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Energetics of the AK13 semilocal Kohn-Sham exchange energy functional
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0001-5439-711X
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-5571-0814
2016 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 94, no 15, article id 155143Article in journal (Refereed) Published
Abstract [en]

The recent nonempirical semilocal exchange functional of Armiento and Kummel [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.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC , 2016. Vol. 94, no 15, article id 155143
National Category
Theoretical Chemistry
Identifiers
URN: urn:nbn:se:liu:diva-133756DOI: 10.1103/PhysRevB.94.155143ISI: 000390031400002OAI: oai:DiVA.org:liu-133756DiVA, id: diva2:1063078
Note

Funding Agencies|Swedish Research Council (VR) [621-2011-4249]; Linnaeus Environment at Linkoping on Nanoscale Functional Materials (LiLi-NFM) - VR; Swedish e-Science Research Centre (SeRC)

Available from: 2017-01-09 Created: 2017-01-09 Last updated: 2017-11-29
In thesis
1. Theoretical prediction of properties of atomistic systems: Density functional theory and machine learning
Open this publication in new window or tab >>Theoretical prediction of properties of atomistic systems: Density functional theory and machine learning
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The prediction of ground state properties of atomistic systems is of vital importance in technological advances as well as in the physical sciences. Fundamentally, these predictions are based on a quantum-mechanical description of many-electron systems. One of the hitherto most prominent theories for the treatment of such systems is density functional theory (DFT). The main reason for its success is due to its balance of acceptable accuracy with computational efficiency. By now, DFT is applied routinely to compute the properties of atomic, molecular, and solid state systems.

The general approach to solve the DFT equations is to use a density-functional approximation (DFA). In Kohn-Sham (KS) DFT, DFAs are applied to the unknown exchangecorrelation (xc) energy. In orbital-free DFT on the other hand, where the total energy is minimized directly with respect to the electron density, a DFA applied to the noninteracting kinetic energy is also required. Unfortunately, central DFAs in DFT fail to qualitatively capture many important aspects of electronic systems. Two prime examples are the description of localized electrons, and the description of systems where electronic edges are present.

In this thesis, I use a model system approach to construct a DFA for the electron localization function (ELF). The very same approach is also taken to study the non-interacting kinetic energy density (KED) in the slowly varying limit of inhomogeneous electron densities, where the effect of electronic edges are effectively included. Apart from the work on model systems, extensions of an exchange energy functional with an improved KS orbital description are presented: a scheme for improving its description of energetics of solids, and a comparison of its description of an essential exact exchange feature known as the derivative discontinuity with numerical data for exact exchange.

An emerging alternative route towards the prediction of the properties of atomistic systems is machine learning (ML). I present a number of ML methods for the prediction of solid formation energies, with an accuracy that is on par with KS DFT calculations, and with orders-of-magnitude lower computational cost.

Abstract [sv]

Att kunna förutsäga egenskaper hos atomistiska system utgör en viktigdel av vår teknologiska utveckling, samt spelar en betydande roll i defysikaliska vetenskaperna. Sådana förutsägelser bygger på en kvantmekaniskbeskrivning av mångelektronsystem. En av de mest framståendeteorierna för att behandla den här typen av system är täthetsfunktionalteorin(DFT). Den främsta orsaken till dess framgång är attden lyckas kombinera skaplig noggrannhet med en bra beräkningseffektivitet.DFT används numera rutinmässigt för att beräkna storheterhos atomer, molekyler, och fasta kroppar.

Generellt sett löses ekvationerna inom DFT genom att man inför entäthetsfunktionalapproximation (DFA). I Kohn-Sham (KS) DFT, användsDFAer för att approximera utbytes-korrelationsenergin. Inom orbitalfriDFT, där målet är att direkt minimera den totala energin med avseendepå elektrontätheten, så approximerar man också den icke-interageranderörelseenergin hos elektronerna. Dessvärre så fallerar många centralaDFAer att kvalitativt beskriva många viktiga aspekter hos elektronsystem.Två viktiga exempel är beskrivningen av lokaliserade elektroner,samt beskrivningen av system där det förekommer elektronytor.

I denna avhandling använder jag modellsystem för att konstruera enDFAför elektronlokaliseringsfunktionen (ELF). Samma tillvägagångssättappliceras sedan för att studera den kinetiska energitätheten i gränsen avlångsamt varierande elektrontätheter, där effekten av elektronytor effektivtinkluderas. Förutom arbetet som berör modellsystem, så presenterasen utökad variant av en utbytes-energifunktional med en förbättrad KSorbitalbeskrivning: ett schema för att förbättra dess energiegenskaperför solida material, samt en jämförelse av dess beskrivning av en viktigegenskap hos den exakta utbytesenergin, vilket utgörs av diskontinuiteteri dess derivata.

Ett mera nyligen uppkommet samt alternativt sätt att kunna förutsägaegenskaper hos atomistiska system utgörs av maskinlärning (ML).Jag presenterar ett antal ML-modeller för att kunna förutsäga formeringsenergierhos fasta material med en noggrannhet som är i linje medresultat som uppnås av beräkningar med hjälp av KS DFT, och med enberäkningseffektivitet som är flera storleksordningar snabbare.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2017. p. 68
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1868
National Category
Theoretical Chemistry Other Physics Topics Condensed Matter Physics Control Engineering Other Engineering and Technologies not elsewhere specified
Identifiers
urn:nbn:se:liu:diva-139767 (URN)10.3384/diss.diva-139767 (DOI)978-91-7685-486-0 (ISBN)
Public defence
2017-09-08, Planck, Fysikhuset, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2017-08-15 Created: 2017-08-15 Last updated: 2017-08-18Bibliographically approved

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