Direct calculation of energy differences, such as ionization potentials

Abstract

Indirect methods for the calculation of energy differences imply that two separate calculations of the involved states are performed first and then the difference is taken. In a ‘direct’ method the transition energy is calculated without an attempt to calculate either of the states between which transition takes place. The theory of direct calculations of energy differences is reviewed with emphasis on ionization potentials and special attention to the method of a common unitary transformation of two model states. Results for the ionization potentials of a few small molecules are presented. The elements of a more general theory are outlined in which the Liouvillean superoperator (and its resolvent) as well as the Fock space formulation of quantum chemistry (especially the concept of effective Hamiltonians in Fock space) play a key role.