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1
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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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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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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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 as shell structure, or atoms in molecules, could be characterised as regions of constant shape chemical potential. Our third investigation concerned the homogeneous scaling of the Kohn-Sham kinetic energy. We disproved certain existing relations in the literature; we then went on to derive simple bounds on the kinetic energy, and to numerically calculate the approximate scaling of the kinetic energy in atomic systems. Our fourth investigation concerned an improved Lieb-Oxford bound for the exchange-correlation energy. By improving the numerical optimisation in the last part of the proof, we were able to tighten the bound. The second part of our work focused on the search for new energy functionals, and procedures for developing new functionals. Our efforts have been in two areas. The first was an investigation of the correlation functional of Hartree-Fock-Kohn-Sham theory. We observed the deficiencies of current functionals in the reproduction of the correlation potential, and attempted to correct this by fitting a functional to best reproduce numerical correlation potentials. In doing so, we observed the highly non-local nature of correlation in Hartree-Fock-Kohn-Sham theory, and the important effect of the derivative discontinuity on the energy. The second investigation attempted an exhaustive study of the Generalised Gradient Approximation (GCA), within a well-defined ab initio model. We developed a rigorous fitting methodology, and constructed well-converged fits to conclusively explore the limits of the accuracy of the GCA. A large number of observations were made concerning the choice of functional basis, the importance of additional gradient corrections, and the role of exact exchange. We also applied our fitting methodology to the construction of approximate Kohn-Sham kinetic energy functionals, with some success.
5
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.
6
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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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 in α-quartz. Ab initio total energycalculations, based on the EMTO theory, have been used todetermine the elastic properties of Al1-xLixrandom alloys in the face-centered cubiccrystallographic phase. The obtained overall good agreementwith experiment demonstrates the applicability of the quantummechanics formulated within the framework of the DensityFunctional Theory for mapping the structural and mechanicalproperties of random alloys against chemical composition.
7
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.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (p. 117-136).
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 improves upon it by including higher level treatments of electronic correlation which are not readily available in Density-Functional Theory but are a keystone of wavefunction-based electronic structure methods. The method involves using CDFT to construct a small basis of hand-picked states which suffice to reasonably describe the static correlation present in a particular system, and efficiently computing electronic coupling elements between them. Analytical gradients were also implemented, involving computational effort roughly equivalent to the evaluation of an analytical Hessian for an ordinary DFT calculation. The routines were implemented within Q-Chem in a fashion accessible to end users; calculations were performed to assess how CDFT-CI improves reaction transition state energies, and to assess its ability to produce conical intersections, as compared to ordinary DFT. The analytical gradients enabled optimization of reaction transition-state structures, as well as geometry optimization on electronic excited states, with good results.
by Benjamin James Kaduk.
Ph.D.
8
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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Schenk, Stefan. "Density functional theory on a lattice". kostenfrei, 2009. http://d-nb.info/998385956/34.
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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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11
Bhattacharyya, Anirban. "Application of effective field theory to density functional theory for finite systems". Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1124116299.
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Thesis (Ph. D.)--Ohio State University, 2005.Title from first page of PDF file. Document formatted into pages; contains xv, 210 p.; also includes graphics (some col.). Includes bibliographical references (p. 205-210). Available online via OhioLINK's ETD Center
12
Yam, Chi-yung, i 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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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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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.
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 studied under high compressions. Our results confirm the recent high-pressure experimental observations of new complex crystal structures for the Cs-III and Rb-III phases. Thus, it is now certain that the famous isostructural phase transition in Cs is rather a new crystallographic phase transition.
The elastic properties of the new superconductor MgB2 and Al-doped MgB2 have been investigated. Values of all independent elastic constants (c11, c12, c13, c33, and c55) as well as bulk moduli in the a and c directions (Ba and Bc respectively) are predicted. Our analysis suggests that the high anisotropy of the calculated elastic moduli is a strong indication that MgB2 should be rather brittle. Al doping decreases the elastic anisotropy of MgB2 in the a and c directions, but, it will not change the brittle behaviour of the material considerably.
The three most relevant battery properties, namely average voltage, energy density and specific energy, as well as the electronic structure of the Li/LixMPO4 systems, where M is either Fe, Mn, or Co have been calculated. The mixing between Fe and Mn in these materials is also examined. Our calculated values for these properties are in good agreement with recent experimental values. Further insight is gained from the electronic density of states of these materials, through which conclusions about the physical properties of the various phases are made.
The electronic and magnetic properties of the dilute magnetic semiconductor Mn-doped ZnO has been calculated. We have found that for an Mn concentration of 5.6%, the ferromagnetic configuration is energetically stable in comparison to the antiferromgnetic one. A half-metallic electronic structure is calculated by the GGA approximation, where Mn ions are in a divalent state leading to a total magnetic moment of 5 μB per Mn atom.
