Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session A27: Electronic Structure Methods I |
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Sponsoring Units: DCOMP Chair: Brandon Cook, Oak Ridge National Laboratory Room: 501 |
Monday, March 3, 2014 8:00AM - 8:12AM |
A27.00001: Selectively Localized and Symmetric Wannier Functions Runzhi Wang, Emanuel Lazar, Hyowon Park, Andrew Millis, Chris Marianetti The method of Marzari and Vanderbilt for computing maximally localized Wannier functions (MLWF) is widely used to represent localized orbitals in periodic materials. However the standard MLWF method minimizes the global spread of all orbitals in a preselected energy window. In many methods for strongly correlated electronic systems, including the density functional plus dynamical mean field method, one wishes to localize one particular class of orbitals (ie. a transition metal d orbital) without regard for the localization of the other states (eg. oxygen p and s). In addition, guaranteed preservation of pre-specficied point symmetry is desirable. Here we present an approach to this problem and demonstrate its implementation in model systems and real materials. [Preview Abstract] |
Monday, March 3, 2014 8:12AM - 8:24AM |
A27.00002: Failure of hybrid functionals to predict band gaps of materials at nanoscale Xinquan Wang, Zhigang Wu It is well known that density functional theory (DFT) within LDA/GGA severely underestimates band gaps in semiconductors and insulators due to the lack of derivative discontinuity in exchange-correlation, and hybrid functionals have been widely employed to improve band-gap calculations within the framework of DFT. In this work we show that hybrid functionals are not reliable in predicting band gap for nanostructures by comparing the hybrid functionals results of Si nanowires with those obtained using the many-body perturbation theory within the GW approximation. The hybrid functionals give a worse band-gap scaling law than that of LDA/GGA and their success in bulk materials is largely fortuitous, because they cannot correctly describe the response to the variation in screening. [Preview Abstract] |
Monday, March 3, 2014 8:24AM - 8:36AM |
A27.00003: DFT properties of Quasi-One-Dimensional Nanostructured Materials John Mintmire, Junwen Li, Daniel Gunlycke, Carter White Over the past several years we have made substantial progress in developing an approach for density-functional electronic structure calculations on quasi-one-dimensional nanostructures with helical symmetry. In this talk we discuss the application of these first-principles methods using Gaussian basis sets for calculating the electronic band structure of periodic graphitic nanostructures such as carbon nanotubes and graphene nanoribbons In particular we discuss how chemical effects at the edges of saturated graphene nanoribbons can cause ribbons to twist and form three-dimensional helical structures. Our calculations show that F-terminated armchair ribbons twist into helices, unlike flat H-terminated strips. Twisting ribbons of either termination couple the conduction and valence bands, resulting in band gap modulation. [Preview Abstract] |
Monday, March 3, 2014 8:36AM - 8:48AM |
A27.00004: A Self-consistent Mixing Parameter Scheme for Hybrid Functionals Applied to Periodic Systems Jonathan Skone, Marco Govoni, Giulia Galli We present a self-consistent scheme for determining the optimal fraction of exact exchange ($\alpha$) for hybrid functionals applied to condensed phase systems. It has been previously shown that the optimal mixing parameter is related to the inverse of the dielectric constant in solids, which in turn is related to the statically screened exchange term in the electronic self-energy within the GW approximation. We use this relationship to evaluate $\alpha$ self-consistently so as to obtain a mixing-parameter that is independent of the (arbitrary) choice of the initial fraction of exact-exchange. Our self-consistent scheme (sc-EXX) does not rely on any empirical parameters and is straightforward to apply to semiconducting and insulating, periodic systems. We show that for a variety of solids the sc-EXX scheme yields macroscopic dielectric constants in excellent agreement with experiment and provides considerable improvement in quasi-particle gaps over other non-empirical hybrid functionals with fixed exact exchange (e.g. PBE0). Furthermore, this approach provides an affordable way of capturing the static screening effects in a self-consistent manner, thus providing a superior starting point for GW calculations that include full dynamical screening. [Preview Abstract] |
Monday, March 3, 2014 8:48AM - 9:00AM |
