Convergence behavior of the M�ller-Plesset perturbation series: Use of Feenberg scaling for the exclusion of backdoor intruder states

Abstract

The convergence behavior of the Moller–Plesset (MP) perturbation series is investigated utilizing MP correlation energies up to order 65 calculated at the full CI (FCI) level. Fast or slow convergence, initial oscillations, or divergence of the MPn series depend on the electronic system investigated and the basis set used for the FCI calculation. Initial oscillations in the MPn series are observed for systems with electron clustering due to the fact that MP theory exaggerates electron-correlation effects at even orders and corrects this at odd orders. In such cases, it is important that the s, p basis is first saturated before diffuse functions are added. With a VDZ+diff basis, too much weight is given to high-order correlation effects described by pentuple and higher excitations, which leads to the formation of artificial intruder states and to the divergence of the MPn series. This can be corrected by extending to VQZ or VPZ basis sets before one adds diffuse functions. Alternatively, one can use m-order Feenberg scaling to exclude backdoor intruder states from the convergence region of the MPn series. For all cases considered, divergence of the MPn series caused by unbalanced basis sets including diffuse functions can be suppressed by Feenberg scaling. Also, initial oscillations of the MPn series can be dampened and convergence acceleration of the MPn series achieved if the appropriate order of Feenberg scaling is determined for the problem in question. The relationship between electronic structure, basis set, and convergence of the MPn series is discussed. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 306–330, 2000