14
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 applicable on different systems such as molecules and solids?'' is still on the agenda. The main problem is that of finding the ground state of the considered system. Density functional theory (DFT) methods apparently are the most widely spread self-consistent methods to investigate the ground state properties. This is due to their high computational efficiency and very good accuracy. In the framework of DFT, usually the total energy is decomposed into kinetic energy, Coulomb energy, and a term called the exchange-correlation energy. Taking into account the relativistic kinetic energy leads to direct and indirect relativistic effects on the electronic structure of a solid. The most pronounced direct effect (although not the biggest in magnitude) is the spin-orbit splitting of band states. A well-known indirect relativistic effect is the change of screening of valence electrons from the nuclear charge by inner-shell electrons. One can ask that how relativistic effects come into play in ordinary density functional theory. Of course ordinary density functional theory does not include those effect. Four-current density functional theory (CDFT), the quantum electrodynamic version of the Hohenberg-Kohn theory is a powerful tool to treat relativistic effects. Although it is principally designed for systems in strong magnetic fields, CDFT can also be applied in situations where currents are present without external magnetic fields. As already pointed out by Rajagopal and Callaway (1973), the most natural way to incorporate magnetism into DFT is the generalization to CDFT. These authors, however, treated its most simple approximation, the spin density functional theory (SDFT), which keeps the spin current only and neglects completely correlation effects of orbital currents. By using the Kohn-Sham-Dirac (KSD) equation, spin-orbit coupling is introduced kinematically. The part of the orbital magnetism that is a consequence of Hund's second rule coupling is absent in this theory and there is not any more a one-to-one mapping of spin densities onto external fields. In solids, in particular in metals, the importance of Hund's second rule coupling (orbital polarization) and Hund's third rule (spin-orbit coupling) is usually interchanged in comparison to atoms. Thus, in applications of the relativistic CDFT to solids, the usual way has been to keep the spin-orbit coupling in the KSD equation (an extension to ordinary Kohn-Sham (KS) equation) and to neglect the orbital contribution to the total current density and approximate exchange-correlation energy functional with spin density only. This scheme includes a spontaneous exchange and correlation spin polarization. Orbital polarization, on the other hand, comes into play not as a correlation effect but also as an effect due to the interplay of spin polarization and spin-orbit coupling: In the presence of both couplings, time reversal symmetry is broken and a non-zero orbital current density may occur. Application of this scheme to 3d and 4f magnets yields orbital moments that are smaller than related experimental values by typically a factor of two. Orbital magnetism in a solid is strongly influenced by the ligand field, originating from the structural environment and geometry of the solid. The orbital moments in a solid with cubic symmetry are expected to be quenched if spin-orbit coupling is neglected. However, spin-orbit coupling induces orbital moments, accordingly. The relativistic nature of the spin-orbit coupling requires orbital magnetism to be treated within QED, and the treatment of QED in solids is possible in the frame of current density functional theory. The kinematic spin-orbit coupling is accounted for in many DFT calculations of magnetic systems within the LSDA. However, a strong deviation of the LSDA orbital moments from experiment is found in such approaches. To avoid such deviations, orbital polarization corrections would be desirable. In this Thesis, those corrections have been investigated in the framework of CDFT. After a short review for CDFT in Chapter 2, in Chapter 3, an "ad hoc" OP correction term (OPB) suggested by Brooks and Eriksson is given. This correction in some cases gives quite reasonable corrections to orbital moments of magnetic materials. Another OP correction (OPE), which has been introduced recently, was derived from the CDFT in the non-relativistic limit. Unfortunately, the program can only incompletely be carried through, as there are reasonable but uncontrolled approximations to be made in two steps of the derivation. Nevertheless, the result is quite close to the "ad hoc"ansatz. The calculated OPE energies for 3d and 4f free ions are in qualitative agreement with OPB energies. In Chapter 4, both corrections are implemented in the FPLO scheme to calculate orbital moments in solids. We found that both OPB and OPE corrections implemented in FPLO method, yield reasonably well the orbital magnetic moments of bcc Fe, hcp Co and fcc Ni compared with experiment. In Chapter 5, the effect of spin-orbit coupling and orbital polarization corrections on the spin and orbital magnetism of full-Heusler alloys is investigated by means of local spin density calculations. It is demonstrated, that OP corrections are needed to explain the experimental orbital moments. Model calculations employing one ligand field parameter yield the correct order of magnitude of the orbital moments, but do not account for its quantitative composition dependence. The spin-orbit coupling reduces the degree of spin polarization of the density of states at Fermi level by a few percent. We have shown that the orbital polarization corrections do not change significantly the spin polarization degree at the Fermi level. We also provide arguments that Co2FeSi might not be a half-metal as suggested by recent experiments. In Chapter 6, to understand recent XMCD data for Co impurities in gold, the electronic structure of Co impurities inside gold has been calculated in the framework of local spin density approximation. The orbital and spin magnetic moment have been evaluated. In agreement with experimental findings, the orbital moment is enhanced with respect to Co metal. On the other hand, internal relaxations are found to reduce the orbital moment considerably, whereas the spin moment is less affected. Both OPB and OPE yield a large orbital moment for Co impurities. However, those calculated orbital moments are almost by a factor of two larger than the experimental values. We also found that the orbital magnetic moment of Co may strongly depend on pressure.
15
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
parametersrescaled interaction strength, dipole-dipole energy and the trap parameter which determine the trap geometry based on this theory. The thesis starts with a brief outline of the density functional theory and theory of our system, continues with calculations based on this theory, which are free of any variational assumptions for the density profile. Moreover, results of density graphics for harmonic trap will be followed by discussion of comparison and contrast with Thomas-Fermi method based on the paper of Goral et al.. These discussions are mainly about the shape of the density distribution, variation of the cloud parameters and energy behaviours according to the rescaled interaction strength. The thesis concludes with an analysis of contribution of density functional theory to this fermionic system.
