The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
Carsten A. Ullrich - One of the best experts on this subject based on the ideXlab platform.
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(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer
Physical Review A, 2019Co-Authors: Carsten A. UllrichAbstract:According to the Hohenberg-Kohn Theorem of density-functional theory (DFT), all observable quantities of systems of interacting electrons can be expressed as functionals of the ground-state density. This includes, in principle, the spin polarization (magnetization) of open-shell systems; the explicit form of the magnetization as a functional of the total density is however unknown. In practice, open-shell systems are always treated with spin-DFT, where the basic variables are the spin densities. Here the relation between DFT and spin-DFT for open-shell systems is illustrated and the exact magnetization density functional is obtained for the half-filled Hubbard trimer. Errors arising from spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are analyzed and partially resolved via the exact magnetization functional.
Paul W Ayers - One of the best experts on this subject based on the ideXlab platform.
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Legendre-transform functionals for spin-density-functional theory.
Journal of Chemical Physics, 2006Co-Authors: Paul W Ayers, Weitao YangAbstract:We provide a rigorous proof that the Hohenberg-Kohn Theorem holds for spin densities by extending Lieb’s Legendre-transform formulation to spin densities. The resulting spin-density-functional theory resolves several troublesome issues. Most importantly, the present paper provides an explicit construction for the spin potentials at any point along the adiabatic connection curve, thus providing a formal basis for the use of exchange-correlation functionals of the spin density in the Kohn-Sham density-functional theory (DFT). The practical implications of this result for unrestricted Kohn-Sham DFT calculations is considered, and the existence of holes below the Fermi level is discussed. We argue that an orbital’s energy tends to increase as its occupation number increases, which provides the basis for a computational algorithm for determining the occupation numbers in Kohn-Sham DFT and helps explain the origin of Hund’s rules and holes below the Fermi level.
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generalizations of the hohenberg kohn Theorem i legendre transform constructions of variational principles for density matrices and electron distribution functions
Journal of Chemical Physics, 2006Co-Authors: Paul W Ayers, Sidney Golden, Mel LevyAbstract:Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn Theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Lieb’s Legendre transform ansatz to the generalized Hohenberg-Kohn functional not only solves the υ-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the v- and N-representability problems based on the constrained search ...
Mel Levy - One of the best experts on this subject based on the ideXlab platform.
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On the simple constrained‐search reformulation of the Hohenberg–Kohn Theorem to include degeneracies and more (1964–1979)
International Journal of Quantum Chemistry, 2010Co-Authors: Mel LevyAbstract:The constrained-search reformulation provides a transparent proof of the Hohenberg–Kohn Theorem, while extending it to include degeneracies, solving the w-representability problem, and more. This proof, as first presented at the 1979 Sanibel meeting, is reviewed within the context of a brief historical perspective and my interactions at that meeting. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010
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generalizations of the hohenberg kohn Theorem i legendre transform constructions of variational principles for density matrices and electron distribution functions
Journal of Chemical Physics, 2006Co-Authors: Paul W Ayers, Sidney Golden, Mel LevyAbstract:Given a general, N-particle Hamiltonian operator, analogs of the Hohenberg-Kohn Theorem are derived for functions that are more general than the particle density, including density matrices and the diagonal elements thereof. The generalization of Lieb’s Legendre transform ansatz to the generalized Hohenberg-Kohn functional not only solves the υ-representability problem for these entities, but, more importantly, also solves the N-representability problem. Restricting the range of operators explored by the Legendre transform leads to a lower bound on the true functional. If all the operators of interest are incorporated in the restricted maximization, however, the variational principle dictates that exact results are obtained for the systems of interest. This might have important implications for practical work not only for density matrices but also for density functionals. A follow-up paper will present a useful alternative approach to the v- and N-representability problems based on the constrained search ...
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Basic time-independent density-functional Theorems for ground states and excited states
AIP Conference Proceedings, 2001Co-Authors: Mel LevyAbstract:Several basic time-independent density-functional Theorems are reviewed for ground states and excited states. In particular, the simple constrained-search formulation is utilized to prove the Hohenberg-Kohn Theorem for degenerate as well as for non-degenerate situations. Then, a time-independent Kohn-Sham theory is presented for an individual excited state, and first-order adiabatic connection perturbation theory is compared with a common approximation within time-dependent theory for excited states.
