c CCLRC
Section 3.4
where is d
P M F
the constraint distance between the two groups used to define the reaction coordi-
nate.
The routines pmf shake and pmf rattle are called to apply corrections to the atomic positions
and respectively the atomic velocities of all particles constituting pmf units.
In presence of both bond constraints and pmf constraints. The constraint procedures, i.e. SHAKE
or RATTLE, for both types of constraineds are applied iteratively in order bonds-pmfs until con-
vergence of W
P M F
reached. The number of iteration cycles is limited by the same limit as for the
constraint procedures.
3.4
Thermostats
The system may be coupled to a heat bath to ensure that the average system temperature is
maintained close to the requested temperature, T
ext
. When this is done the equations of motion
are modified and the system no longer samples the microcanonical ensemble. Instead trajectories
in the canonical (NVT) ensemble, or something close to it are generated. DL POLY 3 comes with
four different thermostats: Langevin [
], Evans (Gaussian constraints) [
]. Of these only the Nos´e-Hoover algorithm generates trajectories in the canonical
(NVT) ensemble. Evans and Berendsen algorithms will produce properties that typically differ
from canonical averages by O(1/N ) [
], as the Evans algorithm generates trajectories in the
(NVE
kin
) ensemble. The Langevin method does not generate any proper enesemble at all as it
impose Brownian Dynamics (or Stochastic Dynamics) on the system.
3.4.1
Langevin Thermostat
The Langevin thermostat works by coupling every particle to a viscous background and a stochastic
heath bath such that
dr
i
(t)
dt
= v
i
(t)
dv
i
(t)
dt
=
f
i
(t) + R
i
(t)
m
i
- v
i
(t) ,
(3.20)
where is a constant (user defined) friction parameter (in units of ps
-1
) and R(t) is stochastic
force with zero mean that satisfies the fluctuation-dissipation theorem:
R
i
(t) R
j
(t ) = 2 m
i
k
B
T
ij
(t - t ) ,
(3.21)
where superscripts denote Cartesian indices, subscripts particle indices, k
B
is the Boltzmann con-
stant, T the target temperature and m
i
the particle's mass. The effect of this algorithm is thermo-
stat the system on a local scale. Particles that are too "cold" are given more energy by the noise
term and particles that are too "hot" are slowed down by the friction. Numerical instabilities,
which usually arise from inaccurate calculation of a local collision-like process, are thus efficiently
kept under control and cannot propagate.
The generation of random forces is implemented in the routine langevin forces.
The VV implementation the algorithm is straight forward. A conventional VV1 and VV2 (thermally
unconstrained) steps are carried out. At the end of VV2 the thermal constraint applied on the
unthermostated velocities at full step t + t in the following manner
48