A27.00005: Charged excitations in extended nanostructures from Koopmans-compliant functionals Nicolas Poilvert, Ismaila Dabo Koopmans-compliant (K) functionals aim to restore the piecewise linearity of approximate density-functional theory (DFT) functionals, generalizing ideas first introduced in the case of DFT+U functionals, but not restricted to predefined atomic orbitals. K functionals enable one to recover meaningful energy levels, which can thus be interpreted as charged excitation energies. Although it has been shown that K calculations yield energy levels and cross sections in excellent agreement with photoelectron spectroscopies, applications to crystalline materials have been lacking. Here, we report on recent progress in describing the band structures of periodic systems within K approximations. Our approach proceeds by analyzing the response of the electron density upon charged excitation in the limit of increasingly large systems. This analysis underscores important differences between conventional DFT approximations and their K counterparts, and enables us to generalize K functionals to extended systems. Validation of this approach is provided by the accurate description of $sp^{2}$-bonded carbon nanostructures. In the process, we highlight the performance of common DFT approximate functionals in capturing charged excitations in materials, provided that electronic localization is enforced [Preview Abstract] |
Monday, March 3, 2014 9:00AM - 9:12AM |
A27.00006: Hybrid functional and quasiparticle calculations of the Schottky barrier height at TiN/HfO$_{2}$ interface Young Jun Oh, Alex Taekyung Lee, Hyeon-Kyun Noh, K.J. Chang In high-k/metal gate transistors, it is important to control the metal work function such that it should be close to the valence and conduction band edges of Si in $p$- and $n$-channel devices, respectively. The Schottky barrier height (SBH) is affected by composition of metal gate, impurity, and deposition process. In theoretical studies, using the local density functional approximation, the SBH is severely underestimated because of the underestimation of the dielectric band gap. In this work, we perform both hybrid functional and quasiparticle calculations to improve the band gap and effective work function in TiN/HfO$_{2}$ interface. We consider two types of TiN/HfO$_{2}$ interface structures, which consist of either Ti-O or N-Hf interface bonds. Depending on the type of interface bonds, the SBH differs by 0.36 eV. In the many-body perturbation theory, the \textit{GW}$_{0}$ approach, which employs the self-consistent Green's function and the full frequency-dependent dielectric function, greatly improves the agreement of the SBH with experiments. We discuss the effects of the self-consistency and the plasmon-pole approximation on the SBH. On the other hand, with the hybrid functional, the SBH is overestimated due to the larger downward shift of the valence band edge of HfO$_{2}$. [Preview Abstract] |
Monday, March 3, 2014 9:12AM - 9:24AM |
A27.00007: Unfolding the Berry curvature of supercell calculations Raffaello Bianco, Raffaele Resta, Ivo Souza Unfolding band structures of supercell calculations has become a valuable tool for visualizing the influence of point impurities on the electronic states in crystals. In the same spirit, we introduce a procedure which maps the $k$-space Berry curvature of the occupied states from the small BZ of a supercell onto the normal BZ of the perfect (or virtual) crystal. As an application, we analyze the $k$-space distribution of the unfolded curvature of bcc Fe$_{1-x}$Co$_x$ ordered alloys, to better understand the influence of alloying on the anomalous Hall conductivity. Comparing with the ordinary curvature calculated in the virtual-crystal approximation, we find that the lowering of translational symmetry by the Co ``impurities'' introduces ``extrinsic'' contributions, which correlate with changes in the spectral function near the Fermi surface. In particular, the unfolded curvature displays additional sharp peaks associated with low-energy \textit{pseudovertical} transitions. These occur in regions of $k$-space where two unfolded bands, which in the virtual crystal would be separated in $k$-space (and therefore would not jointly contribute to its Berry curvature), lie on either side of the Fermi level and are coupled by the impurity potential. [Preview Abstract] |
Monday, March 3, 2014 9:24AM - 9:36AM |
A27.00008: Relaxation of atomic orbitals in a plane-wave basis set Jose Luis Martins, Carlos L. Reis We investigate a first-principles calculations scheme that uses a small or even minimal atomic orbital basis-set which is expanded in plane-waves and is subsequently augmented by a simple relaxation procedure in that same plane-wave basis set. Our results show good agreement between the standard pseudopotential plane-wave method and the novel hybrid methodology. The proposed method is simple to implement in existing plane-wave computer programs and leads to substantial gains in computation speed while maintaining reasonable accuracy. We show results for some test cases, including local-density band-structures of silicon and graphite and radial distribution functions of liquid silicon. [Preview Abstract] |
