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.