Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional

Lucero, Melissa J.; Henderson, Thomas M.; Scuseria, Gustavo E.

doi:10.1088/0953-8984/24/14/145504

Cited by 88 publications

(90 citation statements)

References 91 publications

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“…For this task we used the PBEsol functional and the S(13) subset as a representative enough combination for testing convergence. We found perfect agreement between our results and those obtained by Heyd et al 4 and more recently by Lucero et al 49 These calculations all use the m-6-311G* Gaussian basis with periodic boundary conditions (G-PBC). 25 by using a plane-waves projector augmented wave (PW-PAW) method, and the results obtained by Hao et al 26 by using a mix of Slater-type and numerical orbitals at the quadruple zeta plus quadruple polarization (STO+NO/QZQP) level; see references cited for the details of these methodologies and calculations.…”

Section: B Software Basis Sets Relativistic Effectssupporting

confidence: 89%

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

Peverati¹,

Truhlar²

2012

The Journal of Chemical Physics

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The recently developed SOGGA11 and M11-L density functionals have been tested for the prediction of bandgaps and lattice constants by comparing to databases containing 31 bandgaps and 34 lattice constants. To make a comparative assessment we also test several other density functionals against the same databases; in particular, we test the local spin density approximation, PBE, PBEsol, SOGGA, TPSS, revTPSS, and M06-L local density functionals and the HSE screened-exchange hybrid nonlocal density functional; and for a subset of 13 lattice constants we also compare the mean errors to those of the AM05 and WC local density functionals and the HISS and HSEsol nonlocal density functionals. The tests show that, of the ten functionals tested against all 65 data, the SOGGA, PBEsol, and HSE functionals are the most accurate for lattice constants, whereas the HSE, M11-L, and M06-L density functionals are the most accurate for bandgaps. However, the SOGGA11 density functional is the most accurate generalized gradient approximation for bandgaps.

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Section: B Software Basis Sets Relativistic Effectssupporting

confidence: 89%

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

Peverati¹,

Truhlar²

2012

The Journal of Chemical Physics

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“…For lattice parameters and bulk moduli, GGA and related hybrid functionals for solids (e.g., PBEsol family) give improved results with respect to common functionals devised for molecules (e.g., PBE family). Interestingly, we confirm results by Lucero et al 74 for the HISS functional, which gives overall good results when compared to One could attempt a ranking based on MSE and RMSD statistics. At this level, the best performing methods are characterized by two criteria: (1) the errors are nearly centered on zero; and (2) they have a small dispersion.…”

Section: Validation Datasupporting

confidence: 90%

Prediction Uncertainty of Density Functional Approximations for Properties of Crystals with Cubic Symmetry

et al. 2015

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The performance of a method is generally measured by an assessment of the errors between the method's results and a set of reference data. The prediction uncertainty is a measure of the confidence that can be attached to a method's prediction. Its estimation is based on the random part of the errors not explained by reference data uncertainty, which implies an evaluation of the systematic component(s) of the errors. As the predictions of most density functional approximations (DFA) present systematic errors, the standard performance statistics, such as the mean of the absolute errors (MAE or MUE), cannot be directly used to infer prediction uncertainty. We investigate here an a posteriori calibration method to estimate the prediction uncertainty of DFAs for properties of solids. A linear model is shown to be adequate to address the systematic trend in the errors. The applicability of this approach to modest-size reference sets (28 systems) is evaluated for the prediction of band gaps, bulk moduli, and lattice constants with a wide panel of DFAs.

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“…Practical GKS schemes often rely on the Fock operator, or variants thereof. Such GKS calculations were performed, e.g., by employing the screened exchange approach [69,[71][72][73][74][75], by using global hybrid functionals [76][77][78][79][80][81][82][83][84][84][85][86], range-separated hybrid functionals [80,81,[87][88][89][90][91][92][93][94][95][96], and by applying a scaling correction to the Hartree and exchange functionals [97,98]. Alternatively, one can step outside the KS scheme by introducing orbital-specific corrections, where different electrons of the KS system are subject to different potentials.…”

Section: Introductionmentioning

confidence: 99%

Fundamental gaps with approximate density functionals: The derivative discontinuity revealed from ensemble considerations

Kraisler

Kronik

2014

The Journal of Chemical Physics

101

102

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The fundamental gap is a central quantity in the electronic structure of matter. Unfortunately, the fundamental gap is not generally equal to the Kohn-Sham gap of density functional theory (DFT), even in principle. The two gaps differ precisely by the derivative discontinuity, namely, an abrupt change in slope of the exchange-correlation (xc) energy as a function of electron number, expected across an integer-electron point. Popular approximate functionals are thought to be devoid of a derivative discontinuity, strongly compromising their performance for prediction of spectroscopic properties. Here we show that, in fact, all exchange-correlation functionals possess a derivative discontinuity, which arises naturally from the application of ensemble considerations within DFT, without any empiricism. This derivative discontinuity can be expressed in closed form using only quantities obtained in the course of a standard DFT calculation of the neutral system. For small, finite systems, addition of this derivative discontinuity indeed results in a greatly improved prediction for the fundamental gap, even when based on the most simple approximate exchange-correlation density functional -the local density approximation (LDA). For solids, the same scheme is exact in principle, but when applied to LDA it results in a vanishing derivative discontinuity correction. This failure is shown to be directly related to the failure of LDA in predicting fundamental gaps from total energy differences in extended systems.

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Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional

Cited by 88 publications

References 91 publications

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

Prediction Uncertainty of Density Functional Approximations for Properties of Crystals with Cubic Symmetry

Fundamental gaps with approximate density functionals: The derivative discontinuity revealed from ensemble considerations

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