Generalized Kohn-Sham schemes and the band-gap problem

Seidl, A.; Görling, Andreas; Vogl, P.; Majewski, J. A.; Levy, Mel

doi:10.1103/physrevb.53.3764

Cited by 1,191 publications

(1,051 citation statements)

References 51 publications

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“…[5][6][7] This has led to the development of two main first-principles alternative frameworks for quasiparticle excitations: many-body perturbation theory, mainly within the so-called GW approximation 8 on top of DFT, [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and generalized-KS DFT. [26][27][28][29][30] Recently, range-separated hybrid (RSH) functionals 31-37 combined with an optimally-tuned range parameter 38,39 were shown to very successfully predict quasiparticle band gaps, band edge energies and excitation energies for a range of interesting small molecular systems, well matching both experimental results and GW predictions. [40][41][42][43] The key element of the range parameter tuning is the minimization of the deviation between the highest occupied orbital energy and the ionization energy 39,40 or the direct minimization of the energy curvature.…”

Section: Introductionmentioning

confidence: 74%

Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory

et al. 2015

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We develop a stochastic formulation of the optimally-tuned range-separated hybrid density functional theory which enables significant reduction of the computational effort and scaling of the non-local exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band-edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a selfconsistent Hamiltonian which is central for additional post-processing, for example in the stochastic Bethe-Salpeter approach.

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Section: Introductionmentioning

confidence: 74%

Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory

et al. 2015

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“…These are still well within density functional theory, using the generalized Kohn-Sham (GKS) framework [13,14,31], and their non-local Fock-like exchange component assists in the inclusion of long-range contributions. Although the time-dependent GKS equations have yet to be formally derived, hybrid functionals are already widely used for calculating optical properties.…”

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confidence: 99%

Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory

et al. 2015

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We present a framework for obtaining reliable solid-state charge and optical excitations and spectra from optimally-tuned range-separated hybrid density functional theory. The approach, which is fully couched within the formal framework of generalized Kohn-Sham theory, allows for accurate prediction of exciton binding energies. We demonstrate our approach through first principles calculations of one-and two-particle excitations in pentacene, a molecular semiconducting crystal, where our work is in excellent agreement with experiments and prior computations. We further show that with one adjustable parameter, set to produce an accurate bandgap, this method accurately predicts band structures and optical spectra of silicon and lithium flouride, prototypical covalent and ionic solids. Our findings indicate that for a broad range of extended bulk systems, this method may provide a computationally inexpensive alternative to many-body perturbation theory, opening the door to studies of materials of increasing size and complexity.

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“…x F x (s, q, α, x u ) (53) and using the generalized Kohn-Sham method [81], the XE potential can be computed in the same manner, as has been shown in Equation (50), and will differ from a regular meta-GGA potential only due to an extra integration. Finally, we remark that the exact nuclear behavior can be reproduced only by high level functionals, which include the exact-XE density, such as the optimized-effective potential (OEP) method [82][83][84] or hyper-GGAs methods [85][86][87], which are significantly more expensive than the proposed Equation (53).…”

Section: Exchange Energymentioning

confidence: 99%

Kinetic and Exchange Energy Densities near the Nucleus

2016

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Abstract:We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.

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Generalized Kohn-Sham schemes and the band-gap problem

Cited by 1,191 publications

References 51 publications

Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory

Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory

Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory

Kinetic and Exchange Energy Densities near the Nucleus

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