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Dissertations / Theses on the topic 'Periodic density functional theory'

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Published: 6 September 2023

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1

Todorova, Tanya Kumanova. "Periodic density functional study on supported vanadium oxides." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2007. http://dx.doi.org/10.18452/15680.

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Geträgerte Vanadiumoxidkatalysatoren sind wegen ihrer Vielseitigkeit bei Oxidationsreaktionen von großem Interesse. Der Schlüssel zum Verständnis der zugrunde liegenden Mechanismen ist ein weitreichendes Verständnis in die mikroskopische Struktur der Vanadiumoxide unter verschiedenen Bedingungen sowie die Art der Bindung an die Oberfläche des Trägers. In der vorliegenden Arbeit werden die Systeme Vanadiumoxid/Aluminiumoxid und Vanadiumoxid/Siliziumoxid mittels Dichtefunktionaltheorie in Kombination mit statistischer Thermodynamik untersucht. Als Modelle für Aluminiumoxid werden die s
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2

Lourenço, Mirtha Alejandra de Oliveira. "Tuning functionalized periodic mesoporous organosilicas for CO2/CH." Doctoral thesis, Universidade de Aveiro, 2016. http://hdl.handle.net/10773/21817.

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Doutoramento em Ciência e Engenharia de Materiais<br>Esta tese de doutoramento teve como principal objetivo a conceção de novas organossílicas mesoporosas periódicas (PMOs) para aplicação na separação de misturas gasosas de dióxido de carbono e metano. Materiais PMOs, com grupos fenileno e bifenileno bissililados, foram modificados por introdução de grupos funcionais amina, utilizando uma das seguintes metodologias: i) reação de co-condensação; ii) pós-modificação da ponte orgânica; iii) "grafting". O tamanho dos poros das PMOs funcionalizadas e não funcionalizadas foi definido pelo t
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3

Laino, Teodoro. "Multigrid QM/MM approaches in ab initio molecular dynamics." Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/85799.

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4

Burow, Asbjörn Manfred. "Methoden zur Beschreibung von chemischen Strukturen beliebiger Dimensionalität mit der Dichtefunktionaltheorie unter periodischen Randbedingungen." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2011. http://dx.doi.org/10.18452/16415.

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Die vorliegende Arbeit ist ein Beitrag auf dem Gebiet der theoretischen Chemie und beschäftigt sich mit der Entwicklung effizienter Berechnungsmethoden für die Elektronendichte und die Energie des Grundzustands molekularer und periodischer Systeme im Rahmen der Kohn-Sham-Dichtefunktionaltheorie (Kohn-Sham-DFT) und unter Verwendung von lokalen Basisfunktionen. Im Vordergrund steht dabei die einheitliche Beschreibung von Molekülen und ausgedehnten Systemen beliebiger Periodizität (zum Beispiel Volumenkristalle, dünne Filme und Polymere) mit einfachen Algorithmen bei einem hohen Maß an numerische
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5

Schweigert, Igor Vitalyevich. "Ab initio Density Functional Theory." [Gainesville, Fla.] : University of Florida, 2005. http://purl.fcla.edu/fcla/etd/UFE0011614.

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6

Laming, Gregory John. "Density functional theory for molecules." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336907.

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7

Chan, G. K. L. "Aspects of density functional theory." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597413.

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The first part of our work, we describe investigations into the formal and conceptual aspects of density functional theory. These have been in four main areas. The first, is the theory of the derivative discontinuity, where we extended the theory to density matrix functionals, and carried out calculations of the effects of the discontinuity. Our second investigation concerned a new channel concept, namely, the shape and local chemical potentials. These describe the electron donating or accepting power of a density fragment. We demonstrated in simple model systems, that chemical features such a
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8

Esplugas, Ricardo Oliveira. "Density functional theory and time-dependent density functional theory studies of copper and silver cation complexes." Thesis, University of Sussex, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.496931.

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A particular emphasis of this thesis has been to provide insight into the underlying stability of these complexes and hence interpret experimental data, and to establish the development of solvation shell structure and its effect on reactivity and excited states. Energy decomposition analysis, fragment analysis and charge analysis has been used throughout to provide deeper insight into the nature of the bonding in these complexes. This has also been used successfully to explain observed preferential stability and dissociative loss products.
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9

Taga, Adrian. "Materials Engineering Using Density Functional Theory." Doctoral thesis, KTH, Materials Science and Engineering, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3809.

