Ab initio regularization in many-body perturbation theory: A size-consistent Brillouin-Wigner approach

Wave function theory is widely used to systematically improve the accuracy of quantum chemistry calculations by including electron correlation effects from first principles. However, the simplest post-Hartree-Fock approach, second-order Møller-Plesset perturbation theory (MP2), is divergent in small-gap systems. Cases of near or exact degeneracy in MP2 lead to large errors for dispersion-bound noncovalent complexes, dative bonding in transition metal systems, and for thermochemistry in general. Alternatively, Brillouin-Wigner perturbation theory can offer strictly regular correlation energies, but it has not been widely adopted for single-reference post-Hartree-Fock calculations because it is not size-extensive. We present a tensor formulation of second-order Brillouin-Wigner perturbation theory that is size-extensive, size-consistent, and invariant to orbital rotations in occupied or virtual subspaces. Our chosen ansatz for the regularizer tensor (henceforth called the second-order size-consistent Brillouin-Wigner functional, or scBW2) augments the orbital-energy gap by a factor that is related to the correlation contribution to the ionization potential. We show that the scBW2 regularizer can be applied in its native form (i.e., without parameters) to dissociate H₂ in a minimal basis set, achieving the exact dissociation limit with spin-restricted or spin-polarized orbitals. We also find that scBW2 can faithfully dissociate the C—C σ bond in ethane to an asymptotic limit that is invariant to the spin-polarization of the reference orbitals, and that scBW2 produces smooth dissociation curves for multiply-bonded atoms. Finally, we benchmark the performance of scBW2 on datasets encompassing noncovalent interaction energies, transition metal reaction energies, and broad thermochemical properties. Overall, our results suggest that the parameter-free scBW2 outperforms MP2 and performs similarly to empirically parameterized orbital-energy-gap-dependent Δ-regularizers (such as κ-MP2) in most cases, and even approaches the accuracy of coupled-cluster with single and double substitutions (CCSD) for thermochemical properties. Owing to its explicit amplitude-dependent regularization, scBW2 appears to be more transferable than Δ-regularizers for a wide variety of problems of chemical interest.