Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session T24: Focus Session: Recent Developments in Density Functional Theory II |
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Sponsoring Units: DCOMP Chair: Timo Thonhauser, Wake Forest University Room: 326 |
Thursday, March 21, 2013 8:00AM - 8:12AM |
T24.00001: Comparing Exact Charge Gaps to Exact DFT and DFT Approximations for Extended 1D Continuum Systems Edwin Miles Stoudenmire, Lucas O. Wagner, Steven R. White, Kieron Burke With recent technical advances, the density matrix renormalization group (DMRG) can solve model electronic structure systems with long-range interactions in the 1D continuum exactly. We have been studying these systems as a laboratory for understanding and improving density functional theory (DFT). In this setting we can compute both the exact Kohn-Sham (KS) system and implement key DFT approximations. I will present exact data for charge gaps of extended chains of atoms and molecules driven through metal-insulator transitions, then compare various methods for computing these gaps in DFT. For example, we can compute the KS band gap exactly then compare to the KS band gap or integer gap computed within approximations such as LDA or LDA+U. Our results clarify how KS-DFT captures, or fails to capture, weakly and strongly correlated insuators and highlights the key challenges for improving approximate functionals. [Preview Abstract] |
Thursday, March 21, 2013 8:12AM - 8:24AM |
T24.00002: Development of accurate electron-hole exchange-correlation functional for calculation of exciton binding energy and electron-hole recombination probability in quantum dots Arindam Chakraborty, Christopher Blanton Development of electron-hole exchange-correlation functional (eh-Exc) is challenging because of various factors such as distance dependent dielectric function, different effective masses, and presence of core/shell interfaces. Calculation of eh-recombination probability is also challenging because of its sensitivity to the form of the wavefunction at small electron-hole separation. This talk will focus on systematic development of eh-Exc to address these challenges. In this approach an orbital based functional is constructed by combining the strategy of direct minimization of the optimized effective potential (OEP) with the OEP-MBPT method. The eh-Exc functional was used for computational of exciton binding energy and eh-recombination in a series of CdSe qdots. Comparison of the eh-Exc results with pseudopotential+CI calculations, Kohn-Sham perturbation theory calculations, and experimental values will be presented. The results indicate that the search for the ground state densities can be restricted to a set of N-representable densities which satisfy the electron-hole Kato cusp condition. Assessment and benchmarking of the quality of the eh-recombination probability will be presented by comparing eh-Exc results with explicitly correlated methods such as PIMC and QMC calculations. [Preview Abstract] |
Thursday, March 21, 2013 8:24AM - 8:36AM |
T24.00003: A DFT-based method of calculating optical properties of transition metal oxide materials John E. Coulter, Adam Gali, Manousakis Efstratios As part of an ongoing investigation of optical properties of transition metal oxide materials, we have examined the optical properties of Vanadium Dioxide using an \emph{ab-initio} method. Starting from hybrid DFT, we apply the GW approximation and solve the Bethe-Salpeter Equation (BSE) on the wavefunctions obtained from the DFT starting point. We find that the hybrid functional is not fully satisfactory for description of the optical spectrum of VO2, and that corrections are required. The hybrid functional results may be a good starting place for many-body perturbation theory. We apply the GW approximation and then solve the BSE from that starting point. We show that including single particle-hole quasiparticles is not sufficient for the optical spectrum, and that two-particle-two-hole effects must be included via the BSE to give agreement between the integrated strength of the optical spectrum at low energies and the experimental spectrum. We also find that a large number of high energy states must be included for a convergent description of the low energy optical spectrum. [Preview Abstract] |
Thursday, March 21, 2013 8:36AM - 8:48AM |
