Complete basis set correlation energies. III. The total correlation energy of the neon atom

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Abstract
Within the framework of many-body perturbation theory, the total correlation energy can be partitioned into: intraorbital pair energies, eii; interorbital pair energies, αβeij and ααeij; double-excitation pair-coupling terms eij,kl(D); and higher-excitation pair-coupling terms, eij,kl(S,T,Q,...). The asymptotic convergence of pair natural orbital expansions for each of these terms is determined for the model problem of n infinitely separated helium-like ions with infinite nuclear charge. For example, the asymptotic form of the basis set truncation error in an αβ-interorbital pair energy is LimitNij→∞Δαβeij =αβfij (𝒥μ=1Nij Cμij)2 ((−225/ 4608)) (Nij+δij)−1 , where Nij is the number of pair natural orbitals and Cμij is the coefficient of pair natural orbital configuration μij. Numerical studies of the neon atom verify that this model behavior applies to real many-electron systems. The pair-coupling terms beyond third-order contribute less than 1% of the total correlation energy in a variety of atoms and molecules and can therefore be neglected. As a practical test of the use of the asymptotic forms to extrapolate the remaining terms, a double zeta plus polarization set of pair natural orbitals was used. Extrapolation of each of the neon pair energies to the value for a complete basis set yields an independent electron pair approximation equal to −0.4233 hartree, which is 108.6% of the experimental correlation energy (−0.3896±0.001 hartree). Including the third-order MP-MBPT pair-coupling terms and extrapolating to a complete basis set gives a total correlation energy equal to −0.3904 hartree, which is 100.2±0.2% of the experimental value. A similar calculation on H2O gave equally good results (calc. −0.3706; expt. −0.370±0.003 hartree) indicating that this DZ+P CBS method is applicable to polyatomic potential energy surfaces.