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<p>This doctoral thesis presents density functionalcalculations applied in several domains of interest in solidstate physics and materials science. Non-collinear magnetismhas been studied both in an artificial multi-layer structure,which could have technological relevance as a magnetic sensordevice, and as excitations in 3d ferromagnets. The intricatebulk crystal structure of γ-alumina has been investigated.An improved embedded cluster method is developed and applied tostudy the geometric and electronic structures and opticalabsorption energies of neutral and positively charged oxygenvacancies
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10

Kaduk, Benjamin James. "Constrained Density-Functional Theory--Configuration Interaction." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/73175.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2012.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (p. 117-136).<br>In this thesis, I implemented a method for performing electronic structure calculations, "Constrained Density Functional Theory-- Configuration Interaction" (CDFT-CI), which builds upon the computational strengths of Density Functional Theory and improv
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11

Watson, Mark Adrian. "Density-functional theory and molecular properties." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615929.

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12

Schenk, Stefan. "Density functional theory on a lattice." kostenfrei, 2009. http://d-nb.info/998385956/34.

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13

Yasuda, Koji. "Correlation energy functional in the density-matrix functional theory." American Physical Society, 2001. http://hdl.handle.net/2237/8742.

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14

Helbig, Nicole. "Orbital functionals in density-matrix- and current-density-functional theory." [S.l.] : [s.n.], 2006. http://www.diss.fu-berlin.de/2006/442/index.html.

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15

Wlodarczyk, Radoslaw Stanislaw. "Surface structure predictions and development of global exploration tools." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17207.

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Diese Arbeit ist ein Beitrag zur theoretischen Chemie sowie zur Oberflächenchemie. Durch Kombination von computergestützten und experimentellen Untersuchungen wird die atomare Struktur von dünnen SiO2-Filmen auf Ru(0001)-Unterlagen, von eisendotierten SiO2-Filmen auf diesen Unterlagen und von H2O-Filmen auf MgO(001)-Oberflächen bestimmt. Die atomaren Strukturmodelle wurden entweder mit dem neu entworfenen und im Paket DoDo implementierten genetischen Algorithmus oder mittels auf Sachkenntnis gestützter Vermutungen erhalten. Die simulierten Eigenschaften der so erhaltenen Strukturen stimmen seh
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16

Osorio, Guillén Jorge Mario. "Density Functional Theory in Computational Materials Science." Doctoral thesis, Uppsala University, Department of Physics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4496.

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<p>The present thesis is concerned to the application of first-principles self-consistent total-energy calculations within the density functional theory on different topics in materials science.</p><p>Crystallographic phase-transitions under high-pressure has been study for TiO2, FeI2, Fe3O4, Ti, the heavy alkali metals Cs and Rb, and C3N4. A new high-pressure polymorph of TiO2 has been discovered, this new polymorph has an orthorhombic OI (Pbca) crystal structure, which is predicted theoretically for the pressure range 50 to 100 GPa. Also, the crystal structures of Cs and Rb metals have been
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17

Sargolzaei, Mahdi. "Orbital Polarization in Relativistic Density Functional Theory." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2007. http://nbn-resolving.de/urn:nbn:de:swb:14-1167841057730-69007.

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The description of the magnetic properties of interacting many-particle systems has been one of the most important goals of physics. The problem is to derive the magnetic properties of such systems from quantum mechanical principles. It is well understood that the magnetization in an atom described by quantum numbers, spin (S), orbital (L), and total angular momentum (J) of its electrons. A set of guidelines, known as Hund's rules, discovered by Friedrich Hermann Hunds help us to determine the quantum numbers for the ground states of free atoms. The question ``to which extent are Hund's rules
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18

Akyar, Ozge. "Density Functional Theory For Trapped Ultracold Fermions." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610948/index.pdf.

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Recently a new outlook on dealing with dipolar ultracold fermions based on density functional methods has received attention. A Thomas-Fermi treatment coupled with a variational approach has been developed for a collection of fermions trapped in a harmonic potential interacting via dipole-dipole forces. In this thesis, firstly our alternative formalism for Thomas-Fermi method by performing some calculations based on the Kohn-Sham formalism which is one of the main idea of density functional theory is investigated. Furthermore, density distributions are obtained dependent to the parameters<br>r
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19

Pawluk, Tiffany. "Iridium nanoparticles : a density functional theory study /." Available to subscribers only, 2005. http://proquest.umi.com/pqdweb?did=1075692711&sid=20&Fmt=2&clientId=1509&RQT=309&VName=PQD.

