A Partitioned Correlation Function Interaction approach for describing electron correlation in atoms

The traditional multiconfiguration Hartree–Fock (MCHF) and configuration interaction (CI)methods are based on a single orthonormal orbital basis. For atoms with many closed coreshells, or complicated shell structures, a large orbital basis is needed to saturate the differentelectron correlation effects such as valence, core–valence and correlation within the coreshells. The large orbital basis leads to massive configuration state function (CSF) expansionsthat are difficult to handle, even on large computer systems. We show that it is possible to relaxthe orthonormality restriction on the orbital basis and break down the originally very largecalculations into a series of smaller calculations that can be run in parallel. Each calculationdetermines a partitioned correlation function (PCF) that accounts for a specific correlationeffect. The PCFs are built on optimally localized orbital sets and are added to a zero-ordermultireference (MR) function to form a total wave function. The expansion coefficients of thePCFs are determined from a low dimensional generalized eigenvalue problem. The interactionand overlap matrices are computed using a biorthonormal transformation technique (Verdeboutet al 2010 J. Phys. B: At. Mol. Phys. 43 074017). The new method, called partitionedcorrelation function interaction (PCFI), converges rapidly with respect to the orbital basis andgives total energies that are lower than the ones from ordinary MCHF and CI calculations. ThePCFI method is also very flexible when it comes to targeting different electron correlationeffects. Focusing our attention on neutral lithium, we show that by dedicating a PCF to thesingle excitations from the core, spin- and orbital-polarization effects can be captured veryefficiently, leading to highly improved convergence patterns for hyperfine parameterscompared with MCHF calculations based on a single orthogonal radial orbital basis. Bycollecting separately optimized PCFs to correct the MR function, the variational degrees offreedom in the relative mixing coefficients of the CSFs building the PCFs are inhibited. Theconstraints on the mixing coefficients lead to small off-sets in computed properties such ashyperfine structure, isotope shift and transition rates, with respect to the correct values. By(partially) deconstraining the mixing coefficients one converges to the correct limits and keepsthe tremendous advantage of improved convergence rates that comes from the use of severalorbital sets. Reducing ultimately each PCF to a single CSF with its own orbital basis leads to anon-orthogonal CI approach. Various perspectives of the new method are given