c CCLRC
Section 3.1
3.1
Introduction
As a default the DL POLY 3 integration algorithms are based on the Velocity Verlet (VV) scheme,
which is both simple and time reversible [
]. It generates trajectories in the microcanonical (NVE)
ensemble in which the total energy (kinetic plus potential) is conserved. If this property drifts or
fluctuates excessively in the course of a simulation it indicates that the timestep is too large or the
potential cutoffs too small (relative r.m.s. fluctuations in the total energy of 10
-5
are typical with
this algorithm).
The VV algorithm has two stages (VV1 and VV2). At the first stage it requires values of position
(r), velocity (v) and force (f ) at time t. The first stage is to advance the velocities to t + (1/2)t
by integration of the force and then to advance the positions to a full step t + t using the new
half-step velocities:
1. VV1:
v(t +
1
2
t) v(t) +
t
2
f (t)
m
,
(3.1)
where m is the mass of a site and t is the timestep
r(t + t) r(t) + t v(t +
1
2
t)
(3.2)
2. FF:
Between the first and the second stage a recalculation of the force at time t + t is required
since the positions have changed
f (t) f (t + t)
(3.3)
3. VV2:
In the second stage the half-step velocities are advanced to to a full step using the new force
v(t + t) v(t +
1
2
t) +
t
2
f (t + t)
m
(3.4)
DL POLY 3 also offers integration algorithms based on the leapfrog Verlet (LFV) scheme [
Although LFV scheme is somewhat simpler and numerically faster than the VV scheme, it is
usually not time reversible and does not offer the numerical stability the VV scheme does.
The LFV algorithm is one staged. It requires values of position (r) and force (f ) at time t and
velocity (v) at half a timestep behind: t - (1/2)t. Firstly, the forces are recalculated afresh at
time t (from time t + t) since the positions have changed from the last step:
1. FF:
f (t) f (t - t) ,
(3.5)
where t is the timestep
2. LFV:
The velocities are advanced by a timestep to t + (1/2)t by integration of the new force
v(t +
1
2
t) v(t -
1
2
t) + t
f (t)
m
,
(3.6)
where m is the mass of a site, and then the positions are advanced to a full step t + t using
the new half-step velocities
r(t + t) r(t) + t v(t +
1
2
t)
(3.7)
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