A refined version of the ‘‘shape consistent’’ effective potential procedure of Christiansen, Lee, and Pitzer was used to compute averaged relativistic effective potentials (AREP) and spin–orbit operators for the elements Rb through Xe. Particular attention was given to the partitioning of the core and valence space and, where appropriate, more than one set of potentials is provided. These are tabulated in analytic form. Gaussian basis sets with contraction coefficients for the lowest energy state of each atom are given. The reliability of the transition metal AREPs was examined by comparing computed atomic excitation energies with accurate all-electron relativistic values. The spin–orbit operators were tested in calculations on selected atoms.

A b initio averaged relativistic effective core potentials (AREP) and spin–orbit (SO) operators are reported for the elements Cs through Rn. Two sets have been calculated for certain elements to provide AREPs with varying core/valence space definitions thereby permitting the treatment of core–valence correlation interactions. The AREPs and SO operators are tabulated as expansions in Gaussian-type functions (GTF). GTF valence basis sets for the lowest energy state of each atom are tabulated. The reliability of the AREPs and SO operators is gauged by comparing calculated atomic excitation energies and SO splitting energies with all-electron relativistic values. Calculated atomic excitation energies are found to agree to 0.12 eV and SO energies to 3.4%.

A refined version of the ‘‘shape consistent’’ effective potential procedure of Christiansen, Lee, and Pitzer was used to compute averaged relativistic effective potentials (AREP) and spin-orbit operators for the atoms K through Kr. Particular attention was given to the partitioning of the core and valence space, and where appropriate more than one set of potentials is provided. These are tabulated in analytic form. Gaussian basis sets with expansion coefficients for the lowest energy state of each atom are given. The reliability of the transition metal AREPs was determined by comparing computed atomic excitation energies with accurate all-electron relativistic values. In all cases the maximum error was found to be less than 0.1 eV. The reliability of the spin-orbit operators was also considered.

Ab initio averaged relativistic effective core potentials (AREP), spin-orbit (so) operators, and valence basis sets are reported for the elements Fr through Pu in the form of expansions in Gaussian-type functions. Gaussian basis sets with expansion coefficients for the low-energy states of each atom are given. Atomic orbital energies calculated under the j -j coupling scheme within the self-consistent field approximation and employing the AREP'S in their unaveraged form (REP'S) agree to within 10% of orbital energies due to numerical all-electron Dirac-Fock calculations. The accuracy of the AREP'S and so operators is also shown to be good through comparisons of calculated so splitting energies with all-electron Dirac-Fock results.

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and

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Articles you may be interested inA b i n i t i o effective core potentials including relativistic effects. V. SCF calculations with ω-ω coupling including results for Au2 +, TlH, PbS, and PbSe Relativistic effects in a b i n i t i o effective core potential studies of heavy metal compounds. Application to HgCl2, AuCl, and PtH A b i n i t i o effective core potentials including relativistic effects. IV. Potential energy curves for the ground and several excited states of Au2 A b i n i t i o effective core potentials including relativistic effects. II. Potential energy curves for Xe2, Xe+ 2, and Xe*2 An effective core potential system has been developed for heavy atoms in which relativistic effects are included in the effective potentials (EP). The EP's are based on numerical Dirac-Hartree-Fock calculations for atoms and on the Phillips-Kleinman transformation with other aspects similar to the treatments of Goddard and Melius and Kahn, Baybutt, and Truhlar. The EP's may be writtenwhere Iljm> is a two-component angular basis function that is a product of a two-component Pauli spinor and spherical harmonics. The numerical functions UIjEP(r) are approximated as expansions in terms of Gaussian or exponential functions. The use of these EP's enables one to use the .ii -coupling scheme for subsequent applications in all-valence-electron calculations on heavy atoms and their molecules. A standard atomic SCF program has been modified to accommodate these EP's and Gaussian and exponential basis sets having the proper j angular dependence. Energy levels for many atomic states of Xe and Au were calculated. The study of Xe excited states indicates that the spin-orbit splittings are reasonably approximated and that the numerical DHF calculations are adequately reproduced. Au has been treated as an atom with I, 11, 17, 19, or 33 valence electrons to investigate the effects of redefinition of the core. P is the momentum operator (-iV). Also, .. (~ ~)with r:r being a Pauli matrix and