Direct ΔMBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers

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 equation of motion coupled cluster singles and doubles 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. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4790626]