Ab initio asymptotic-expansion coefficients for pair energies in MP2 perturbation theory for atoms

Author： Jankowski Karol SŁupski Romuald Flores Jesus R.

ISSN： 1362-3028

Source： Molecular Physics, Vol.104, Iss.13-14, 2006-07, pp. : 2213-2223

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Abstract

The leading asymptotic expansion (AE) coefficients for two partial-wave (PW) expansions in powers of ( l +1/2) −1 are derived for the second-order symmetry-adapted pair (SAP) energies defining the second-order Møller–Plesset (MP2) correlation energies for closed-shell N -electron atoms. In the main expansion, the PW increments (PW/m) are directly defined by the pair of angular momenta of the orbitals used in their computation. In the auxiliary expansion the PW increments (PW/a) are defined by the order, l , of the Legendre polynomial P l (cos ϑ 12 ) in the expansion of the pair function. Our approach differs in several respects from that put forward a decade ago by Kutzelnigg and Morgan, who derived the leading AE coefficients in the PW/a expansion for all states of He-like ions within the framework of the 1/ Z expansion perturbation theory. However, we use their results concerning many technical details. It is shown that the expressions for the AE coefficients of the main expansion can be obtained from those for the He-like ions if some terms are multiplied by simple rational factors and the radial integrals are expressed in terms of Hartree–Fock orbitals defining the pair instead of hydrogen-like wave functions. To obtain the formulae for the AE coefficients for the main expansion, we have derived expressions relating the PW/m and PW/a energy increments. The AE coefficients for the main expansion are calculated for the Ne atom and compared with their counterparts determined from computed MP2 energy increments. Very close agreement is found.