c CCLRC
Section 3.5
3.5.3
The Hoover Barostat
DL POLY 3 uses the Melchionna modification of the Hoover algorithm [
of motion involve a Nos´e-Hoover thermostat and a barostat in the same spirit. Additionally, as
shown in [
], a modification allowing for coupling between the thermostat and barostat is also
introduced.
Cell size variation
For isotropic fluctuations the equations of motion are:
d
dt
r(t) = v(t) + (t) (r(t) - R
0
(t))
d
dt
v(t) =
f (t)
m
- [(t) + (t)] v(t)
d
dt
(t) =
2E
kin
(t) - 2
q
mass
q
mass
= 2
2
T
(3.69)
d
dt
(t) = 3V (t)
P(t) - P
ext
p
mass
- (t)(t)
p
mass
= (f + 3) k
B
T
ext
2
P
d
dt
V (t) = [3(t)] V (t) ,
where is the barostat friction coefficient, R
0
(t) the system centre of mass at time t, q
mass
the
thermostat mass,
T
a specified time constant for temperature fluctuations, p
mass
the barostat
mass,
P
a specified time constant for pressurweightinge fluctuations, P the instantaneous pressure
and V the system volume.
The conserved quantity is, to within a constant, the Gibbs free energy of the system:
H
NPT
= H
NVE
+
q
mass
(t)
2
2
+
p
mass
(t)
2
2
+ P
ext
V (t) + (f + 1) k
B
T
ext
t
o
(s)ds .
(3.70)
y
The VV flavour of the algorithm is implemented in the DL POLY 3 routine npt h1 vv in the
following manner:
1. Thermostat: Note 2E
kin
(t) changes inside
(t +
1
8
t) (t) +
t
8
2E
kin
(t) - 2
q
mass
v(t) v(t) exp -(t +
1
8
t)
t
4
(3.71)
(t +
1
4
t) (t +
1
8
t) +
t
8
2E
kin
(t) - 2
q
mass
2. Barostat: Note E
kin
(t) and P(t) have changed and change inside
(t) (t) exp -(t +
1
4
t)
t
8
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