c CCLRC
Section 2.2
with
ab
= 1 if a = b and
ab
= 0 if a = b . In the absence of screening terms S(r), this formula
reduces to:
-
r
U (
jik
, r
ij
, r
ik
) = -
r
A(
jik
) .
(2.26)
The derivative of the angular function is
-
r
A(
jik
) =
1
sin(
jik
)
jik
A(
jik
)
r
r
ij
· r
ik
r
ij
r
ik
,
(2.27)
with
r
r
ij
· r
ik
r
ij
r
ik
= (
j
-
i
)
r
ik
r
ij
r
ik
+ (
k
-
i
)
r
ij
r
ij
r
ik
-
cos(
jik
) (
j
-
i
)
r
ij
r
2
ij
+ (
k
-
i
)
r
ik
r
2
ik
.
(2.28)
The atomic forces are then completely specified by the derivatives of the particular functions A()
and S(r) .
The contribution to be added to the atomic virial is given by
W = -(r
ij
· f
j
+ r
ik
· f
k
) .
(2.29)
It is worth noting that in the absence of screening terms S(r), the virial is zero [
The contribution to be added to the atomic stress tensor is given by
= r
ij
f
j
+ r
ik
f
k
(2.30)
and the stress tensor is symmetric.
In DL POLY 3 valence forces are handled by the routine angles forces.
2.2.4
Angular Restraints
In DL POLY 3 angle restraints, in which the angle subtended by a triplet of atoms, is maintained
around some preset value
0
is handled as a special case of angle potentials. As a consequence
angle restraints may be applied only between atoms in the same molecule. Unlike with application
of the "pure" angle potentials, the electrostatic and van der Waals interactions between the pair
of atoms are still evaluated when distance restraints are applied. All the potential forms of the
previous section are avaliable as angular restraints, although they have different key words:
1. Harmonic: (-hrm)
2. Quartic: (-qur)
3. Truncated harmonic: (-thm)
4. Screened harmonic: (-shm)
17