Chemistry Reference
In-Depth Information
modes, i.e., bond stretching. The fastest period relevant to organic and biomo-
lecules is around 10 fs (associated, e.g., with C-H, O-H, and N-H stretching).
Resolving these fast motions adequately dictates that time steps of length 1 fs
or less should be used. Because of this the slower and more computationally
expensive force components are updated at each step, resulting in CPU limita-
tions of simulation length and system size. Solving the problems of efficient
time stepping and fast evaluation of nonbonded forces without distance cut-
offs is an ongoing activity.
Multiple Time Steps
In multiple time-step (MTS) time discretization methods the short-range
forces, which can change rapidly in time, are updated frequently with small
time steps. The long-range forces can be treated with larger steps in time
(appropriate to the time scale on which they vary). We will discuss later the
fundamental impact that the high-frequency force components have on MTS
methods as well. In this chapter we trace the development of MTS methods
and present a tutorial that illustrates an elementary application of these tech-
niques.
Reaction Paths
A very different set of methodologies involves trying to compute trajec-
tories between two states of a molecular system. These ''double-ended'' algo-
rithms, usually called reaction path approaches, differ from integrators of the
Newton equations of motion, Eq. [6], in that only the initial positions and
velocities of the particles in the system are needed. The two boundary points,
i.e., the states of the system, can represent a reactant and product configura-
tion or a transition (or intermediate) state and reactant (product) configura-
tion. The calculated path provides a qualitative description of the structural
changes as function of a parameter(s) [reaction coordinate(s)] that charac-
terizes the reaction path. The path then represents a series of replicas of the
molecular system
parameterized accord-
ing to a parameter
s.
In this notation,
X
represents the coordinates of the mole-
cule in a given slice of the path.
Most of the reaction path approaches make use of a spatial step and
accordingly are not affected by the time-scale limitation of other MD methods.
For complex systems, however, the ruggedness of the potential energy surface
limits the applicability and accuracy of these paths because the number of con-
formations in the trajectory needs to increase. Another fundamental limitation
is that these methods are not applicable for the study of molecular events for
which very few details are known about the conformations of products or key
intermediates. It is for those processes where theoretical approaches are more
helpful.
f
X
ð
s
Þg ¼ f
X
ð
s
1
Þ;
X
ð
s
2
Þ; ...;
X
ð
s
N
Þg
