In the density functional theory (DFT), the elec­tronic energy of a system can be written as a func­tional of its electron density:

U = F [p(r)]

The embedded atom model (EAM)7 postulates that in a metal, where electrostatic screening is good, one might approximate this nonlocal functional by a local function. And furthermore, that the change in energy due to adding a proton to the system could be treated by perturbation theory (i. e., no change in p). Hence, the energy associated with the hydrogen atom would depend only on the electron density that would exist at that point r in the absence of the hydrogen.

UH(r) = FH(p(r))

The idea can be extended further, where one con­siders the energy of any atom ‘embedded’ in the effective medium of all the others.8 Now, the energy of each (ith) atom in the system is written in the same form,

Ut = Fi (p(r))

To this is added the interionic potential energy, which in the presence of screening, they took as a short-ranged pairwise interaction. This gives an expression for the total energy of a metallic system:

Utot = Y< Fi(p(r,))+£ V(r, y)

iij

To make the model practicable, it is assumed that p can be evaluated as a sum of atomic densities f(r), that is, p(ri) = ^2j f(rij) and that F and V are unknown functions which could be fitted to empirical data. The ‘modified’ EAM incorporates screening of f and addi­tional contributions to p from many-body terms.