Arimondo / Yelin Advances in Atomic, Molecular, and Optical Physics

1. Auflage 2015
ISBN: 978-0-12-802335-8
Verlag: Academic Press
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, Band Volume 64, 454 Seiten, Format (B × H): 152 mm x 229 mm

Reihe: Advances in Atomic, Molecular, and Optical Physics

Advances in Atomic, Molecular, and Optical Physics provides a comprehensive compilation of recent developments in a field that is in a state of rapid growth, as new experimental and theoretical techniques are used on many problems, both old and new.

Topics covered include related applied areas, such as atmospheric science, astrophysics, surface physics, and laser physics, with timely articles written by distinguished experts that contain relevant review material and detailed descriptions of important developments in the field.



- Presents the work of international experts in the field
- Comprehensive articles compile recent developments in a field that is experiencing rapid growth, with new experimental and theoretical techniques emerging
- Ideal for users interested in optics, excitons, plasmas, and thermodynamics
- Topics covered include atmospheric science, astrophysics, surface physics, and laser physics, amongst others

Autoren/Hrsg.

Arimondo, Ennio

Yelin, Susanne

Weitere Mitwirkende

Arimondo, Ennio

Yelin, Susanne F.

Fachgebiete

• Naturwissenschaften Physik Quantenphysik Atom- und Molekülphysik
• Naturwissenschaften Physik Elektromagnetismus Quantenoptik, Nichtlineare Optik, Laserphysik

Inhaltsverzeichnis

- Paradox of Self-Interaction Correction: How Can Anything So Right Be So Wrong?
John P. Perdew, Adrienn Ruzsinszky, Jianwei Sun, and Mark R. Pederson
- Local Spin Density Treatment of Substitutional Defects in Ionic Crystals with Self-Interaction Corrections
Koblar Jackson
- Electronic Transport as a Driver for Self-Interaction-Corrected Methods
Anna Pertsova, Carlo Canali, Mark R. Pederson, Ivan Rungger and S. Sanvito
- The Two-Set and Average-Density Self-Interaction Corrections Applied to Small Electronic Systems
Phuong M. Dinh, Paul-Gerhard Reinhard, Eric Suraud and Marc Vincendon
- Koopmans-Compliant Self-Interaction Corrections
Nicolas Poilvert, Giovanni Borghi, Ngoc Linh Nguyen, Nathan Keilbart, Kevin Wang and Ismaila Dabo
- Constrained Local Potentials for Self Interaction Correction
Nikitas I. Gidopoulos and Nektarios N. Lathiotakis
- Self-interaction Correction as a Kohn-Sham Scheme in Ground-State and Time-Dependent Density Functional
Stephan Kümmel
- Self-Interaction Corrections within the Fermi-Orbital-Based Formalism
Mark R. Pederson and Tunna Baruah
- Laser Spectroscopy and Quantum Optics in GaAs and InAs Semiconductor Quantum Dots
Duncan G. Steel
- Ultracold Neutral Plasmas Well into the Strongly Coupled Regime
Michael S. Murillo and Scott D. Bergeson
- Coherent Population Trapping, Nuclear Spin Cooling And Lévy Ights in Solid State
Atom-Like Systems
Swati Singh, Y. Chu, Mikhail D. Lukin, Susanne F. Yelin
- Thermodynamics of Quantum Systems under Dynamical Control
David Gelbwaser-Klimovsky, Wolfgang Niedenzu and Gershon Kurizki

