Embedded atom model
Encyclopedia
In computational chemistry
Computational chemistry
Computational chemistry is a branch of chemistry that uses principles of computer science to assist in solving chemical problems. It uses the results of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids...

 and computational physics
Computational physics
Computational physics is the study and implementation of numerical algorithms to solve problems in physics for which a quantitative theory already exists...

, the embedded atom model, embedded-atom method 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 represent the electron density. EAM is related to the second moment approximation to tight binding
Tight binding (physics)
In solid-state physics, the tight binding model is an approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site. The method is closely related to the LCAO method used...

 theory, also known as the Finnis-Sinclair model. These models are particularly appropriate for metallic systems. Embedded-atom methods are widely used in molecular dynamics
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...

simulations.

Model simulation

In a simulation, the potential energy of an atom, , is given by
,
where is the distance between atoms and , is a pair-wise potential function, is the contribution to the electron charge density from atom of type at the location of atom , and is an embedding function that represents the energy required to place atom of type 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.
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