Multireference perturbation theory with nonorthogonal determinants

Abstract

We introduce NOCI-RSPT, a framework for constructing perturb-then-diagonalize multireference perturbation theories for model spaces defined by nonorthogonal determinants. NOCI-RSPT realizes order-by-order size consistency by orthogonalizing the effective Hamiltonian before perturbatively truncating it and removes problematic internal excitations through model-space projection. The resulting second- and third-order theories, NOCI-RS2 and NOCI-RS3, recover MP2 and MP3 in the single-reference limit and exhibit the same respective cost scaling at fixed model-space size. Calculations on assemblies of multireference $\mathrm{H}_2$ fragments demonstrate size consistency, while calculations of the low-energy states of $\mathrm{H}_2$ along its dissociation curve demonstrate improved numerical stability and characterize the influence of intruder states. The latter calculations demonstrate the exceptional accuracy achieved by NOCI-RS3 and illustrate how model-space expansion and amplitude regularization can mitigate the effects of large perturbative corrections. Altogether, NOCI-RSPT provides a systematic route to low-scaling multireference perturbation theories built from single-reference methods.