Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session H21: General Theory: Density Functional Theory |
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Sponsoring Units: DCOMP Chair: Giulia Galli, University of California, Davis Room: Colorado Convention Center 106 |
Tuesday, March 6, 2007 8:00AM - 8:12AM |
H21.00001: Effects of semicore d-electrons in screened-exchange density functional methods Byounghak Lee, Lin-Wang Wang We report a theoretical study on the role of shallow $d$ states in the screened-exchange local density approximation (sX-LDA) band structure of binary semiconductor systems. We found that the inaccurate pseudo-wavefunctions can lead to 1) an overestimation of the screened-exchange interaction between the localized $d$ states and the delocalized higher energy $s$ and $p$ states and 2) an underestimation of the screened-exchange interaction between the $d$ states. The resulting sX-LDA band structures have substantially smaller band gaps compared with experiments. We correct the pseudo-wavefunctions of $d$ states by including the $s$ and $p$ states of the same shell in the valence states. The correction of pseudo-wavefunctions yields band gaps and the $d$ state binding energy in good agreement with experiments. Compared with the quasi-particle GW method, our sX-LDA results shows not only similar quality band gaps but also much better $d$ state binding energy. As an example, we present sX-LDA results of $s-d$ coupling in zinc-blende semiconductors and compare them with LDA+U results. We also present an efficient method to correct the pseudo-wavefunction exchange-integral error by using projection of wavefunctions onto atomic orbitals. [Preview Abstract] |
Tuesday, March 6, 2007 8:12AM - 8:24AM |
H21.00002: Asymptotic Near Nucleus Structure of the Electron-Interaction Potential in Local Effective Potential Theories Viraht Sahni, Zhixin Qian In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near nucleus structure of the electron-interaction potential is $v_{ee}(r) = v_{ee}(0) + \beta r + \gamma r^{2}$. In this paper we prove via time-independent Quantal Density Functional Theory[1](Q-DFT): (i) correlations due to the Pauli exclusion principle and Coulomb repulsion do not contribute to the linear structure;(ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is \emph{solely} due to Correlation-Kinetic effects, the coefficient $\beta$ being determined analytically. By application of adiabatic coupling constant perturbation theory via QDFT we further prove: (iv) the Kohn-Sham (KS-DFT) `exchange' potential $v_{x}(r)$ approaches the nucleus linearly, this structure being due \emph{solely} to lowest- order Correlation-Kinetic effects: (v) the KS-DFT `correlation' potential $v_{c}(r)$ also approaches the nucleus linearly, being \emph{solely} due to higher-order Correlation-Kinetic contributions. The above conclusions are equally valid for system of arbitrary symmetry, provided spherical averages of the properties are employed. \\ 1 \emph{Quantal Density Functional Theory}, V. Sahni (Springer-Verlag 2004) [Preview Abstract] |
Tuesday, March 6, 2007 8:24AM - 8:36AM |
H21.00003: Wave Function Functional via the Normalization Constraint Xiao-Yin Pan, Viraht Sahni, Lou Massa In this paper we extend our prior work [1] on the construction of approximate wave function functionals $\Psi = \Psi[\chi]$ for the ground state of the $He$ atom by attempting to expand the space of variations of the functional. As in our prior work, we assume $\Psi[\chi] = \Phi\{\phi_{i} \}[1 - f(\chi)]$, where $\Phi\{\phi_{i}\}$ is a normalized Slater determinant of the orbitals $\phi_{i}({\bf x})$, ${\bf x} = {\bf r} \sigma$, and $f(\chi)$ a correlation factor, and employ normalization as the constraint to determine the function $\chi$. However, we expand the space of variations from $\chi = \chi(s)$ to $\chi = \chi(st)$, where $s = r_{1} + r_{2}, t = r_{1} - r_{2}$. Although the constrained search over the entire requisite (\emph{st}) space is not achieved, two solutions of the integral equation for the function $\chi$ have been obtained. These two wave functions have the properties that they are normalized independent of the prefactor, with the density being that of the prefactor. The significance of these attributes of the wave function functionals will be discussed. \\ 1 . X.-Y. Pan et al, Phys. Rev. Lett. \textbf{93}, 130401 (2004) [Preview Abstract] |
