Energy Density Functional Theory of Many-Electron Systems

Ludeña, Eduardo V.; Kryachko, Eugene S.

doi:10.1007/978-94-009-1970-9

Cited by 348 publications

(194 citation statements)

References 588 publications

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“…The background of this theory and its very many applications have been described in numerous text books, e.g. (Parr and Yang, 1989;Kryachko and Ludena, 1990;Koch and Holthausen, 1999;Martin, 2008;Engel and Dreizler, 2011). The success of this computational approach is based on two factors.…”

Section: Introductionmentioning

confidence: 99%

Density functional theory based calculations for high pressure research

Winkler¹,

Milman²

2014

Zeitschrift Für Kristallographie – Crystalline Materials

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Section: Introductionmentioning

confidence: 99%

Density functional theory based calculations for high pressure research

Winkler¹,

Milman²

2014

Zeitschrift Für Kristallographie – Crystalline Materials

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“…The MP2 level has been used together with DFT method, the utility of which has been demonstrated for the description of the physical and chemical molecular properties, [35][36][37][38][39][40] including hydrogen-bond systems. [41][42][43][44] …”

Section: Introductionmentioning

confidence: 99%

Basis set superposition error-counterpoise corrected potential energy surfaces. Application to hydrogen peroxide⋯X (X=F−, Cl−, Br−, Li+, Na+) complexes

Daza¹,

Dobado²,

Molina³

et al. 1999

The Journal of Chemical Physics

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Mo ր ller-Plesset ͑MP2͒ and Becke-3-Lee-Yang-Parr ͑B3LYP͒ calculations have been used to compare the geometrical parameters, hydrogen-bonding properties, vibrational frequencies and relative energies for several X Ϫ and X ϩ hydrogen peroxide complexes. The geometries and interaction energies were corrected for the basis set superposition error ͑BSSE͒ in all the complexes ͑1-5͒, using the full counterpoise method, yielding small BSSE values for the 6-311 ϩG(3d f ,2p) basis set used. The interaction energies calculated ranged from medium to strong hydrogen-bonding systems ͑1-3͒ and strong electrostatic interactions ͑4 and 5͒. The molecular interactions have been characterized using the atoms in molecules theory ͑AIM͒, and by the analysis of the vibrational frequencies. The minima on the BSSE-counterpoise corrected potential-energy surface ͑PES͒ have been determined as described by S. Simón, M. Duran, and J. J. Dannenberg, and the results were compared with the uncorrected PES.

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“…In the framework of the modern density functional theory, [1][2][3][4][5] the physical and chemical properties of a many fermion system may be completely described by means of the single-particle probability density, which is to be denoted by ͑r͒ in position space and ␥͑p͒ in momentum space. The spread or extent of these quantum-mechanical probability densities is measured by the Boltzmann-Shannon information entropy, which for one-dimensional systems is defined as S ϭϪ ͵ Ϫϱ ϱ ͑x͒ln ͑x ͒dx, ͑1͒…”

Section: Introductionmentioning

confidence: 99%

Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates

Sánchez-Ruiz¹

1997

Journal of Mathematical Physics

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The problem of calculating the information entropy in both position and momentum spaces for the nth stationary state of the one-dimensional quantum harmonic oscillator reduces to the evaluation of the logarithmic potential V n (t) ϭϪ͐ Ϫϱdx at the zeros of the Hermite polynomial H n (x). Here, a closed analytical expression for V n (t) is obtained, which in turn yields an exact analytical expression for the entropies when the exact location of the zeros of H n (x) is known. An inequality for the values of V n (t) at the zeros of H n (x) is conjectured, which leads to a new, nonvariational, upper bound for the entropies. Finally, the exact formula for V n (t) is written in an alternative way, which allows the entropies to be expressed in terms of the even-order spectral moments of the Hermite polynomials. The asymptotic (nӷ1) limit of this alternative expression for the entropies is discussed, and the conjectured upper bound for the entropies is proved to be asymptotically valid.

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Energy Density Functional Theory of Many-Electron Systems

Cited by 348 publications

References 588 publications

Density functional theory based calculations for high pressure research

Density functional theory based calculations for high pressure research

Basis set superposition error-counterpoise corrected potential energy surfaces. Application to hydrogen peroxide⋯X (X=F−, Cl−, Br−, Li+, Na+) complexes

Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates

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