c CCLRC
Section 3.4
6. Thermostat:
(t + t)
1 +
t
T
E
kin
(t + t)
- 1
1/2
v(t + t) v(t + t) .
(3.44)
The LFV implementation the Berendsen algorithm is iterative as an initial estimate of (t) at full
step is calculated using an unconstrained estimate of the velocity at full step, v(t).
1. FF:
f (t) f (t - t) ,
(3.45)
2. LFV: The iterative part is as follows
v(t +
1
2
t)
v(t -
1
2
t) + t
f (t)
m
(t)
r(t + t) r(t) + t v(t +
1
2
t)
(3.46)
3. SHAKE
4. Full step velocity:
v(t)
1
2
v(t -
1
2
t) + v(t +
1
2
t)
(3.47)
5. Thermostat:
(t) 1 +
t
T
E
kin
(t)
- 1
1/2
.
(3.48)
Several iterations are required to obtain self consistency. In DL POLY 3 the number of iterations
is set to 2 (3 if bond constraints are present).
The Berendsen algorithms conserve total momentum but not energy.
The VV and LFV flavours of the Berendsen algorithm are implemented in the DL POLY 3 routines
nvt b1 vv and nvt b1 lfv respectively.
3.4.4
Nos´
e-Hoover Thermostat
In the Nos´e-Hoover algorithm [
] Newton's equations of motion are modified to read:
dr(t)
dt
= v(t)
dv(t)
dt
=
f (t)
m
- (t) v(t)
(3.49)
The friction coefficient, , is controlled by the first order differential equation
d(t)
dt
=
2E
kin
(t) - 2
q
mass
(3.50)
where is the target thermostat energy, equation (
q
mass
= 2
2
T
(3.51)
is the thermostat mass, which depends on a specified time constant
T
(for temperature fluctuations
normally in the range [0.5, 2] ps).
The VV implementation the algorithm takes place in symplectic manner as follows:
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