Chemistry Reference
In-Depth Information
In MD trajectories it is easy to extract dynamical properties by comput-
ing an average over time. The extraction of these properties is more difficult to
do in reaction path approaches because trajectories are computed in configura-
tion space (with only coordinate information for each structure in the path).
Dynamical information can be computed, though, if an ensemble of many
reactive trajectories is obtained. But such an ensemble is not generally deter-
mined (this can be done with transition path sampling). Reaction path meth-
ods are very useful for determining of rates and free energy profiles for fast
but rare events that are inefficiently probed with other MD algorithms
because trajectories obtained with reaction path approaches filter out the wait-
ing periods the system spends in the reactant wells, in contrast to standard MD
trajectories.
The reaction path methods consist of a number of different theoretical
formulations and algorithms and therefore are difficult to describe by a com-
mon framework (the second part of this chapter reviews some of the path tech-
niques developed in the past 10 years). All of these techniques describe the
system with atomic detail and use a potential function of the form of Eq.
[9]. We will also describe, in more detail, one of these methods, which is based
on a discretized formulation of the action of classical mechanics. In this action
formalism (called stochastic difference in length, SDEL), reaction paths are
obtained by linking two conformations of the system. These paths, parameter-
ized according to arc length, can be obtained with a large length step. There-
fore, this algorithm tries to solve the time-scale limitation of normal MD
simulations by using a boundary value formulation of the classical equations
of motion. Although this method has been used to compute approximate paths
for processes that are impossible to study using normal MD simulations, it is
difficult to compute dynamical properties from these paths (e.g., the time of
the trajectory computed directly from the algorithm is underestimated by sev-
eral orders of magnitude!). Still, the method can be used to determine large
conformational changes that can be resolved by the trajectory. This chapter
provides a tutorial section about how to run a program associated with this
algorithm and reviews some recent applications and improvements in the
methodology.
MULTIPLE TIME-STEP METHODS
In an effort to lengthen the feasible simulation time scale of molecular
simulations, Streett and co-workers introduced the multiple time-step method
in 1978.
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These authors recognized that the components of the force that vary
most rapidly, and hence require small time steps for numerical resolution, are
typically associated with atom pair interactions at small separations. This spa-
tial localization is important because each of the
N
particles in the simulation
has such an interaction with only a few, say
k
N
, neighboring particles.