16
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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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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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 pseudo-atom confined to a spherical potential, as used in the SIESTA linear scaling DFT program, and consist of a radial function multiplied by a spherical harmonic. Code to evaluate overlap and kinetic energy matrix elements between PAOs has been written, and tested using Gaussian PAOs, whose overlap integrals can be computed analytically. The PAO code has been integrated into the CON QUEST program and used to perform tests of the linear scaling algorithms on Silicon. Conventional plane wave DFT has been applied to calculate the energetics of a dislocation network in InAs grown on GaAs(110). Both InAs and GaAs have the zinc-blende crystal structure but the lattice constant of InAs is seven percent greater than that of GaAs. Experiments show that during deposition of the InAs by molecular beam epitaxy (MBE) compressive strain leads to formation of a strain relieving dislocation network after a critical amount of InAs coverage. In this thesis DFT is applied to calculate the energetically favoured location for the dislocation core and the resulting structure. In addition the critical InAs coverage necessary for dislocation formation is also calculated and compared to that measured by experiment.
19
Stauffert, Oliver [Verfasser], i Michael [Akademischer Betreuer] Walter. "Electron-phonon coupling with density functional theory". Freiburg : Universität, 2019. http://d-nb.info/1191689328/34.
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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 performed. Important
properties calculated from the simulations such as the equilibrium structure, isothermal
equation of state, and bulk moduli were compared with available experimental data to
assess the agreement of the calculation method. The largest contribution to the error was
believed to be caused by a poor description of van der Waals (vdW) interactions within
the DFT formalism.
An empirical van der Waals correction to DFT was added to VASP to increase
agreement with experiment. The average agreement of the calculated unit-cell volumes
for six energetic crystals improved from approximately 9% to 2%, and the isothermal
EOS showed improvement for PETN, HMX, RDX, and nitromethane. A comparison was
made between DFT results with and without the vdW correction to identify possible
advantages and limitations.
Uniaxial compressions perpendicular to seven low-index crystallographic planes
were performed on PETN, HMX, RDX, nitromethane, and NEST-1. The principal
stresses, shear stresses, and band gaps for each direction were compared with available
experimental information on shock-induced sensitivity to determine possible correlations
between physical properties and sensitivity. The results for PETN, the only system for
which the anisotropic sensitivity has been thoroughly investigated by experiment,
indicated a possible correlation between maximum shear stress and sensitivity. The
uniaxial compressions that corresponded to the greatest maximum shear stresses in HMX,
RDX, solid nitromethane, and NEST-1 were identified and predicted as directions with
possibly greater sensitivity. Experimental data is anticipated for comparison with the
predictions.
21
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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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 exchange and correlation potential. The central approximation in DFT is the functional form of the exchange-correlation potential. The most basic approximate functionals are explicit functions of the electron density. More sophisticated approximations are orbital dependent functionals or hybrids of density and orbital dependent functionals. In this work we present the implementation of some accurate local exchange potentials, the exact exchange (EXX) potential, the local Fock exchange (LFX) potential and an approximation to EXX, the common energy denominator approximation (CEDA) potential. The EXX potential minimises the Hartree-Fock (HF) total energy and is calculated using perturbation theory and the Hylleraas variational method, improving upon previous implementations. Optimising a local potential that adopts the HF density as its own ground state density, gives the LFX potential, which is simple to calculate and physically equivalent to the EXX potential. Both the EXX and LFX methods are extended to be applicable to metallic systems. The implemented potentials are used to calculate the electronic band structures for semiconductors, insulators, antiferromagnetic insulators and metals. For the semiconducting, insulating and metallic systems studied, the LFX method gives very similar results to EXX. In the systems characterised by stronger correlations, we observe a small disparity between the two exchange methods. When compared to experiment, the results are surprisingly accurate, given the complete neglect of correlation in these calculations. This is remarkable for the strongly correlated systems and also for the simple metals, given the well-known qualitative failure of Hartree-Fock for metals. The fundamental gap of a system is the sum of the KS eigenvalue gap and a correction known as the derivative discontinuity. The exact derivative discontinuity for a system is derived from ensemble density functional theory, thus allowing the full calculation of fundamental band gaps. Approximate forms of the discontinuity for the local density approximation (LDA), generalised gradient approximations (GGA), EXX and LFX are also derived and implemented. Contrary to the accepted wisdom, that the derivative discontinuity for local approximations (LDA/GGA) vanishes, calculated LDA and GGA fundamental band gaps give a much improved result over the corresponding Kohn-Sham band gaps, with accuracy comparable to EXX and LFX KS band gaps. Finally the derivative discontinuity using exact exchange and an orbital dependent correlation functional was also derived but not implemented.
