Quasi‐particle equation from the configuration‐interaction ( CI ) wave‐function method

Abstract The Green‐function method is a well‐known way to reduce the quantum mechanical problem of n electrons moving in the field of clamped nuclei to the problem of solving a one‐electron Schrödinger equation (the quasi‐particle equation) involving a pseudopotential (the self‐energy). This method is widely used in solid‐state, low‐energy electron‐molecule scattering, ionization, and electron attachment theory, and much work has focused on finding accurate self‐energy approximations. Unfortunately, the operator nature of the fundamental quantity (Green function) in the usual quasi‐particle equation formalism significantly complicates the derivation of self‐energy approximations, in turn significantly complicating applications to inelastic scattering and multiconfigurational bound‐state problems. For these problems or wherever the operator approach becomes inconvenient, we propose an alternative quasi‐particle equation derived wholely within a configuration interaction wave‐function formalism and intended to describe the same phenomenology as does the Green function quasi‐particle equation. Our derivation refers specifically to electron removal but is readily generalized to electron attachment and scattering. Although the Green function and wave‐function quasi‐particle equations are different, we emphasize the parallels by rederiving both equations within the equations‐of‐motion formalism and then producing a wave‐function analog of the Green function two‐particle‐hole Tamm–Dancoff approximation.