Explicitly correlated Green's function methods for calculating electron binding energies

Single-particle Green's function method is a direct way of calculating electron binding energy, which relies on expanding the Fock subspace in a finite single-particle basis. However, these methods suffer from slow asymptotic decay of basis set incompleteness error. An energy-dependent explicitly correlated (F12) formalism for Green's function is presented that achieves faster convergence to the basis set limit. The renormalized second-order Green's function method (NR2-F12) scales as iterative N^5 where N is the system size. These methods are tested on a set of small (O21) and medium-sized (OAM24) organic molecules. The basis set incompleteness error in ionization potential (IP) obtained from the NR2-F12 method and aug-cc-pVDZ basis for OAM24 is 0.033 eV compared to 0.067 eV for NR2 method and aug-cc-pVQZ basis. Hence, accurate electron binding energies can be calculated at a lower cost using NR2-F12 method. For aug-cc-pVDZ basis, the electron binding energies obtained from NR2-F12 are comparable to EOM-IP-CCSD method that uses a CCSD reference and scales as iterative N^6.