23
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 accurately realistic devices. On the one hand, Density-Functional Theory (DFT), the most convenient tool to obtain the electronic structure of complex materials, yields only qualitatively descriptions of the low-temperature physical properties of quantum dot devices. On the other hand, a quantitative description of low-temperature transport properties of the SET, such that obtained through the solution of the Anderson model via exact methods, is nonetheless unable to account for realistic features of experimental devices, such as geometry, band structure and electron-electron interactions in the electron gases. DFT describes the electron gases very well, but proves inadequate to treat the electronic correlations introduced by the quantum dot. This thesis proposes a way out of this frustrating dilemma. Our contribution is founded on renormalization-group (RG) concepts. Specifically, we show that, under conditions of experimental interest, the high and low temperatures regimes of a SET corresponds to the weakly-coupling and strongly-coupling fixed points of the Anderson Hamiltonian. Based on an RG analysis, we argue that, at this low-temperature fixed point, the entanglement between impurity and gas-electron spins introduces non-local correlations that lie beyond the reach of local- or quasi-local-density approximations, hence rendering inadequate approximations for the exchange-correlation energy functional. By contrast, the weak-coupling fixed point is within the reach of local-density approximations. With a view to describing realistic properties of quantum dot devices, we therefore propose a hybrid self-consistent procedure that starts with the weak-coupling fixed point and takes advantage of a reliable numerical method to drive the Hamiltonian to the strong-coupling fixed point. Our approach employs traditional DFT to treat the weak-coupling system and the Numerical Renormalization-Group (NRG) method to obtain properties in the strongcoupling regime. As an illustration, we apply the procedure to a single-electron transistor modeled by a generalized one-dimensional Hubbard Hamiltonian. We analyze the thermal dependence of the conductance in the SET and discuss its behavior at low-temperatures, comparing our results with other self-consistent approaches and with experimental data.O estudo de propriedades de transporte em dispositivos nano estruturados e junções moleculares tornou-se um tópico de grande interesse com a recente demanda por novas tecnologias quânticas. Grande parte do nosso conhecimento tem sido guiado por trabalhos experimentais e teóricos de um dispositivo conhecido como transístor de um elétron (SET), o qual é constituído por um ponto quântico acoplado a dois gases de elétrons independentes. O SET é particularmente interessante devido as suas propriedades de transporte a baixas temperaturas, as quais são governadas pelo efeito Kondo. Uma dificuldade metodológica, no entanto, tem barrado novos avanços teóricos para se obter uma descrição precisa de dispositivos realistas. Por um lado, a teoria do funcional da densidade (DFT), uma das ferramentas mais convenientes para calcular a estrutura eletrônica de materiais complexos, provê uma descrição apenas qualitativa das propriedades de transporte de transístores quânticos a baixas temperaturas. Por outro lado, uma descrição quantitativa satisfatória do SET a baixas temperaturas, tal como a modelagem e solução do modelo de Anderson via métodos exatos, é incapaz de levar em conta características realistas de dispositivos complexos, tal como geometria, estrutura de bandas e interações inter eletrônicas nos gases de elétrons. Embora a DFT os descreva bem, ela é inadequada para tratar correlações introduzidas pelo ponto quântico. Na presente tese propomos uma alternativa para este dilema. Nossa contribuição é fundamentada em conceitos de grupo de renormalização (RG). Especificamente, mostramos que, em condições de interesse experimental, os regimes de altas e baixas temperaturas em um SET correspondem aos pontos fixos de acoplamento fraco e forte do Hamiltoniano de Anderson. Baseando-nos em na análise do RG, mostramos que, no ponto fixo de baixas temperaturas, o emaranhamento entre a impureza e os spins dos gases eletrônicos introduz correlações não-locais que não podem ser descritas com abordagens DFT baseadas em aproximações locais ou quase locais para o potencial de troca e correlação. Em contraste, o ponto fixo de acoplamento fraco pode ser descrito por aproximações locais. Com o objetivo de obter uma descrição realista das propriedades de transístores quânticos, propomos um procedimento auto-consistente que começa do ponto fixo de acoplamento fraco e se aproveita de um método numérico eficiente para levar o Hamiltoniano para o ponto fixo de acoplamento forte. Nossa abordagem emprega DFT para tratar o sistema no limite de acoplamento fraco e o método de Grupo de Renormalização Numérico (NRG) para obter propriedades no regime de acoplamento forte. Como ilustração, aplicamos o procedimento para um transístor de um elétron modelado através do Hamiltoniano de Hubbard generalizado. Analisamos a dependência térmica da condutância no SET discutindo seu comportamento a baixas temperatura e comparamos nossos resultados com outras abordagens auto-consistentes e resultados experimentais.
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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 collaboration with the Nellist group at Oxford materials. We explore the binding of atomic oxygen to cuboctahedral platinum nanoparticles of up to 1000 atoms using DFT calculations in ONETEP. We demonstrate convergence to the infinite slab limit for single oxygen adsorption in chapter 4 and correlate adsorption strength against popular descriptors for catalytic activity, such as the d-band centre approach. This approach is possible because of work which will be described in chapter 3 to implement angular momentum projected density of states calculations in ONETEP. The effects of oxygen coverage on the Pt55 and Pt147 cuboctahedral nanoparticles will also be analysed, which serves to advance our simulations towards realistic conditions. We show in our investigation into half monolayer, hemispherical oxygen coverage on platinum nanoparticles that oxygen tends to gravitate towards the edges and lower coordinated sites in the nanoparticle and away from the centres of facets. This effect correlates with the site specific, single oxygen adsorption energies on Pt309 and experimental platinum nanoparticles which is presented in chapter 5. We show that when subdividing the binding of monolayers of oxygen into only (111) and (100) facets that these have a lower adsorption strength per oxygen atom than combined (100) and (111) facets as well as lower binding strength than single oxygen adsoprtion. In the next part of the study, which is discussed in chapter 5, we show large scale DFT calculations on real platinum nanoparticles, which were measured by the Nellist group at Oxford materials using advanced electron microscopy techniques. These DFT calculations provide the electronic structure of the experimentally measured nanoparticles, which allowed us to apply electron density based catalytic activity descriptors to the nanoparticles, such as the d-band centre approach, or our own electronic density based descriptor described in chapter 3. We find that surface roughness of the experimental nanoparticles contributes to more potential oxygen binding sites with low electron density, which correlatates with stronger oxygen adsorption strength in our model, when compared with the relative smoothness of cuboctahedral and truncated octahedral facets. In the analysis which is presented in chapter 5, the proportion of sites which lie within 0.2 eV of the oxygen binding strength required for optimum catalytic activity is predicted with high efficiency, based on our catalytic activity descriptor. Finally, in chapter 6 we describe a new method for large scale DFT calculations on metallic systems which we call the AQuA-FOE method. We show how this method can have a computational cost which increases effectively linearly with the number of atoms. The AQuA-FOE method works by implicitly heating and quenching the electrons in the system to find the oneparticle density matrix, while conserving the electron number. We show validation of this method inside the EDFT procedure by comparing numerically with the diagonalisation based EDFT that is already implemented in ONETEP showing agreement in the energies to better than 10⁻⁵ EH per atom. We will also demonstrate the effectively linear-scaling computational cost of our method with calculation times on regular truncated octahedral Palladium nanoparticles ranging from 2,406 to 12,934 atoms.
