  We present an explicitly correlated formalism for the second-order
single-particle Green's function method (GF2-F12) that does not assume the
popular diagonal approximation, and describes the energy dependence of the
explicitly correlated terms. For small and medium organic molecules the basis
set errors of ionization potentials of GF2-F12 are radically improved relative
to GF2: the performance of GF2-F12/aug- cc-pVDZ is better than that of
GF2/aug-cc-pVQZ, at a significantly lower cost.
