The standard Pauli Hamiltonian is highly singular for Coulomb potentials near the nuclei of the atoms. It is shown that the theory of effective Hamiltonians allows the determination of Pauli-like Hamiltonians that are regular enough to be used in variational calculations. A numerical illustration is given for hydrogenic atoms with atomic number varying from Z = 1 to Z = 86. These calculations yield relativistic correction potentials which are used for studying the series of neutral rare gas atoms. Our approach opens the way for accurate two-component calculations for molecules.
Articles you may be interested inNumerical application of the coupled cluster theory with localized orbitals to polymers. IV. Band structure corrections in model systems and polyacetylene Valence effective Hamiltonian technique for nitrogen containing polymers: Electronic structure of polypyrrole, pyrolized polyacrylonitrile, paracyanogen, polymethineimine, and derivativesThe recently proposed ab initio effective Hamiltonian technique is extended to polymer calculations and applied to various conformations of polyacetylene (all-trans, cis-transoid, and trans-cisoid) and polydiacetylene (acetylenic and butatrienic backbones). Band structures, density of states (DOS), and XPS theoretical spectra are presented. Comparison of the band structures and DOS with those obtained by ab initio SCF (self-consistent-field) Hartree---Fock calculations of double zeta quality is excellent. The XPS theoretical spectrum for all-trans polyacetylene is in good agreement with experiment. In polyacetylene, it is found that the 1T bands are quite similar for all three backbone conformations, though the a bands differ significantly. For polydiacetylene, low ionization potentials are predicted-a few tenths of an eV larger than polyacetylene for the acetylenic backbone and a few tenths of an eV smaller than polyacetylene for the butatrienic backbone.
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