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In such a simulation, the energy due to an atom, ''i'', is given by
:<math>E_i = F_\alpha\left(\sum_{i\neq j} \rho_\alpha (r_{ij}) \right) + \frac{1}{2} \sum_{i\neq j} \phi_{\alpha\beta}(r_{ij})</math>
where <math>r_{ij}</math> is the distance between atoms <math>i</math> and <math>j</math>, <math>\phi_{\alpha\beta}</math> is a pair-wise potential function, <math>\rho_\alpha</math> is the contribution to the electron charge density from atom <math>j</math> at the ___location of atom <math>i</math>, and <math>F</math> is an embedding function that represents the energy required to place atom <math>i</math> of type <math>\alpha</math> into the electron cloud.
Since the electron cloud density is a summation over many atoms, usually limited by a cutoff radius, the EAM potential is a multibody potential. For a single element system of atoms, three scalar functions must be specified: the embedding function, a pair-wise interaction, and an electron cloud contribution function. For a binary alloy, the EAM potential requires seven functions: three pair-wise interactions (A-A, A-B, B-B), two embedding functions, and two electron cloud contribution functions. Generally these functions are provided in a tabularized format and interpolated by cubic splines.
==See also==
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