Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session L13: Ground State Density Functional Theory: Theory Development |
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Sponsoring Units: DCOMP Chair: Andreas Savin, Université Pierre et Marie Curie Room: Morial Convention Center 204 |
Tuesday, March 11, 2008 2:30PM - 2:42PM |
L13.00001: Strictly correlated electrons in density-functional theory: A general formulation with applications to spherical densities Michael Seidl, Paola Gori-Giorgi, Andreas Savin We reformulate the strong-interaction limit of electronic density functional theory in terms of a classical problem with a degenerate minimum. This allows us to clarify many aspects of this limit, and to write a general solution, which is explicitly calculated for spherical densities. We then compare our results with previous approximate solutions and discuss the implications for density functional theory. [Preview Abstract] |
Tuesday, March 11, 2008 2:42PM - 2:54PM |
L13.00002: Spherically and system-averaged pair densities in the strong-interaction limit of density functional theory Paola Gori-Giorgi, Andreas Savin, Michael Seidl The spherically and system-averaged pair density (also known in chemistry as intracule density) plays a central role in the construction and understanding of exchange-correlation energy functionals in density functional theory. We have calculated the intracule density for several atoms in the strong-interaction limit of density functional theory. Comparison of our results with the same quantities calculated in the opposite limit, the non-interacting Kohn-Sham system, provides useful insight on the nature of electronic correlation in density functional theory. [Preview Abstract] |
Tuesday, March 11, 2008 2:54PM - 3:06PM |
L13.00003: Internally Consistent Local Approximation to Density Functional theory Antonios Gonis, Don M. Nicholson, G. Malcolm Stocks We propose a new non-local functional for the implementation of density functional theory (DFT) within a local approximation. This functional is obtained through the replacement of the conventional form $T_s+\frac{1}{2}\int{\rm d}{\bf r}_1\int{\rm d}{\bf r}_2\frac{n({\bf r}_1)n({\bf r}_2)}{|{\bf r}_1-{\bf r}_2|}$ to represent the kinetic and Coulomb energy of a non-interacting system with the expression $T_s+\frac{1}{2}\int{\rm d}{\bf r}_1\int{\rm d}{\bf r}_2\frac{n_s({\bf r}_1,{\bf r}_2)}{|{\bf r}_1-{\bf r}_2|}$ where $n_s({\bf r}_1,{\bf r}_2)$ is the two-particle density formed from the non-interacting wave function, and $n({\bf r})$ is the single-particle density. Based on this new functional we develop a local approximation and show that it is self-interaction free and also leads to energies that form an upper bound to the exact ground-state energy. We provide a brief comparison with the conventional Kohn-Sham local density approximation and some of the schemes introduced to correct for the presence of self-interaction in the conventional formalism, and comment on our immediate plans for future development. [Preview Abstract] |
Tuesday, March 11, 2008 3:06PM - 3:18PM |
L13.00004: A new approach to density functional theory Kieron Burke, Peter Elliott, Attila Cangi, Donghyung Lee I will explain a new way to think about density functional theory, based on a simple principle: asymptotic exactness for large particle number. This explains many features of existing functionals [1], and makes the connection between semiclassical and density functional approximations. It underlies the restoration of the gradient expansion in PBEsol[2]. It also provides a path toward highly accurate, orbital-free, non-local functionals of the potential, for both the density itself and the non-interacting kinetic energy.\newline [1] J.P. Perdew, L.A. Constantin, E. Sagvolden, and K. Burke, Phys. Rev. Lett. {\bf 97}, 223002 (2006).\newline [2] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, and K. Burke, arXiv:0707.2088 (2007). [Preview Abstract] |
Tuesday, March 11, 2008 3:18PM - 3:30PM |
L13.00005: The Role of Quantum Stress in Descriptive Chemistry Ilya Tokatly, Giovanni Vignale, Jianmin Tao We show that key concepts of descriptive chemistry, such as atomic shells, bonding electron pairs and lone electron pairs, may be described in terms of {\it quantum stress focusing}, i.e. the spontaneous formation of closed surfaces upon which the electronic pressure has an extremum. This description subsumes previous mathematical constructs, such as the Laplacian of the density and the electron localization function, and provides a new tool for visualizing chemical structure. We also show that the full anisotropic stress tensor can be easily calculated from density functional theory. [Preview Abstract] |
Tuesday, March 11, 2008 3:30PM - 3:42PM |
