Paola Gori-Giorgi

Local-spin-density functional for multideterminant density functional theory

(Dated: February 6, 2008)Based on exact limits and quantum Monte Carlo simulations, we obtain, at any density and spinpolarization, an accurate estimate for the energy of a modified homogeneous electron gas where elec-trons repel each other only with a long-range coulombic tail. This allows us to construct an analyticlocal-spin-density exchange-correlation functional appropriate to new, multideterminantal versionsof the density functional theory, where quantum chemistry and approximate exchange-correlationfunctionals are combined to optimally describe both long- and short-range electron correlations.I. INTRODUCTION

Short-range correlation in the uniform electron gas: Extended Overhauser model

shows very good agreement in the range 0.5&r/r s&1. We thus have a strong indication that the Overhauser model potential gives accurate quantitative results also in the ‘‘unknown’’ shortest-range region 0 <r/r s&0.5. In this way we are able to present a quantitative, reliable estimate for the r s dependence of the r 2 coefficient of the small-r expansion of g(r). This coefficient is important for energy density functionals which include the gradient correction to the r 2 coefficient of the exchange-correlation hole, while its spin resolution ~i.e., its and # contributions, also available in the present treatment! is of interest for functionals based on the Fermi hole curvature. 21 Other possible applications are dis

Density functional Theory for Strongly Interacting Electrons

We present an alternative to the Kohn-Sham formulation of density-functional theory for the ground-state properties of strongly interacting electronic systems. The idea is to start from the limit of zero kinetic energy and systematically expand the universal energy functional of the density in powers of a coupling constant that controls the magnitude of the kinetic energy. The problem of minimizing the energy is reduced to the solution of a strictly correlated electron problem in the presence of an effective potential, which in our theory plays the same role as the Kohn-Sham potential plays in the traditional formulation. We discuss several schemes for approximating the energy functional, and report preliminary results for low-density quantum dots.

Density functional theory for strongly-interacting electrons: perspectives for physics and chemistry

Improving the accuracy and thus broadening the applicability of electronic density functional theory (DFT) is crucial to many research areas, from material science, to theoretical chemistry, biophysics and biochemistry. In the last three years, the mathematical structure of the strong-interaction limit of density functional theory has been uncovered, and exact information on this limit has started to become available. The aim of this paper is to give a perspective on how this new piece of exact information can be used to treat situations that are problematic for standard Kohn-Sham DFT. One way to use the strong-interaction limit, more relevant for solid-state physical devices, is to define a new framework to do practical, non-conventional, DFT calculations in which a strong-interacting reference system is used instead of the traditional non-interacting one of Kohn and Sham. Another way to proceed, more related to chemical applications, is to include the exact treatment of the strong-interaction limit into approximate exchange-correlation energy density functionals in order to describe difficult situations such as the breaking of the chemical bond.

Properties of short-range and long-range correlation energy density functionals from electron-electron coalescence

The combination of density-functional theory with other approaches to the many-electron problem through the separation of the electron-electron interaction into a short-range and a long-range contribution is a promising method, which is raising more and more interest in recent years. In this work some properties of the corresponding correlation energy functionals are derived by studying the electron-electron coalescence condition for a modified (long-range-only) interaction. A general relation for the on-top (zero electron-electron distance) pair density is derived, and its usefulness is discussed with some examples. For the special case of the uniform electron gas, a simple parametrization of the on-top pair density for a long-range only interaction is presented and supported by calculations within the extended Overhauser model. The results of this work can be used to build self-interaction corrected short-range correlation energy functionals.

Electronic Zero-Point Oscillations in the Strong-Interaction Limit of Density Functional Theory.

The exchange-correlation energy in Kohn-Sham density functional theory can be expressed exactly in terms of the change in the expectation of the electron-electron repulsion operator when, in the many-electron Hamiltonian, this same operator is multiplied by a real parameter λ varying between 0 (Kohn-Sham system) and 1 (physical system). In this process, usually called adiabatic connection, the one-electron density is kept fixed by a suitable local one-body potential. The strong-interaction limit of density functional theory, defined as the limit λ→∞, turns out to be like the opposite noninteracting Kohn-Sham limit (λ→0) mathematically simpler than the physical (λ = 1) case and can be used to build an approximate interpolation formula between λ→0 and λ→∞ for the exchange-correlation energy. Here we extend the systematic treatment of the λ→∞ limit [Phys. Rev. A 2007, 75, 042511] to the next leading term, describing zero-point oscillations of strictly correlated electrons, with numerical examples for small spherical atoms. We also propose an improved approximate functional for the zero-point term and a revised interpolation formula for the exchange-correlation energy satisfying more exact constraints.

Study of the discontinuity of the exchange‐correlation potential in an exactly soluble case

It was found by Perdew et al. (Phys Rev Lett, 1982, 49, 1691) and by Sham and Schluter (Phys Rev Lett. 1983, 51, 1884) that the exact Kohn–Sham exchange-correlation potential of an open system may jump discontinuously as the particle number crosses an integer, with important physical consequences. Recently, Sagvolden and Perdew (Phys Rev A 2008, 77, 012517) have analyzed the discontinuity of the exchange-correlation potential as the particle number crosses one, with an illustration that uses a model density for the H− ion. In this work, we extend their analysis to the case in which the external potential is the simple harmonic confinement, choosing spring-constant values for which the two-electron hamiltonian has an analytic solution. This way, we can obtain the exact, analytic, exchange and correlation potentials for particle number fluctuating between zero and two, illustrating the discontinuity as the particle number crosses one without introducing any model or approximation. We also discuss exchange and correlation separately.

Energy densities in the strong-interaction limit of density functional theory

We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small atoms and small model quantum dots (Hookes atoms) are compared with available approximations defined in the same gauge. The idea of a local interpolation along the adiabatic connection is discussed, comparing the energy densities of the Kohn-Sham, the physical, and the strong-interacting systems. We also use our results to analyze the local version of the Lieb-Oxford bound, widely used in the construction of approximate exchange-correlation functionals.

Simple model for the spherically and system-averaged pair density : Results for two-electron atoms

As shown by Overhauser and others, accurate pair densities for the uniform electron gas may be found by solving a two-electron scattering problem with an effective screened electron-electron repulsion. In this paper we explore the extension of this approach to nonuniform systems, and we discuss its potential for density functional theory. For the spherically- and system-averaged pair density of two-electron atoms we obtain very accurate short-range properties, including, for nuclear charge Z{>=}2, on-top values (zero electron-electron distance) essentially indistinguishable from those coming from precise variational wave functions. By means of a nonlinear adiabatic connection that separates long- and short-range effects, we also obtain Kohn-Sham correlation energies whose error is less than 4 mhartree, again for Z{>=}2, and short-range-only correlation energies whose accuracy is one order of magnitude better.

System-adapted correlation energy density functionals from effective pair interactions

This article discusses some ideas concerning an ‘average-pair-density functional theory’, in which the ground-state energy of a many-electron system is rewritten as a functional of the spherically and system-averaged pair density. These ideas are further clarified with simple physical examples. Then it is shown that the proposed formalism can be combined with density functional theory to build system-adapted correlation energy functionals. A simple approximation for the unknown effective electron–electron interaction that enters in this combined approach is described, and results for the He series and for the uniform electron gas are briefly reviewed.