Chemistry Reference
In-Depth Information
The total potential energy for the system is obtained by summing the
V
bond
terms for all six bonds, and
V
elec
for the eight electrostatic pairs. Note that
because the oxygen atoms are not subjected to any force, we need not compute
interactions between them, resulting in 3
8 nonbonded pairs. The
forces are then computed as the negative gradient of
V
elec
. The form of the
total forces can be seen in the MATLAB code twowaters.m. We have imple-
mented the time-stepping algorithms [6]-[20]. Simulations using the various
algorithms are coordinated and dispatched by the file dyntwowat.m.
3
1
¼
High- and Low-Frequency Motion: The Importance of
Electrostatic Forces
For typical configurations of the model system, in which the molecules
are separated by about 5
˚
, it is seen that the forces due to the bonded interac-
tions have magnitude on the order of 10
1
, while the electrostatic forces have
magnitude on the order of 10
3
. It is natural to wonder about the overall
importance of the tiny electrostatic forces. We performed long MD simulations
using [6] in the presence and absence of electrostatic forces in the model. The
left view in Figure 2 shows O-H bond distance over a few dozen time steps—
enough to capture several periods of the fastest motions due to the bond forces.
It can be observed that the fastest oscillations have a period of approximately
9 fs. The right view in Figure 2 shows a much longer trajectory of the dipole
angle
for one of the molecules. The presence of the electrostatic forces can
be seen to result in very low frequency motions—several orders of magnitude
slower than the fast bond-induced motions. Without electrostatic interaction,
the dipole angle remains essentially constant, with small fluctuations due to
y
Figure 2
Model exhibits motion across a wide range of frequencies. The left view shows
a short trajectory of O-H bond distance in the model system showing the period of the
fastest motion to be approximately 8.8 fs. The right view shows the trajectory of one
dipole angle. Note that the electrostatic interactions result in a low-frequency motion
with period approximately 10 ps. This motion is absent when the electrostatic
component is removed from the potential energy model.