Monday, March 3, 2014 9:36AM - 9:48AM |
A27.00009: Consistent treatment of charged systems within periodic boundary conditions: The Projector Augmented-Wave and pseudopotential methods revisited Jean-Paul Crocombette, Fabien Bruneval, Xavier Gonze, Boris Dorado, Marc Torrent, Francois Jollet The \textit{ab initio} calculation of charged defect properties in solids is not straightforward because of the delicate interplay between the long-range Coulomb interaction and the periodic boundary conditions. We derive the Projector Augmented-Wave (PAW) energy and hamiltonian with a special care on the potentials from Coulomb interaction. By explicitly treating the background compensation charge, we find a new term in the total energy of charged cells and in the potential. We show that this background term is needed to accurately reproduce all-electron calculations of the formation energy of a charged defect. In particular, the previous PAW expressions were spuriously sensitive to the pseudization conditions and this artifact is removed by the background term. This PAW derivation also provides insights into the norm-conserving pseudopotential framework. We propose then an alternative definition for the total energy of charged cells and for the potential within this framework. [Preview Abstract] |
Monday, March 3, 2014 9:48AM - 10:00AM |
A27.00010: A finite-size supercell correction scheme for charged defects in one-dimensional systems: Application to impurities in silicon nanowires Sunghyun Kim, Ji-Sang Park, K.J. Chang The formation energies of defects in solids are important to determine their stability and charge transition levels. In first-principles calculations for charged defects, supercells subject to periodic boundary conditions are commonly used. However, this approach suffers from spurious interactions between the defect and its image charges. Due to the long-ranged Coulomb interaction, a very large supercell is inevitable to obtain the numerical convergence. To overcome this problem, several finite-size supercell corrections have been proposed for bulk solids and two-dimensional systems. In this work, we propose a new finite-size correction scheme for charged defects in one-dimensional systems, where the medium is surrounded by vacuum in radial directions. The energy correction is obtained by solving the Poisson equation with the macroscopic dielectric constant. We show that the macroscopic dielectric constant and the defect charge distribution can be derived from the electrostatic potential in first-principles calculations. We test our scheme for charged B and P impurities in silicon nanowires. We find that the corrected formation energies converge rapidly with either increasing of the wire length or increasing of the vacuum pad, providing reliable charge transition levels. [Preview Abstract] |
Monday, March 3, 2014 10:00AM - 10:12AM |
A27.00011: Optimized Gaussian Basis Sets for Plane-Wave Compatible Calculations Jin Cheng, Florian Libisch, Mohan Chen, Emily Carter The Wu-Yang optimized effective potential method (WY-OEP) is becoming widely used in embedding theories to get the exact kinetic energy potential for a given density. Our group implemented this scheme in the plane-wave code (ABINIT) and showed that it performs well for potential functional embedding on the density functional theory (DFT)/DFT level. To extend this embedding scheme and the WY-OEP method to correlated-wavefunction (CW)/DFT embedding, it is necessary to perform a WY-OEP calculation with a CW density. However, the incompleteness of Gaussian basis sets used in CW calculations causes numerical instabilities and leads to unphysical behavior in the kinetic energy potential. We propose a method to construct a basis set that systematically approaches the plane-wave basis density while retaining the quality of the CW. By doing so, basis set incompatibility has been eliminated. Test calculations show that good agreement for the density can be reached and the CW calculations give reasonable results. Furthermore, the WY-OEP has been performed with densities from a variety of CWs. The densities are well-reproduced and the kinetic energy potential is free of unphysical behavior, boding well for such potential-functional-embedded CW calculations. [Preview Abstract] |
Monday, March 3, 2014 10:12AM - 10:24AM |
