Chemistry Reference
In-Depth Information
extrapolation method is largely independent of
, allowing for large MTS steps
while maintaining the underlying behavior of the single-step Langevin method.
t
EXTENDING THE TIME SCALE: PATH
METHODOLOGIES
Molecular dynamics (MD) is the most widely used computational meth-
od to study the kinetic and thermodynamic properties of atomic and molecular
systems.
59-61
These properties are obtained by solving the microscopic equa-
tions of motion (Eq. [1]) for the system under consideration. The multiple
time-step algorithms discussed earlier have extended the time scale that can
be reached, but, the gain is still insufficient for the study of many processes;
for many systems, such as biomolecules, this simulation time is inadequate
to study large conformational changes or to study rare but important events
as examples.
A different approach for such systems can be considered, however, that
invokes a different set of methodologies that attempt to compute trajectories
connecting conformations from the reactant state to conformations of the pro-
duct state, i.e., the reaction path. Transition path sampling, MaxFlux, discrete
path sampling, string methods, and optimization of actions are examples of
methodologies that search for these transition paths. We now will review
briefly the first four methods and then present the theory and implementation
of the action formalism in more detail.
Transition Path Sampling
Transition path sampling (TPS) is a methodology that can be used to
study slow activated processes. This technique, first developed by the Chandler
group
62,63
and further improved by Bolhuis et al.,
64-67
is based on a polymer-
like representation of the complete trajectory (Figure 7). TPS is an iterative
method that starts by computing a dynamical pathway connecting conforma-
tions of the reactant and product state. That can be done using simpler meth-
ods that generate approximate trajectories connecting two boundary points.
Starting from this initial path, further trajectories are then generated using
an iterative strategy. Specifically, a configuration snapshot (i.e., nuclear posi-
tions and velocity vectors) is taken from the previous trajectory and modified
(Monte Carlo shooting method
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) in a manner consistent with the correspond-
ing distribution ensemble. Usually, the incorporated change is a momentum var-
iation. Then, starting from this modified configuration, forward and backward
trajectories are generated using MD, and, if this pathway connects the reactant
and product state, it is used to generate another new pathway as above. An
accurate sampling of trajectory space can be generated by iterating this
process many times. From these trajectories, reaction mechanisms and transition