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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 applicable on different systems such as molecules and solids?'' is still on the agenda. The main problem is that of finding the ground state of the considered system. Density functional theory (DFT) methods apparently are the most widely spread self-consistent methods to investigate the ground state properties. This is due to their high computational efficiency and very good accuracy. In the framework of DFT, usually the total energy is decomposed into kinetic energy, Coulomb energy, and a term called the exchange-correlation energy. Taking into account the relativistic kinetic energy leads to direct and indirect relativistic effects on the electronic structure of a solid. The most pronounced direct effect (although not the biggest in magnitude) is the spin-orbit splitting of band states. A well-known indirect relativistic effect is the change of screening of valence electrons from the nuclear charge by inner-shell electrons. One can ask that how relativistic effects come into play in ordinary density functional theory. Of course ordinary density functional theory does not include those effect. Four-current density functional theory (CDFT), the quantum electrodynamic version of the Hohenberg-Kohn theory is a powerful tool to treat relativistic effects. Although it is principally designed for systems in strong magnetic fields, CDFT can also be applied in situations where currents are present without external magnetic fields. As already pointed out by Rajagopal and Callaway (1973), the most natural way to incorporate magnetism into DFT is the generalization to CDFT. These authors, however, treated its most simple approximation, the spin density functional theory (SDFT), which keeps the spin current only and neglects completely correlation effects of orbital currents. By using the Kohn-Sham-Dirac (KSD) equation, spin-orbit coupling is introduced kinematically. The part of the orbital magnetism that is a consequence of Hund's second rule coupling is absent in this theory and there is not any more a one-to-one mapping of spin densities onto external fields. In solids, in particular in metals, the importance of Hund's second rule coupling (orbital polarization) and Hund's third rule (spin-orbit coupling) is usually interchanged in comparison to atoms. Thus, in applications of the relativistic CDFT to solids, the usual way has been to keep the spin-orbit coupling in the KSD equation (an extension to ordinary Kohn-Sham (KS) equation) and to neglect the orbital contribution to the total current density and approximate exchange-correlation energy functional with spin density only. This scheme includes a spontaneous exchange and correlation spin polarization. Orbital polarization, on the other hand, comes into play not as a correlation effect but also as an effect due to the interplay of spin polarization and spin-orbit coupling: In the presence of both couplings, time reversal symmetry is broken and a non-zero orbital current density may occur. Application of this scheme to 3d and 4f magnets yields orbital moments that are smaller than related experimental values by typically a factor of two. Orbital magnetism in a solid is strongly influenced by the ligand field, originating from the structural environment and geometry of the solid. The orbital moments in a solid with cubic symmetry are expected to be quenched if spin-orbit coupling is neglected. However, spin-orbit coupling induces orbital moments, accordingly. The relativistic nature of the spin-orbit coupling requires orbital magnetism to be treated within QED, and the treatment of QED in solids is possible in the frame of current density functional theory. The kinematic spin-orbit coupling is accounted for in many DFT calculations of magnetic systems within the LSDA. However, a strong deviation of the LSDA orbital moments from experiment is found in such approaches. To avoid such deviations, orbital polarization corrections would be desirable. In this Thesis, those corrections have been investigated in the framework of CDFT. After a short review for CDFT in Chapter 2, in Chapter 3, an "ad hoc" OP correction term (OPB) suggested by Brooks and Eriksson is given. This correction in some cases gives quite reasonable corrections to orbital moments of magnetic materials. Another OP correction (OPE), which has been introduced recently, was derived from the CDFT in the non-relativistic limit. Unfortunately, the program can only incompletely be carried through, as there are reasonable but uncontrolled approximations to be made in two steps of the derivation. Nevertheless, the result is quite close to the "ad hoc"ansatz. The calculated OPE energies for 3d and 4f free ions are in qualitative agreement with OPB energies. In Chapter 4, both corrections are implemented in the FPLO scheme to calculate orbital moments in solids. We found that both OPB and OPE corrections implemented in FPLO method, yield reasonably well the orbital magnetic moments of bcc Fe, hcp Co and fcc Ni compared with experiment. In Chapter 5, the effect of spin-orbit coupling and orbital polarization corrections on the spin and orbital magnetism of full-Heusler alloys is investigated by means of local spin density calculations. It is demonstrated, that OP corrections are needed to explain the experimental orbital moments. Model calculations employing one ligand field parameter yield the correct order of magnitude of the orbital moments, but do not account for its quantitative composition dependence. The spin-orbit coupling reduces the degree of spin polarization of the density of states at Fermi level by a few percent. We have shown that the orbital polarization corrections do not change significantly the spin polarization degree at the Fermi level. We also provide arguments that Co2FeSi might not be a half-metal as suggested by recent experiments. In Chapter 6, to understand recent XMCD data for Co impurities in gold, the electronic structure of Co impurities inside gold has been calculated in the framework of local spin density approximation. The orbital and spin magnetic moment have been evaluated. In agreement with experimental findings, the orbital moment is enhanced with respect to Co metal. On the other hand, internal relaxations are found to reduce the orbital moment considerably, whereas the spin moment is less affected. Both OPB and OPE yield a large orbital moment for Co impurities. However, those calculated orbital moments are almost by a factor of two larger than the experimental values. We also found that the orbital magnetic moment of Co may strongly depend on pressure.