A27.00012: Shirley Reduced Basis DFT: plane-wave generality and accuracy at reduced computational cost Maxwell Hutchinson, David Prendergast The Shirley Reduced Basis (SRB) provides a means for performing density functional theory electronic structure calculations with plane-wave accuracy and generality in a basis of significantly reduced size. The SRB is comprised of linear combinations of periodic Bloch functions sampled coarsely over the Brillouin zone (BZ) and selected for maximal information content using proper orthogonal decomposition [E. Shirley, Phys. Rev. B 54, 464 (1996)]. A basis produced from only order 10 samples, lying on the BZ boundary, is able to reproduce energies and stresses to sub meV and kbar accuracy, respectively, with order 10 basis functions per electronic band. Unlike other electronic structure bases of similar sizes, the SRB is adaptive and automatic, making no model assumptions beyond the use of pseudopotentials. We provide the first self-consistent implementation of this approach, enabling both relaxations and molecular dynamics. We demonstrate the usefulness of the method on a variety of physical systems, from crystalline solids to reduced dimensional systems under periodic boundary conditions, realizing order of magnitude performance improvements while kept within physically relevant error tolerances. [Preview Abstract] |
Monday, March 3, 2014 10:24AM - 10:36AM |
A27.00013: Relativistic Optimized Norm-Conserving Vanderbilt Pseudopotentials D.R. Hamann Two-projector fully non-local pseudopotentials obeying the generalized norm-conserving condition\footnote{D. Vanderbilt, Phys. Rev. B \textbf{41}, 7892 (1990).} and incorporating systematic convergence optimization\footnote{A. M. Rappe\textit{ et al.}, Phys. Rev. B \textbf{41}, 1227 (1990).} have been shown to accurately reproduce all-electron results with high computational efficiency.\footnote{D. R. Hamann, Phys. Rev. B \textbf{88}, 085117 (2013).} The generalized norm-conservation theorem guarantees exact reproduction of all-electron norms, radial log-derivatives, and first energy derivatives of radial log derivatives at several energies, as well as the hermiticity of the non-local pseudopotential operator. This theorem is exact only for non-relativistic all-electron wave functions.\footnote{Vanderbilt} Averaging out small asymmetries of the non-local operators generated using scalar-relativistic Schr\"{o}dinger equation solutions preserves agreement of these quantities to order 10$^{-4}$, and yields excellent results for solids.\footnote{Hamann} I show that fully-relativistic Dirac-equation solutions can be treated in the same manner, with comparably small errors. Spin-orbit band splittings as well as other properties of several solids calculated with these pseudopotentials will be compared to fully-relativistic all-electron results. [Preview Abstract] |
Monday, March 3, 2014 10:36AM - 10:48AM |
A27.00014: Visualizing the Kohn-Sham kinetic energy density in molecules Antonio C. Cancio, Aeryk Kuna In recent years, driven by applications at high temperature and large system size, interest has turned to the construction of orbital-free density functionals, modeling the kinetic energy solely as a functional of the electron density and its derivatives. We visualize the Kohn-Sham kinetic energy density (KED) for the AE6 test set of molecules commonly used to test density functional performance for atomization energies. Calculations are performed using the ABINIT plane-wave code with over-converged cutoffs and simulation cell sizes to produce as accurate results as possible within a pseudopotential approximation. The orbital-dependent KED is compared to simple orbital-free models such as the Thomas-Fermi and von-Weiszacker KED's and to a sophisticated metaGGA-level functional proposed by Perdew and Constantin (PC). All models fail to reproduce the Kohn-Sham KED reasonably in high density regions -- covalent and polar bonds and valence lone-pairs. In particular, the PC model actually disimproves on the simpler gradient expansion model in these regions. A simple fix is proposed for the PC functional, substantially modifying its behavior for regions of high values of the Laplacian of the density and low density gradient. [Preview Abstract] |
Monday, March 3, 2014 10:48AM - 11:00AM |
A27.00015: An investigation of the generalized phase shifts and the integrated density of states for full-potential single site scattering G. Malcolm Stocks, Yang Wang, J. Sam Faulkner In the conventional multiple scattering theory approach to {\em ab initio} electronic structure calculations, the integrated density of states (IDOS) is determined by taking the imaginary part of the Green function integrated along an energy contour. In this presentation, we show a numerically more reliable approach that uses an analytical expression for the IDOS, derived from the Krein's theorem. We compare both approaches, Krein's theorem versus the Green function method, in single site cases (e.g., Cu, Al, Mo). And we discuss the concept of generalized phase shifts, which are the diagonal elements of a unitary transformation of the S-matrix for the full-potential single site scattering, and show their applications in the determination of the IDOS. [Preview Abstract] |
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