Analysis and Characterization of Surface Potentials

We have shown in earlier work that it is possible to quantitatively relate a variety of liquid, solid and solution phase properties to the electrostatic potential patterns on the surfaces of the individual molecules [64-66]. Among these properties are pKa, boiling points and critical constants, enthalpies of fusion, vaporization and sublimation, solubilities, partition coefficients, diffusion constants and viscosities. For these purposes, we take the molecular surface to be the 0.001 au contour of the molecular electronic density p(r), following the suggestion of Bader et al [67], 

The electrostatic potential that is produced at any point r in the space around a molecule by its nuclei and electrons is given by eq (1)  

Za is the charge on nucleus A, located at Ra- The sign and magnitude of V(r) are the net result of the positive and negative contributions of the nuclei and electrons, respectively, at the point r. For V(r) computed on the molecular surface, we determine the local maxima and minima (i.e. the most positive and negative values, Vs,max and Vs,min), the average deviation II and the total variance a t- The latter two are defined by eqs. (2) and (3)  

We view n as an indicator of the internal charge separation, or local polarity, that is present even in molecules with zero dipole moments. It has been shown to correlate with dielectric constants [68] and with an experimentally-based measure of polarity [65]. The total variance, Ot0t which is the sum of the positive and negative variances, reflects the spread, or range of values, of the surface electrostatic potential. It is particularly sensitive to the positive and negative extremes, because of the terms being squared. We have found Otot to be effective as a measure of a molecule s tendency for noncovalent interactions for example, it enters into our expressions for boiling point [69], enthalpy of vaporization [64], solubilities [70,71], etc. 

Two classes of unsaturated compounds that are of interest in the present context, as energetic materials, are trinitroaromatics and nitroheterocycles, e.g. imidazoles and triazoles. The electrostatic potential on the molecular surface of 1,3,5-trinitrobenzene, 11, which is the parent molecule for the trinitroaromatics that we shall consider, has local maxima above the ring and near each of the C-NO2 bonds [77], This pattern is modified somewhat when other substituents are introduced, but its basic features remain even under the influence of electron-donating groups, e.g. in 2,4-diamino-l,3,5-trinitrobenzene 12, although the maxima are now less positive [76]. The 

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