The Embedded-Atom-Method

The more complex Cu-Cu interaction was computed in accord with the embedded atom method (EAM) [4], [5], [6].

In this approach the overall electron density in a metal is assumed to be a linear-superposition of the contribution of each atom. It is mainly affected by the contribution of the atom of reference whence one approximates the other atoms by a constant term. The total energy can then be written as

$$E_{tot} = \sum_i F_i(\rho_{h,i}) + \frac{1}{2}\sum_i\sum_{j(\ne i)} \rho_{ij}(R_{ij}).$$

In this equation $F(\rho_{h,i})$ stands for the energy due to the background electronic density $\rho_{h,i}$ at atom $i$. The second term represents the Coulombic repulsion between the cores.

The electronic density $\rho_{h,i}$ is computed from the atomic densities $\rho_j^a(R_{ij})$ as follows:

$$\rho_{h,i}=\sum_{j(\ne i)}\rho_j^a(R_{ij})$$

In advance of simple pair potentials this approach allows for many body interactions.