EAM + electrostatic potential

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The EAM + electrostatic potential is a combination of the regular EAM model with an additional coulomb term.

$$ E_{tot}=E_{EAM} + \frac{1}{2} \sum_{i\neq j} E(r_{ij}) \quad \text{with} \quad E(r_{ij}) \sim \frac{q_{i}q_{j}}{r_{ij}} $$

Number of potential functions

To describe a system with $N$ atom types you need $N(N+5)/2$ potentials.

# atom types	$\Phi_{ij}$	$\rho_j$	$F_i$	Total # potentials
$N$	$N(N+1)/2$	$N$	$N$	$N(N+5)/2$
1	1	1	1	3
2	3	2	2	7
3	6	3	3	12
4	10	4	4	18

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 EAM potentials in the potential file for N atom types is:

$\Phi_{00}, \ldots, \Phi_{0N}, \Phi_{11}, \ldots, \Phi_{1N}, \ldots, \Phi_{NN},$
$\rho_0, \ldots, \rho_N,$
$F_0, \ldots, F_N,$