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The many-electron energy in density functional theory: from exchange-correlation functional design to applied electronic structure calculations
KTH, School of Engineering Sciences (SCI), Theoretical Physics.
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [sv]

Att förutsäga egenskaper hos material och kemiska system är en viktig komponent för teoretisk och teknisk utveckling i fysik, kemi och biologi. Ett systems egenskaper styrs till stor del av dess elektrontillstånd. Datorprogram som baseras på täthetsfunktionalsteori kan beskriva elektronkonfigurationer mycket noggrant. Täthetsfunktionalsteorin hanterar all kvantmekanisk energi exakt, förutom ett mindre bidrag, utbytes-korrelationsenergin. Avhandlingen diskuterar existerande approximationer av utbytes-korrelationsenergin och presenterar en ny metod för konstruktion av funktionaler som hanterar detta bidrag---delsystems-funktionalmetoden. Flera teoretiska resultat relaterade till funktionalutveckling ges. En utbytes-korrelations-funktional har konstruerats helt utan empiriska antaganden (dvs, från första-princip). Funktionalen har använts för att beräkna gitterkonstant, bulkmodul och vakansenergi för aluminium, platina och kisel. Arbetet förväntas vara generellt tillämpbart inom området för täthetsfunktionalsteoriberäkningar

Abstract [en]

The prediction of properties of materials and chemical systems is a key component in theoretical and technical advances throughout physics, chemistry, and biology. The properties of a matter system are closely related to the configuration of its electrons. Computer programs based on density functional theory (DFT) can calculate the configuration of the electrons very accurately. In DFT all the electronic energy present in quantum mechanics is handled exactly, except for one minor part, the exchange-correlation (XC) energy. The thesis discusses existing approximations of the XC energy and presents a new method for designing XC functionals---the subsystem functional scheme. Numerous theoretical results related to functional development in general are presented. An XC functional is created entirely without the use of empirical data (i.e., from so called first-principles). The functional has been applied to calculations of lattice constants, bulk moduli, and vacancy formation energies of aluminum, platinum, and silicon. The work is expected to be generally applicable within the field of computational density functional theory.

Place, publisher, year, edition, pages
Stockholm: KTH , 2005. , ix, 85 p.
Series
Trita-FYS, ISSN 0280-316X ; 2005:48
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-428ISBN: 91-7178-150-1 (print)OAI: oai:DiVA.org:kth-428DiVA: diva2:11599
Public defence
2005-09-30, Sal FR4, AlbaNova, Roslagstullsbacken 21, Stockholm, 14:00
Opponent
Supervisors
Note
QC 20100830Available from: 2005-09-23 Created: 2005-09-23 Last updated: 2010-08-31Bibliographically approved
List of papers
1. Subsystem functionals: investigating the exchange energy per particle
Open this publication in new window or tab >>Subsystem functionals: investigating the exchange energy per particle
2002 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 66, no 16, 1651171-16511717 p.Article in journal (Refereed) Published
Abstract [en]

A viable way of extending the successful use of density-functional theory into studies of even more complex systems than are addressed today has been suggested by Kohn and Mattsson [W. Kohn and A. E. Mattsson, Phys. Rev. Lett. 81, 3487 (1998); A. E. Mattsson and W. Kohn, J. Chem. Phys. 115, 3441 (2001)], and is further developed in this work. The scheme consists of dividing a system into subsystems and applying different approximations for the unknown (but general) exchange-correlation energy functional to the different subsystems. We discuss a basic requirement on approximative functionals used in this scheme; they must all adhere to a single explicit choice of the exchange-correlation energy per particle. From a numerical study of a model system with a cosine effective potential, the Mathieu gas, and one of its limiting cases, the harmonic oscillator model, we show that the conventional definition of the exchange energy per particle cannot be described by an analytical series expansion in the limit of slowly varying densities. This indicates that the conventional definition is not suitable in the context of subsystem functionals. We suggest alternative definitions and approaches to subsystem functionals for slowly varying densities and discuss the implications of our findings on the future of functional development.

Keyword
Generalized Gradient Approximation, Electron-Gas, Potential Approximation, Metallic Surface, Expansion, Molecules, Formalism, Accurate, Solids, State
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-6784 (URN)10.1103/PhysRevB.66.165117 (DOI)000179286400053 ()
Note
QC 20100830Available from: 2005-09-23 Created: 2005-09-23 Last updated: 2017-12-14Bibliographically approved
2. How to tell an atom from an electron gas: a semi-local index of density inhomogeneity
Open this publication in new window or tab >>How to tell an atom from an electron gas: a semi-local index of density inhomogeneity
2003 (English)In: Acta physica et chimica debrecina, Vol. 36, no 25Article in journal (Refereed) Published
Abstract [en]

From a global perspective, the density of an atom is strongly inhomogeneous and not at all like the density of a uniform or nearly-uniform electron gas. But, from the semi-local or myopic perspective of standard density functional approximations to the exchange-correlation energy, it is not so easy to tell an atom from an electron gas. We address the following problem:  Given the ground-state electron density n and orbital kinetic energy density in the neighborhood of a point r, can we construct an inhomogeneity index which approaches zero for weakly-inhomogeneous densities and unity for strongly-inhomogeneous ones? The solution requires not only the usual local ingredients of a meta-generalized gradient approximation, but also r and r2. The inhomogeneity index is displayed for atoms, and for model densities of metal surfaces and bulk metals. Scaling behavior and a possible application to functional interpolation are discussed.



