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  • Atomic, Molecular and Optical Physics  (8)
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  • 1
    Electronic Resource
    Electronic Resource
    Ionization potentials of atoms calculated with a nonlocal exchange and a local correlation functional (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 52 (1994), S. 993-1010 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We calculate the first ionization potential of atoms (3 ≤ Z ≤ 54) by means of a nonlocal density functional approach and the results are compared with those obtained using other recent density functional approaches based on density gradients. In these calculations, we use a nonlocal weighted spin-density approximation of exchange effects and a local spin-density approximation of Coulomb correlation, both based on novel forms of the pair-correlation functions. We also calculate the total energies of the He, Be, and Ne isoelectronic series. © 1994 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560520425
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  • 2
    Electronic Resource
    Electronic Resource
    Nonlocal functionals for exchange and correlation in density functional theory: Application to atoms and to small atomic clusters (1995)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 499-508 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The local density approximation (LDA) to exchange and correlation effects has well-known limitations. The nonlocal weighted density approximation (WDA) corrects some of those defects. This is illustrated here by applications to free atoms and small atomic clusters. The WDA also induces a nonlocal kinetic energy functional that is tested for atoms. © 1995 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560560508
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  • 3
    Electronic Resource
    Electronic Resource
    A mass formula for the energy of metal clusters (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 52 (1994), S. 767-797 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We obtain an analytic expression for the total energy of a metallic cluster formed by N atoms of valence v and with net charge Q, by solving variationally the extended Thomas-Fermi version of density functional theory within the spherical jellium model. The energy is expressed as an expansion (mass formula) in decreasing powers of the cluster radius RI = rsZ1/3, with Z = vN, and rs, the one electron radius of the bulk, \documentclass{article}\pagestyle{empty}\begin{document}$$ E\left( {r_s ,Z,Q} \right) = \sum\limits_{n = - 2}^3 {a_n \left( {r_s } \right)Z^{n/3} + Q\sum\limits_{n = 0}^2 {W_n \left( {r_s } \right)Z^{ - n/3} + \frac{1}{2}\frac{{Q2}}{{R_I + d\left( {r_s } \right)}},} } $$\end{document} and the coefficients of this mass formula are functions of rs. Contributions of volume (RI3), surface (RI2), curvature (RI), constant (RI0), (1/RI), and (1/RI2) are clearly separated in the formula. The Chemical potential, work function, electron affinity, and ionization potential are easily obtained for neutral and charged clusters of any electronic density in the metallic range. A general estimation of the critical size for stability against electron detachment of negatively charged clusters is also obtained. The stability of highly charged clusters against fragmentation is also studied. © John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560520407
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  • 4
    Electronic Resource
    Electronic Resource
    Nonlocal exchange and kinetic-energy density functionals for electronic systems (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 44 (1992), S. 347-358 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The nonlocal weighted density approximation (WDA) to the exchange and kinetic-energy functionals of many electron systems proposed several years ago by Alonso and Girifalco is used to compute, within the framework of density functional theory, the ground-state electronic density and total energy of noble gas atoms and of neutral jellium-like sodium clusters containing up to 500 atoms. These results are compared with analogous calculations using the well known Thomas-Fermi-Weizsäcker-Dirac (TFWD) approximations for the kinetic (TFW) and exchange (D) energy density functionals. An outstanding improvement of the total and exchange energies, of the density at the nucleus and of the 〈r-1〉 expectation values is obtained for atoms within the WDA scheme. For sodium clusters we notice a sizeable contribution of the nonlocal effects to the total energy and to the density profiles. In the limit of very large clusters these effects should affect the surface energy of the bulk metal. © 1992 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560440830
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  • 5
    Electronic Resource
    Electronic Resource
