A wavefunction approach to equations of motion—Green's function methods

Abstract

A derivation is presented of the equations of motion—Green's function method which is formulated entirely within a wavefunction representation. Such a pedagogical approach simplifies, clarifies, and organizes many aspects of the theory introduced by propagator techniques, diagram summations, hierarchy truncations, equations of motion methods, etc. The theory indicates relationships with standard configuration interaction approaches and generalized Koopmans' methods. The derivation emphasizes the purely linear matrix eigenvalue nature of the problem and the possibility for wholly nonperturbative approaches involving “configurational selection” methods analogous to those employed in configuration interaction computations. The theory is analyzed for the two limiting cases where the exact ground state wavefunction is known and where the exact excitation operator is known. In the latter case the exact excitation energy is obtained, while the former may generate only an approximation. For finite space calculations, we show that both the complete configuration interaction calculation and the complete equations of motion results within the space are the same. The theory illuminates various features of previous calculations, and it is applied in separate papers to calculations of excitation energies and ionization potentials in the nitrogen molecule.