Tuesday, March 6, 2007 8:36AM - 8:48AM |
H21.00004: A new approach to in full potential multiple scattering theory electronic structure calculations G.M. Stocks, Yang Wang, Aurelian Rusanu, Don M. Nicholson, Markus Eisenbach, Yevgeniy Puzyrev Despite the wide use of first principles electronic multiple scattering theory methods there realization as full potential methods has proved problematical with the consequence that atomic relaxation in not typically performed due to the lack of accurate forces. Here we describe some new techniques that facilitate an easy implementation of these full potential methods. In the determination of the scattering path matrix(t-matrix) we eschew the expansion of the shape function and use surface integrals to determine scattering t-matrix. We also use a new method is the treatment of Poisson problem where the charge density is divided in a spherical non-overlapping charge, which is treated using standard methods, and a pseudo charge which is treated by FFT-methods. [Preview Abstract] |
Tuesday, March 6, 2007 8:48AM - 9:00AM |
H21.00005: Optical properties of real surfaces: local field effects at oxidized Si(100)(2x2) computed with an efficient numerical scheme Lucia Caramella, Giovanni Onida, Fabio Finocchi, Lucia Reining, Francesco Sottile We show the application of an efficient numerical scheme to obtain the independent-particle dynamic polarizability matrix $\chi^{(0)}({\bf r}, {\bf r}', \omega)$, a key quantity in modern \emph{ab initio} excited state calculations. The method has been applied to the study of the optical response of a realistic oxidized silicon surface, including the effects of the local fields. The latter are shown to substantially increase the surface optical anisotropy in the energy range below the bulk bandgap. Our implementation in a large-scale \emph{ab initio} computational code allows us to make a quantitative study of the CPU time scaling with respect to the system size, and demonstrates the real potential of the method for the study of excited states in large systems. [Preview Abstract] |
Tuesday, March 6, 2007 9:00AM - 9:12AM |
H21.00006: Quantum mechanical models of energy dependence on fractional charge Steven Valone, Susan Atlas When subsystems interact sufficiently, the subsystems can exchange electrons and the effective number of electrons on each subsystem can take on fractional values. The energy of the system can be expressed as a function of that fractional charge. Pioneering work of Perdew, Parr, Levy, and Balduz [1] showed that when the subsystems interact weakly, the energy depends linearly with the fractional charge. We explain recently derived energy dependencies, based on a 2-state model, for the case when the subsystems interact strongly [2]. Those results are extended to a more general 3-state case. Insights into the properties of the chemical potentials of the subsystems are discussed. \newline \newline [1] J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Jr., Phys. Rev. Lett. {\bf 49}, 1691 (1982). \newline [2] S. M. Valone and S. R. Atlas, Phys. Rev. Lett. accepted. [Preview Abstract] |
Tuesday, March 6, 2007 9:12AM - 9:24AM |
H21.00007: Wave Function Functionals via the Constraint of the Expectations of Hermitian Single-Particle Operators Marlina Slamet, Xiao-Yin Pan, Viraht Sahni Recently, the idea [1] of 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, has been proposed. A constrained search over all functions $\chi$ such that $\Psi[\chi]$ satisfies a physical constraint or leads to a known value of an observable, is performed. A rigorous upper bound to the energy is then obtained via the variational principle. In this paper we extend this work on the ground state of the He atom by imposing the constraint that $\Psi[\chi]$ reproduce the exact expectations of the Hermitian single-particle operators $W = \sum_{i} r_{i}^{n}, n = -2, -1, 1, 2$, and $W =\sum_{i}\delta ({\bf r}_{i})$. By employing the form $\Psi[\chi] = \Phi [1 - f (\chi)]$, where $\Phi$ is a prefactor and $f(\chi)$ a correlation factor, two solutions to the resulting integral equation for the functions $\chi$ are determined for each operator $W$. In each case, the two wave function functionals lead to upper bounds to the energy that differ minimally from those of [1] in which only the constraint of normalization is imposed, while simultaneously reproducing the exact expectation of the operator $W$ .\\ 1. X.-Y. Pan, et al, Phys. Rev. Lett. \textbf{93}, 130401 (2004) [Preview Abstract] |
