c CCLRC
Section 2.2
3. Truncated harmonic: (thrm)
U (
jik
) =
k
2
(
jik
-
0
)
2
exp[-(r
8
ij
+ r
8
ik
)/
8
]
(2.15)
4. Screened harmonic: (shrm)
U (
jik
) =
k
2
(
jik
-
0
)
2
exp[-(r
ij
/
1
+ r
ik
/
2
)]
(2.16)
U (
jik
) =
k
8(
jik
- )
2
(
0
- )
2
- (
jik
- )
2 2
×
exp[-(r
ij
/
1
+ r
ik
/
2
)]
(2.17)
U (
jik
) = k [
a
jik
(
jik
-
0
)
2
(
jik
+
0
- 2)
2
-
a
2
a-1
(
jik
-
0
)
2
( -
0
)
3
] exp[-(r
8
ij
+ r
8
ik
)/
8
]
(2.18)
7. Harmonic cosine: (hcos)
U (
jik
) =
k
2
(cos(
jik
) - cos(
0
))
2
(2.19)
8. Cosine: (cos)
U (
jik
) = A [1 + cos(m
jik
- )]
(2.20)
U (
jik
) = A (
jik
-
0
) (r
ij
- r
o
ij
) (r
ik
- r
o
ik
)
(2.21)
In these formulae
jik
is the angle between bond vectors r
ij
and r
ik
:
jik
= cos
-1
r
ij
· r
ik
r
ij
r
ik
.
(2.22)
In DL POLY 3 the most general form for the valence angle potentials can be written as:
U (
jik
, r
ij
, r
ik
) = A(
jik
)S(r
ij
)S(r
ik
) ,
(2.23)
where A() is a purely angular function and S(r) is a screening or truncation function. All the
function arguments are scalars. With this reduction the force on an atom derived from the valence
angle potential is given by:
f
= -
r
U (
jik
, r
ij
, r
ik
) ,
(2.24)
with atomic label
being one of i, j, k and indicating the x, y, z component. The derivative is
-
r
U (
jik
, r
ij
, r
ik
) = -S(r
ij
)S(r
ik
)
r
A(
jik
)
-A(
jik
)S(r
ik
)(
j
-
i
)
r
ij
r
ij
r
ij
S(r
ij
)
-A(
jik
)S(r
ij
)(
k
-
i
)
r
ik
r
ik
r
ik
S(r
ik
) ,
(2.25)
16