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Robert D. Cowan

Bio: Robert D. Cowan is an academic researcher from Los Alamos National Laboratory. The author has contributed to research in topics: Spectral line & Ionization. The author has an hindex of 29, co-authored 67 publications receiving 3413 citations.
Topics: Spectral line, Ionization, Ab initio, Ion, Electron


Papers
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Journal ArticleDOI
TL;DR: The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms as discussed by the authors.
Abstract: The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms. Introduction of the quantum number j is avoided by omitting the spin-orbit term of the Pauli equation. The major relativistic effects, both direct and indirect, are thereby incorporated into the wave functions, while allowing retention of the commonly used nonrelativistic formulation of energy level calculations. The improvement afforded in calculated total binding energies, excitation energies, spin-orbit parameters, and expectation values of rm is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations.

849 citations

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TL;DR: In this article, an analytical expression for the energy-matrix coefficients of the electrostatic-interaction parameters Fk(li,lj) and Gk(lj, lj) was derived for any configuration with less than five open subshells, starting from only a table of the terms, parents, and coefficients of fractional parentage for each lini.
Abstract: For an arbitrary electron configuration l1n1l2n2l3n3⋯, analytical expressions are derived for the energy-matrix coefficients of the electrostatic-interaction parameters Fk(li,lj) and Gk(li,lj) and of the spin–orbit parameters ζ(li). A computer program is described which calculates decimal values of these coefficients for any configuration with less than five open subshells, starting from only a table of the terms, parents, and coefficients of fractional parentage for each open subshell lini. Given also a set of values of the parameters, the program evaluates and diagonalizes the energy matrices to obtain the eigenvalues and eigenvectors of the states belonging to this configuration. If so specified, the program does the above for two configurations of opposite parity, differences eigenvalues to obtain wavelengths for dipole transitions, and from the eigenvectors computes line strengths and (given an absolute value for the reduced dipole matrix element) transition probabilities.

373 citations

Journal ArticleDOI
TL;DR: The Hartree-Fock (HF) equations, with or without Latter's cutoff in the tail of the potential function, leads to serious errors when applied to excited configurations of atoms as mentioned in this paper, and a more accurate approximation (HX) is suggested in which Hartree's method is used for the selfinteraction correction, and a modification of the Slater ${\ensuremath{\rho}}^{\frac{1}{3}}$ term is used to approximate the remainder of the HF exchange terms.
Abstract: The ${\ensuremath{\rho}}^{\frac{1}{3}}$ approximation introduced by Slater for the exchange terms in the Hartree-Fock (HF) equations, with or without Latter's cutoff in the tail of the potential function, leads to serious errors when applied to excited configurations of atoms. A more accurate approximation (HX) is suggested in which Hartree's method is used for the self-interaction correction, and a modification of the Slater ${\ensuremath{\rho}}^{\frac{1}{3}}$ term is used to approximate the remainder of the HF exchange terms. The HX scheme is fairly simple; iterative convergence to self-consistent-field solutions is quite stable; and the resulting one-electron radial wave functions produce acceptably accurate values of one-electron and total binding energies, interaction parameters ${F}^{k}$, ${G}^{k}$, and ${\ensuremath{\zeta}}_{i}$, and expectation values of ${\mathcal{r}}^{n}$. Perturbation-theory relativistic and correlation corrections are computed; the latter are based on the free-electron approximation, with empirical modifications to allow for differences between free and bound electrons. Results agree well with experimental ionization and excitation energies for a wide variety of configurations.

196 citations

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TL;DR: Theoretical calculation of energy levels and spectra ab initio are described for transitions of the type pm-pm−1l, especially 3pm-3pm−13d transitions in the Ar i and Cl i isoelectronic sequences as mentioned in this paper.
Abstract: Theoretical calculation of energy levels and spectra ab initio are described for transitions of the type pm–pm−1l, especially 3pm–3pm−13d transitions in the Ar i and Cl i isoelectronic sequences. Strong changes of wavefunction composition occur in going from neutral atoms to ions as a result of collapse of the 3d wavefunction; for m = 2 and 6 these take the form of coupling changes, and for m = 3–5 they take the form of changes of parentage composition. Abnormally low Ti v 3p6–3p54d intensities are explained as an interference effect in evaluation of the dipole radial integral.

