Fifth-order many-body perturbation theory for molecular correlation energies

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Abstract
Full fifth‐order many‐body perturbation theory (MBPT) correlation energy contributions have been calculated for the molecules: BH, CH2 , H2 O, HF, SiH2 , CO, C2 H2, and O3 at the double zeta plus polarization level. The connected T4 component of the fifth‐order energy has been computed with only an N6 basis set dependence due to a new factorization introduced for the ‘‘connected’’ quadruple T4 diagrams. For the systems where MBPT is converging smoothly the fifth‐order recovers 30%–50% of the difference between MBPT(4) and the full configuration interaction (FCI) values. The E5 based [2,1] Padé approximants generally provide a better approximation to the FCI energy. The absolute values of E5 corrections vary from 1–2 mhartrees for the hydrides at the equilibrium geometry up to 22 mhartrees for the O3 molecule, which is poorly described by a single self‐consistend‐field reference function.