where solvent molecules are directly per-tmbed by the presence of solute molecule) that surrounds each solute molecule in the solvent bulk, have usually raised a need for empirical approximations to the determination of a parameter encompassing solvent polarity and polarizability. An alternative approach to... 

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