The potential energy curve for the X1Σg+ state of Mg2 calculated with many-body perturbation theory

Abstract

The ground state potential curve for the van der waals molecule, Mg₂, is calculated by adding to the Hartree–Fock potential curve those many‐body perturbation theory (MBPT) correlation corrections which arise from double excitation type diagrams through fourth order (DE–MBPT). The fourth‐order binding energy is shown to be unaffected by higher order double excitation diagrams. The DE–MBPT potential curve is compared to the fourth‐order Rayleigh–Schrödinger perturbation theory (RSPT) approximation of the double excitation configuration interaction (DECI) potential curve. The DE–MBPT curve is found to be in much better agreement with experiment. Since the only difference between the MBPT equation and the RSPT equation is the size‐inconsistent E₂Δ renormalization term contained in the double CI and its fourth‐order RSPT approximation, the importance of having a size‐consistent model for molecular binding is demonstrated. The inclusion of additional correlation effects, due to the fourth‐order EPV rearrangement diagrams, are found to further improve the computed binding energy. Unlike the terms in the DE–MBPT method, these EPV terms are not invariant to a unitary transformation of degenerate orbitals, and this lack of invariance causes an incorrect dissociation limit. A breakdown of the correlation energy into pair contributions is made and discussed with particular emphasis on the origin of the molecular binding energy.