Reaching Full Correlation through Nonorthogonal Configuration Interaction: A Second-Order Perturbative Approach

Nonorthogonal multireference methods can predict statically correlated adiabatic energies while providing chemical insight through the combination of diabatic reference states. However, reaching quantitative accuracy using nonorthogonal multireference expansions remains a significant challenge. In this work, we present the first rigorous perturbative correction to nonorthogonal configuration interaction, allowing the remaining dynamic correlation to be reliably computed. Our second-order "NOCI-PT2" theory exploits a zeroth-order generalized Fock Hamiltonian and builds the first-order interacting space using single and double excitations from each reference determinant. This approach therefore defines the rigorous nonorthogonal extension to conventional multireference perturbation theories. We find that NOCI-PT2 can quantitatively predict multireference potential energy surfaces and provides state-specific ground and excited states for adiabatic avoided crossings. Furthermore, we introduce an explicit imaginary-shift formalism requiring shift values that are an order of magnitude smaller than those used in conventional multireference perturbation theories.