Statistically-Based Interaction Indices

In the preceding sections of this chapter, we have focused on the use of extrema in the electrostatic potential, i.e. Vmin. Vs,min and Vs,max. for th interpretation and prediction of site-specific molecular interactions. However, additional information about a molecule s ability to interact with other molecules can be obtained by an analysis of the overall pattern of the electrostatic potential on the molecular surface. Politzer and co-workers have in recent years developed a number of statistically-based interaction indices that are defined in terms of the entire surface electrostatic potential [100-102]. They have further shown 

It is not within the scope of this article to present a full review of all the applications of statistically-based interaction indices. We will instead give a short presentation of the most important indices followed by an example of the use of these indices in the analysis of a solvation process the partitioning of solutes between octanol and water. 

As a measure of local polarity, a quantity H has been defined by [100] 

The quantity ofot, which is defined by eq. 16, reflects the variabihty of the electrostatic potential on the molecular surface [101]. 

The first summation is over the surface points with positive potential and the second over the points with negative potential. Vg and Vg are the positive and negative surface averages in V(r), respectively, Since the terms in eq. 10, are squared, Otot is, in contrast to fl, particularly sensitive to the extremes in V(r). The two quantities have also been found to be quite different and even been found to vary in opposite directions for some groups of molecules [106]. atot i considered to be indicative of a molecule s electrostatic interaction tendencies. For example, has been used in conjunction with measures of molecular size, i.e. surface area or volume, for correlating solubilities in supercritical fluids [101, 105]. It has been suggested that Ojot in these relationships reflect solute-solute interactions, since the supercritical solubility mainly is determined by the solute vapor pressure [105]. 

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Statistically Based Interaction Indices Derived from... 

Murray, J. S., T. Brinck, P. Lane, K. Paulsen, and P. Politzer. 1994. Statistically-Based Interaction Indices Derived From Molecular Surface Electrostatic Potentials A General Interaction Properties Function (GIPF). J. Mol. Struct. (Theochem) 307, 55. 

Statistically Based Interaction Indices Derived from Molecular Surface Electrostatic Potentials A General Interaction Properties Function (GIPF). 

Murray, J.S., Brinck, T, Lane, P Paulsen, K. and Politzer, P. (1994) Statistically-based interaction indices derived from molecular surface electrostatic potentials a general interaction properties function (GIPF)./. Mol. Struct. (Theochem), 307, 55-64. 

We believe that relationships like eq. 20 that combines the use of global statistically based interaction indices with local interaction indices, such as the Vmin, can be very useful for stud dng solvation processes. In particular, for... 

The density functional theory of Hohenberg, Kohn and Sham [173,205] has become the standard formalism for first-principles calculations of the electronic structure of extended systems. Kohn and Sham postulate a model state described by a singledeterminant wave function whose electronic density function is identical to the ground-state density of an interacting /V-clcctron system. DFT theory is based on Hohenberg-Kohn theorems, which show that the external potential function v(r) of an //-electron system is determined by its ground-state electron density. The theory can be extended to nonzero temperatures by considering a statistical electron density defined by Fermi-Dirac occupation numbers [241], The theory is also easily extended to the spin-indexed density characteristic of UHF theory and of the two-fluid model of spin-polarized metals [414],... 

The aforementioned macroscopic physical constants of solvents have usually been determined experimentally. However, various attempts have been made to calculate bulk properties of Hquids from pure theory. By means of quantum chemical methods, it is possible to calculate some thermodynamic properties e.g. molar heat capacities and viscosities) of simple molecular Hquids without specific solvent/solvent interactions [207]. A quantitative structure-property relationship treatment of normal boiling points, using the so-called CODESS A technique i.e. comprehensive descriptors for structural and statistical analysis), leads to a four-parameter equation with physically significant molecular descriptors, allowing rather accurate predictions of the normal boiling points of structurally diverse organic liquids [208]. Based solely on the molecular structure of solvent molecules, a non-empirical solvent polarity index, called the first-order valence molecular connectivity index, has been proposed [137]. These purely calculated solvent polarity parameters correlate fairly well with some corresponding physical properties of the solvents [137]. 

D Reference Interaction Site Model The 3D RISM [80-82, 93] is a theoretical method for modeling solution phase systems based on classical statistical mechanics. The 3D RISM equations relate 3D intermolecular solvent site—solute total correlation functions (hjr)), and direct correlation functions (c (r)) (index a corresponds to the solvent sites) [80, 82] ... 

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