Excited states in Hartree–Fock theory

Abstract

Hartree Fock theory is extended to excited states of interacting N-particle Fermionic systems. In contrast to the orbital-by-orbital and state-by-state approach followed by previous attempts to such an extension, the present methodology provides, in principle, a systematic determination of all excited states in the Hartree Fock treatment of electronic many-particle states. The excited states are defined as the eigenstates of the Nth order density matrix for a Slater determinant of order KN that represents the ground state of a non-interacting collection of K replicas of an interacting N-particle system. The equations determining the KN orbitals entangled in the collection ground state increase linearly with K, while they give rise to CNKN=KNN excited states of all orders, 1 to N. The entire spectrum is populated as K→∞. The method goes beyond Koopman’s theorem allowing the incorporation into the ground state of the effects of particle excitations to states of higher energy.