Repartitioning the Hamiltonian in Many-Body Second-Order Brillouin-Wigner Perturbation Theory: Uncovering New Size-Consistent Models.

Second-order Møller-Plesset perturbation theory is well-known as a computationally inexpensive approach to the elec- tron correlation problem that is size-consistent, but fails to be regular. On the other hand, the less well-known many- body version of Brillouin-Wigner (BW) perturbation theory has the reverse properties: it is regular but fails to be size-consistent when used with the standard MP partitioning. For this reason it is not widely used. In this work, we analyze the ways in which it is possible to use alternative non-MP partitions of the Hamiltonian to yield variants of BW2 that are size-consistent as well as regular. We show that there is a vast space of such BW2 theories, and also show that it is possible to define a repartitioned BW2 theory from the ground state density alone, which regenerates the exact correlation energy. We also provide a general recipe for deriving regular, size-consistent and size-extensive partitions from physically meaningful components and we apply the result to small model systems. The scope of these results appears to further set the stage for a revival of BW2 in quantum chemistry.