New formula to estimate the ground state energy, E

Abstract

The one‐electron reduced local energy function, E_L(1), is introduced which has the properties 〈E_L〉=〈H〉, and 〈E²_L〉 ⩽〈H²〉. It is suggested that the accuracy of E_L reflects the local accuracy of an approximate wavefunction. From the properties of E_L a modified form of Weinstein’s formula, E_w′, is defined which is bounded as follows: E_w⩽E_w′⩽〈H〉, where E_w is Weinstein’s lower bound formula for the ground state energy, E₀. The estimate to E₀ provided by E_w′ 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.