    Nonlocal exchange and kinetic energy density functionals with correct asymptotic behavior for electronic systems (1994)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 171-184 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The search for a density functional theory (DFT) free of one-electron orbitals needs the development of good kinetic energy functionals beyond the venerable Thomas-Fermi and gradient expansion functionals. With this goal in mind, we previously solved for several atoms and positive ions the Euler equation associated with the exchange and kinetic energy functionals of the nonlocal weighted density approximation (WDA). In this work, we improve the theory by enforcing the correct asymptotic behavior of the exchange potential following a prescription of Przybilsky and Borstel (PB). We have calculated electronic densities, density moments 〈rn〉 (n = -1,1,2) and the density at the nucleus ρ(0), as well as total and exchange energies and chemical potentials for neutral and charged atoms. All those quantities show a better agreement with Hartree-Fock results than those obtained using gradient-corrected Thomas-Fermi functionals. The radial densities, 4πr2(r), show two local maxima at positions close to those of the first two maxima of Hartree-Fock radial densities. This effect, which is absent in the self-consistent densities from the usual gradient-corrected Thomas-Fermi functions, can be interpreted, in our view as an incipient emergence of the shell effect. © 1994 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560490309
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  • 6
    Electronic Resource
    Electronic Resource
    Relation between total energy, electronic potential at the nucleus, and chemical potential of positive ions (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 145-149 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Simple density functional theory gives the following relation between the energy EZ, N of an ion of nuclear charge Z and N electrons, the potential V(0) created at the nucleus by the electronic cloud, and the chemical potential μ \documentclass{article}\pagestyle{empty}\begin{document}$$ E_{Z,N} = \frac{3}{7}(ZV(0) + N_\mu). $$\end{document}Using Hartree - Fock values for V(0) and μ, this equation has been tested in several isoelectronic series with 3 ≤ N ≤ 28. The importance of the term 3Nμ/7 increases as the degree of ionization increases.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560260110
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  • 7
    Electronic Resource
    Electronic Resource
    Study of an approximate relation between the energy of an atom and the electronic potential at the nucleus (1982)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 22 (1982), S. 989-997 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: This paper provides an analysis of the reasons for the approximate validity of the relation \documentclass{article}\pagestyle{empty}\begin{document}$ E = \frac{3}{7}NV(0) $\end{document}, between the total energy E of a neutral atom, the number N of electrons, and the electronic potential at the nucleus V(0). Using the density functional formalism we find that the right-hand side of the above equation also appears (and is the leading term) in density functional approximations more sophisticated than the Thomas-Fermi (TF) approximation (the above equation is exact in the TF approximation). Systematic improvements to the equation appear to be difficult because the main corrections come from those terms which are more difficult to handle in the density functional formalism. After this analysis we propose a kinetic energy functional for neutral atoms in the Hartree-Fock approximation. The first term of this new functional is a rescaled Thomas-Fermi term \documentclass{article}\pagestyle{empty}\begin{document}$$ T_0^\gamma = (1 + \gamma)\int {\frac{3}{{10}}(3\pi ^2){}^{2/3}\rho ^{5/3} d{\rm r}} $$\end{document}, where γ = -0.0063 for light atoms and γ = 0.0085 for the others. The second term is the first gradient correction due to Kirzhnits \documentclass{article}\pagestyle{empty}\begin{document}$$ T_2 = \frac{1}{{72}}\int {\frac{{(\nabla \rho)^2 }}{\rho }d{\rm r}} $$\end{document}.For lithium to krypton atoms, this new functional gives an average error of 0.22%.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560220510
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  • 8
    Electronic Resource
    Electronic Resource
    Local behavior of the kinetic energy in density functional theory (1985)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 393-406 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The local behavior of several approximate kinetic energy functionals is analyzed, for the case of free atoms and ions, by comparison with the local kinetic energy of Hartree-Fock theory. The atomic electron densities used are, in all cases, Hartree-Fock electron densities. The kinetic energy functional obtained by the gradient expansion method (with a small number of terms) is, locally, not very accurate, but its integrated value is fortuitously accurate, due to a strong cancellation of errors. Functionals which have the Weizsäcker term tw = (Δ ρ)2/8ρ as a key ingredient are more accurate locally. The explicit incorporation of the shell structure and nonlocal density effects into the kinetic energy functional leads to the best results. The motivation for this work is that only a kinetic energy functional with an accurate local behavior will give good electron densities on solution of the Euler equation derived from it.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560270404
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