Tuesday, March 6, 2007 9:24AM - 9:36AM |
H21.00008: Molecular grand-canonical ensemble density functional theory O. Anatole von Lilienfeld, Mark E. Tuckerman The fundamental challenge of compound design, \textit{i.e.}~the reverse engineering of stable chemical compounds with predefined specific properties, originates in the high-dimensional and combinatorial nature of the \textit{chemical} space [1] which is spanned by the grand-canonical variables (superimposed particle densities of electrons and nuclei). A rigorous description of chemical space, using a grand-canonical multi-component density functional theory framework, will be presented [2]. Specifically, a total energy density functional for molecular systems in contact with an electron and a proton bath is introduced using Lagrange multipliers which correspond to the energetic response to changes of the elementary particle densities. Results will be shown for a molecular Fukui function, for finite temperature estimates of the redox potential of ammonia, and for alchemical variation of the intermolecular energy of formic acid interacting non-covalently with 10 proton systems [2,3]. Implications for rational compound design [4] and multi-scale modeling shall be discussed.\newline [1] P Kirkpatrick, C Ellis \textit{Nature} {\bf 432} 823 (2004) \newline [2] OAvL, M E Tuckerman \textit{J Chem Phys} {\bf 125} 154104 (2006) \newline [3] OAvL, M E Tuckerman \textit{submitted} \newline [4] OAvL, R Lins, U Rothlisberger \textit{Phys Rev Lett} {\bf 95} 153002 (2005) [Preview Abstract] |
Tuesday, March 6, 2007 9:36AM - 9:48AM |
H21.00009: The Accuracy of calculated electronic ground state energies Bernard Delley, Russell D. Johnson Ground-state enthalpies, calculated by a wide variety of electronic structure methods, are compared with experimentally well established values across a sizable database of 577 molecules and 15 atoms. With the diversity of species and bonding types available in this compilation it is possible to detect deficiencies that may escape with smaller test sets. The present analysis relying on ``Database optimized Atomic Enthalpies of Formation'' (DAtEF) yields error statistics which relate to reaction enthalpies among the species much more directly than extrapolations based on atomization enthalpies. The evaluation is applied to methods ranging from high level first principles wavefunction calculations to density functionals and to semiempirical approaches. It is found that computationally efficient and broadly applicable density functional methods with relatively small but adequate numerical basis sets can provide ground state enthalpies within $\approx$ 20 kJ/mol RMS ( $\approx$ 4.8 kcal/mol). This must be considered an excellent result, as presently only the heaviest available methods may provide about a factor of 2 more accuracy, if the conclusions inferred from a subset of the database hold up. [Preview Abstract] |
Tuesday, March 6, 2007 9:48AM - 10:00AM |
H21.00010: Time-dependent optimized effective potential for quantum wells Harshani Wijewardane, Carsten A. Ullrich Most present applications in time-dependent density-functional theory employ adiabatic approximations for the exchange- correlation (XC) potential, ignoring all functional dependence on densities at previous times. In this talk, we describe the electron dynamics in quantum wells beyond the adiabatic approximation, using the time-dependent optimized effective potential (TDOEP) method. In TDOEP, the XC potential is a functional of the time-dependent orbitals, and follows from an integral equation over space and time. We solve the full TDOEP integral equation for quantum well intersubband dynamics in exact exchange as well as self-interaction corrected ALDA. Various properties of the resulting time-dependent XC potential, such as its asymptotics, memory dependence, and discontinuity upon population of a new subband level are discussed. This work is supported by NSF DMR-0553485 and Research Corporation. [Preview Abstract] |
Tuesday, March 6, 2007 10:00AM - 10:12AM |
