Natural orbital function energetics

The calculation of electronic spectra of lanthanide or actinide compounds poses a considerable challenge to relativistic electronic structure methods. Apart from the mandatory relativistic Hamiltonians, the small energetic separation of valence / and d orbitals in lanthanide and actinide atoms gives rise to a prominent multi-reference nature of the N-electron wave function. Even the most accurate methods of calculating multiple spin-orbit-coupled states such as MRCl+SO and CASPT2+SO suffer from the limited number of configura-... 

All parameters are either of a one-center nature or involve two-center integrals that fall off rapidly with distance (i.e., two-center Coulomb integrals are not parametrized). The reference ab initio data set was defined by STO-3G calculations, which quantitatively reproduce Mulliken charges, intemuclear distances, and relative energies derived from pure Slater orbital calculations. The error function minimized includes intemuclear distances, Mulliken charges, and energetics. Four parameters were defined for each atom, except for second major row atoms with d orbitals, which have a fifth parameter. Their effect on the integrals is as follows ... 

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