Single-Particle Green Function Approach and Correlated Atomic or Molecular Orbitals

In this paper, we propose a generic and systematic approach for study of the electronic structure for atoms or molecules. In particular, we address the issue of single particle states, or orbitals, which should be one of the most important aspects of a quantum many-body theory. We argue that the single-particle $\it{Green}$ function provides a most general scheme for generating these single particle states or orbitals. We call them the $\it{correlated}$ atomic or molecular orbitals to make a distinction from those determined from $\it{Hartree-Fock}$ equation. We present the calculation of the single particle properties (i.e., the electron affinities $(EA's)$ and ionization potentials $(IP's)$) for the $H_{2}O$ molecule using the correlated molecular orbitals in the context of quantum chemistry with a second-order self energy. We also calculate the total ground state energy with a single $Slater$ wavefunction determined only from the hole states. Comparisons are made with available experimental data as well as with those from the $\it{Hartree-Fock}$ or density functional theory $(DFT)$ calculations. We conclude that the correlated atomic or molecular orbital approach provides a strictest and most powerful method for studying the single-particle properties of atoms or molecules. It also gives a better total energy than do the $\it{Hartree-Fock}$ and $\it{DFT}$ even at the single $\it{Slater}$ determinant level. It promises that a correlation theory based on the correlated atomic or molecular orbitals will become an approach which possesses the advantages and also overcomes their shortcomings of current quantum chemistry methods based on either the conventional quantum many-body theory or the $DFT$.