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20

Osorio, Guillén Jorge Mario. "Density functional theory in computational materials science /." Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4496.

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21

Choudhury, Rathin. "Application and development of density functional theory." Thesis, University College London (University of London), 2006. http://discovery.ucl.ac.uk/1444572/.

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This thesis concerns developments and applications using the density functional theory (DFT) ab initio electronic structure method. Implementation of a pseudo atomic orbital (PAO) basis set in the linear scaling DFT program CONQUEST is reported and used to test aspects of the linear scaling algorithm. Also a separate study using plane-wave DFT (VASP code) to model the strained growth of Indium Arsenide (InAs) on the (110) surface of Gallium Arsenide (GaAs), in particular the formation of a strain relieving dislocation network, has been performed. Pseudo atomic orbitals are the eigenstates of a
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22

Yam, Chi-yung, and 任志勇. "Linear-scaling time-dependent density functional theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B31246199.

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23

Stauffert, Oliver [Verfasser], and Michael [Akademischer Betreuer] Walter. "Electron-phonon coupling with density functional theory." Freiburg : Universität, 2019. http://d-nb.info/1191689328/34.

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24

Conroy, Michael W. "Density Functional Theory Studies of Energetic Materials." Scholar Commons, 2009. http://scholarcommons.usf.edu/etd/3691.

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First-principles calculations employing density functional theory (DFT) were performed on the energetic materials PETN, HMX, RDX, nitromethane, and a recently discovered material, nitrate ester 1 (NEST-1). The aims of the study were to accurately predict the isothermal equation of state for each material, improve the description of these molecular crystals in DFT by introducing a correction for dispersion interactions, and perform uniaxial compressions to investigate physical properties that might contribute to anisotropic sensitivity. For each system, hydrostatic-compression simulations were
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25

Nair, Nikhil. "New directions in hybrid density functional theory." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620224.

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26

Hollins, Thomas William. "Local exchange potentials in density functional theory." Thesis, Durham University, 2014. http://etheses.dur.ac.uk/10932/.

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DFT is a method that deals eciently with the ground state any-electron problem. It replaces the solution of the many-electron Schrodinger's equation with an equation to determine the electronic density alone. In the Kohn-Sham (KS) scheme, this density is obtained as the ground state density of a ctitious system of non-interacting electrons. The aim is to determine the local potential for these electrons so that their density equals the interacting density of the physical system. This potential is the sum of the electron-nuclear attraction, the Hartree repulsion from the density and nally the e
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27

Zawadzki, Krissia de. "Density-functional theory for single-electron transistors." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-24102018-165237/.

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The study of transport in nano-structured devices and molecular junctions has become a topic of great interest with the recent call for quantum technologies. Most of our knowledge has been guided by experimental and theoretical studies of the single-electron transistor (SET), an elementary device constituted by a quantum dot coupled to two otherwise independent free electron gases. The SET is particularly interesting because its transport properties at low temperatures are governed by the Kondo effect. A methodological difficulty has nonetheless barred theoretical progress in describing accura
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28

Aarons, Jolyon. "Density functional theory applied to metallic nanoparticles." Thesis, University of Southampton, 2018. https://eprints.soton.ac.uk/418013/.

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This thesis will focus on DFT for calculations of large metallic nanoparticles. It will show new algorithms that were developed for reduced scaling DFT methods for metals; the testing, verification and design of new descriptors for predicting the catalytic activity of metallic nanoparticles; application of large-scale DFT calculations to model nanoparticle sequences to show size and oxygen adsorption coverage trends, and finally the application of these techniques and knowledge to perform a study of oxygen adsorption on real-world, experimentally determined platinum nanoparticles in collaborat
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29

Sargolzaei, Mahdi. "Orbital Polarization in Relativistic Density Functional Theory." Doctoral thesis, Technische Universität Dresden, 2006. https://tud.qucosa.de/id/qucosa%3A24939.

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The description of the magnetic properties of interacting many-particle systems has been one of the most important goals of physics. The problem is to derive the magnetic properties of such systems from quantum mechanical principles. It is well understood that the magnetization in an atom described by quantum numbers, spin (S), orbital (L), and total angular momentum (J) of its electrons. A set of guidelines, known as Hund's rules, discovered by Friedrich Hermann Hunds help us to determine the quantum numbers for the ground states of free atoms. The question ``to which extent are Hund's rules
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30

Johnson, Erin R. "A density-functional theory including dispersion interactions." Thesis, Kingston, Ont. : [s.n.], 2007. http://hdl.handle.net/1974/926.

