Environmental Engineering Reference
In-Depth Information
The velocity Verlet method updates the position and velocity
through the two-step evaluation as:
1
2
a
(
t
)
t
2
,
r
(
t
+
t
)
=
r
(
t
)
+
v
(
t
)
t
+
(1.20)
v
t
+
t
2
1
2
a
(
t
)
t
,
=
v
(
t
)
+
(1.21)
+
V
(
r
(
t
t
))
+
=−
a
(
t
t
)
,
(1.22)
m
v
(
t
+
t
)
=
v
t
+
t
2
1
2
a
(
t
+
t
)
t
.
+
(1.23)
It is obvious that in any integration algorithm, the time step is
always an important factor. Too large time step may arise in the
integration algorithm due to high energy overlaps between atoms
andleadtoaprogramfailure.Toosmalltimestepwillresultinmuch
more computer time. Usually, in one time step, the motion of the
particle should be approximately one order of magnitude smaller
than the atom-atom bond length. For most solid state materials, the
suggested time step at room temperature is from 0.1 fs to 1 fs (1 fs
=
10
−
15
s).
1.4 Temperature in Molecular Dynamics
1.4.1
Heat Bath
Based on equipartition theorem, the temperature of a system in MD
simulation isdefined as
N
T
=
m
i
v
i
·
v
i
/
(3
Nk
B
),
(1.24)
=
i
1
where
N
is total number of atoms in the system,
k
B
is Boltzmann's
constant,
m
i
and
v
i
is the mass and velocity (vector form) of atom
i
,
respectively,andtheangularbracketdenotestheensembleaverage.
To set the system at aimed temperature, heat bath is used to realize
thecanonicalensemble,thatis,constanttemperature.Dependingon
the nature of excitation, there are two kinds of heat baths widely