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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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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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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.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, molecular geometries, exchange-repulsion, and hydrogen-bond interactions. To improve the quality of DFT, one popular idea is to apply empirical corrections to existing density functionals. Such an approach is both conceptually simple and computationally affordable. Despite many successful applications, most existing DFT empirical correction methods focus only on the dispersion corrections. In this thesis, we introduce system-specific empirical corrections to DFT. Our method not only provides corrections for dispersion, but also addresses problems such as deficiencies with molecular geometries, exchange-repulsion, and hydrogen bonding. The empirical correction, named "supplemental potential" (SP), is created by fitting the force differences between a functional and a high quality post-Hartree-Fock method. We tested the performance of SPs for three types of systems: water, methane-water, and molecular crystals. For the water system, the Becke-Lee-Yang-Parr (BLYP) functional description ofthe water potential energy surface (PES) can be improved to coupled-cluster quality with our water SP. For (H20)n (n=l-6), the relative cluster energies, cluster binding energies, and optimized energy structures are correctly predicted with the water SP correction. The developed methane-water SP is able to improve the BLYP PES to coupled-cluster quality in the study of methane water system. In the molecular crystal studies, the DFT-SP method correctly predict the most stable crystal structures among the sets of low-energy polymorphs, for four out of five studied organic molecules.
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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 in conclusion the extension of Density Functional Perturbation Theory for non-local functional is introduced, showing the results obtained on graphite. In the appendix we also present for the first time Moka (MOdeling pacKage for Atomistic simulations) an open-source modeling GUI for atomistic simulations.
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Tian, Wei Quan. "Density-functional theory, chemical tests and evaluation of exchange-correlation functionals". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58314.pdf.
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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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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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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 gain molecular insight into the chemical composition, thermochemical and structural properties of this type of ultrathin GO films on silicon carbide substrates.
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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 with (n=1,2,3,4) on the clean and oxygen depleted lepidocrocite surface. Through systematic investigation of various cases we conclude that Au preferres O
vacancy sites rather than clean surface in accordance with previous metal adsorption studies on TiO2 surfaces. For the clean surface, we observe that Au clusters with an odd number of atoms are weakly bonded and metallizes the system while even number of Au atoms results in small band gap semiconductors with relatively higher binding energies.
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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. For dilute concentrations of Mn (~ 5%) the ordering temperature of the system is low, due to the short ranged character of the exchange interactions and disorder effects. The clustering tendency of the Co atoms in a ZnO matrix was also studied. The electronic structure, and in turn the magnetic interactions among the Co atoms, is strongly dependent on the exchange-correlation functional used. It is found that Co impurities tend to form nanoclusters and that the interactions among these atoms are antiferromagnetic within the local spin density approximation + Hubbard U approach. The electronic structure, as well as the chemical and magnetic interactions in Co and (Co,Al)-doped ZnO, was investigated by joined experimental and theoretical techniques. For a good agreement between the two, approximations beyond the local density approximation must be used. It is found that the Co atoms prefer to cluster within the semiconducting matrix, a tendency which is increased with Al co-doping. We envision that it is best to describe the system as superparamagnetic due to the formation of Co nanoclusters within which the interactions are antiferromagnetic. The magnetic anisotropy and evolution of magnetic domains in Fe81Ni19/Co(001) superlattices were investigated both experimentally, as well as using model spin dynamics. A magnetic reorientation transition was found.
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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 solvent-solvent interaction but is nonetheless quite accurate. We use this approach to reproduce transfer free energies reported elsewhere, and show that the cDFT model captures the desolvation barrier and the temperature dependence of the transfer free energy. We use experimental values that we have analyzed to define the parameter space of a model density functional theory approach. We then extend the classical density functional theory to capture protein-water interactions, thus developing a new implicit solvent model. Along the way we give a proof that the free energy of a bath of particles in a finite external potential is independent of the external potential in the isothermal-isobaric ensemble. We finally discuss the challenges remaining in implementing our implicit solvent model.Science, Faculty of
Physics and Astronomy, Department of
Graduate
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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.The LSD GX exchange density is corrected for self-interaction (SI) by splitting the total Fermi hole correlation factor into pure-exchange and self-interaction holes.
These new LSD and SI corrected schemes are compared to each other. They also compare very well theoretically and numerically (total energies and eigenvalues) with other local schemes current in the literature.
New equations for the IP and electronegativities of the atoms in these local schemes are derived which give good results.
