Fourth‐order constant denominator perturbation theory

A constant denominator perturbation theory based on a zeroth‐order Hamiltonian characterized by degenerate subsets of orbitals is developed to fourth order. This formulation allows a decoupling of the numerators of the perturbation sequence, allowing for a much more rapid evaluation of the resulting sums. Although the theory is general, a constant denominator is chosen as a scaled difference between the average occupied and average virtual orbital energies. The correction for this choice is folded back into the perturbation. The scale can be chosen such that the first‐order wave‐function yields the lowest possible variational bound, or it can be chosen based upon the sequence of energy terms and the size of the wave function corrections. Results are presented within the localized bond model utilizing both the Pariser‐Parr‐Pople and CNDO model Hamiltonians. When the scale is chosen variational the second‐order theory yields a useful bound, usually containing most of the basis set correlation. The third order appears as a scaled Langhoff‐Davidson correction. The fourth‐order theory displays remarkable stability, even in those cases in which Nesbet‐Epstein partitioning seems poorly converged and Moller‐Plesset theory uncertain. Other possible scalings are introduced and discussed, but the utility of these must await the more accurate predictions of fifth order for comparison.