Third-order size-consistent Brillouin-Wigner perturbation theory

<jats:p>Low order Rayleigh-Schrödinger (RS) perturbation theory with Møller-Plesset partitioning is size-consistent but not regular, and for this reason, the third order variant, MP3, is not commonly used in computational quantum chemistry. Recently, it has become clear how to modify Brillouin-Wigner perturbation theory at second order to be both size-consistent and regular, by using a non-Møller-Plesset partitioning to define BWs2. In this work, a solution is presented for the problem of defining an iterative third-order generalization, iBWs3, that is size-consistent, regular, and exact for the electron correlation of 2 electrons in 2 orbitals. iBWs3 is closely related to coupled cluster theory with doubles, with the same compute scaling. An implementation and a series of tests on restricted orbital dissociations and relative energies are reported.</jats:p>