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31

Woodward, Clifford Edwin. "A density functional theory of polar fluids." Thesis, The University of Sydney, 1985. https://hdl.handle.net/2123/26797.

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32

Song, Yang. "Correcting density functional theory with supplemental potentials." Thesis, Boston University, 2013. https://hdl.handle.net/2144/12850.

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Thesis (Ph.D.)--Boston University PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.<br>Density Functional Theory (DFT) is a widely used method in quantum mechanics for modeling atoms and molecules. Commonly used DFT functionals have many shortcomings that include a poor description of dispersion,
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33

Sabatini, Riccardo. "Non-local correlation in Density Functional Theory." Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4710.

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In this thesis we present several advancements in the field of non-local Density Functional Theory (DFT). After a short theoretical introduction, both on DFT and some of its extensions, we introduce the non-local functional formalism as proposed by Dion et al. [PRL 92, 246401 (2004)] discussing the most important implementations. Then three main contributions are presented, starting from the stress derivation, with an application on aminoacid crystal; a new non-local functional formulation, the rVV10, derived from the original Vydrov and Van Voorhis implementation [JCP 133, 244103 (2010)], and
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34

Karlsson, Daniel. "Nuclear density functional theory calculations for the r-process nucleosynthesis : Nuclear density functional theory calculations for the r-process nucleosynthesis." Thesis, KTH, Fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-250775.

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35

Dal, Corso Andrea. "Density-functional theory beyond the pseudopotential local density approach: a few cases studies." Doctoral thesis, SISSA, 1993. http://hdl.handle.net/20.500.11767/4059.

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36

Sayin, Ceren Sibel. "Density Functional Theory Investigation Of Tio2 Anatase Nanosheets." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12611075/index.pdf.

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In this thesis, the electronic properties of nanosheets derived from TiO2 anatase structure which acts as a photocatalyst, are investigated using the density functional theory. We examine bulk constrained properties of the nanosheets derived from the (001) surface and obtain their optimized geometries. We investigate properties of lepidocrocite-type TiO2 nanosheets and nanotubes of different sizes formed by rolling the lepidocrocite nanosheets. We show that the stability and the band gaps of the considered nanotubes increase with increasing diameter. We also study adsorption of Aun clusters wi
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37

Iusan, Diana Mihaela. "Density Functional Theory Applied to Materials for Spintronics." Doctoral thesis, Uppsala universitet, Materialteori, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119887.

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The properties of dilute magnetic semiconductors have been studied by combined ab initio, Monte Carlo, and experimental techniques. This class of materials could be very important for future spintronic devices, that offer enriched functionality by making use of both the spin and the charge of the electrons. The main part of the thesis concerns the transition metal doped ZnO. The role of defects on the magnetic interactions in Mn-doped ZnO was investigated. In the presence of acceptor defects such as zinc vacancies and oxygen substitution by nitrogen, the magnetic interactions are ferromagnetic
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38

Mills, Eric A. "Protein-solvent interactions and classical density functional theory." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/55761.

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We use classical density functional theory to investigate the interactions between solvents and proteins. We examine a diverse experimental literature to establish thermodynamic properties of protein-cosolute interaction, particularly the compensation between transfer entropy and transfer enthalpy. We develop a method of analysing the uncertainties in such measurements and use the method to resolve a long-standing debate over entropy-enthalpy compensation. We develop a classical density functional theory for interactions between proteins and cosolutes. The theory developed here ignores the sol
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39

Manoli, Soheil Dimitri. "The generalized exchange local spin density-functional theory /." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75359.

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An orbital dependent local spin density-functional (LSD) scheme with a generated exchange, the LSD GX scheme, has been developed based on the correct normalization conditions of an electron gas. This scheme contains no adjustable parameters; the B$ sb1$, B$ sb2$ and $ alpha sp lim$ are constant for all atoms once the shape of the Fermi hole is chosen. These parameters are rigorously calculated using an unspecified Fermi hole correlation factor and they give an exchange density which reduces exactly to the homogeneous free electron gas one at the high electron density limit.<br>The LSD GX excha
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40

Zhou, Si. "Density functional theory study of oxidized epitaxial graphene." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/52264.