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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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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 stoichiometries in the range of U2O5 to UO3. While UO2 is well characterised, both experimentally and computationally, there is a paucity of data concerning higher stoichiometry oxides in the literature. Experiments and simulations are emerging that deal with individual phases, however a comprehensive study that assesses the properties of all polymorphs and provides comparison over the full range of stoichiometries has been lacking from the literature First the nuclear fuel cycle is introduced, as well as UO2 as a nuclear fuel (Chapter 1), before the quantum mechanical methodology used throughout is explained (Chapter 2). Applying a number of different density functionals (including GGAs, meta-GGAs and hybrids) to UO2 in Chapter 3 it emerges that the PBE + U formalism reproduces the experimentally observed properties to a good degree of accuracy, and so is selected for the rest of the simulations. Following this Chapter 4 examines defect clusters in UO2, finding split interstitials to dominate at low stoichiometry (UO2 – UO2.0625), chains of 2:2:2 Willis clusters at higher stoichiometry (UO2.125 – UO2.25 (U4O9)) and split quad interstitials at higher stoichiometry (UO2.33 (U3O7)). Chapter 5 is an investigation of layered U2O5, where it emerges that the Np2O5 structure is more stable than δ-U2O5 and all uranium ions are in the U5+ oxidation state. Next Chapter 6 considers layered U3O8, which is structurally oxygen rich U2O5, where it is found that U5+ and U6+ ions exist in pentagonal bipyramidal and octahedral coordination respectively. The final set of results in Chapter 7 concern the polymorphs of UO3, where it is found that U6+ adopts a range of coordination environments and the predicted relative stability of each modification matches well with experiment. Finally the conclusions are presented in Chapter 8 along with plans for future work.
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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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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 n'est pas toujours suffisant, notamment dans les matériaux fortement corrélés. Par ailleurs, l'expression des observables du système en terme de la matrice densité n'est pas toujours connue. Tel est le cas, par exemple, pour la fonction spectrale, qui est liée aux spectres de photoémission. Dans ce cas, il y a des annulations d'erreur entre l'approximation à la corrélation électronique et l'approximation à l'observable, ce qui affaiblit la théorie. Dans cette thèse, nous recherchons des approximations plus précises en exploitant le lien entre les matrices densité et les fonctions de Green. Dans la première partie de la thèse, nous nous concentrons sur la fonction spectrale. En utilisant le modèle de Hubbard, qui peut être résolu exactement, nous analysons les approximations existantes à cette observable et nous soulignons leurs points faibles. Ensuite, à partir de sa définition en terme de la fonction de Green à un corps nous dérivons une expression pour la fonction spectrale qui dépend des nombres d'occupation naturels et d'une énergie efficace qui prend en compte toutes les excitations du système. Cette énergie efficace dépend de la matrice densité à un corps ainsi que des ordres supérieurs. Des approximations simples à cette énergie efficace donnent des spectres précis dans des systèmes modèles dans des régimes à la fois de faible et de forte corrélation. Pour illustrer notre méthode sur les matériaux réels, nous calculons le spectre de photoemission du NiO massif: notre méthode donne une image qualitativement correcte dans la phase antiferromagnétique et dans la phase paramagnétique, contrairement aux méthodes de champ moyen utilisés actuellement, qui donnent un métal dans le dernier cas. La deuxième partie de la thèse est plus explorative et traite des phénomènes dépendant du temps dans la RDMFT. En général, l'évolution temporelle des matrices densité est donnée par la hiérarchie des équations de Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY), dans lequel l'équation du mouvement de la matrice densité a n corps est donnée en termes de la matrice densité à n+1 corps. La première équation de la hiérarchie relie la matrice densité à un corps à la matrice densité à deux corps. La tâche difficile est de trouver des approximations à la matrice densité à deux corps. Les approximations existantes sont des extensions adiabatiques des approximations de l'état fondamental. Nous explorons cette question en examinant de nouvelles approximations qui nous tirons de la théorie à plusieurs corps (MBPT) basée sur les fonctions de Green ainsi que de la solution exacte du modèle de Anderson à deux niveaux dans son état fondamental. Nos premiers résultats sur le modèle de Anderson soumis à divers champs externes montrent quelques caractéristiques intéressantes, qui suggèrent d'explorer davantage ces approximations aussi sur des systèmes modèles plus grandsThis thesis addresses the description of electron correlation and spectroscopy within the context of Reduced Density-Matrix Functional Theory (RDMFT). Within RDMFT the ground-state properties of a physical system are functionals of the ground-state reduced density matrix. Various approximations to electron correlation have been proposed in literature. Many of them, however, can be traced back to the work of Müller, who has proposed an approximation to the correlation which is similar to the Hartree-Fock approximation but which can produce fractional occupation numbers. This is not always sufficient. Moreover, the expression of the observables of the system in terms of the reduced density matrix is not always known. This is the case, for example, for the spectral function, which is closely related to photoemission spectra. In this case there are error cancellations between the approximation to correlation and the approximation to the observable, which weakens the theory. In this thesis we look for more accurate approximations by exploiting the link between density matrices and Green's functions. In the first part of the thesis we focus on the spectral function. Using the exactly solvable Hubbard model as illustration, we analyze the existent approximations to this observable and we point out their weak points. Then, starting from its definition in terms of the one-body Green's function, we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the one-body as well as higher-order reduced density matrices. Simple approximations to this effective energy give accurate spectra in model systems in the weak as well as strong-correlation regimes. To illustrate our method on real materials we calculate the photoemission spectrum of bulk NiO: our method yields a qualitatively correct picture both in the antiferromagnetic and in the paramagnetic phases, contrary to currently used mean-field methods, which give a metal in the latter case. The second part of the thesis is more explorative and deals with time-dependent phenomena within RDMFT. In general the time evolution of the reduced density matrices is given by the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations, in which the equation of motion of the n-body reduced density matrix is given in terms of the (n + 1)-body reduced density matrix. The first equation of the hierarchy relates the one-body to the two-body reduced density matrix. The difficult task is to find approximations to the two-body reduced density matrix. Commonly used approximations are adiabatic extension of ground-state approximations. We explore this issue by looking at new approximations derived from Many-Body Perturbation Theory (MBPT) based on Green's functions as well as from the exact solution of the two-level Anderson impurity model in its ground state. Our first results on the two-level Anderson model subjected to various external fields show some interesting and, at the same time, puzzling features, which suggest to explore further these approximations
