Construction of Fermi Potentials from Electronic Wave Functions.

The Fermi potential, v(r), is the nonclassical part of the multiplicative effective potential appearing in the one-particle Schrödinger-type equation for the square root of the electron density. The usual way of constructing v(r) by inverting that equation produces unsatisfactory results when applied to electron densities expanded in Gaussian basis sets. We suggest a different method that is based on an explicit formula for v(r) in terms of the interacting one- and two-electron reduced density matrices of the system. This method is exact in the basis-set limit and yields accurate approximations to the basis-set-limit v(r) when applied to reduced density matrices represented in terms of finite basis sets. Illustrative applications involve atomic and molecular wave functions generated at various levels of ab initio theory. It is also shown how to construct the Pauli and exchange-correlation potentials of any system starting with only v(r).