University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Embeddedatom and related methods for metallic systems (I)
As we discussed above, pair potentials, even with an additional densitydependent term
cannot provide an adequate description of metallic systems.
An alternative simple but rather
realistic approach to the description of bonding in metallic systems is based on the
concept
of local density
that is considered as the key variable. This allows one to account for the
dependence of the strength of individual bonds on the local environment which is especially
important for simulation of surfaces and defects.
Many methods, that have been proposed since early 1980s, have different names (e.g.
embeddedatom method  EAM, effective medium theory, FinnisSinclair potential, the glue
model, corrected effective medium potential  CEM, etc.) and are based on different physical
arguments (e.g. tightbinding model, effectivemedium theory), but result in a similar
expression for the total energy of the system of N atoms:
(
)
∑
≠
+
=
i
j
ij
ij
i
i
i
)
(r
φ
2
1
ρ
F
E
Interpretation and functional form of F, f, and
φ
depend on a particular method. From the
point of view of effective medium theory or the embeddedatom method, the energy of the
atom
i
is determined by the local electron density at the position of the atom and the function
f describes the contribution to the electronic density at the site of the atom i from all atoms j.
The sum over function
f
is therefore a measure of
local electron density
ρ
i
.
The
embedding
energy F
is the energy associated with placing an atom in the electron environment described
by
ρ
.
The pairpotential term
φ
describes electrostatic contributions.
The general form of
the potential can be considered as a generalization of the basic idea of the Density Functional
Theory – the local electron density can be used to calculate the energy.
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 Fall '11
 Zhigilei
 Quantum Chemistry, Energy, Kinetic Energy, electron density, density functional theory, Leonid Zhigilei

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