L13.00006: Semiclassical Approaches in Density Functional Theory Peter Elliott, Attila Cangi, Donghyung Lee, Kieron Burke We discuss the use of semiclassical methods in understanding, and improving, density functional theory (DFT). It has been found[1] that semiclassical approaches can explain many features of modern exchange-correlation approximations, such as the local density approximation or generalized gradient approximations. In this work, we continue this line of inquiry, showing how semiclassical approximations may be used to construct a form for the non-interacting kinetic energy density. A semiclassical approximation to the Green's function is made[2], which, when integrated appropriately, yields leading corrections to the Thomas-Fermi result. It can be regarded as a functional of the potential. We test this approximation for various 1D systems confined within a box and present the results. This, coupled with the corresponding form of the density[2], could provide an orbital-free DFT which would allow more complex systems to be studied.\newline [1] J. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, and K. Burke, arXiv:0707.2088 (2007).\newline [2] W. Kohn and L.J. Sham, Phys. Rev. {\bf 137}, A1697 (1965). [Preview Abstract] |
Tuesday, March 11, 2008 3:42PM - 3:54PM |
L13.00007: Correlation Energy of 3D Spin-Polarized Electron Gas: A Single Interpolation Between High- and Low-Density Limits Jianwei Sun, John Perdew, Michael Seidl We present an analytic model for the correlation energy per electron $e_c (r_s ,\zeta)$ in the three-dimensional (3D) uniform electron gas, covering the full range $0\le r_s <\infty $ and $0\le \zeta \le 1$ of the density parameter $r_s $ and the relative spin polarization $\zeta$. An interpolation is made between the exactly known high-density ($r_s \to 0)$ and low-density ($r_s \to \infty)$ limits, using a formula which (unlike previous ones) has the right analytic structures in both limits. We find that there is almost enough information available from these limits to determine the correlation energy over the full range. By minimal fitting to numerical quantum Monte Carlo data, we predict the value of $b_1 (\zeta)$ at $\zeta $=0 close to the theoretical value [1], where $b_1 (\zeta)$ is the coefficient of the $r_s $term in the high-density expansion. The model finds correlation energies for the unpolarized ($\zeta $=0) and fully polarized ($\zeta $=1) cases in excellent agreement with Monte Carlo data. \newline [1] T. Endo, M. Horiuchi, Y. Takada and H. Yasuhara, Phys. Rev. B 59, 7367 (1999) [Preview Abstract] |
Tuesday, March 11, 2008 3:54PM - 4:06PM |
L13.00008: Semiclassical Origin of Density Functionals Attila Cangi, Peter Elliott, Donghyung Lee, Kieron Burke We use methods of semiclassical physics [1] to study the basic ingredients of DFT in terms of an asymptotic expansion in powers of the particle number. As an example we derive an approximate many-particle density [2] of a general potential in a one-dimensional system with hard walls. If the Fermi level lies above the maximum of the potential, we obtain densities very close to the exact answer, even for a small particle number. Density oscillations due to the effect of the boundaries are also present.\newline [1] M. V. Berry and K. E. Mount, Reports of Progress in Physics 35, 315 (1972).\newline [2] W. Kohn and L. J. Sham, Phys. Rev. 137, A1697 (1965). [Preview Abstract] |
Tuesday, March 11, 2008 4:06PM - 4:18PM |
L13.00009: Construction of an analytic exchange-correlation hole for the Perdew-Burke-Ernzerhof GGA Matthias Ernzerhof, Hilke Bahmann The Perdew-Burke-Ernzerhof (PBE) [1] approximation to the exchange-correlation energy is employed as a starting point for the construction of an approximate, spherically averaged exchange-correlation hole. In a first step, we develop a new model for the PBE exchange hole. This model satisfies the homogeneous electron gas limit; it is normalized and yields the correct small-gradient limit in the system average. A correlation factor [2], i.e., a function multiplying the exchange hole, is proposed that turns the exchange into an exchange-correlation hole. The correlation factor has a simple form and its parameters are determined through a number of known conditions that ought to be satisfied by a PBE exchange-correlation hole. The homogeneous-electron-gas limit of the new hole model is compared to the LSD hole [3]. \newline [1] J.P. Perdew, K. Burke, M. Ernzerhof, PRL 77, 3865 (1996); 78, 1396(E) (1997). \newline [2] P. Gori-Giorgi, J.P. Perdew, PRB 66, 165118 (2002). \newline [3] J.P. Perdew, Y. Wang, PRB 46, 12947 (1992). [Preview Abstract] |
Tuesday, March 11, 2008 4:18PM - 4:30PM |
L13.00010: Orbital-free Kinetic Energy Density Functionals of GGA Type with Positive-definite, Finite Pauli Potentials S.B. Trickey, V.V. Karasiev, R.S. Jones, Frank Harris A reliable, orbital-free expression for the Kohn-Sham kinetic energy functional $T_s$ would provide Born-Oppenheimer forces for first-principles molecular dynamics with a computational cost scaling as the relevant system volume rather than some power of the electron count $N_e$. In previous work (J. Computer-Aided Mat. Des. {\bf 13}, 111 (2006)) we obtained improved (compared to published) generalized gradient approximate KE functionals by requiring positive-definiteness of the Pauli potential, $v_\theta = \delta T_\theta / \delta n$, with $T_s = T_w + T_\theta$ and $T_w$ the von Weizs\"acker KE functional. However, such modified conjoint functionals still generate unphysical singularities at the nuclei. Here we discuss a systematic use of gradient expansion truncations to generate constrained enhancement factors for GGA functionals that are guaranteed to yield $v_\theta$ that is both everywhere positive definite and finite at the nuclei. Illustrative results will be reported. [Preview Abstract] |
