A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals

► A computationally practical antisymmetric product of nonorthogonal geminals wavefunction is proposed. ► A generalized Richardson eigenstate is a size-consistent, computationally efficient, model for strong correlation. ► Correlated wavefunctions for open shells based on geminals are proposed. ► The projected Schrödinger equation is used to determine the parameters in a nonorthogonal geminal product wavefunction. ► The APr2G wavefunction (antisymmetric product of rank two geminals) is proposed.