Reviews in Computational Chemistry Volume 18

Electronegativity Equalization Models 115
electronic potential (i.e., a large frequency for the oscillations about the exact
trajectory in Figure 4), but large enough so that reasonable length time steps
can still be used. In addition, the mass should be chosen so that the coupling
between the charge and nuclear degrees of freedom is relatively weak. Any
such coupling enables the cold charges to absorb energy from the rest of the
system, eventually reaching equilibrium with the warmer parts of the system.
Weak coupling results in relatively slow energy transfer, taking hundreds of
picoseconds or longer before the charge temperature and amplitude of the
charge oscillations become large enough to require reminimization. For
many applications, standard 1 femtosecond time steps can be used, and the
charges will remain at a temperature less than 6 K for a 50-ps simulation without
thermostatting. Thus EE combined with the extended Lagrangian method
is not much more computationally demanding than nonpolarizable simulations.
126,148 Finding the optimum masses can be difficult for systems with
many different atom types, each fluctuating on a different time scale. 10 For
these cases, different Mq must be used for the different charge masses. The
expression for la becomes
P
i
la ¼
wi=Mq;i P
i 1=Mq;i
½53Š
For more complex systems, thermostatting may be required to keep the
charges near 0 K. 10
Polarizable models based on EE implement the electrostatic interactions
using either point or diffuse charges, and can thus be combined quite easily
with other methods of treating polarizability to create hybrid models. The
EE and the dipole polarizable models have some features in common, but
they are not equivalent. They have, for example, different distance dependences
and polarizability responses. Some hybrid models have included both
dipole polarizability and fluctuating charges. 131,144,150,166 The fluctuating
charge model has also been combined with a shell-type model, as a method
of allowing polarization in single-atom species such as simple ions, without
having to introduce the added complication of the dipole field tensor. 82,104,167
The w i and J ij parameters for the EE models can be optimized so that the
resulting charges match gas-phase values as determined from either ab initio
quantum mechanical calculations or the experimental dipole
moment. 125,126,136–138,148 Parameters derived along these lines can give accurate
gas-phase charge values. Information about many-body interactions can
be included in the parameterization in several ways. First, quantities including
ESP charges, geometries, and the strength of many-body interactions can be
obtained from ab initio calculations on clusters. 142,145,150,166 Second, the
polarization response from an applied electric field can be used. 146 Third,
one can optimize the parameters to give the optimal charges both in the gas
phase and in the presence of a solvent, as modeled using reaction field