National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-6785 (URN)
Note
QC 20100830Available from: 2005-09-23 Created: 2005-09-23 Last updated: 2010-08-31Bibliographically approved
3. Alternative separation of exchange and correlation in density-functional theory
Open this publication in new window or tab >>Alternative separation of exchange and correlation in density-functional theory
2003 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 68, no 24, 2451201-2451205 p.Article in journal (Refereed) Published
Abstract [en]

It has recently been shown that local values of the conventional exchange energy per particle cannot be described by an analytic expansion in the density variation. Yet, it is known that the total exchange-correlation (XC) energy per particle does not show any corresponding nonanalyticity. Indeed, the nonanalyticity is here shown to be an effect of the separation into conventional exchange and correlation. We construct an alternative separation in which the exchange part is made well behaved by screening its long-ranged contributions, and the correlation part is adjusted accordingly. This alternative separation is as valid as the conventional one, and introduces no new approximations to the total XC energy. We demonstrate functional development based on this approach by creating and deploying a local-density-approximation-type XC functional. Hence, this work includes both the theory and the practical calculations needed to provide a starting point for an alternative approach towards improved approximations of the total XC energy.

Keyword
article, calculation, correlation analysis, density functional theory, elementary particle, energy, mathematical analysis, screening
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-6786 (URN)10.1103/PhysRevB.68.245120 (DOI)000188391900043 ()
Note
QC 20100831Available from: 2005-09-23 Created: 2005-09-23 Last updated: 2017-12-14Bibliographically approved
4. Functional designed to include surface effects in self-consistent density functional theory
Open this publication in new window or tab >>Functional designed to include surface effects in self-consistent density functional theory
2005 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 72, no 8, 085108- p.Article in journal (Refereed) Published
Abstract [en]

We design a density-functional-theory (DFT) exchange-correlation functional that enables an accurate treatment of systems with electronic surfaces. Surface-specific approximations for both exchange and correlation energies are developed. A subsystem functional approach is then used: an interpolation index combines the surface functional with a functional for interior regions. When the local density approximation is used in the interior, the result is a straightforward functional for use in self-consistent DFT. The functional is validated for two metals (Al, Pt) and one semiconductor (Si) by calculations of (i) established bulk properties (lattice constants and bulk moduli) and (ii) a property where surface effects exist (the vacancy formation energy). Good and coherent results indicate that this functional may serve well as a universal first choice for solid-state systems and that yet improved functionals can be constructed by this approach.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-6787 (URN)10.1103/PhysRevB.72.085108 (DOI)000231564600033 ()2-s2.0-33644936253 (Scopus ID)
Note
QC 20100831Available from: 2005-09-23 Created: 2005-09-23 Last updated: 2017-12-14Bibliographically approved
5. Nonequivalence of the generalized gradient approximations PBE and PW91
Open this publication in new window or tab >>Nonequivalence of the generalized gradient approximations PBE and PW91
2006 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 73, no 19, 195123- p.Article in journal (Refereed) Published
Abstract [en]

Two of the most popular generalized gradient approximations used in the applications of the density functional theory, PW91 and PBE, are generally regarded as essentially equivalent. They produce similar numerical results for many simple properties, such as lattice constants, bulk moduli, and atomization energies. We examine more complex properties of systems with electronic surface regions, with the specific application of the monovacancy formation energies of Pt and Al. A surprisingly large and consistent discrepancy between PBE and PW91 results is obtained. This shows that despite similarities found between some simple material properties, PBE and PW91 are not equivalent. The differences obtained for the monovacancy formation energies are related to differences in surface intrinsic errors which are substantiated using the idealized, well-controlled, jellium surface model. In view of the differences obtained with the PW91 and PBE functionals we develop separate surface intrinsic error corrections for these and revisit some earlier results.

Keyword
Density-Functional Approximations, Electron-Gas, Ultrasoft Pseudopotentials, Energy, Accurate, Systems, Transition, Exchange, Surfaces
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-6788 (URN)10.1103/PhysRevB.73.195123 (DOI)000237950400056 ()2-s2.0-33744492305 (Scopus ID)
Note
QC 20100831. Tidigare titel: PBE and PW91 are not the same. Titel ändrad samt uppdaterad från Submitted till Published 20100831.Available from: 2005-09-23 Created: 2005-09-23 Last updated: 2017-12-14Bibliographically approved
6. Numerical Integration of functions originating from quantum mechanics
Open this publication in new window or tab >>Numerical Integration of functions originating from quantum mechanics
(English)Report (Other academic)
Abstract [en]

Applications in quantum physics commonly involve large batches of integrals of smooth but veryoscillatory functions. The purpose of this work is to benchmark and compare different numerical algorithms for evaluating such integrals. The routines studied include: two from the QUADPACK package based on Gauss-Kronrod quadrature; one routine based on Patterson’s improvements of Gauss-Kronrod quadrature; and two routines that use a non-standard algorithm of applying quadrature-like rules of unrestricted order. The last algorithm has been seen in previous works,but is not in wide-spread use. The present work includes optimized implementations of this algorithm for both serial and parallel computation.

Place, publisher, year, edition, pages
Stockholm: KTH
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-6789 (URN)
Note
QC 20100831Available from: 2005-09-23 Created: 2005-09-23 Last updated: 2010-08-31Bibliographically approved

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