First-Order Symmetry-Adapted Perturbation Theory with Double Exchange for Multireference Systems

We extend first-order multiconfigurational symmetry-adapted perturbation theory, SAPT(MC), [Hapka, M. J. Chem. Theory Comput. 2021, 17, 5538–5555], to account for double-exchange effects, where up to two electron pairs are exchanged between interacting monomers. To achieve this, we derive density-matrix-based expressions for the first-order exchange energy to arbitrary orders in the overlap expansion. As a numerical demonstration, we apply the double-exchange approximation to strongly orthogonal geminal wave functions. Additionally, we propose an approximate method for evaluating double-exchange energy with complete active space (CAS) wave functions of the valence type, i.e., with n active electrons distributed over n orbitals. We analyze the performance of these methods on model dimers in both ground and excited states.