Angular Coulomb Potentials

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The angular coulomb potentials are a combination of the regular coulomb potentials and a angular dependent term similar to MEAM:

$$ V=V_{Coulomb}+\frac{1}{2}\sum f_{ij}(r_{ij})f_{ik}(r_{ik})g_i(\cos(\theta_{ijk})) $$

Number of potential functions

To describe a system of $N$ atom types you need $N(N+2)$ potentials.

# atom types	$\phi_{ij}$	$f_{ij}$	$g_i$	Total # potentials
$N$	$N(N+1)/2$	$N(N+1)/2$	$N$	$N(N+2)$
1	1	1	1	3
2	3	3	2	8
3	6	6	3	15
4	10	10	4	24

Order of potential functions

The potential table is assumed to be symmetric, i.e. the potential for the atom types 1-0 is the same as the potential 0-1.

The order of the potentials in the potential file for $N$ atom types is:

$\phi_{00}, \ldots, \phi_{0N}, \phi_{11}, \ldots, \phi_{1N}, \ldots, \phi_{NN}$
$f_{00}, \ldots, f_{0N}, f_{11}, \ldots, f_{1N}, \ldots, f_{NN}$
$g_0, \ldots, g_N$