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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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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 show different reactivities to the Cr2O3(0001) surface. The different terminations provide insight on the reactivity of the surface to the molecules under varying oxygen chemical potential as background environment. Various chemical complexes have been investigated, each having applications in chemical catalysis, including the growth of an H2O layer in a hexagonal 2D lattice and an array of Cl atoms in a honeycomb lattice. Poisoning of materials by sulfuric acid is among the daily problems worldwide, with significant loss of resources. A mechanistic design on how to avert the problem is at the heart of scientific activities. This study, paper III, investigates the interaction of molecular, intermediately decomposed, and fully decomposed states of H2S with the Cr2O3(0001) surface, allowing for the possibility of a varying oxygen chemical potential as background environment. Based on the difference in reactivity of the adsorbate species with the differently terminated surfaces, we have suggested that a higher oxygen chemical potential as background environment has a potential to be unreactive to the adsorbate species or at least minimize the surface poisoning. Titanium-nickelide is an important biomaterial with various applications in medical technology. However, it is still a matter of a continued research effort on how to establish the best biocompatible version of the material. Existence of nickel atoms at contact points of the biomaterial has been reported to hamper the quality of the biomaterial. As a consequence, several experimental activities have been carried out to remedy a surface treatment of the material, mostly by oxidation. This study, paper IV, characterizes the oxidation of various low indexes of the biomaterial surface. Based on this characterization, a conclusion is reached that doping the material with potassium atoms improves the performance quality of the biomaterial and a method of achieving the doping is suggested. The use of two or more DFT packages, with different basis sets, may be motivated for consistency verification of results obtained so as to make quality conclusions, or to take advantage of a reduced computational time. In this report, paper V, we have shown that the Dacapo DFT package and the BAND DFT package with very different basis sets, i.e., plane waves and atomic orbitals, respectively, can be used together in a single study by satisfying the above motivation points. We have reported that the pseudopotentials (frozen cores) used in the calculations play a crucial role for the outcome of calculations and computation time demand, and suggested a possible discrepancy in the magnitudes of energy differences. The alloy between rare earths and novel transition metals Pt and Pd is of renewed research interest. This is in part motivated by the desire to tailor some of the properties of these widely applied transition metals or the rare earths. To be able to have control over the quantitative changes in the properties, a clear establishment of the alloy structures is crucial. There have been considerable experimental research efforts carried out reporting the investigated alloy structures. However, a consistent conclusion has not been obtained. This study, paper VI, is based on the various experimentally predicted structures and systematically suggests the most stable structure.
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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 thèse, les effets de cette séparation de portée sur les énergies d'un système en interaction partielle sont d'abord étudiés le long de la connection adiabatique dans le cas indépendant du temps afin d'aider le développement des méthodes à séparation de portée pour les énergies d'excitation. La séparation de portée est ensuite appliquée dans le cadre de la TDDFT aux noyaux d'échange et de corrélation, où dans le cas d'une approximation monodéterminentale, la longue portée du noyau de corrélation est absente. Afin de prendre en compte l'effet des doubles excitations, un noyau de corrélation de longue portée dépendant de la fréquence est développé en s'inspirant du noyau Bethe-Salpeter. Ce noyau est alors ajouté de façon perturbative au noyau TDDFT à séparation de portée afin de prendre en compte les effets des excitations doublesLinear-response time-dependent density-functional theory (TDDFT) is nowadays a method of choice to compute molecular excitation energies. However, within the usual adiabatic semi-local approximations, it is not able to describe properly Rydberg, charge-transfer or multiple excitations. Range separation of the electronic interaction allows one to mix rigorously density-functional methods at short range and wave function or Green’s function methods at long range. When applied to the exchange functional, it already corrects most of these deficiencies but multiple excitations remain absent as they need a frequency-dependent kernel. In this thesis, the effects of range separation are first assessed on the excitation energies of a partially-interacting system in an analytic and numerical study in order to provide guidelines for future developments of range-separated methods for excitation energy calculations. It is then applied on the exchange and correlation TDDFT kernels in a single-determinant approximation in which the long-range part of the correlation kernel vanishes. A long-range frequency-dependent second-order correlation kernel is then derived from the Bethe-Salpeter equation and added perturbatively to the range-separated TDDFT kernel in order to take into account the effects of double excitations
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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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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-Sham orbital energies.
Then we want to rebut the theory of "unconventional density variation" proposed more than 20 years ago. Supported by theoretical analysis and numericalevidence, we proved that all density variations are the same in nature.
We have also extended two total energy functionals suggested before to the Hartree-Fock method. Numerical tests on different molecules show these functionals are very promising in accelerating the SCF convergence of quantum chemistry calculations.
Finally, we completed a comprehensive theoretical study on the tautomers of pyridinethiones. Many molecular properties predicted from theory are comparedwith those got from experiments. The dominant forms of the tautomers are confirmed to be the thione forms. This demonstrates the power of DFT methods, and this work can serve as a reference for studying similar molecules.
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Coe, Jeremy Patrick. "Entanglement and density-functional theory in two-electron systems". Thesis, University of York, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.521163.
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Brown, Philip. "Fast Density Functional Theory on A Massively Parrallel Arxhitecture". Thesis, University of Bristol, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.499909.
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Leithall, Gavin Ralph. "Density functional theory for hard hyperspheres in odd dimensions". Thesis, University of Bristol, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.535219.
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