9 research outputs found
Ultranonlocality and accurate band gaps from a meta-generalized gradient approximation
No full textThe proper description of step structures in the exchange correlation potential, of charge localization, and a reasonable prediction of band gaps have been long-standing, serious challenges for semilocal density functionals. In practice, obtaining all of these properties from the functional derivative of an energy functional was possible only at the price of incorporating exact exchange. We here show that they can be achieved at significantly lower, semilocal computational expense by using kinetic-energy density-dependent functionals. The key to obtaining these features is a functional construction strategy that focuses on the derivative discontinuity and the density response
Exploring local range separation: The role of spin scaling and one-electron self-interaction
No full textRight band gaps for the right reason at low computational cost with a meta-GGA
No full textIn density functional theory, traditional explicit density functionals such as the local density approximation and generalized gradient approximations cannot accurately predict the band gap of solids for a fundamental reason: They lack the exchange-correlation derivative discontinuity. By comparing Kohn-Sham and generalized Kohn-Sham calculations, we here show that the nonempirical meta-generalized-gradient-approximation (meta-GGA) TASK from Aschebrock and Kümmel [Phys. Rev. Res. 1, 033082 (2019)2643-156410.1103/PhysRevResearch.1.033082] predicts the right gaps for the right reason, i.e., as a combination of a proper Kohn-Sham gap and a substantial derivative discontinuity contribution. For many materials from small-gap semiconductors to large-gap insulators, the proper band gap is thus obtained. We further study a group of metal-halide perovskites for which the band gap is notoriously hard to predict. For these materials, TASK yields band gaps very similar to the nonlocal screened hybrid Heyd-Scuseria-Ernzerhof functional, yet at a fraction of the hybrid functional's computational cost. We discuss the influence of correlation functionals, and open questions in the comparison of calculated band gaps with experimental ones.</p
Challenges for semilocal density functionals with asymptotically nonvanishing potentials
No full textThe Becke-Johnson model potential [A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 ( 2006)] and the potential of the AK13 functional [R. Armiento and S. Kummel, Phys. Rev. Lett. 111, 036402 ( 2013)] have been shown to mimic features of the exact Kohn-Sham exchange potential, such as step structures that are associated with shell closings and particle-number changes. A key element in the construction of these functionals is that the potential has a limiting value far outside a finite system that is a system-dependent constant rather than zero. We discuss a set of anomalous features in these functionals that are closely connected to the nonvanishing asymptotic potential. The findings constitute a formidable challenge for the future development of semilocal functionals based on the concept of a nonvanishing asymptotic constant.Funding Agencies|German-Israeli Foundation for Scientific Research and Development; University of Bayreuth Graduate School; Swedish Research Council (V.R.) [2016-04810]; Swedish e-Science Research Centre (SeRC)</p
Meta-generalized gradient approximations in time dependent generalized Kohn–Sham theory: Importance of the current density correction
No full textFirst steps towards achieving both ultranonlocality and a reliable description of electronic binding in a meta-generalized gradient approximation
No full textIt has been demonstrated that a meta-generalized gradient approximation (meta-GGA) to the exchange-correlation energy of density functional theory can show a pronounced derivative discontinuity and significant ultranonlocality similar to exact exchange, and can accurately predict the band gaps of many solids. We here investigate whether within the meta-GGA form these properties are compatible with a reasonable accuracy for electronic binding energies. With the help of two transparent and inexpensive correlation functional constructions we demonstrate that this is the case. We report atomization energies, show that reliable bond lengths are obtained for many systems, and find promising results for reaction barrier heights, while keeping the strong derivative discontinuity and ultranonlocality, and thus accuracy for band gaps
Orbital nodal surfaces: Topological challenges for density functionals
No full textNodal 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 density-functional approximations. For the functional derivatives of the Armiento-Kummel (AK13) [Phys. Rev. Lett. 111, 036402 (2013)] and Becke88 [Phys. Rev. A 38, 3098 (1988)] energy functionals, i.e., the corresponding semilocal exchange potentials, as well as the Becke-Johnson [J. Chem. Phys. 124, 221101 (2006)] and van Leeuwen-Baerends (LB94) [Phys. Rev. A 49, 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.Funding Agencies|German-Israeli Foundation for Scientific Research and Development; University of Bayreuth Graduate School; Swedish Research Council (VR) [2016-04810]; Swedish e-Science Research Centre (SeRC)</p