Leseproben

Chapter One Paradox of Self-Interaction Correction
How Can Anything So Right Be So Wrong?
John P. Perdew*,†; Adrienn Ruzsinszky*; Jianwei Sun*; Mark R. Pederson‡,1    * Department of Physics, Temple University, Philadelphia, Pennsylvania, USA
† Department of Chemistry, Temple University, Philadelphia, Pennsylvania, USA
‡ Department of Chemistry, Johns Hopkins University, Baltimore, Maryland, USA
1 Corresponding author: email address: [e-mail] Abstract
Popular local, semilocal, and hybrid density functional approximations to the exchange-correlation energy of a many-electron ground state make a one-electron self-interaction error which can be removed by its orbital-by-orbital subtraction from the total energy, as proposed by Perdew and Zunger in 1981. This makes the functional exact for all one-electron ground states, but it does much more as well: It greatly improves the description of negative ions, the dissociation curves of radical molecules and of all heteronuclear molecules, the barrier heights for chemical reactions, charge-transfer energies, etc. PZ SIC even led to the later discovery of an exact property, the derivative discontinuity of the energy. It is also used to understand strong correlation, which is beyond the reach of semilocal approximations. The paradox of SIC is that equilibrium properties of molecules and solids, including atomization energies and equilibrium geometries, are at best only slightly improved and more typically worsened by it, especially as we pass from local to semilocal and hybrid functionals which by themselves provide a ladder of increasing accuracy for these equilibrium properties. The reason for this puzzling ambivalence remains unknown. In this speculative chapter, we suggest that the problem arises because the uncorrected functionals provide an inadequate description of compact but noded one-electron orbital densities. We suggest that a meta-generalized gradient approximation designed to satisfy a tight lower bound on the exchange energy of a one-electron density could resolve the paradox, providing after self-interaction correction the first practical “density functional theory of almost everything.” Keywords Density functional theory Exchange Correlation Self-interaction correction Semilocal functionals Equilibrium bonds One-electron densities Noded orbitals 1 Introduction
Kohn–Sham density functional theory (Kohn and Sham, 1965) is a formally exact construction of the ground-state energy and electron density for a system of electrons with mutual Coulomb repulsion in the presence of a multiplicative scalar external potential. The construction proceeds by solving self-consistent one-electron equations for the occupied Kohn–Sham orbitals, fictional objects used to build up the electron density, and the noninteracting part of the kinetic energy. The many-electron effects are incorporated via the exchange-correlation energy as a functional of the density, Exc[n?,n?], and its functional derivative or exchange-correlation potential vxcs([n?,n?];r). In practice, the exchange-correlation energy has to be approximated. This approach is very widely used for the computation of atoms, molecules, and condensed matter, because of its useful balance between computational efficiency and accuracy. The exact exchange-correlation energy is defined (Gunnarsson and Lundqvist, 1976; Langreth and Perdew, 1975, 1977) so that [n]+Exc[n?,n?]=?01d?.   (1) Here, [n]=12?d3r?d3r'n(r)n(r')|r-r'|,   (2) is the Hartree electrostatic self-repulsion energy of the total electron density n(r) = n?(r) + n?(r), the sum of up-spin and down-spin contributions. ˆee is the electron–electron Coulomb repulsion operator. And ?? is the ground-state wavefunction for electrons with interaction Vˆee and with density (r)= independent of coupling constant ?. The spin-dependent external scalar potential vs?(r) varies between the Kohn–Sham effective potential at ? = 0 and the physical external potential at ? = 1. We can write Exc as the sum of exchange and correlation energies, where the exchange energy Ex is defined by [n]+Ex[n?,n?]=.   (3) Typically ?0 is a single Slater determinant of Kohn–Sham orbitals, and Ex differs from Hartree–Fock exchange only via the small difference between Kohn–Sham and Hartree–Fock orbitals. The exchange energy and the correlation energy are nonpositive. They arise because, as an electron moves through the density, it creates around itself exchange and correlation holes (Gunnarsson and Lundqvist, 1976) which reduce its repulsion energy with the other electrons. The exchange hole arises from self-interaction correction and wavefunction antisymmetry under particle exchange, and its density integrates to - 1, while the correlation hole arises from Coulomb repulsion, and its density integrates to 0. While the exchange-correlation energy can be a small fraction of the total energy, it is nature's glue (Kurth and Perdew, 2000) that creates most of the binding of one atom to another in a molecule or solid. For any spin-up one-electron density n1(r), the Coulomb repulsion operator vanishes so [n1]+Ex[n1,0]=0,   (4) c[n1,0]=0.   (5) The functional Exc of Eq. (1) is defined for ground-state spin-densities, but it has a natural continuation to all fully-spin-polarized one-electron densities, given by Eqs. (4) and (5), since the Coulomb repulsion operator vanishes for all such densities. This continuation is not only natural but also physical: It makes the solutions of the Kohn–Sham orbital equations exact for one-electron systems, not only in their ground states but also in their excited states and time-dependent states. It is also the choice made in the Hartree–Fock and self-interaction-corrected Hartree approximations. Approximate functionals that satisfy Eqs. (4) and (5) are said to be one-electron self-interaction-free (Perdew and Zunger, 1981). For other functionals, the numerical values of the right-hand sides are self-interaction errors (SIE) for exchange and correlation, respectively, and their sum is the total self-interaction error. Semilocal approximations have single-integral form, xcsl[n?,n?]=?d3rn?xcsl(n?,n?,?n?,?n?,t?,t?),   (6) and are popular because of their computational efficiency. The original local spin-density approximation (Gunnarsson and Lundqvist, 1976; Kohn and Sham, 1965) uses only the spin-density arguments, the generalized gradient approximation (GGA) (Becke, 1988; Langreth and Mehl, 1983; Lee et al., 1988; Perdew and Wang, 1986; Perdew et al., 1996) adds the spin-density gradients, and the meta-GGA (Becke and Roussel, 1989; Perdew et al., 1999; Sun et al., 2012, 2013; Tao et al., 2003; Van Voorhis and Scuseria, 1998) adds the positive kinetic energy densities s(r)=Saoccupied12|??as|2   (7) of the Kohn–Sham orbitals ?as. The exchange-correlation energy per particle xcsl may be constructed to satisfy exact constraints on Exc, and the addition of more arguments permits the satisfaction of more constraints with resulting greater accuracy. For some GGA s (e.g., PBE) and meta-GGA s (e.g., TPSS), this construction is nonempirical. But no semilocal functional can satisfy Eq. (4), because of the full nonlocality of U[n], and only the meta-GGA can satisfy Eq. (5). Hybrid functionals (Becke, 1993; Ernzerhof and Scuseria, 1999; Stephens et al., 1994) add an exact-exchange ingredient, e.g., xchybrid=(1-a)Exsl+aExexact+Ecsl.   (8) Typically they achieve higher accuracy through empirical selection of the mixing parameter (e.g., 0.25) and not through...

Über Autor(innen)

Arimondo, Ennio
Ennio Arimondo is Professor of Physics at the University of Pisa, Italy. In a a long research career, Professor Arimondo has been engaged in experimental and theoretical research related to laser spectroscopy, the interaction of radiation with matter, laser cooling and new phenomena of ultracold atomic gases. Professor Arimondo is a Fellow of the American Physical Society and of the Institute of Physics. He is editor of Conference and School Proceedings.