We explore the concept of seniority number (defined as the number of unpaired electrons in a determinant) when applied to the problem of electron correlation in atomic and molecular systems. Although seniority is a good quantum number only for certain model Hamiltonians (such as the pairing Hamiltonian), we show that it provides a useful partitioning of the electronic full configuration interaction (FCI) wave function into rapidly convergent Hilbert subspaces whose weight diminishes as its seniority number increases. The primary focus of this study is the adequate description of static correlation effects. The examples considered are the ground states of the helium, beryllium, and neon atoms, the symmetric dissociation of the N(2) and CO(2) molecules, as well as the symmetric dissociation of an H(8) hydrogen chain. It is found that the symmetry constraints that are normally placed on the spatial orbitals greatly affect the convergence rate of the FCI expansion. The energy relevance of the seniority zero sector (determinants with all paired electrons) increases dramatically if orbitals of broken spatial symmetry (as those commonly used for Hubbard Hamiltonian studies) are allowed in the wave function construction.

A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic minimal-basis-set orbitals that deviate as little as possible from free-atom SCF minimal-basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed "quasiatomic minimal-basis-sets" is independent of the calculational atomic orbital basis used. The resulting resolution of molecular orbitals in terms of quasiatomic minimal basis set orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimal-basis orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn-Sham density functional theory orbitals and is easily generalized to valence MCSCF orbitals.

An analytical expression is found for the accurate ab initiopotential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F2 are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5cm−1 over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30cm−1 of the experimental value of 12953±8cm−1. The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation,spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev.41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants. KeywordsAb initio calculations, Dissociation energies, Polynomials, Dissociation, Electron correlation calculations Disciplines Chemistry CommentsThe following article appeared in Journal of Chemical Physics 127 (2007) An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F 2 are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5 cm −1 over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30 cm −1 of the experimental value of 12 953± 8 cm −1 . The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis ͓Phys. Rev. 41, 721 ͑1932͔͒ of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.