Essentials of Computational Chemistry

446 12 EXPLICIT MODELS FOR CONDENSED PHASES
A slightly more complex representation is to put equal positive atomic charges on the
hydrogen atoms and a negative charge on the symmetry axis, or equal negative charges
in the lone pair regions, again to mimic water’s dipole moment, but also to better represent
its overall charge distribution. Such very simple models, with careful parameterization,
do remarkably well in reproducing many properties of liquid water, e.g., bulk density,
heat of vaporization, compressibility, heat capacity, etc. The most successful models along
these lines, that are widely used in modern simulations, are the transferable-intermolecularpotentials-3-
and -4-point-charge water models (TIP3P and TIP4P; Jorgensen et al. 1983).
The similarly designed SPC (simple point charge) water model also continues to see modern
use (Berendsen et al. 1981) including forms recently modified to improve its dielectric and
diffusive properties (Glattli, Daura, and van Gunsteren 2003).
For non-aqueous solvents, the approximation of the solvent as a LJ sphere is usually less
practical. However, substantial time savings can be realized by employing a united-atom
approach for carbon atoms and their attached hydrogens. The most complete parameterization
of organic solvents has been accomplished as part of the OPLS force field, including
inter alia alkanes, aromatics, carbon tetrachloride, chloroform, furan, n-octanol, and pyrrole,
many in both UA and AA representations (see Table 2.1 and also Jorgensen, Briggs, and
Contreras 1990; Kaminski et al. 1994; McDonald and Jorgensen 1998). In these cases, as for
water, solvent parameters were optimized based on comparison of bulk solvent properties to
experimental measurements.
At the next level of complexity, the polarity of solvent models, as made manifest by
their atomic partial charges, can be augmented with a polarizability. This allows the solvent
molecule to respond to its surroundings in a fashion conceptually similar to the electronic
component of the solvent polarization described in Section 11.1.1. Typically a polarizability
tensor α is assigned either to the solvent molecule as a whole or to individual atoms. Then,
the induced dipole moment at each polarizable position can be determined from
µ ind = αE (12.30)
where E is the total electric field arising from all of the atomic point charges and all of
the induced dipoles. Thus, µ ind must be determined iteratively, with convergence potentially
being problematic. Once converged, the additional contribution to the total electrostatic
energy from the charge-induced dipole interactions can be computed according to
V = 1
2
i
j
qiµ ind
j · rij
r 3 ij
(12.31)
where i runs over charge sites and j runs over polarizability sites and r is the intersite
distance. In addition, induced-dipole–induced-dipole interactions contribute according to
Eq. (2.23).
Owing to its particular importance, polarizable solvent models have largely been restricted
to water, for which a sizable number have been developed (see, for example, Dang 1992;
Rick, Stuart, and Berne 1994; Bernardo et al. 1994; Zhu and Wong 1994; Lefohn, Ovchinnikov,
and Voth 2001). Because evaluating the terms deriving from solvent polarizability