c CCLRC
Section 3.5
4. Full step velocity:
v(t)
1
2
v(t -
1
2
t) + v(t +
1
2
t)
(3.60)
5. Thermostat:
(t +
1
2
t) (t -
1
2
t) + t
2E
kin
(t) - 2
q
mass
(t)
1
2
(t -
1
2
t) + (t +
1
2
t)
.
(3.61)
Several iterations are required to obtain self consistency. In DL POLY 3 the number of iterations
is set to 3 (if no bond constraints are present). If bond constraints are present an extra iteration
is required due to the call to the SHAKE routine. Note that the SHAKE corrections need only be
applied during the first iteration as subsequent to this the velocities, relative to the bond c.o.m.
velocity, will be orthogonal to the bond vectors. The velocity scaling imposed by the thermostat is
isotropic so does not destroy this orthogonality.
The conserved quantity is derived from the extended Hamiltonian for the system which, to within
a constant, is the Helmholtz free energy
H
NVT
= H
NVE
+
q
mass
(t)
2
2
+ f k
B
T
ext
t
o
(s)ds .
(3.62)
The VV and LFV flavours of the Nos´e-Hoover algorithm are implemented in the DL POLY 3
routines nvt h1 vv and nvt h1 lfv respectively.
3.5
Barostats
The size and shape of the simulation cell may be dynamically adjusted by coupling the system to
a barostat in order to obtain a desired average pressure (P
ext
) and/or isotropic stress tensor ().
DL POLY 3 has three such algorithms: the Berendsen barostat [
], the Hoover type barostat [
and the Martyna-Tuckerman-Klein (MTK) barsotat [
]. Only the last two have a well defined
conserved quantities.
3.5.1
Instantaneous pressure and stress
The instantaneous pressure in a system,
P(t) =
[2E
kin
(t) - W
atomic
(t) - W
constrain
(t - t) - W
PMF
(t - t)]
3V (t)
,
(3.63)
is a function of the system volume, kinetic energy and virial, W.
Note that when bond constraints or/and PMF constraints are present in the system P will not
converge to the exact value of P
ext
. This is due to iterative nature of the constrained motion in
which the virials W
constrain
and W
PMF
are calculated retrospectively to the forcefield virial W
atomic
.
The instantaneous stress tensor in a system,
(t) =
kin
(t) +
atomic
(t) +
constrain
(t - t) +
PMF
(t - t) ,
(3.64)
is a sum of the forcefield,
atomic
, constrain,
constrains
, and PMF,
PMF
, stresses.
Note that when bond constraints or/and PMF constraints are present in the system, the quantity
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