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On Time-Independent Density-Functional Theories for Excited States
Electron Correlations and Materials Properties, 1999Co-Authors: Mel LevyAbstract:Ground-state density-functional theory (DFT) is now routinely used and generally provides the most powerful and efficient method today for electronic structure calculations [1, 2, 3, 4, 5, 6, 7, 8, 9]. My purpose here is to briefly review aspects of several excited-state formulations that are closely related to the ground-state time-independent Hohenberg-Kohn Theorem. The appealing time-dependent theory forexcited states [10] was described at this conference by Gross.
Masahiko Higuchi - One of the best experts on this subject based on the ideXlab platform.
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A restrictive condition on approximate forms of the kinetic energy functional of the pair density functional theory
International Journal of Quantum Chemistry, 2010Co-Authors: Masahiko Higuchi, Mitiyasu Miyasita, Katsuhiko HiguchiAbstract:By using the N-representability condition and the Hohenberg-Kohn Theorem on the pair density (PD), we have derived a property of the kinetic energy functional of the PD functional theory. This property can be regarded as a restrictive condition on approximate forms of the kinetic energy functional, and gives a useful guideline to develop them. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010
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Density functional theory with arbitrary basic variables
Journal of Magnetism and Magnetic Materials, 2004Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:Abstract By modifying the Levy constrained-search formulation, the Hohenberg–Kohn Theorem of the density functional theory is extended. The new Theorem allows us to choose arbitrary physical quantities as basic variables, which uniquely determine the ground-state properties of the system. The Theorem also establishes the variational principle with respect to the basic variables chosen. By using this Theorem, self-consistent single-particle equations are derived. If the occupation matrix of localized orbitals is chosen as a basic variable, these equations are equivalent to those of the LDA+U method.
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A Relativistic Current- and Spin-Density Functional Theory and a Single-Particle Equation
Journal of the Physical Society of Japan, 1997Co-Authors: Masahiko Higuchi, Akira HasegawaAbstract:In order to calculate the electronic structure for f -electron compounds, in which the f electrons are itinerant and responsible to magnetism, it is necessary to take into account the magnetic effects which originate from the spin polarization and the orbital current besides relativistic effects. For a system of interacting electrons in an external electromagnetic field, a nonrelativistic current- and spin-density functional theory of Vignale and Rasolt (1987) is generalized to a relativistic current- and spin-density functional theory. A generalized Hohenberg-Kohn Theorem is shown to hold, and a single-particle equation of the Kohn-Sham-Dirac type is derived. In the single-particle equation, which is appropriate to an isolated atom, the magnetic interaction is expressed in a form similar to the Zeeman term in which the spin and the orbital angular momenta couple with an effective magnetic field.
Roberto López Boada - One of the best experts on this subject based on the ideXlab platform.
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Analysis of the stability of finite subspaces in density functional theory
Theoretical Chemistry Accounts, 2009Co-Authors: Ramiro Pino, Olivier Bokanowski, Eduardo V. Ludeña, Roberto López BoadaAbstract:We study the problem of the stability of finite subspaces with respect to the external potential in the formulation of the Hohenberg-Kohn Theorem in density functional theory. We provide general procedures to construct potentials that make any finite dimensional subspace unstable, i.e., we construct potentials that acting over functions that belong to the subspace, generate functions that do not belong to that subspace. Explicit calculations of these instability generating potentials are carried out for the particle-in-a-box problem and for the hydrogen atom. We also discuss the consequences of these instabilities on the Kohn–Sham equations, as well as conditions for stability and the relation between instability and nonuniqueness of potentials.
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A re-statement of the Hohenberg–Kohn Theorem and its extension to finite subspaces
Theoretical Chemistry Accounts, 2007Co-Authors: Ramiro Pino, Olivier Bokanowski, Eduardo V. Ludeña, Roberto López BoadaAbstract:Bearing in mind the insight into the Hohenberg–Kohn Theorem for Coulomb systems provided recently by Kryachko (Int J Quantum Chem 103:818, 2005), we present a re-statement of this Theorem through an elaboration on Lieb’s proof as well as an extension of this Theorem to finite subspaces.