Chemistry Reference
In-Depth Information
CHAPTER 7
Extending the Time Scale in Atomically
Detailed Simulations
Alfredo E. C ´ rdenas
a
and Eric Barth
b
a
Department of Chemistry, University of South Florida,
Tampa, Florida
b
Department of Mathematics and Computer Science, Kalamazoo
College, Kalamazoo, Michigan
INTRODUCTION
The Verlet Method
The current practice of molecular dynamics simulation dates back to the
pioneering work on smooth potential models for monatomic fluids of Rahman
1
and Verlet
2
in the 1960s. In the 1970s, interest developed in applying molecular
dynamics methods to more complicated molecular fluids such as water,
3
mole-
cular fluids with internal degrees of freedom,
4
and large flexible molecules.
5
Given a potential energy function
V
(about which we have much more to say
below) that models the interatomic forces in a molecular system with
N
atoms,
the Newtonian equations of motion can then be expressed as
M
€
r
¼
F
ð
r
Þ¼r
r
V
ð
r
Þ
½
1
where
M
is a diagonal mass matrix with diagonal
½
m
1
m
1
m
1
m
2
m
2
m
2
...
m
N
m
N
m
N
