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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 30 (1986), S. 451-451 
    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
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 49 (1994), S. 539-548 
    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: A set of exact conditions is compiled for the purpose of developing and testing approximations for the exchange-correlation energy as a functional of the electron density. Special emphasis is placed upon recently developed density-scaling relationships. Commonly used generalized gradient approximations are compared against several of these conditions. A direct tabular comparison of these functionals (not of calculated properties) with one another is also made. © 1994 John Wiley & Sons, Inc.
    Additional Material: 2 Tab.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 48 (1993), S. 93-100 
    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: In many situations, the most long-ranged parts of the exchange and correlation holes surrounding an electron cancel one another. Apparently for this reason, local spin density and generalized gradient approximations are more accurate for exchange and correlation together than for either alone. A study is made of the ability of these density functionals, and also the unmodified second-order gradient expansion, to describe various short-range effects in atoms: the correlation contribution to the interacting kinetic energy, the antiparallel-spin correlation energy, and the correction to the random phase approximation. Generalized gradient approximations, constructed with no adjustable parameter from the electron gas of slowly varying density, are found to give results of useful accuracy for real atoms. Prospects are discussed for use of the new functionals to improve the accuracy of electronic-structure calculations. © 1993 John Wiley & Sons, Inc.
    Additional Material: 4 Tab.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 935-941 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Correlation of a quantum many-body state makes the one-particle density matrix nonidempotent. Therefore, the Shannon entropy of the natural occupation numbers measures the correlation strength on the one-particle level. Here, it is shown how this general idea of a correlation entropy must be adapted for two-electron systems in view of conservation laws which mix Slater determinants even in the noninteracting limit. Results are presented for the correlation entropy s of H2 as a function of the nucleus-nucleus separation R. In the ground state, the entropy of the spatial factor of the wave function maximizes 1.7 bohr beyond the Coulson-Fischer separation. The role of the correlation entropy in density functional theory is also discussed. © 1997 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 48 (1993), S. 249-261 
    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 evaluate binding energies, ionization energies, and second-order energy differences as functions of valence electron number for small spherical clusters of stabilized jellium, using the Kohn-Sham equations with the local-spin-density (LSD) approximation. Cohesive energies are also reported. A comparison is made with semiclassical formulas (liquid drop model and Padé approximant, with surface and curvature coefficients derived from first principles). These formulas nicely average the shell-structure oscillations of the energy, which are found to be almost the same as for ordinary jellium. Spherical clusters with 1, 7, and 9 electrons have binding energies very close to those of the semiclassical predictions. © 1993 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 64 (1997), S. 285-295 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The local spin-density (LSD) functional and Perdew-Wang 91 (PW91) generalized gradient approximations to atomization energies of molecules are investigated. We discuss the coupling-constant dependence of the atomization energy and why exchange errors of the functionals are greater than exchange-correlation errors. This fact helps to justify hybrid schemes which mix some exact exchange with density functional approximations for exchange and correlation. It is shown that the biggest errors in the atomization energies occur when there is a strong interaction between different electron pairs, which vanishes upon atomization. We argue that the amount of exchange character of a molecular property, such as the atomization energy, depends on the property itself. We define an exact mixing coefficient b, which measures this exchange character, and show that both LSD and PW91 typically overestimate this quantity. Thus, nonempirical hybrid schemes which approximate this quantity by its LSD or PW91 value typically do not improve the exchange-correlation energy.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 285-295, 1997
    Additional Material: 3 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 197-205 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The on-top pair density P(r, r) gives the probability that one electron will be found on top of another at position r. We find that the local spin density (LSD) and generalized gradient (GGA) approximations for exchange and correlation predict this quantity with remarkable accuracy. We show how this fact and the usual sum-rule arguments explain the success of these approximations for real atoms, molecules, and solids, where the electron spin densities do not vary slowly over space. Self-consistent LSD or GGA calculations make realistic predictions for the total energy E, the total density n(r), and the on-top pair density P(r,r), even in those strongly “abnormal” systems (such as stretched H2) where these approximations break symmetries and yield unrealistic spin magnetization densities m(r). We then suggest that ground-state ferromagnetic iron is a “normal” system, for which for LSD or GGA m(r) and the related local spin moment are trustworthy, but that iron above the Curie temperature and antiferromagnetic clusters at all temperatures are abnormal system for which the on-top pair density interpretation is more viable than the standard physical interpretation. As an example of a weakly abnormal system, we consider the four-electron ion with nuclear charge Z → ∞ © 1997 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 61 (1997), S. 835-845 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We present an analysis of local or semilocal density functionals for the exchange-correlation energy by decomposing them into their gradients rs (local Seitz radius), ζ (relative spin polarization), and s (reduced density gradient). We explain the numerical method pertaining to this kind of analysis and present results for a few atoms and ions. The atomic shell structure is prominent, and only the ranges 0 〈 rs 〈 10 and 0 〈 s 〈 3 are important. The low-density and large-gradient domains, where the approximations for the exchange-correlation energy are least trustworthy, have very little weight. © 1997 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 56 (1995), S. 199-210 
    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 exchange-correlation energy of a many-electron system may be written as the electrostatic interaction between the electron density at position r and the density of the exchange-correlation hole at position r + u. If we average the hole over the entire system, we find that the energy is uniquely decomposed into contributions from various electronic separations u. We may also decompose the hole into contributions from parallel and antiparallel spins. We give several exact conditions which this system-averaged, spindecomposed exchange-correlation hole satisfies. Local spin density (LSD) and generalized gradient approximations (GGAS), are more appropriate for u → 0 than for large u and more trustworthy for antiparallel spins than for parallel spins. We illustrate how good LSD is as u = 0 with explicit examples, but also note that, contrary to expectation, LSD is not exact for u=0, except in certain limiting cases. We show that the dramatic failure of the second-order gradient expansion for large u can be cured by a real-space cutoff procedure which generates a nonempirical GGA, the Pw91 functional. We conclude with some thoughts about the search for greater accuracy in the next 30 years of density functional theory. © 1995 John Wiley & Sons, Inc.
    Additional Material: 3 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 57 (1996), S. 309-319 
    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: Gradient corrections to the local spin density (LSD) approximation for the exchange-correlation energy are making density functional theory as useful in quantum chemistry as it is in solid-state physics. But which of the many gradient-corrected density functionals should be preferred a priori? We make a graphical comparison of the gradient dependencies of some popular approximations, discussing the exact formal conditions which each obeys and identifying which conditions seem most important. For the exchange energy, there is little formal or practical reason to choose among the Perdew-Wang 86, Becke 88, or Perdew-Wang 91 functionals. But, for the correlation energy, the best formal properties are displayed by the nonempirical PW91 correlation functional. Furthermore, the real-space foundation of PW91 yields an insight into the character of the gradient expansion which suggests that PW91 should work especially well for solids. Indeed, while improving dissociation energies over LSD, PW91 remains the most “local” of the gradient-corrected exchange-correlation functionals and, thus, the least likely to overcorrect the subtle errors of LSD for solids. To show that our analysis of spin-unpolarized functionals is sufficient, we also compute spin-polarization energies for atoms, finding PW91 values only slightly more negative than LSD values. © 1996 John Wiley & Sons, Inc.
    Additional Material: 8 Ill.
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