Essentials of Computational Chemistry

12.4 SOLVENT MODELS 447
increases the amount of time required for a simulation by roughly an order of magnitude,
the use of polarizable solvents has been primarily either for technical comparisons in model
development, or for the simulation of particularly simple systems, where convergence for a
given property of interest may be expected to occur quickly. Developers tend to focus on
properties for which non-polarizable water models do poorly, e.g., the density anomaly in
water where below 4 ◦ C the liquid density begins to decrease with decreasing temperature.
However, the failures of prior models to function well for such properties is not necessarily
intrinsic, but may simply reflect a failure to have considered the property in the development
of the non-polarizable model (Mahoney and Jorgensen 2000). More recent work with
polarizable acetonitrile and acetone solvent models has indicated, not surprisingly, that polarizability
critically improves the description of solvation structures and interaction energies
associated with the solvation of monatomic ions in these solvents (Fischer et al. 2002).
A yet more complete but still formally classical solvent model has been developed for use
when the solute is represented quantum mechanically. The electrostatic interactions between
a classical solvent and a quantum mechanical solute are relatively simple to represent, and
are discussed in detail in the next chapter on mixed QM/MM methods. The non-bonded
interactions are somewhat more challenging. Gordon et al. (2001) have described an approach
that they call the effective fragment potential (EFP) method that, by analogy to ECPs, replaces
the direct computation of dispersion and exchange-repulsion interactions between solute and
solvent electrons by an interaction between solute electrons and a solvent pseudopotential.
The solvent pseudopotentials (and the representation of its electrostatic distribution and
polarizability) are determined parametrically in order to create a transferable solvent model
especially suitable for use in QM/MM calculations using HF theory as the QM component.
The EFP model has since been extended to DFT as the QM component as well (Adamovic,
Freitag, and Gordon 2003).
12.4.2 Quantal Models
When one refers to a quantum mechanical solvent model, the word ‘model’ reverts to its
usual sense in the context of QM methods: it is the level of electronic structure theory
used to describe the solvent. Thus, there is no real distinction between the solvent and
the solute in terms of computational technology – the wave function for the complete supersystem
(or the DFT equivalent) is computed without resort to methodological approximations
beyond those inherent to the level of electronic structure theory. To avoid problems with
basis-set imbalances, one might expect calculations representing the solvent in a fully QM
fashion to employ a common level of theory for all particles, but this does not have to be
the case.
At several points in this book, it has been emphasized that the prevalence of classical MC
and MD simulations derives from the impracticality of carrying out fully QM dynamics.
While this is largely true, for systems of only modest size where short trajectories may
be profitably analyzed, fully QM MD simulations using the so-called Car–Parrinello technique
are a viable option (Car and Parrinello 1985). In its most widely used formulation,
the Car–Parrinello method employs DFT as the electronic-structure method of choice. In