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Section 3.5


Rp (t)
∆t  σ(t) − Pext V (t) 1 2Ekin (t) 1

+
+
4
pmass
f
pmass
pmass
·
µ
·
¸¶
(3.100)
¸
1
1
1
∆t
v(t) ← exp − η(t + ∆t) + Tr η(t + ∆t)
· v(t)
4
f
4
2
·
¸
1
1
r(t + ∆t) ← exp η(t + ∆t) ∆t · r(t) + ∆t v(t + ∆t)
2
2
Similarly, for the LFV couched algorithms these are
1
η(t + ∆t) ← exp (−χp (t)∆t)
2




 σ(t) − P
R
(t)
p
V
(t)
1
1
∆t
2E
(t)
ext
kin
η(t −

+
+
) + ∆t

2
pmass
f
pmass
pmass 
·
scale
=
scale v
=
scale f
=
µ
¶
¸
3
∆t
1+ χ 1+ 1+
η(t)
f
2
2
−1
scale
∆t
scale
(3.101)
f (t) + R(t)
1
1
v(t + ∆t) ← scale v · v(t − ∆t) + scale f ·
2
2
m
½
¾
1
1
1
r(t + ∆t) ← r(t) + ∆t v(t + ∆t) + η(t + ∆t) · r(t + ∆t)
2
2
2
It is worth noting DL POLY 4 uses Taylor expansion truncated to the quadratic term to approximate exponentials of tensorial terms.
This ensemble is optionally extending to constant normal pressure and constant surface area,
NPn AT [56], by semi-isotropic constraining of the barostat equation of motion to:
d
ηαβ (t) =
dt
(
σzz (t)−Pext V (t)
pmass
+
0
2Ekin (t) 1
f
pmass
− χp ηzz (t) +
Rp,zz (t)
pmass
:
:
(α = β) = z
(α, β) 6= z .
(3.102)
Similarly, this ensemble is optionally extending to constant normal pressure and constant surface
tesnison, NPn γT [56], by semi-isotropic constraining of the barostat equation of motion to:

Rp,αα (t)
(t) 1
σαα (t)−[Pext −γext /hz (t)] V (t)

+ 2Ekin

pmass
f
pmass − χp ηαα (t) + pmass



d
ηαβ (t) =

dt


σzz (t)−Pext V (t)
pmass
2Ekin (t) 1
f
pmass
− χp ηzz (t) +
Rp,zz (t)
pmass
(α = β) = x, y
(α = β) = z
0
(α 6= β) = x, y, z ,
(3.103)
where γext is the user defined external surface tesnion and hz (t) = V (t)/Axy (t) is the instantenious
hight of the MD box (or MD box volume over area).


+
:
:
:
:
The VV and LFV flavours of the non-isotropic Langevin barostat (and Nosé-Hoover thermostat)
are implemented in the DL POLY 4 routines nst l0 vv and nst l0 lfv respectively. Both make
use of the DL POLY 4 module langevin module. The routines nst l1 vv and nst l1 lfv
implement the same but also incorporate RB dynamics.
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