The cavity surface area

In solubility studies of some substituted biphenyls, it was found (see 5.5.3.1) fliat gA evaluated via eq. [5.5.23] was linearly correlated wifli die nonpolar surface area of the solutes rather than with dieir total surface area the correlation equation was gA = 0.37 A poiar- K was concluded diat die A in the parameter gA is the nonpolar surface area of die solute. This conclusion, however, was based on die assumption diat g is fixed. But the correlation equation can also be written gA = 0.37 F p ,3Aoiai, where F p ,b,= A,K.npoiar/A, is the fraction of solute surface area that is nonpolar. Suppose it is admiUed that g may depend upon the solute (more particularly, it may depend upon the solute s polarity) then the correlation is consistent with the identities A = A fai and g = 0.37 

Thus differences in gA may arise from differences in solute polarity, acting through g. But A may itself change, rather obviously as a result of solute size, but also as a consequence of change of solvent, for the solvent size and geometry will affect die shape and size of the cavity that houses the solute. 

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In this relationship. S is alkane solubility, A is the cavity surface area and a is the hydrophobic free energy per unit area. Extensive fitting of this equation [24] yields a value of 88 kJ mol A for the proportionality constant a. This value corresponds to an unfavourable free energy of about 3.6 kJ mol for the transfer of a CH2 group to aqueous solution. 

Free energy of solubility = Proportional to the cavity surface area... 

To improve the accuracy of implicit-solvent potential energy surfaces, non-electrostatic interactions must be included, although such interactions have received only a brief mention here. The smooth, linear-scaling PCM technology that is discussed here is immediately ready for use in MM/PBSA applications [36, 38], as a replacement for finite-difference electrostatics. Other formulas for the non-electrostatic interactions [47] can also be used in PCM calculations, possibly after some re-parameterization. In general these non-electrostatic interaction formulas depend in some way on the cavity surface area, which is smooth and easily calculable by means of the PCM algorithms discussed herein. 

For several years use has been made of a computed geometric property of molecules. This property, which can be examined to see if these indices carry relevant structure information, is the cavity surface area . This is a computer-calculated property which is based on a spherical shape for each atom in a molecule and takes into account a suitable overlapping of these spheres in the formation of bonds. To each radius of an atom is added a radius for a solvent water molecule which would be in closest contact. The radii for the atoms, including the water molecule (taken as a sphere), are the van der Waals radii. The surface area is then computed over this composite of interpenetrating spheres. 

The results recorded in Table 3 suggest that the index is parallel to the cavity surface area. It is unreasonable to think that a single numerical index for each molecule could capture the complete essence of the structure and provide an entire basis for describing a complex property like the cavity surface area or the many properties of a given molecule. Several indices describing the many facets of molecular structure must be necessary to relate to any single property and, most certainly, to the many properties of a molecule. 

In other words, since the free energy of cavity formation, AG, is a function of the cavity surface area, it is proportional to the regular increase in molecular volume upon addition of each homologous structural unit. 

Sinanoglu and co-workers [2, 19, 59] calculated the cavity surface area. S, from the relation... 

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