Towards benchmark second-order correlation energies for large atoms. II. Angular extrapolation problems

Abstract

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.