Abstract
A direct method (D-Delta-MBPT(2)) to calculate second-order ionization potentials (IPs), electron affinities (EAs), and excitation energies is developed. The Delta-MBPT(2) method is defined as the correlated extension of the Delta-HF method. Energy differences are obtained by integrating the energy derivative with respect to occupation numbers over the appropriate parameter range. This is made possible by writing the second-order energy as a function of the occupation numbers. Relaxation effects are fully included at the SCF level. This is in contrast to linear response theory, which makes the D-Delta-MBPT(2) applicable not only to single excited but also higher excited states. We show the relationship of the D-Delta-MBPT(2) method for IPs and EAs to a second-order approximation of the effective Fock-space coupled-cluster Hamiltonian and a second-order electron propagator method. We also discuss the connection between the D-Delta-MBPT(2) method for excitation energies and the CIS-MP2 method. Finally, as a proof of principle, we apply our method to calculate ionization potentials and excitation energies of some small molecules. For IPs, the Delta-MBPT(2) results compare well to the second-order solution of the Dyson equation. For excitation energies, the deviation from EOM-CCSD increases when correlation becomes more important. When using the numerical integration technique, we encounter difficulties that prevented us from reaching the Delta-MBPT(2) values. Most importantly, relaxation beyond the Hartree Fock level is significant and needs to be included in future research.