Source: https://www.potfit.net/wiki/doku.php?id=adp
The angular-dependent potential is a generalization of the EAM model for the simulation of the covalent component of bonding.
The angular-dependent potential model was suggested by Y. Mishin, M.J. Mehl, and D. Papaconstantopoulos, Acta Mater., 53 (15), 4029-4041, (2005). it is based on the EAM potential model, and the first two terms in the expression for the energy are exactly the same as for EAM potentials:
1
2
N
1
2
1
2
1
6
E
total
=
∑
Φ
i
j
(
r
i
j
)
+
∑
F
i
(
n
i
)
+
∑
(
μ
α
i
)
2
+
∑
(
λ
α
i
β
)
2
−
∑
i
ν
2
i
i
,
j
(
j
≠
i
)
i
i
,
α
i
,
α
,
β
i
i
and j
j
enumerate atoms and the superscripts α
,
β
=
1
,
2
,
3
α,β=1,2,3
refer to the Cartesian directions. The first two terms are explained in detail on the EAM page.
The additional three terms introduce non-central components of bonding through the vectors
μ
α
i
=
∑
u
i
j
(
r
i
j
)
r
α
i
j
j
≠
i
and tensors
λ
α
i
β
=
∑
w
i
j
(
r
i
j
)
r
α
i
r
β
j
i
j
j
≠
i
i
are traces of the λ
νi
λ
-tensor:
ν
i
=
∑
λ
α
α
i
α
These additional terms can be thought of as measures of the dipole (
) and quadrupole (λ
μ
μ
λ
) distortions of the local environment of an atom.