Calculation and interpretation of total energies in electron propagator theory

Abstract

Ground state total energies and one-electron density matrices can be calculated from contour integrals over the electron propagator. Ionization energies and corresponding Feynman–Dyson amplitudes are related simply to ground state properties. Total energy formulas derived from electron propagator theory are transparent generalizations of Hartree–Fock expressions. Computationally useful methods for evaluating integrals over the Coulson contour are derived. An approximate integration scheme is introduced and compared to exact results. Several decouplings of the electron propagator that have been employed frequently for electron binding energies are used to calculate size-extensive total energies. These methods do not yield satisfactory correlation energies, but they provide a reasonable account of bending potentials for water, ammonia, and methane. Total energy contributions derived from propagator poles and residues are calculated as a function of bond angle distortions. These results are compared with simple molecular orbital notions that seek to explain the instability of D∞h water, D3h ammonia, and D4h methane with respect to the equilibrium geometries of these molecules.