Third-Order Perturbation Theory Made Regular: A Noniterative Correction to the Size-Consistent Second-Order Brillouin–Wigner Perturbation Theory

While second- and third-order Møller-Plesset perturbation theories are a useful description of weak electron correlations in molecules, they fail catastrophically in the presence of strong correlations. A promising recent alternative to MP2 is the size-consistent second-order Brillouin-Wigner perturbation theory, BWs2, which is both regular and size-consistent. Here we develop and assess a noniterative third-order correction to BWs2, called BWs2.5. This method has identical computational costs to MP3 and is both regular and size-consistent. For the model problem of two electrons in two orbitals, it removes the leading error of BWs2 if 50% of the third-order contribution is included. BWs2.5 is stable across a variety of tests of bond breaking using spin-restricted orbitals, with dissociation limits above the spin-polarized solution as needed for size consistency. Numerical tests on a variety of chemical energy differences establish that BWs2.5 is notably more accurate than BWs2.