Comparison between exact and semilocal exchange potentials: An all-electron study for solids

Tran, Fabien; Blaha, Peter; Betzinger, Markus; Blügel, Stefan

doi:10.1103/physrevb.91.165121

Cited by 44 publications

(71 citation statements)

References 114 publications

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“…We find this to be very much the case for our own attempts at converging AK13 results for systems with nodal surfaces, and also other authors have reported numerical problems with self-consistent calculations [78]. Furthermore, unusual oscillations in the AK13 potential have also been observed in the interstitial region of Si crystals [35], and these might be another consequence of the features that we discussed here for finite systems. Quite generally, one might speculate that similar issues could have influenced the convergence of some of the many published values obtained with B88-and BJ-based potential functionals.…”

Section: Discussionmentioning

confidence: 48%

“…Various modifications of the BJ exchange potential functional are used quite frequently in the literature [29][30][31][32][33][34][35]. Therefore, we begin our application of the minimal model with the BJ expression.…”

Section: A the Bj Potential Functional In The Vicinity Of Nodal Surfmentioning

confidence: 99%

“…Many attempts have been made to incorporate some of the missing features into semilocal DFT [17][18][19][20][21][22][23][24][25][26][27]. In recent years, it was the Becke-Johnson (BJ) model potential [28] in particular that sparked interest in this respect [22,[29][30][31][32][33][34][35]. Its key characteristic is to effectively mimic nonlocal exchange features in the asymptotic behavior of the potential by means of having a nonzero limiting value far away from a finite system.…”

Section: Introductionmentioning

confidence: 99%

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Orbital nodal surfaces: Topological challenges for density functionals

2017

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Nodal surfaces of orbitals, in particular of the highest occupied one, play a special role in Kohn-Sham density-functional theory. The exact Kohn-Sham exchange potential, for example, shows a protruding ridge along such nodal surfaces, leading to the counterintuitive feature of a potential that goes to different asymptotic limits in different directions. We show here that nodal surfaces can heavily affect the potential of semilocal densityfunctional approximations. For the functional derivatives of the Armiento-Kümmel (AK13) 2421 (1994)] model potentials, we explicitly demonstrate exponential divergences in the vicinity of nodal surfaces. We further point out that many other semilocal potentials have similar features. Such divergences pose a challenge for the convergence of numerical solutions of the Kohn-Sham equations. We prove that for exchange functionals of the generalized gradient approximation (GGA) form, enforcing correct asymptotic behavior of the potential or energy density necessarily leads to irregular behavior on or near orbital nodal surfaces. We formulate constraints on the GGA exchange enhancement factor for avoiding such divergences.

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Section: Discussionmentioning

confidence: 48%

Section: A the Bj Potential Functional In The Vicinity Of Nodal Surfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Orbital nodal surfaces: Topological challenges for density functionals

2017

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“…For atoms and small molecules, Cerceira et al found an overall improvement of the first ionization potential as obtained from the highest occupied KS eigenvalue [12]. A recent all-electron study of solids [13] reveals that the orbitals obtained from the AK13 potential greatly improves on EXX total energies, as well as the general features of the potential shape. The combined picture from these works is that both the KS states and their respective eigenvalues (i.e., band structure) have generally improved.…”

Section: Introductionmentioning

confidence: 99%

Energetics of the AK13 semilocal Kohn-Sham exchange energy functional

Lindmaa

Armiento

2016

Phys. Rev. B

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The recent nonempirical semilocal exchange functional of Armiento and Kümmel [Phys. Rev. Lett. 111, 036402 (2013)], AK13, incorporates a number of features reproduced by higher-order theory. The AK13 potential behaves analogously with the discontinuous jump associated with the derivative discontinuity at integer particle numbers. Recent works have established that AK13 gives a qualitatively improved orbital description compared to other semilocal methods, and reproduces a band structure closer to higher-order theory. However, its energies and energetics are inaccurate. The present work further investigates the deficiency in energetics. In addition to AK13 results, we find that applying the local-density approximation (LDA) non-self-consistently on the converged AK13 density gives very reasonable energetics with equilibrium lattice constants and bulk moduli well described across 13 systems. We also confirm that the attractive orbital features of AK13 are retained even after full structural relaxation. Hence, the deficient energetics cannot be a result of the AK13 orbitals having adversely affected the quality of the electron density compared to that of usual semilocal functionals; an improved orbital description and good energetics are not in opposition. This is also confirmed by direct calculation of the principal component of the electric field gradient. In addition, we prove that the non-self-consistent scheme is equivalent to using a single external-potential-dependent functional in an otherwise consistent, nonvariational Kohn-Sham density-functional theory (KS DFT) scheme. Furthermore, our results also demonstrate that, while an internally consistent KS functional is presently missing, non-self-consistent LDA on AK13 orbitals works as a practical nonempirical computational scheme to predict geometries, bulk moduli, while retaining the band structure features of AK13 at the computational cost of semi-local DFT.

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“…However, for these functionals total-energy related quantities are not accessible [60][61][62]. New types of GGAs can yield significantly improved potential properties [63][64][65], but at the cost of being less accurate for total energies. Global hybrid functionals [66][67][68][69][70][71], which linearly combine (semi-)local xc energy components, with a weight (1 − a), and exact exchange (EXX, i.e., the Fock-integral evaluated with KS orbitals), with a weight a, mitigate the oneelectron self-interaction error and often yield an excellent description of properties related to the total energy, for a ≈ 0.25.…”

Section: Introductionmentioning

confidence: 99%

Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue

Kraisler

Schmidt

Kümmel

et al. 2015

The Journal of Chemical Physics

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There are several approximations to the exchange-correlation functional in density-functional theory that accurately predict total energy-related properties of many-electron systems, such as binding energies, bond lengths, and crystal structures. Other approximations are designed to describe potential-related processes, such as charge transfer and photoemission. However, the development of a functional which can serve the two purposes simultaneously is a long-standing challenge. Trying to address it, we employ in the current work the ensemble generalization procedure proposed in Phys. Rev. Lett. 110, 126403 (2013). Focusing on the prediction of the ionization potential via the highest occupied Kohn-Sham eigenvalue, we examine a variety of exchange-correlation approximations: the local spin-density approximation, semi-local generalized gradient approximations, and global and local hybrid functionals. Results for a test set of 26 diatomic molecules and single atoms are presented. We find that the aforementioned ensemble generalization systematically improves the prediction of the ionization potential, for various systems and exchange-correlation functionals, without compromising the accuracy of total energy-related properties. We specifically examine hybrid functionals. These depend on a parameter controlling the ratio of semi-local to non-local functional components. The ionization potential obtained with ensemble-generalized functionals is found to depend only weakly on the parameter value, contrary to common experience with non-generalized hybrids, thus eliminating one aspect of the so-called 'parameter dilemma' of hybrid functionals.

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Comparison between exact and semilocal exchange potentials: An all-electron study for solids

Cited by 44 publications

References 114 publications

Orbital nodal surfaces: Topological challenges for density functionals

Orbital nodal surfaces: Topological challenges for density functionals

Energetics of the AK13 semilocal Kohn-Sham exchange energy functional

Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue

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