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Molecular Physics

An International Journal at the Interface Between Chemistry and Physics
Volume 111, 2013 - Issue 9-11: Special Issue: In Honour of Trygve Helgaker
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Invited Article

The Møller–Plesset perturbation revisited: origin of high-order divergences

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Pages 1092-1099
Received 23 Jan 2013
Accepted 13 Mar 2013
Accepted author version posted online: 15 Apr 2013
Published online: 24 Apr 2013
 

Contrarily to what happens with the Epstein–Nesbet (EN) zeroth-order Hamiltonian, the Møller–Plesset (MP) perturbation operator has diagonal matrix elements, the expression of which is recalled. It is a balance between hole–hole and particle–particle repulsions on one hand and of hole–particle attractions on the other hand. For the double excitations, which dominate the correlation effects, the attractive terms prevail and the second-order MP energy is underestimated, at least for atoms of the first rows of the periodic table. It will be shown that when the perturbation expansion reaches multiple excitations, the diagonal terms of the MP perturbation operator may become larger than the zeroth-order MP excitation energy and creates an oscillating divergence of the series. Several situations of this type will be presented. This divergence is linked to the non-additivity of excitation energies, while this additivity is an underlying assumption for the linked cluster theorem and the coupled cluster method. This analysis may also explain why for heavy atoms the second-order MP energies overshoot the exact correlation energies.

Acknowledgement

The Laboratoire de Chimie et Physique Quantiques in UMR 5626 of the CNRS. C.A. has been financed by the Italian MILUR through its PRIN 2009 funds.

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