We have studied the use of the asymptotic expansions (AEs) for the angular momentum extrapolation (to l --> infinity) of atomic second-order Moller-Plesset (MP2) correlation energies of symmetry-adapted pairs (SAPs). The AEs have been defined in terms of partial wave (PW) increments to the SAP correlation energies obtained with the finite element MP2 method (FEM-MP2), as well as with the variational perturbation method in a Slater-type orbital basis. The method employed to obtain AEs from PW increments is general in the sense that it can be applied to methods other than MP2 and, if modified, to molecular systems. Optimal AEs have been determined for all types of SAPs possible in large atoms using very accurate FEM PW increments up to lmax = 45. The impact of the error of the PW increments on the coefficients of the AEs is computed and taken into account in our procedure. The first AE coefficient is determined to a very high accuracy, whereas the second involves much larger errors. The optimum l values (lopt) for starting the extrapolation procedures are determined and their properties, interesting from the practical point of view, are discussed. It is found that the values of the first AE coefficients obey expressions of the type derived by Kutzelnigg and Morgan [J. Chem. Phys. 96, 4484 (1992); 97, 8821(E) (1992)] for He-type systems in the bare-nucleus case provided they are modified by fractional factors in the case of triplet and unnatural singlet SAPs. These expressions give extremely accurate values for the first AE coefficient both for the STO and the FEM Hartree-Fock orbitals. We have compared the performance of our angular momentum extrapolations with those of some of the principal expansion extrapolations performed with correlation consistent basis sets employed in the literature and indicated the main sources of inaccuracy.

To provide very accurate reference results for the second-order Møller-Plesset (MP2) energy and its various components for Zn(2+), which plays for 3d-electron systems a similar role as Ne for smaller atoms and molecules, we have performed extensive calculation by two completely different implementations of the MP2 method: the finite element method (FEM) and the variation-perturbation (VP) method. The FEM and VP calculations yield partial wave contributions up to l(max)=45 and 12, respectively. Detailed comparison of all FEM and VP energy components for l(max)=12 has disclosed an extraordinary similarity, which justifies using the present results as benchmarks. The present correlation energies are compared with other works. The dependability of an earlier version of FEM, already applied to very large closed-shell atoms, is confirmed. It has been found that for larger atoms the accuracy of the analytical Hartree-Fock results has an impact on the accuracy of the MP2 energies greater than for smaller atoms. Fields of applications of the present results in studies of various electron correlation effects in 3d-electron atoms and molecules are indicated.

The leading asymptotic expansion (AE) coefficients for two partial-wave (PW) expansions in powers of ðl þ 1=2Þ À1 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 ðcos # 12 Þ 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.

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