clearly depends on the solute size; (2) the energy of weak solute-solvent “disper-
sion” forces; (3) solvent “reorganization energy” caused by disturbing solvent–
solvent dispersion forces, and (4) the electrostatic interaction energy between
charges on the solute and charges on solvent molecules (in a continuum context
the solute polarizes even a nonpolar medium like pentane, engendering electrostatic
interactions). These divisions are somewhat arbitrary; thus reorganization energy
does not have to be defined to exclude electrostatic interactions [ 19 , 21 ]. Terms
(1)–(3) can be subsumed intoGCDS, a cavitation-dispersion-solvent-reorganization
free energy term that is a sum of contributions from the atoms of groups in the
molecule, each contribution being the product of an effective exposed surface area
Aand a so-called surface tensions(which has no particular connection with
conventional surface tension [ 16 , 18 ]):
GCDS¼
X
iAisi (8.1)This very empirically parameterized equation for nonelectrostatic terms is a
characteristic of the SMx series (solvent model 1, 2,..., now up to SM8) of Cramer
and Truhlar [ 22 ].
The calculation of the electrostatic part of the interaction energy, the fourth term,
uses as the starting point the Poisson equation, which relates electrostatic potential
fto charge distributionrand dielectric constante;fandr(and possiblye), vary
from place to place, hence the position vectorr:
r^2 fðrÞ¼4 prðrÞ
e(8.2)
The equation applies to a dielectric medium which responds linearly to (under-
goes polarization linearly with) the charge distributionr. A dielectric medium is a
nonconducting, that is, insulating, medium that when subjected to the field of an
electric charge shifts its charge distribution slightly along the direction of the field,
i.e. becomes polarized;eis the ratio of the electrical conductivity of the medium to
the conductivity of the vacuum. For a solvent it is an approximate measure of
polarity (an index of which is dipole momentm), if we constrain our domain to
certain classes. For 24 solvents encompassing nonpolar (e.g. pentane,m0.00,e1.8),
polar aprotic (e.g. dimethyl sulfoxide,m3.96,e46.7), and polar protic (e.g. water,
m1.85e80) dispositions, the correlation coefficientr^2 ofewithmwas only 0.36
(removing formic acid and water raised it to 0.75). For nine nonpolar, seven polar
aprotic, and 8 polar protic solvents, considered as separate classes,r^2 was 0.90,
0.87, and 0.0009 (sic), respectively [ 23 ]. Note that because of parameterization for
other factors e.g. Eq.8.1, modern continuum methods do not depend only (if at all –
see COSMO and COSMO-RS, below) on dielectric constant.
The key to current continuum algorithms for calculating the properties of
a molecule in solution is to formulate a solution Hamiltonian operator H^
(Section 4.3.4) in which these energy terms appear in addition to the in vacuo
526 8 Some “Special” Topics