Kohn-Sham Self-Consistent Calculation of the Structure of Metallic Sodium

Tong, B. Y.

doi:10.1103/physrevb.6.1189

Cited by 53 publications

(19 citation statements)

References 41 publications

(2 reference statements)

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“…Since self-consistent Hartree-Fock band calculations are not yet practical, current band calculations are inevitably based on simplified exchange approximations, for example, the Slater free-electron exchange approximation [23, 241, or variations thereof [7,. Some of these variations are based on theoretical considerations [26,29,301 , while others are essentially empirical in character [7,25,27,281. It is not yet clear which form of the free-electron exchange approximation is most suitable for band calculations, but this question is more likely to be settled empirically than on purely theoretical grounds.…”

Section: B Exchange Effectsmentioning

confidence: 99%

Energy band structure of diamond, cubic silicon carbide, silicon, and germanium

Herman

Kortum

Kuglin

2009

Int. J. Quantum Chem.

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We have developed a method for determining the band structure of crystals which combines the best features of a first-principles approach with the best features of an empirical approach. The first step in our method is a first-principles OPW band calculation based on the free-electron exchange approximation. In the second step, we depart from a purely first-principles approach, and introduce a small empirical correction which brings key features of the calculated energy level scheme into exact (or close) agreement with the most reliably established features of the experimental level scheme. In addition to obtaining reliable energy band models valid over a wide energy range, we obtain the electronic wave functions for a large number of levels, the core and valence electronic charge distributions, and many other "first-principles" quantities. Following a summary of the shortcomings of purely first-principles and purely empirical band calculations, we sketch the essential features of our intermediate treatment. Recent studies of the band structure of diamond, cubic silicon carbide, silicon, and germanium-carried out both by our method and other methods-are then discussed and compared. It is shown how improved band models for these crystals can be generated with the aid of some crucial information about the band structure derived from experiment. Finally, we observe that although the use of a universal exchange potential is an important simplification, and one that has greatly accelerated recent progress in energy band calculations, this approximation is to some extent an oversimplification. I t appears likely that some of the empirical corrections that we now have to introduce in order to bring theory and experiment closer together could be reduced substantially if we could define one exchange potential for s-like electrons, another for p-like electrons, and still another for d-like electrons. This idea of I-dependent exchange potentials represents a middle ground between the Hartree-Fock extreme of different exchange potentials for different orbitals, and the Slater extreme of the same exchange potential for all orbitals.

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Section: B Exchange Effectsmentioning

confidence: 99%

Energy band structure of diamond, cubic silicon carbide, silicon, and germanium

Herman

Kortum

Kuglin

2009

Int. J. Quantum Chem.

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“…where X = rs(r)/A; ( 4~/ 3 ) r:(r) = p(r)-l, and A = 21, C = 0.045, B = 0.7734, and LY = 0.52106 are numerical constants. Equation (3) with the functionals of the type given in Equations ( 6 ) - ( 8 ) have been previously solved for atoms [9] and some molecules [ 101 (in a spin-polarized scheme), yielding very good results for charge densities and total ground-state energies. The total ground-state electronic energy is given by where KE is the kinetic energy and…”

Section: Singwi and Coworkers [ 8 ] For Fcorr[p(r)] As Fitted Numericmentioning

confidence: 99%

Combined fourier transform and discrete variational method approach to the self-consistent solution of the electronic band structure problem within the local density formalism

Zunger

Freeman

2009

Int. J. Quantum Chem.

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This novel approach combines a discrete variational treatment of all potential terms arising from the superposition of the spherical overlapping atomic charge densities with a rapidly convergent Fourier series representation of all multicenter nonspherical potential terms. The basis set consists of the exact numerical atomic valence orbitals, augmented by charge transfer states, virtual atomic states, and single analytic Slater orbitals for increased variational flexibility. The initial potential is a non-muffin-tin overlapping atomic potential including nongradient local density exchange and correlation terms. Full self-consistency is obtained by a procedure that combines an iterative scheme within the superposition model with a self-consistent optimization of the Fourier components of the nonspherical charge density terms. Ground-state properties such as structure factors and cohesive energy are computed. The results for diamond show very good agreement with experiment.Comparison of the results with the Hartree-Fock calculation is discussed.

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“…Ref. [53]). However, it is only in the 1970s that theoreticians started to systematically develop local correlation functionals for calculations on solids in the framework of Kohn-Sham equations [54,55].…”

Section: In This Issue)mentioning

confidence: 99%

The role of density functional theory in chemistry: Some historical landmarks and applications to zeolites

Corminbœuf

Tran

Weber

2006

Journal of Molecular Structure: THEOCHEM

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Density functional theory (DFT) has progressively emerged in the last 40 years as a leading methodology for the modelling and simulation of chemical systems. In this paper, some historical landmarks in the development of this method are outlined, emphasizing on its main characteristic being an electron density-based theory. This is in contrast with wavefunction-based methodologies which were exclusively employed previously. Interestingly, DFT has been first applied to solids, with a rather late recognition by chemists and molecular scientists. After this historical survey, several applications of DFT to the structure and properties of zeolites are reviewed as a tribute to Dr Annick Goursot. q

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Kohn-Sham Self-Consistent Calculation of the Structure of Metallic Sodium

Cited by 53 publications

References 41 publications

Energy band structure of diamond, cubic silicon carbide, silicon, and germanium

Energy band structure of diamond, cubic silicon carbide, silicon, and germanium

Combined fourier transform and discrete variational method approach to the self-consistent solution of the electronic band structure problem within the local density formalism

The role of density functional theory in chemistry: Some historical landmarks and applications to zeolites

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