T24.00004: Quasiparticle Spectra from a Nonempirical Optimally Tuned Range-Separated Hybrid Density Functional Sivan Refaely-Abramson, Sahar Sharifzadeh, Niranjan Govind, Jochen Autschbach, Jeffrey B. Neaton, Roi Baer, Leeor Kronik We present a method for obtaining outer-valence quasiparticle excitation energies from a density-functional-theory-based calculation, with an accuracy that is comparable to that of many-body perturbation theory within the GW approximation. The approach uses a range-separated hybrid density functional, with an asymptotically exact and short-range fractional Fock exchange. The functional contains two parameters, the range separation and the short-range Fock fraction. Both are determined nonempirically, per system, on the basis of the satisfaction of exact physical constraints for the ionization potential and many-electron self-interaction, respectively. The accuracy of the method is demonstrated on four important benchmark organic molecules: perylene, pentacene, 3,4,9,10-perylene-tetracarboxylic dianhydride (PTCDA), and 1,4,5,8-naphthalene-tetracarboxylic dianhydride (NTCDA). We envision that for finite systems the approach could provide an inexpensive alternative to GW, opening the door to the study of presently out of reach large-scale systems (Phys. Rev. Lett., in press). [Preview Abstract] |
Thursday, March 21, 2013 8:48AM - 9:00AM |
T24.00005: Plasmon-pole models affect band gaps in GW calculations Paul Larson, Zhigang Wu Density functional theory calculations have long been known to underestimate the band gaps in semiconductors. Significant improvements have been made by using GW calculations that uses the self energy, defined as the product of the Green function (G) and screened Coulomb exchange (W). However, many approximations are made in the GW method, specifically the plasmon-pole approximation. This approximation replaces the integration necessary to produce W with a simple approximation to the inverse dielectric function. Four different plasmon-pole approximations have been tested using the tight-binding program ABINIT: Godby-Needs, Hybertsen-Louie, von der Linden-Horsch, and Engel-Farid. For many materials, the differences in the GW band gaps for the different plasmon-pole models are negligible, but for systems with localized electrons, the difference can be larger than 1 eV. The plasmon-pole approximation is generally chosen to best agree with experimental data, but this is misleading in that this ignores all of the other approximations used in the GW method. Improvements in plasmon-pole models in GW can only come about by trying to reproduce the results of the numerical integration rather than trying to reproduce experimental results. [Preview Abstract] |
Thursday, March 21, 2013 9:00AM - 9:12AM |
T24.00006: Many-body effects on the zero-point renormalization of diamond: a frozen-phonons approach Gabriel Antonius, Samuel Ponc\'e, Michel C\^ot\'e, Xavier Gonze Electron-phonon interaction has a sizeable effect on the electronic structure of materials. Even at zero temperature, the zero-point renormalization (ZPR) can reduce the band gap of insulators by several hundreds of meV. The method of choice to compute this effect is based on the AHC theory, performing perturbative calculations with DFT wavefunctions and energies, possibly with a scissor shift. However, previous studies suggest that inclusion of many-body effects might change substantially the DFT electron-phonon coupling coefficients. We study the ZPR of the optical band gap of diamond, using a frozen-phonons method. This allows us to perform $G_0W_0$ and self-consistent quasi-particle $GW$ calculations on the distorted lattice, thus including many-body effects in the electron-phonon coupling coefficients. The frozen-phonons method also allows us to study other neglected components of the AHC theory, such as the non-diagonal Debye-Waller term, and the anharmonic effects. [Preview Abstract] |
Thursday, March 21, 2013 9:12AM - 9:24AM |
T24.00007: Going beyond Kohn and Sham (KS): determining accurate ground and first excited states Luiz Ferreira, Marcelo Marques, Lara Teles, Ronaldo Pela The Total energy in KS is written as \[E=\frac{1}{2}\sum\int\nabla\psi^*\cdot\nabla\psi+ \frac{1}{2}\int\frac{\sum\psi^*\psi(r)\sum\psi^*\psi(r^{\prime})} {(r-r^{\prime})}+\int\sum\psi^{*}\psi V_{nuclei}+Exc\] The KS procedure continues by minimizing the energy with respect the wavefunctions $\psi$. The equation for the wave functions is similar to the one-particle Schroedinger equation. In our talk we will present results obtained in the following way: we add an external potential $V_{add}$ to the nuclei potential $V_{nuclei}$ and, after the calculation is completed, we subtract what we added, namely. $-\int\sum\psi^{*}\psi V_{add}$. The result is a calculation according to the Eq. above but with wavefunctions not satisfying the KS equations. If the exchange-correlation term were reliable one would expect that the calculated energy would be larger than the KS energy. The added potential $V_{add}$ is what is being used in the {\it LDA-1/2} method and is dependent on a cut-off parameter $C$. Making the extremization of the total energy with respect to $C$ we obtain (1) a point of maximum, which frequently will be shown to be the first excited state, (2) a minimum, with an energy lower than the KS ($C=0$) ground state and with improved lattice parameter. [Preview Abstract] |
Thursday, March 21, 2013 9:24AM - 9:36AM |
