Essentials of Computational Chemistry

448 12 EXPLICIT MODELS FOR CONDENSED PHASES
principle, every MD step should involve taking a phase point, computing the energy and the
gradients for that point given the nuclear positions, and propagating a short time step prior
to repeating this process. This formalism is extremely time-consuming. Car and Parrinello
showed, however, that one does not need to fully converge the KS wave function at every
step. Instead, the KS MO coefficients are treated as dynamical variables. That is, they are
assigned a fictitious mass and have their ‘coordinates’ added to the usual 3N positional
dimensions of phase space. By careful choice of the masses for the electronic degrees of
freedom, and the time steps for the electronic and nuclear movements, it is possible to
obtain a relevant MD sampling of phase space in favorable systems. To further increase
speed, the method usually uses a plane-wave basis set, which is ideally suited to the periodic
boundary conditions usually imposed in a condensed-phase simulation and allows fast Fourier
transform methods to facilitate solution of the SCF equations.
The obvious advantage of a fully QM solvent representation is that intimate solvent participation
in reactions, say as a proton donor or acceptor, or simply a charge-transfer partner
with the solute, is handled entirely naturally. With improved DFT functionals and everincreasing
computer speeds, this method holds great promise for the future, although it is
still sufficiently time-consuming that present day applications remain somewhat limited.
12.5 Relative Merits of Explicit and Implicit Solvent Models
The fundamental difference between the explicit and implicit solvent models is not that one
has solvent and the other does not. Rather, the difference is that the implicit model employs
a homogeneous medium to represent the solvent where the explicit model uses atomistically
represented molecules. While the latter choice is clearly the more physically realistic, the
practical limitations imposed by explicit representation dictate that it is not necessarily the
best choice for a given problem of interest. This section compares and contrasts the relative
strengths and weaknesses of the two models, including some illustrative applications.
12.5.1 Analysis of Solvation Shell Structure and Energetics
A reaction that has received a substantial amount of study using a variety of alternative
solvent (and solute) models is the Claisen rearrangement, a [3,3] sigmatropic shift that
converts an allyl vinyl ether into a γ ,δ-unsaturated aldehyde (Figure 11.5). The motivation
for its study has been two-fold. First, the conversion of chorismate to prephenate,
which is the first committed step in the biosynthesis of aromatic amino acids in plants,
involves an enzyme-catalyzed Claisen rearrangement. Secondly, although pericyclic reactions
are conventionally thought of as being relatively insensitive to solvent effects, the rate
acceleration for rearrangement of the parent allyl vinyl ether comparing the gas phase to
aqueous solution has been estimated to be on the order of 1000-fold. How does aqueous
solvation effect this large rate acceleration?
Storer et al. (1994) employed a SMx GB continuum solvent model to investigate this
question. Because of the efficiency of the continuum model, they were able to examine
various levels of electronic-structure theory in assessing the influence of aqueous solvation