Tuesday, March 11, 2008 4:30PM - 4:42PM |
L13.00011: Exact condition on the non-interacting kinetic energy for real matter Donghyung Lee, Kieron Burke From the analysis of the asymptotic expansion [1,2] for the total energies of neutral atoms, we suggest a modified gradient expansion approximation to the kinetic energy which satisfies the exact asymptotic condition as the number of electrons N $\rightarrow$ $\infty$. The resulting functional determines the small gradient limit of any generalized gradient approximation, and conflicts with the standard gradient expansion. We apply this new functional to the atoms up to Z $\sim$ 88 in comparison with the 2nd and 4th gradient expansion approximations. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.\newline \newline $[1]$ Thomas-Fermi model: The second correction, J. Schwinger, Phys. Rev. A {\bf 24}, 2353 (1981).\newline $[2]$ Semiclassical atom, B.-G. Englert and J. Schwinger, Phys. Rev. A {\bf 32}, 26 (1985). [Preview Abstract] |
Tuesday, March 11, 2008 4:42PM - 4:54PM |
L13.00012: Construction of Wave Function Functionals Marlina Slamet, Xiao-Yin Pan, Viraht Sahni We recently proposed [1] expanding the space of variations in calculations of the energy by considering the approximate wave function $\Psi$ to be a functional of functions $\chi$, $\Psi = \Psi[\chi]$, rather than a function. A constrained search is first performed over all functions $\chi$ such that $\Psi[\chi]$ satisfies a physical constraint or leads to a known value of an observable. A rigorous upper bound to the energy is then obtained via the variational principle. In this paper we apply this idea to the ground state of the He atom by constructing $\Psi[\chi]$ that reproduce the exact expectations of the Hermitian single- and two-particle operators $W = \sum_{i} r_{i}^{n}, n = -2, -1, 1, 2$; $W =\sum_{i}\delta ({\bf r}_{i})$; $W=|{\bf r}_{1}-{\bf r}_{2}|^{m}, m=-1,-2,1,2$. The functionals are of the form $\Psi[\chi] = \Phi [1 - f(\chi)]$, where $\Phi$ is a prefactor and $f(\chi)$ a correlation factor. The $\Psi[\chi]$ (\emph{i}) lead to the exact expectation value of $W$; (\emph {ii}) are automatically normalized; and (\emph{iii}) provide a rigorous upper bound to the energy. [1] X.-Y. Pan, \textit {et al}, PRA \textbf{72}, 032505 (2005). [Preview Abstract] |
Tuesday, March 11, 2008 4:54PM - 5:06PM |
L13.00013: LDA+DMFT Charge self-consistency applied to Yb valence transition Erik R. Ylvisaker, W. E. Pickett, A. K. McMahan Ytterbium metal, in a pressure range of 0 to 34 GPa, is known to undergo a gradual transition from a $v^2f^{14}$ state to a $v^3f^{13}$ state where $v$ and $f$ represent valence (spd) and f-orbital occupations, respectively. We present, first, conventional LDA+DMFT studies of this transition using both the Hirsch-Fye QMC and Hubbard I atomic solvers. This application of DMFT to the correlated f-orbitals gives reasonable agreement with the experimental transition. However, the neglect of charge self-consistency is questionable for a valence transition where the concentration of valence electrons changes. Therefore we generalize the procedure and compare and contrast LDA+DMFT results (transition pressure, energy and equation of state) with and without charge self-consistency for Yb using the Hubbard I impurity solver. [Preview Abstract] |
Tuesday, March 11, 2008 5:06PM - 5:18PM |
L13.00014: Fock exchange in FLAPW method Tatsuya Shishidou, Tamio Oguchi Fock exchange potential has distinct features which cannnot be seen in the LDA exchange potential. (i) It is self-interaction free potential and (ii) nonlocal potential and thus state-dependent potential. With appropriate correlation effects added, these two features may produce significantly improved results over the conventional LDA results, as one can witness in the GW calculations. Massidda et al.\ (1993) proposed a way to calculate Fock exchange potential of extended solids within the FLAPW method. Their idea was to apply Weinert's Poisson solver to infinite lattice summation as is done for the Hartree potential calculation. Due to the long range nature of Coulomb interaction, one encounters singularity problem in this process. They handled it by simply extending Gygi's prescription (1986), which was originally developed for the norm-conserving pseudopotential framework. In this paper, we present our formula in calculating Fock exchange matrix of solids based on the FLAPW method. Following Massidda's idea, we use Weinert's Poisson solver. However, in treating the Coulomb singularity, we have developed more accurate way: the occupied eigenfunctions in Fock operator are expanded upto the second order in terms of $q$ vector based on the $k\cdot p$ perturbation theory, whearas Gygi's way corresponds to the zeroth order expansion. With this higher order expansion, one can achieve faster convergence for the Brillouin zone integration appearing in the Fock operator. [Preview Abstract] |
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