T24.00008: Efficient optimal effective potential approach for pe- riodic plane-wave density functional theory Florian Libisch, Johannes M. Dieterich, Chen Huang, Emily A. Carter Kohn-Sham (KS) density functional theory (DFT) formulates equations for non-interacting electrons subject to a mean-field KS potential. The exchange and correlation (XC) between electrons are accounted for by density-based XC-functionals. The introduction of orbital-dependent functionals allows for a more accurate treatment of exchange and correlation, a prominent example being the exact treatment of Hartree-Fock exchange. Such a construction, however, is not straightforward in KS DFT, as all Kohn Sham orbitals fulfill the same KS equation. For a given orbital-dependent functional, direct solutions to find the corresponding KS potential are numerically cumbersome or even unstable. By extending and combining previous approaches [Phys. Rev. B 62, 15521 (2000), Phys. Rev. B 84, 165122 (2011)], we introduce a momentum-space based formulation that allows for an efficient treatment of orbital-dependent functionals. We include the full spin degrees of freedom, as well as periodic boundary conditions and k-point sampling. We show that for the spin-free case, our formulation becomes similar to the orbital-shift approach [Phys. Rev. B 68, 035103 (2003)] but numerically better suited for implementation in plane-wave DFT codes. Finally, we discuss practical applications. [Preview Abstract] |
Thursday, March 21, 2013 9:36AM - 9:48AM |
T24.00009: Reliability of the Tran-Blaha functional in predicting band gaps and widths Gian-Marco Rignanese, Waroquiers David, Aur\'elien Lherbier, Anna Miglio, Martin Stankovski, Samuel Ponce, Micael Oliveira, Matteo Giantomassi, Xavier Gonze For a set of oxides and semiconductors, we compute the electronic band structures (gaps and widths) within Density-Functional theory (DFT) using the Tran-Blaha (TB09) functional [Phys. Rev. Lett. {\bf 102}, 226401 (2009)]. We compare them with those obtained from (i) DFT using the local-density approximation (LDA), (ii) many-body perturbation theory (MBPT), and (iii) experiments. TB09 leads to band gaps in much better agreement with experiment than the LDA. However, the valence (and conduction) band widths are often underestimated (noticeably more than in LDA). MBPT corrections are obtained peforming one-shot $GW$ calculations using DFT eigenenergies and wavefunctions as starting point (both LDA and TB09 are considered). These corrections lead to a much better agreement with experimental data for the band widths. The MBPT band gaps obtained starting TB09 are close to those from quasi-particle self-consistent $GW$ calculations, at a much reduced cost. Finally, we explore the possibility to tune a semi-empirical parameter present in the TB09 functional aiming to obtain simultaneously better gaps and band widths. We find that these requirements are conflicting. [Preview Abstract] |
Thursday, March 21, 2013 9:48AM - 10:00AM |
T24.00010: Construction of a spin-density functional for models of strongly correlated systems: including spin improves the description of charge Klaus Capelle, Daniel Vieira, Vivian Franca An explicit spin-dependence is built into a class of previously developed density functionals for models of strongly correlated systems. As a side effect of accounting for the spin-degrees of freedom, the functional also provides an improved description of the charge-degrees of freedom. In particular, unlike earlier proposals, the present parametrization correctly predicts a positive Mott gap at half filling for any repulsive interaction. Applications to spatially inhomogeneous models, e.g. in the presence of impurities, external fields or trapping potentials are worked out and results are shown to be in excellent agreement with independent many-body calculations, at a fraction of the computational cost. See New J. Phys. 14 073021 (2012). [Preview Abstract] |
Thursday, March 21, 2013 10:00AM - 10:12AM |
T24.00011: Transverse spin gradient functional for non-collinear Spin Density Functional Theory F.G. Eich, G. Vignale, E.K.U. Gross The ab-initio description of non-collinear magnetism is essential for the search of new materials suitable for the construction of spintronic devices. We present a novel functional explicitly constructed for the description of non-collinear magnetism. It is formulated in terms of a Spin Gradient Extension (SGE) to the Local Spin Density Approximation, which introduces a dependence on the transverse gradients of the spin magnetization. While collinear Generalized Gradient Approximations provide a dependence on longitudinal spin gradients the SGE takes into account that longitudinal and transverse variations of the spin magnetization affect the energy differently. The explicit dependence on the transverse gradients is obtained from a reference systems which exhibits non-collinearity, i.e., the spin-spiral-wave state of the uniform electron gas. The inclusion of transverse spin gradients yields exchange-correlation magnetic fields that are non-collinear w.r.t.~the spin magnetization. This implies that the spin-current density of the Kohn-Sham system does not vanish even if no external magnetic field is applied. As an example we present the application of the SGE to the non-collinear ${120^{\circ}}$-N{\'e}el state of a Chromium mono-layer. [Preview Abstract] |
