New formula to estimate the ground state energy, E

The one-electron reduced local energy function, EL(1), is introduced which has the properties 〈EL〉=〈H〉, and 〈E2L〉 ⩽〈H2〉. It is suggested that the accuracy of EL reflects the local accuracy of an approximate wavefunction. From the properties of EL a modified form of Weinstein’s formula, Ew′, is defined which is bounded as follows: Ew⩽Ew′⩽〈H〉, where Ew is Weinstein’s lower bound formula for the ground state energy, E0. The estimate to E0 provided by Ew′ is not guaranteed as an upper or lower bound, but it provides a useful adjunct to 〈H〉 which does not require 〈H2〉. Applications to a variety of approximate wavefunctions for X 1Σ+g H2 and 1 1S He are presented.