116 citations

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TL;DR: In this paper, an ab initio approach is described which enables the valence electrons in heavy atoms to be treated in a standard nonrelativistic manner by including the effect of the relativistic core-valence interactions directly into the ECP.
Abstract: The procedure of deriving ab initio effective core potentials (ECP) to incorporate the Coulomb and exchange effects as well as orthogonality constraints from the inner core electrons is extended to include the dominant relativistic effects on the valence orbitals. An ab initio approach is then described which enables the valence electrons in heavy atoms to be treated in a standard nonrelativistic manner by including the effect of the relativistic core–valence interactions directly into the ECP. The starting point for this procedure is the Pauli Hartree–Fock relativistic treatment of Cowan and Griffin. The pseudo‐orbital transformation and derivation of the l‐dependent effective core potentials are analogous to the nonrelativistic case with certain modifications. Analytic forms for the pseudo‐orbitals and ECP’s are derived for the U atom, and results of valence electron calculations are presented.

110 citations


Cited by
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TL;DR: In this paper, the self-interaction correction (SIC) of any density functional for the ground-state energy is discussed. But the exact density functional is strictly selfinteraction-free (i.e., orbitals demonstrably do not selfinteract), but many approximations to it, including the local spin-density (LSD) approximation for exchange and correlation, are not.
Abstract: The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

16,027 citations

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TL;DR: In this article, the Coulomb, exchange, and core-orthogonality effects of the chemically inert core electron in the transition metal atoms Sc to Hg have been replaced by the ab initio effective core potentials (ECP).
Abstract: Ab initio effective core potentials (ECP’s) have been generated to replace the Coulomb, exchange, and core‐orthogonality effects of the chemically inert core electron in the transition metal atoms Sc to Hg. For the second and third transition series relative ECP’s have been generated which also incorporate the mass–velocity and Darwin relativistic effects into the potential. The ab initio ECP’s should facilitate valence electron calculations on molecules containing transition‐metal atoms with accuracies approaching all‐electron calculations at a fraction of the computational cost. Analytic fits to the potentials are presented for use in multicenter integral evaluation. Gaussian orbital valence basis sets are developed for the (3d,4s,4p), (4d,5s,5p), and (5d,6s,6p) orbitals of the first, second, and third transition series atoms, respectively. All‐electron and valence‐electron atomic excitation energies are also compared for the low‐lying states of Sc–Hg, and the valence‐electron calculations are found to reproduce the all‐electron excitation energies (typically within a few tenths of an eV).

12,141 citations

Journal ArticleDOI
TL;DR: In this article, a consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn.
Abstract: A consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn. The ECP’s are derived from all‐electron numerical Hartree–Fock atomic wave functions and fit to analytical representations for use in molecular calculations. For Rb to Bi the ECP’s are generated from the relativistic Hartree–Fock atomic wave functions of Cowan which incorporate the Darwin and mass–velocity terms. Energy‐optimized valence basis sets of (3s3p) primitive Gaussians are presented for use with the ECP’s. Comparisons between all‐electron and valence‐electron ECP calculations are presented for NaF, NaCl, Cl2, Cl2−, Br2, Br2−, and Xe2+. The results show that the average errors introduced by the ECP’s are generally only a few percent.

8,952 citations

Journal ArticleDOI
D. Andrae1, U. Huermann1, Michael Dolg1, Hermann Stoll1, H. Preu1 
TL;DR: In this paper, nonrelativistic and quasirelativisticab initio pseudopotentials substituting the M(Z−28)+-core orbitals of the second row transition elements and the M (Z−60)+- core orbitals, respectively, and optimized (8s7p6d)/[6s5p3d]-GTO valence basis sets for use in molecular calculations were generated.
Abstract: Nonrelativistic and quasirelativisticab initio pseudopotentials substituting the M(Z−28)+-core orbitals of the second row transition elements and the M(Z−60)+-core orbitals of the third row transition elements, respectively, and optimized (8s7p6d)/[6s5p3d]-GTO valence basis sets for use in molecular calculations have been generated. Additionally, corresponding spin-orbit operators have also been derived. Atomic excitation and ionization energies from numerical HF as well as from SCF pseudopotential calculations using the derived basis sets differ in most cases by less than 0.1 eV from corresponding numerical all-electron results. Spin-orbit splittings for lowlying states are in reasonable agreement with corresponding all-electron Dirac-Fock (DF) results.

7,009 citations

Journal ArticleDOI
TL;DR: In this paper, the authors survey the local density functional formalism and some of its applications and discuss the reasons for the successes and failures of the local-density approximation and some modifications.
Abstract: A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

3,285 citations