Thursday, March 21, 2013 10:12AM - 10:24AM |
T24.00012: Angular Momentum Dependent Orbital Free Density Functional Theory Youqi Ke, Florian Libisch, Junchao Xia, Lin-Wang Wang, Emily A. Carter We report a novel and general formalism for linear scaling, angular momentum dependent (AMD) orbital free (OF) density functional theory (DFT) to advance the accuracy and applicability of OFDFT. To introduce angular momentum dependence in OFDFT, we devise a hybrid scheme by partitioning the system into muffin-tin spheres and an interstitial region: the electron density inside the spheres is expressed by a set of Kohn-Sham (KS) DFT derived atom-centered basis functions combined with an on-site density matrix N$_{R}$. A general OFDFT total energy functional is introduced with a crucial nonlocal energy term E$^{NL}$ which is neglected in conventional implementations of OFDFT. E$^{NL}$ corrects the errors due to the use of approximate kinetic energy density functionals and local pseudopotentials for ion-electron interactions. We approximate E$^{NL}$ to include AMD contributions inside the spheres: as a first step, a linear dependence on the N$_{R}$ is considered with a set of AMD energies E$^{l}_{R}$. E$^{l}_{R}$ are determined by fitting a small set of bulk properties to KSDFT. We find AMD-OFDFT offers substantial improvements over conventional OFDFT, as we show for various properties of the transition metal Ti and its alloys (Ti$_{x}$Al$_{1-x})$. [Preview Abstract] |
Thursday, March 21, 2013 10:24AM - 10:36AM |
T24.00013: Non-Empirical Orbital-Free Approximations from Semiclassical Approaches Stefano Pittalis, A. Cangi, C.R. Proetto, E.K.U. Gross, K. Burke We present a selection of results up to exchange effects obtained from semiclassical approximations aiming at enabling non-empirical and accurate orbital-free methods in models of electronic nanostructures. Insights for improving or better understanding popular density-functional theory approximations will be analyzed. [Preview Abstract] |
Thursday, March 21, 2013 10:36AM - 10:48AM |
T24.00014: The piecewise-linearity of approximate density functionals revisited: implications for frontier orbital energies Eli Kraisler, Leeor Kronik In the exact Kohn-Sham density-functional theory (DFT), the total energy versus the number of electrons is a series of linear segments between integer points. However, commonly used approximate density functionals produce total energies that do not exhibit this behavior. As a result, many system properties can be poorly described. In particular, the ionization potential theorem, equating the highest occupied eigenvalue with the ionization potential, can be grossly disobeyed. Here, we offer a generalization of all energy terms of an arbitrary density functional to systems with a fractional electron number, based on the ensemble form of DFT. Using the local density approximation as an illustrative example, we find that this generalization significantly reduces the deviation from piecewise linearity, while introducing neither empiricism nor further correction terms. With the generalized form, the total energy at integer electron numbers remains intact, but the eigen-energies change and the ionization potential theorem is much more closely obeyed. [Preview Abstract] |
Thursday, March 21, 2013 10:48AM - 11:00AM |
T24.00015: Curvature and frontier orbital energies in density functional theory Leeor Kronik, Tamar Stein, Jochen Autschbach, Niranjan Govind, Roi Baer Perdew et al. [Phys. Rev. Lett 49, 1691 (1982)] discovered and proved two different properties of exact Kohn-Sham density functional theory (DFT): (i) The exact total energy versus particle number is a series of linear segments between integer electron points; (ii) Across an integer number of electrons, the exchange-correlation potential may ``jump'' by a constant, known as the derivative discontinuity (DD). Here, we show analytically that in both the original and the generalized Kohn-Sham formulation of DFT, the two are in fact two sides of the same coin. Absence of a derivative discontinuity necessitates deviation from piecewise linearity, and the latter can be used to correct for the former, thereby restoring the physical meaning of the orbital energies. Using selected small molecules, we show that this results in a simple correction scheme for any underlying functional, including semi-local and hybrid functionals as well as Hartree-Fock theory, suggesting a practical correction for the infamous gap problem of DFT. Moreover, we show that optimally-tuned range-separated hybrid functionals can inherently minimize both DD and curvature, thus requiring no correction, and show that this can be used as a sound theoretical basis for novel tuning strategies. [Preview Abstract] |
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