Reviews in Computational Chemistry Volume 18

128 Polarizability in Computer Simulations
mechanical polarization effect that depends on the specific implementation of
the dispersion and short-range repulsive interactions. Thus each polarizable
site has an effective polarizability that depends on the local environment.
When a shell-model atom is confined in a condensed phase, the steric interactions
with neighboring ions will generally reduce the effective polarizability
compared to the gas-phase value. In a crystalline environment, there are additional
effects to consider: the anions and cations will polarize by different
amounts in an applied electric field (due to the more diffuse electron density
in the anions). The mechanical polarization effects will act to increase the
effective polarizability in cations, and decrease it in anions. 73 These effects
are completely realistic; the polarizabilities of atoms and ions do change
with their environment in just these ways, 238–240 and shell models have at
times been specifically parameterized to include this effect quantitatively. 73,96
Indeed, the inclusion of this mechanical polarizability effect has been shown to
be crucial for reproducing condensed-phase properties such as phonon dispersion
curves. 74,75
Another coupling of the short-range repulsive and long-range electrostatic
interactions has been developed by Chen, Xing, and Siepmann. 147 In
their EE model, the repulsive part of the Lennard–Jones potential is coupled
to the charge. This coupling is consistent with ab initio quantum calculations
that find that the size of an atom increases with its negative charge. 241 Studies
of gas–liquid 61 and solid–liquid 207 coexistence of water also suggest that models
that couple the volume of an atom (through the Lennard–Jones interaction)
to the size of the atom’s charge may be best suited for prediction of molecular
properties in the three phases. Empirical and semiempirical methods provide a
natural way to link the charges to other parts of the potentials, as is done in the
empirical valence bond approach 242 and the two-state peptide bond model. 183
To further illustrate the importance of coupling the electrostatic and
short-ranged repulsion interactions, we consider the example of a dimer of
polarizable rare gas atoms, as presented by Jordan et al. 96 In the absence of
an external electric field, a PPD model predicts that no induced dipoles exist
(see Eq. [12]). But the shell model correctly predicts that the rare gas atoms
polarize each other when displaced away from the minimum-energy (forcefree)
configuration. The dimer will have a positive quadrupole moment at
large separations, due to the attraction of each electron cloud for the opposite
nucleus, and a negative quadrupole at small separations, due to the exchangecorrelation
repulsion of the electron clouds. This result is in accord with
ab initio quantum calculations on the system, and these calculations can
even be used to help parameterize the model. 96
In essence, this difference between shell models and PPD models arises
from the former’s treatment of the induced dipole as a dipole of finite length.
Polarization in physical atoms results in a dipole moment of a small, but finite,
extent. Approximating this dipole moment as an idealized point dipole, as in
the PPD models, is an attractive mathematical approximation and produces