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Graphene oxide (GO) is a material of both fundamental and applied interest. Elucidating this complex material is crucial to both control its physical chemical properties and enable its applications in technology. Graphene oxide films synthesized from epitaxial graphene on silicon carbide constitute a particular -- simplified -- form of GO, suitable for fundamental physical chemistry studies of oxidized sp2 carbon materials. In this thesis work, I used density functional theory calculations and I developed a lattice-model Monte Carlo scheme to elucidate puzzling experimental observations and to
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41

Crawford, P. "A density functional theory study of chemical reactivity." Thesis, Queen's University Belfast, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.431588.

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42

Brincat, Nick. "Density functional theory investigation of the uranium oxides." Thesis, University of Bath, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.665418.

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The aim of this thesis is to provide insight into the structures and properties of the uranium oxides. As UO2 is easily oxidised during the nuclear fuel cycle it is important to have a detailed understanding of the structures and properties of the oxidation products. Experimental work over the years has revealed many stable oxides including UO2, U4O9, U3O7, U2O5, U3O8 and UO3, all with a number of different polymorphs. The oxides are broadly split into two categories, fluorite-based structures with stoichiometries in the range of UO2 to U2O5 and less dense layered-type structures with stoichio
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43

Ioannou, Andrew George. "Applications of time-dependent current density functional theory." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624734.

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44

Di, Sabatino Stefano. "Reduced density-matrix functional theory : correlation and spectroscopy." Thesis, Toulouse 3, 2015. http://www.theses.fr/2015TOU30137.

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Cette thèse traite de la description de la corrélation électronique et de la spectroscopie dans le cadre de la Théorie de la Fonctionnelle de la Matrice Densité Réduite (RDMFT). Dans la RDMFT, les propriétés de l'état fondamental d'un système physique sont des fonctionnelles de la matrice densité à un corps. Plusieurs approximations à la corrélation électronique ont été proposées dans la littérature. Beaucoup d'entre elles peuvent être reliés au travail de Müller, qui en a proposé une similaire à l'approximation Hartree-Fock mais qui peut produire des nombres d'occupation fractionnaires. Cela
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45

Rohra, Stefan Bruno. "Exact exchange Kohn-Sham spin current density functional theory." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=98054078X.

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46

Nigussa, Kenate Nemera. "Density Functional Theory Investigations of Surface Structure and Reactivity." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-14345.

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The Cr2O3(0001) surface is assumed to terminate by chromium atoms, chromyl groups, and oxygen atoms. This essentially models the industrial surface when subjected to different oxygen chemical potentials. The issue of high temperature surface states is also of particular importance concerning various effects such as corrosion. The investigation of the interaction of selected atomic adsorbates, paper I, has not only been important from a fundamental physics point of view, but also offered useful insight on applied subjects such as corrosion. Various diatomic molecules, paper II, are found to sho
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47

Rebolini, Elisa. "Range-separated density-functional theory for molecular excitation energies." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066214/document.

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La théorie de la fonctionnelle de la densité dépendante du temps (TDDFT) est aujourd'hui une méthode de référence pour le calcul des énergies d'excitation électroniques. Cependant, dans les approximations usuelles, elle n'est pas capable de décrire correctement les excitations de Rydberg, à transfert de charge ou présentant un caractère multiple. La séparation de portée de l'interaction électronique permet de combiner rigoureusement les méthodes fonctionnelles pour décrire la courte portée de l'interaction et les méthodes fonctions d'onde ou fonctions de Green pour la longue portée. Dans cette
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48

Tu, Guangde. "Studies of self-interaction corrections in density functional theory /." Stockholm : Bioteknologi, Kungliga Tekniska högskolan, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4450.

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Tu, Guangde. "Studies of Self-interaction Corrections in Density Functional Theory." Doctoral thesis, Stockholm : School of Biotechnology, Royal Institute of Technology, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4740.

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50

Zhang, Yu. "Mathematical aspects and chemical applications of density functional theory." Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/5306.

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My Ph. D. work is about theoretical basis and applications of density functional theory (DFT). DFT has demonstrated a good balance between computing costand accuracy, so it has become one of the most popular daily-used quantum chemistry methods. The first part of my work is about the asymptotic behavior of finite-system wave-functions. The exponential decaying asymptotic behavior is confirmed andthe structure of the prefactors is further explored. By comparing the asymptotic behavior of the Dyson orbitals and the Kohn-Sham orbitals, we have also provided a physical interpretation of the Kohn-S
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