Reviews in Computational Chemistry Volume 18

96 Polarizability in Computer Simulations
molecular polarizabilities are not that far off, with the Applequist method
tending to overestimate the polarization anisotropies.
Various computer simulation models have used either the Applequist
parameters and no screening 15,16,24,27,28,32,34 or the Thole parameters and
screening of Tij. 19,31,38 Different screening functions have been used as well.
A large number of polarizable models have been developed for water, many
of them with one polarizable site (with a ¼ 1:44 A ˚ 3 ) on or near the oxygen
position. 20–23,26,29,30,33,35–37 For these models, the polarizable sites do not
typically get close enough for polarization catastrophes {ð4aaÞ 1=6 ¼ 1:4 A ˚ ,
see comments after Eq. [16]}, so screening is not as necessary as it would be
if polarization sites were on all atoms. However, some water models with a
single polarizable site do screen the dipole field tensor. 20,22,37 Another model
for water places polarizable sites on bonds. 25 Other polarizable models have
been used for monatomic ions and used no screening of T or E 0 . 15,16,27,34
Polarizable models have been developed for proteins as well, by Warshel
and co-workers (with screening of T but not E 0 ), 44,45 and by Wodak and
co-workers (with no screening). 46
An attractive feature of the dipole polarizable model is that the assignment
of electrostatic potential parameters is more straightforward than for
nonpolarizable models. Charges can be assigned on the basis of experimental
dipole moments or ab initio electrostatic potential charges for the isolated
molecule. The polarizabilities can be assigned from the literature (as in
Table 1) or calculated. Contrarily, with nonpolarizable models, charges may
have some permanent polarization to reflect their enhanced values in the condensed
phase. 6,47 The degree of enhancement is part of the art of constructing
potentials and limits the transferability of these potentials. By explicitly including
polarizability, the polarizable models are a more systematic approach for
potential parameterization and are therefore more transferrable.
Using Eqs. [9] and [11], the energy can be rewritten as
U ind ¼ XN
i ¼ 1
l i E 0 i
1
þ
2
X N
X
li Tij lj þ 1
2
i ¼ 1 j 6¼ i
and the derivative of U ind with respect to the induced dipoles is
=l i U ind ¼ E 0 i
þ X
j 6¼ i
X N
i ¼ 1
l ia 1
i l i ½18Š
Tij l j þ a 1
i l i ¼ 0 ½19Š
The derivative in Eq. [19] is zero because a 1
i li ¼ E0 P
i Tij lj, according
to Eq. [3]. The values of the induced dipoles are therefore those that
minimize the energy. Other polarizable models also have auxiliary variables,
analogous to l, which likewise adjust to minimize the energy.