On the convergence of Z-averaged perturbation theory

Very high order open-shell Z-averaged perturbation theory (ZAPT) energies, equilibrium bond lengths, and harmonic vibrational frequencies have been computed for a suite of small molecules using a determinantal algorithm. The convergence of ZAPTn energies is compared to alternative Moller-Plesset (MP) perturbation theories built on restricted open-shell Hartree-Fock (ROMP, RMP, OPT1, and OPT2) and unrestricted Hartree-Fock (UMP) reference wave functions for NH(2) at three N-H bond lengths and for CN. The ZAPTn energy series closely parallel those of RMPn and ROMPn theories for these systems. Further, we examine the convergence of ZAPTn energies, equilibrium bond lengths (r(e)), and harmonic vibrational frequencies (omega(e)) for X (2)Sigma(g)(+) CN, X (4)Sigma(g) (-) C(2)(+), and b (2)Delta(g) C(2)(+), tracking oscillations in the energy series for the challenging latter system to order 1000. Finally, we obtain r(e) and omega(e) values from explicit ZAPT2 and ZAPT4 computations with a triple-zeta plus double polarization basis set. The ensuing results are very close to those from second- and fourth-order RMP and ROMP for the NO and CN molecules but are significantly closer to experiment in the case of (3)Sigma(g)(-) O(2). The ZAPTn series exhibit all the fascinating diversity of behavior previously observed for closed-shell MPn theory. Particularly encouraging is the ability of Feenberg transformations to remove erratic, strongly oscillatory, and divergent behavior that may occur in ZAPTn series and provide systematic improvements toward the full configuration interaction limit. In light of the appealing mathematical properties of ZAPT and similarity of results to those from the oft-applied RMP theory, coupled with the reductions in computational cost inherent in the ZAPT method relative to theories requiring different orbitals for different spins, we recommend low-order ZAPT for general applications to open-shell systems, particularly in cases where spin contamination is of concern.