Embedded atom model

In computational chemistry, the embedded atom model, or EAM is an approximation describing the energy between two atoms. The energy is a function of a sum of functions of the separation between an atom and its neighbors. In the original model, by Murray Daw and Mike Baskes, the latter functions represented the electron density. EAM is related to the second moment approximation to tight binding theory, also known as the Finnis-Sinclair model. These models are particularly appropriate for metallic systems.

In such a simulation, the energy due to an atom, i, is given by

${\displaystyle E_{i}=F_{\alpha }\left(\sum _{i\neq j}\rho _{\alpha }(r_{ij})\right)+{\frac {1}{2}}\sum _{i\neq j}\phi _{\alpha \beta }(r_{ij})}$,

where ${\displaystyle r_{ij}}$ is the distance between atoms ${\displaystyle i}$ and ${\displaystyle j}$, ${\displaystyle \phi _{\alpha \beta }}$ is a pair-wise potential function, ${\displaystyle \rho _{\alpha }}$ is the contribution to the electron charge density from atom ${\displaystyle j}$ at the ___location of atom ${\displaystyle i}$, and ${\displaystyle F}$ is an embedding function that represents the energy required to place atom ${\displaystyle i}$ of type ${\displaystyle \alpha }$ 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

• Lennard-Jones potential

References

• Daw, M.S. and Baskes, MI. "Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals". Physical Review B 29:12, pp. 6443–6453, 1984, APS.

External links

• http://nickwilson.co.uk/research/bham.ac.uk/PhD/node17.html
• LAMMPS Pair EAM