  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 generalised 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 theory. 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 theory.
