We examine the structure of the time-dependent exchange-correlation potential in the recently developed time-dependent current density functional theory\footnote G. Vignale and W. Kohn, Phys. Rev. Lett. 77, 2037 (1996) . The objective is to derive a rigorous local current-density approximation for slowly varying systems and potentials. In the linear response regime, and for systems that are nonuniform in one direction only, we obtain a simple form, particularly suitable for numerical coding.
[S18.02] PQW Infrared Resonances from New Time-dependent Density Functionals
John F. Dobson (School of Science, Griffith University, Queensland 4111, Australia)
Recent revisions [PRL 73, 2244 (1994): PRL 77, 2037 (1996)] of the theory of linear response in Time Dependent Density Functional Theory have called into question the accuracy of previous analyses of collective electronic resonances, but the size of the necessary corrections was unknown till now. Here we predict the frequency of the Kohn mode and other far infrared resonances of parabolic GaAlAs quantum wells with a view to experimental elucidation of the new many-body effects. Substantial differences are found between the predictions of the various many-body theories.
[S18.03] Effective Action Formulation of Kohn-Sham Density-Functional Theory
Marat Valiev, Gayanath Fernando (University of Connecticut, Physics Department)
We discuss how Kohn-Sham (KS) density-functional theory can be formulated using path-integral effective action formalism of quantum field theory. This approach provides a rigorous theoretical foundation for KS based analysis of various excited and ground state properties of many-body systems. For example, it allows a straightforward systematic analysis of the exchange-correlation potential, excited states, exact one-electron propagator and self-energy entirely in terms of KS derived quantities. Although we mainly concentrate on nonrelativistic many-electron systems, similar treatment can easily be developed for other many-body Hamiltonians.
[S18.04] Separation of the exchange-correlation potential into exchange plus correlation using an optimized effective potential approach: comparison with approximate density- and orbital-dependent functionals.
Claudia Filippi (University of Illinois at Urbana-Champaign), Cyrus Umrigar (Cornell University), Xavier Gonze (Université Catholique de Louvain)
Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. In the past, accurate exchange-correlation potentials have been generated from essentially exact densities but they have not been correctly decomposed into their separate exchange and correlation components (except for two-electron systems). Using a recently proposed method, equivalent to the solution of an optimized effective potential problem with the corresponding orbitals replaced by the exact Kohn-Sham orbitals, we obtain the separation according to the density functional theory definition. We compare the results for the Ne and Be atoms with those obtained by the previously used approximate separation scheme and with the approximate potentials corresponding to the local density and some generalized gradient approximations. A different class of approximate functionals is given by the orbital-dependent functionals. Using the same optimized effective potential scheme with the exact Kohn-Sham orbitals, we obtain the correlation potential corresponding to approximate orbital-dependent correlation functionals, such as the Colle-Salvetti functional.
[S18.05] Local correlation energies of atoms, ions and model systems
Cyrus Umrigar, Chien-Jung Huang (Cornell University)
We present nearly local definitions of the correlation energy density, and its potential and kinetic components, and evaluate them for several atoms, ions and model systems. This information provides valuable guidance in constructing better correlation functionals than those in common use, such as the local density approximation (LDA) and the various generalized gradient approximations (GGAs). The true local correlation energy per electron has oscillations, reflecting the shell-structure, whereas the LDA approximation to it is monotonic. In addition we demonstrate that, for two-electron systems, the quantum chemistry and the density functional definitions of the correlation energy approach each other with increasing atomic number as 1/Z^3.
[S18.06] A quantum Monte Carlo investigation of exchange and correlation of the inhomogeneous electron gas
Maziar Nekovee (Condensed Matter Theory Group, Imperial College, London SW7 2BZ, U.K.), W.M.C. Foulkes (Condensed Matter Theory Group, Imperial College, London SW7 2BZ, U.K.), A.J. Williamson, G. Rajagopal, R.J. Needs (Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 OHE, U.K.)
The exchange-correlation (XC) energy functional, E_xc, plays a fundamental role in the density functional theory of solids. Using an adiabatic connection procedure, E_xc can be expressed in terms of the non-local exchange-correlation hole surrounding each electron. We devised a new method for sampling the exchange-correlation hole of the inhomogeneous electron gas which is based on combining the above adiabatic connection with accurate variational quantum Monte Carlo calculations. We discuss aspects of the method and present results of our calculations for XC holes, XC energy densities and XC potentials in model solids. We compare our findings with those obtained from the local density approximation and generalized gradient approximation.
