Although the various glue-type potentials attribute different aspect of the physics to the N-body and pair­wise terms in the potential, if one has complete free­dom in choosing the functions for V(r), F(p), and f, then it is possible to move energy between the two terms. Johnson and Oh noted that the EAM potential

U = X Vj(rj)+f [ X fj(r’j).

is invariant under a transformation

ъ [X f (rj) ! F [X f (rj) + A X f (rj)

For an alloy,45

1 fb (r) f a (r)

Vab(r) = ‘ TVa(r) + Vb(r)

Thus, it is possible to choose a ‘gauge’ for the poten­tial, for example, by setting F'(p0) = 0 for some ref­erence density p. The advantage of the gauge transformation is that it simplifies fitting the potential. It eliminates terms in F’(p0) for pressure and elastic moduli at the equilibrium volume: these terms are nonlinear in the fitting parameters. Thus, the fitting process can be done by linear algebra.

The downside of the gauge transformation is that it destroys the physical intuition behind the form of the many-body term. Moreover, the gauge is deter­mined by a particular reference configuration, a sim­ple concept for elements, but one which does not transfer readily to alloys.

The FS potentials do not have this freedom, because the function F is predefined as a square root. However, they introduced the ‘effective pair potential’

Veff(rj) = V(r) — f (r)/v’p0

where p0 is a reference configuration (typically the equilibrium crystal structure). Many of the equilibrium properties which they used for fitting depend only on this quantity.

In addition to gauge transformation, MD depends only on the derivative of the total energy. Energy can be partitioned between atoms in any way one likes, without changing the physical results. However, on-atom prop­erties, such as the magnetic moment in magnetic
potentials, typically do depend on the partition of energy between atoms. Such quantities do not have the gauge-invariance property.