Discontinuous approximate molecular electronic wave-functions

Following Kohn (reference 4), Schlosser and Marcus (reference 3), and Weare and Parr (reference 2), an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh–Ritz method in the replacement of the usual kinetic energy operators T?(μ) with operators T?′(μ) = T?(μ) + Î(μ), where Î(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the ?Ψ · ?Ψ way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of ?Ψ and the change of ?Ψ across surfaces of discontinuity.