[S18.07] Quantum Monte Carlo Calculation of the Correlation Hole in Second-row Atoms
Antonio C. Cancio, C. Y. Fong (University of California, Davis), J. S. Nelson (Sandia National Lab., Albuquerque)
We calculate the ground-state correlation holes of the second-row atoms Mg through Ar using a Neon-core nonlocal pseudopotential, and the Variational Monte Carlo method. Dependence on average system density, magnetization, and spin channel is studied and compared to currently used density functional models. In particular we measure the ``on top" correlation hole related to the probability of finding two electrons at zero interparticle separation and its effect on the qualitative features of the correlation hole. Our results are in fair agreement with the linear spin density model of Perdew and Wang(J. P. Perdew and Y. Wang, Phys. Rev. B 46), 12947 (1992-II).
[S18.08] Spin Dependent correlations in atoms
A. Vaught, K. E. Schmidt (Arizona State Univ.), S. A. Vitiello (Iternational Center for Theoretical Physics, Trieste)
Recent microscopic calculations have shown that spin exchange correlations can reproduce the effects of Feynman-Cohen backflow in liquid ^3He. We include these spin dependent correlation in variational Monte Carlo calculations of the electronic structure of the atoms Li through Ne. Our trial wave function is pairwise electron-electron and electron-electron-nuclear correlations of the Boys and Handy form multiplied by a slater determinant constructed from Hartree Fock orbitals. The wave function allows the correlation parameters for singlet and triplet pairs to be different, and correctly enforces the coulomb cusp conditions. This form of the correlation guarantees that it conserves angular momemtum. We use variance minimization to optimize the wave function, and then calculate the energies of these atoms. We compare our results with those of spin independent correlations and simpler spin dependent correlations that do not conserve angular momemtum.
[S18.09] Quantum Monte Carlo Investigation of Exchange and Correlation in Silicon
Randolph Q. Hood (Cavendish Laboratory, Madingley Road, Cambridge, UK), M.Y. Chou (School of Physics, Georgia Institute of Technology, Atlanta, GA, USA), A.J. Williamson, G. Rajagopal, R.J. Needs (Cavendish Laboratory, Madingley Road, Cambridge, UK), W.M.C. Foulkes (The Blackett Laboratory, Imperial College, 17 Prince Consort Road, London, UK)
Utilizing the Monte Carlo variance minimization technique realistic many body wave functions are generated for bulk Silicon with different values of the Coulomb coupling constant. Results of the coupling constant integrated pair-correlation function, the exchange-correlation hole, and the exchange-correlation energy density are presented. These results are directly compared to those obtained from the local density approximation and nonlocal density functional approximations such as the average density approximation and the weighted density approximation. The success of the local density approximation in solids is partly due to a real-space cancelation of errors in the exchange-correlation energy density. Insights from studying the Coulomb coupling constant dependence of the exchange-correlation energy and the exchange-correlation hole are discussed.
[S18.10] Quantum Monte Carlo Calculations of Excitation Energies in Silicon
Andrew Williamson, Guna Rajagopal, Richard Needs (TCM Group, Cavendish Laboratory, Cambridge, UK)
Variational and diffusion quantum Monte Carlo calculations of excitation energies in bulk silicon are reported. The core electrons are represented by a non-local pseudopotential and the trial wavefunctions are optimised using the variance minimisation technique. Excitation energies are calculated both by promoting an electron from the valence band to the conduction band, and by adding and subtracting an electron from the simulation cell. We introduce a new formulation of the electron-electron interaction for systems subject to periodic boundary conditions which is especially adapted for calculating excitation energies and which allows us to distinguish between long and short range effects. We compare the accuracy of excitation energies calculated using the above QMC techniques with the results of calculations using Hartree-Fock methods and the LDA.
[S18.11] Quantum Monte Carlo as a High-Accuracy Method for Treating Chemical Reactions
Jeffrey C. Grossman (University of California at Berkeley), Lubos Mitas (University of Illinois at Urbana-Champaign)
Barrier heights (BH) and heats of formation (\Delta H) have been calculated for a variety of reactions involving sp atoms and molecules by the quantum Monte Carlo (QMC) methods as well as seven other standard first principles methods. QMC calculations of BH and \Delta H are within 1 Kcal/mol (0.04 eV) of experimental values for all reactions considered. By contrast, we have found significant deficiencies of density functional and related methods for these systems. The transition state of the largest reaction studied, involving C_8H_8, has recently been observed experimentally to be an open-shell singlet.(P.G. Wenthold et al, Science 272), 1456 (1996). While this challenging case cannot be correctly described by the traditional approaches, we demonstrate that QMC is the only method which agrees well with experiment.