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Studies of Self-interaction Corrections in Density Functional Theory
KTH, School of Biotechnology (BIO), Theoretical Chemistry.
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The self-interaction error (SIE) in density functional theory (DFT) appears from the fact that the residual self-interaction in the Coulomb part and that in the exchange part do not cancel each other exactly. This error is responsible for the unphysical orbital energies of DFT and the failure to reproduce the potential energy curves of several physical processes.

The present thesis addresses several methods to solve the problem of SIE in DFT. A new algorithm is presented which is based on the Perdew-Zunger (PZ) energy correction and which includes the self-interaction correction (SIC) self-consistently (SC SIC PZ).

When applied to the study of hydrogen abstraction reactions, for which conventional DFT can not describe the processes properly, SC PZ SIC DFT produces reasonable potential energy curves along the reaction coordinate and reasonable transition barriers.

A semi-empirical SIC method is designed to correct the orbital energies. It is found that a potential coupling term is generally nonzero for all available approximate functionals. This coupling term also contributes to the self-interaction error. In this scheme, the potential coupling term is multiplied by an empirical parameter , introduced to indicate the strength of the potential coupling, and used to correct the PZ SIC DFT. Through a fitting scheme, we find that a unique can be used for C, N, O core orbitals in different molecules. Therefore this method is now used to correct the core orbital energies and relevant properties. This method is both efficient and accurate in predicting core ionization energies.

A new approach has been designed to solve the problem of SIE. A functional is constructed based on electron-electron interactions, Coulomb and exchange-correlation parts, which are free of SIE. A post-SCF procedure for this method has been implemented. The orbital energies thus obtained are of higher quality than in conventional DFT. For a molecular system, the orbital energy of the highest occupied molecular orbital (HOMO) is comparable to the experimental first ionization potential energy.

Place, publisher, year, edition, pages
Stockholm: KTH , 2008. , 51 p.
Series
Trita-BIO-Report, ISSN 1654-2312 ; 2008:11
National Category
Theoretical Chemistry
Identifiers
URN: urn:nbn:se:kth:diva-4740ISBN: 978-91-7178-964-8 (print)OAI: oai:DiVA.org:kth-4740DiVA: diva2:13726
Public defence
2008-05-28, FB52, AlbaNova, Roslagstullsbacken, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20100915Available from: 2008-05-09 Created: 2008-05-09 Last updated: 2010-09-15Bibliographically approved
List of papers
1. Core ionization potentials from self-interaction corrected Kohn-Sham Orbital energies
Open this publication in new window or tab >>Core ionization potentials from self-interaction corrected Kohn-Sham Orbital energies
2007 (English)In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 127, no 17, 174110- p.Article in journal (Refereed) Published
Abstract [en]

We propose a simple self-interaction correction to Kohn-Sham orbital energies in order to apply ground state Kohn-Sham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the " ΔKohn -Sham" method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter α is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique α=0.72 and basis set larger than 6-31G, the core ionization energies (IPs) of the self-interaction corrected Kohn-Sham calculations fit quite well to the experimental values. Hence, self-interaction corrected Kohn-Sham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency.

Keyword
Binding energy, Chemical shift, Density functional theory, Electrons, Organic compounds
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-8409 (URN)10.1063/1.2777141 (DOI)000250787300012 ()2-s2.0-35948963605 (Scopus ID)
Note
QC 20100906. Previous title: Self-interaction correction to Kohn-Sham core orbital energies in molecules.Available from: 2008-05-09 Created: 2008-05-09 Last updated: 2017-12-14Bibliographically approved
2. Self-interaction-corrected time-dependent density-functional-theory calculations of x-ray-absorption spectra
Open this publication in new window or tab >>Self-interaction-corrected time-dependent density-functional-theory calculations of x-ray-absorption spectra
Show others...
2007 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 76, no 2, 022506- p.Article in journal (Refereed) Published
Abstract [en]

We outline an approach within time-dependent density functional theory that predicts x-ray spectra on an absolute scale. The approach rests on a recent formulation of the resonant-convergent first-order polarization propagator [P. Norman , J. Chem. Phys. 123, 194103 (2005)] and corrects for the self-interaction energy of the core orbital. This polarization propagator approach makes it possible to directly calculate the x-ray absorption cross section at a particular frequency without explicitly addressing the excited-state spectrum. The self-interaction correction for the employed density functional accounts for an energy shift of the spectrum, and fully correlated absolute-scale x-ray spectra are thereby obtained based solely on optimization of the electronic ground state. The procedure is benchmarked against experimental spectra of a set of small organic molecules at the carbon, nitrogen, and oxygen K edges.

Keyword
Benchmarking, Carbon, Density functional theory, Excited states, Ground state, Nitrogen, Optimization, Oxygen, Polarization, Energy shift, Organic molecules, Polarization propagator, Self-interaction energy
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-8410 (URN)10.1103/PhysRevA.76.022506 (DOI)000249154900062 ()2-s2.0-34548203136 (Scopus ID)
Note
QC 20100914Available from: 2008-05-09 Created: 2008-05-09 Last updated: 2017-12-14Bibliographically approved
3. Perdew-Zunger self-interaction corrections in density functional calculations of transition barriers of hydrogen abstraction reactions
Open this publication in new window or tab >>Perdew-Zunger self-interaction corrections in density functional calculations of transition barriers of hydrogen abstraction reactions
(English)Article in journal (Other academic) Submitted
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-8411 (URN)
Note
QS 20120327Available from: 2008-05-09 Created: 2008-05-09 Last updated: 2012-03-27Bibliographically approved
4. Core electron chemical shifts of hydrogen-bonded structures
Open this publication in new window or tab >>Core electron chemical shifts of hydrogen-bonded structures
2009 (English)In: Chemical Physics Letters, ISSN 0009-2614, E-ISSN 1873-4448, Vol. 468, no 4-6, 294-298 p.Article in journal (Refereed) Published
Abstract [en]

We examine the possibility to study hydrogen-bonded structures through core ionization energies. We use a recently derived self-interaction corrected density functional theory method where the core ionization energies for all chemically shifted elements are obtained by a single calculation of the ground state of the structures. A direct dependency between the hydrogen atom to acceptor atom bond length and the chemical shift of the core ionization energy of the acceptor atom is found, something that has rami. cations for the possibility of effective predictions of hydrogen bond lengths in hydrogen-bonded systems. This observation is verified by the conventional, much more time-consuming, self-consistent field calculations based on density functional theory.

Keyword
self-interaction correction, scalar couplings, level shift, solid-state, systems, acid
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-18101 (URN)10.1016/j.cplett.2008.12.023 (DOI)000262412100040 ()2-s2.0-58149400893 (Scopus ID)
Note
QC 20100525. Tidigare titel: Core electron chemical shifts of hydrogen bonded networks using self interaction corrected DFTAvailable from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
5. An alternative approach to the solution of the self-interaction error in density functional theory with applications to ionization potentials
Open this publication in new window or tab >>An alternative approach to the solution of the self-interaction error in density functional theory with applications to ionization potentials
(English)Manuscript (Other academic)
National Category
Theoretical Chemistry
Identifiers
urn:nbn:se:kth:diva-8413 (URN)
Note
QC 20100915Available from: 2008-05-09 Created: 2008-05-09 Last updated: 2010-09-15Bibliographically approved

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