Embedded atom model

In computational chemistry and computational physics, the embedded atom model, embedded-atom method or EAM, is an approximation describing the energy between atoms and is a type of interatomic potential. 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,^[1] the latter functions represent the electron density. The 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.^[2] Embedded-atom methods are widely used in molecular dynamics simulations.

In a simulation, the potential energy of an atom, i {\displaystyle i} , is given by^[3]

E i = F α ( ∑ j ≠ i ρ β ( r i j ) ) + 1 2 ∑ j ≠ i ϕ α β ( r i j ) {\displaystyle E_{i}=F_{\alpha }\left(\sum _{j\neq i}\rho _{\beta }(r_{ij})\right)+{\frac {1}{2}}\sum _{j\neq i}\phi _{\alpha \beta }(r_{ij})} ,

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

• Interatomic potential
• Lennard-Jones potential
• Bond order potential
• Force field (chemistry)