c CCLRC
Section 2.3
where r
ij
= r
j
- r
i
. The force on atom i is the negative of this.
With the pair forces thus defined the contribution to be added to the atomic virial from each atom
pair is then
W = -r
ij
· f
j
.
(2.88)
The contribution to be added to the atomic stress tensor is given by
= r
ij
f
j
,
(2.89)
where and indicate the x, y, z components. The atomic stress tensor is symmetric.
The long range correction for the system potential is in two parts. Firstly, by analogy with the
short ranged potentials, the correction to the local density is obtained by
i
=
o
i
+ 4 ¯
r
cut
a
r
m
r
2
dr ,
(2.90)
where
o
i
is the uncorrected local density and ¯
is the mean particle density. Evaluating the integral
part of the above equation yields
= 4
¯
a
3
(m - 3)
a
r
cut
m-3
,
(2.91)
which is the local density correction and is identical for all atoms. The correction is applied
immediately after the local density is calculated. The density term of the Sutton-Chen potential
needs no further correction. The pair term correction is obtained by analogy with the short ranged
potentials and is
U
corr
= 2
N ¯
a
3
(n - 3)
a
r
cut
n-3
.
(2.92)
The correction to the local density having already been applied.
To estimate the virial correction we assume the corrected local densities are constants (i.e. in-
dependent of distance - at least beyond the range r
met
). This allows the virial correction to be
computed by the methods used in the short ranged potentials. The result is:
W
corr
= -2 ¯
a
3
nN
(n - 3)
a
r
cut
n-3
-
m
2
C
2
(m - 3)
a
r
cut
m-3 N
i
-1/2
i
.
(2.93)
This correction may be used as it stands, or with the further approximation:
N
i
-1/2
i
=
N
<
1/2
i
>
,
(2.94)
where <
1/2
i
> is regarded as a constant of the system.
In DL POLY 3 the metal forces are handled by the routine metal forces. The local density is cal-
culated by routine metal ld compute. The long range corrections are calculated by metal lrc.
2.3.3
Tersoff Potential
] potential has been developed to be used in multi-component covalent systems. It
has 11 atomic and 2 bi-atomic parameters. The energy is modelled as a sum of pair-like interactions,
28