H21.00011: Time-dependent density functional approach for ultrafast optical phenomena Volodymyr Turkowski, Carsten A. Ullrich We present a formulation of time-dependent density functional theory (TDDFT) in a density-matrix framework, which can be applied to study ultrafast optical phenomena in semiconductor bulk systems and heterostructures. In particular, we derive and analyze the TDDFT version of the semiconductor Bloch equations and study the resulting absorption spectra of simple model insulators for different types of exchange-correlation potentials within and beyond the adiabatic LDA. We discuss the demands that the time-dependent exchange-correlation potential needs to satisfy in order to obtain physically correct absorption spectra, including excitonic features. [Preview Abstract] |
Tuesday, March 6, 2007 10:12AM - 10:24AM |
H21.00012: Dynamical Effects in the Interaction of Energetic Ions and Matter Ryan M. Hatcher, Matthew J. Beck, Sokrates T. Pantelides A theoretical description of the microscopic processes that underlie the interaction of energetic ions traversing a solid faces unique challenges as it is intrinsically a dynamic phenomenon. Here we use time-dependent density-functional theory to explore the exchange of energy between channeled ions, which interact weakly with the solid's nuclei, and electrons in a silicon crystal. We find that the \textbf{dynamic} response of the electron gas is characterized by a drag effect where there is an average accumulation of dynamical electron charge density behind the ion. The drag effect is superposed on additional dynamical patterns. We report the ``stopping powers'' for a number of ion species that are in excellent agreement with experimentally observed oscillations in the stopping powers as a function of the atomic number of the ions. We analyze the result by comparing with results obtained for an ion traversing a thin layer of homogeneous electron gas of various densities. [Preview Abstract] |
Tuesday, March 6, 2007 10:24AM - 10:36AM |
H21.00013: Accelerating self consistent field convergence by rubber sheeting of initial electronic wave functions. G. Eric Matthews, N.A.W. Holzwarth, George Martin, Briana Keeling, Douglas Agopsowicz We develop an algorithm for generating better initial electronic wave function estimates for density functional theory calculations following atomic movement. First principles molecular dynamics and atomic relaxation calculations involve successive movements of atoms followed by self consistent field (SCF) solutions for electronic wave functions. The SCF solutions converge most rapidly when starting from reasonably good estimates. Often estimates are generated directly from the wave functions of the previous atomic positions without adjustments for effects of position changes. Such estimates result in fast convergence to the correct wave function for small atomic movements, but for larger movements, convergence may be much slower. We present a method for improving the estimates of the new wave functions by using information from the movement of the atoms. Our algorithm is based on the ``rubber-sheeting'' method used in overlaying satellite imagery on geographic maps. A warping function is calculated that stretches and shrinks different regions of the wave function so that regions near nuclei are dragged along with the atoms. These estimates yield faster convergence for cases studied thus far. [Preview Abstract] |
Tuesday, March 6, 2007 10:36AM - 10:48AM |
H21.00014: Current-density functional theory of the friction of ions in an interacting electron gas. V. U. Nazarov, J. M. Pitarke, Y. Takada, G. Vignale, Y.-C. Chang Recently [1], the dynamical contribution to the friction coefficient of an electron gas for ions has been obtained quite generally in terms of the exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT). To implement this approach practically, an efficient approximation, like the local-density approximation (LDA), is needed for the dynamical xc kernel. It is, however, known that the {\em scalar} xc kernel of the TDDFT is a nonlocal quantity for which the LDA is not only inaccurate, but also contradictory [2]. Here we recast the theory into the terms of the {\em tensorial} xc kernel of the current-density functional theory [3] in which form the LDA can be applied. Our numerical results are in a considerably better agreement with the experimental stopping power of Al than it has been the case within the LDA to the TDDFT. [1] V.U.Nazarov {\it et al.}, Phys. Rev. B71, 121106 (2005). [2] G.Vignale, Phys. Lett. A209, 206 (1995). [3] G.Vignale and W.Kohn, Phys. Rev. Lett. 77, 2037 (1996). [Preview Abstract] |
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