c CCLRC
Section 2.3
usual to assume g
ab
(r) = 1 for r > r
vdw
. DL POLY 3 sometimes makes the additional assumption
that the repulsive part of the short ranged potential is negligible beyond r
vdw
.
The correction for the system virial is
W
ab
corr
= -2
N
a
N
b
V
r
vdw
g
ab
(r)
r
U
ab
(r)r
3
dr ,
(2.82)
where the same approximations are applied.
Note that these formulae are based on the assumption that the system is reasonably isotropic
beyond the cutoff.
In DL POLY 3 the short ranged forces are calculated by the subroutine vdw forces. The long
range corrections are calculated by routine vdw lrc. The calculation makes use of the Verlet
neighbour list (see above).
2.3.2
Metal Potentials
DL POLY 3 includes density dependent potentials suitable for calculating the properties of metals.
The basic model is due to Finnis and Sinclair [
] as implemented by Sutton and Chen [
form of the potential is: (stch)
U
sc
=
i<j
a
r
ij
n
- C
i
1/2
i
,
(2.83)
where the local density,
i
, is given by
i
=
j
a
r
ij
m
.
(2.84)
The Sutton-Chen potential has the advantage that it is decomposable into pair contributions and
thus falls within the general tabulation scheme of DL POLY 3 , where it is treated as a pair
interaction, although the metal cutoff (r
met
) has nothing to do with short ranged one (r
vdw
). The
same form of potential may be used in alloys, through the appropriate choice of parameters
and
a. The parameters n and m, however, must be the same for all component elements of the alloy.
DL POLY 3 calculates this potential in two stages: the first calculates the local density,
i
, for
each atom; and the second calculates the potential energy and forces. Interpolation arrays, vmet
and gmet (metal generate) - similar to those in van der Waals interactions
both these stages.
The total force f
tot
j
on an atom j derived from this potential is calculated in the standard way:
f
tot
j
= -
j
U
sc
,
(2.85)
which gives
f
tot
j
= -
i=j
n
a
r
ij
n
-
Cm
2
(
-1/2
j
+
-1/2
i
)
a
r
ij
m
1
r
2
ij
r
ij
,
(2.86)
which is recognizable as a sum of pair forces. For example, the force on atom j due to the atom i:
f
j
= -
n
a
r
ij
n
-
Cm
2
(
-1/2
j
+
-1/2
i
)
a
r
ij
m
1
r
2
ij
r
ij
,
(2.87)
27