Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session U24: Focus Session: Recent Developments in Density Functional Theory III |
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Sponsoring Units: DCOMP Chair: Pieremanuele Canepa, Wake Forest University Room: 326 |
Thursday, March 21, 2013 11:15AM - 11:27AM |
U24.00001: Recovering hidden Bloch character: Unfolding Electrons, Phonons, and Slabs Philip B. Allen, Tom Berlijn, David Casavant, Jose Soler One of the main problems of first principles supercell calculations is the band folding problem. As the supercell gets larger, the bands get folded into a smaller Brillouin zone and cease to give information about the Bloch character of the underlying normal cell. To tackle this problem an unfolding formalism has been implemented in first principles calculations via several techniques [1-5]. Here we will present an extended unfolding formalism for finite systems and exemplify it with first principles calculations of a Si (111) slab.\\[4pt] [1] S. Baroni et al, PRL 65, 84 (1990)\\[0pt] [2] F. Giustino et al, PRL 98, 047005 (2007)\\[0pt] [3] W. Ku et al, PRL 104, 216401 (2010)\\[0pt] [4] V. Popescu et al, PRL 104, 236403 (2010)\\[0pt] [5] M. W. Haverkort, arXiv:1109.4036 [Preview Abstract] |
Thursday, March 21, 2013 11:27AM - 11:39AM |
U24.00002: Exponential supercell convergence of the exact exchange energy via truncated coulomb potentials Ravishankar Sundararaman, T. A. Arias Hybrid density functionals have become increasingly popular as a solution to mitigate the self-interaction error in semi-local density functionals, but widespread application to periodic systems has been limited by computational cost. This cost is exacerbated by poor $k$-point convergence due to the $G\to0$ singularity in the exact exchange energy, in spite of several singularity correction methods such as auxilliary function integration,\footnote{P. Carrier, S. Rohra and A. G\"orling, {\it Phys. Rev. B} {\bf 75}, 205126 (2007)}$^{,}$\footnote{I. Duchemin and F. Gygi, {\it Comp. Phys. Comm} {\bf 181}, 855 (2010)} image subtraction,\footnote{J. Paier et al., {\it J. Chem. Phys.} {\bf 122}, 234102 (2005)} and spherical truncation of the coulomb potential.\footnote{J. Spencer and A. Alavi, {\it Phys. Rev. B} {\bf 77}, 193110 (2008)} We analyze these rather disparate methods in an intuitive formalism based on Wannier function localization, which naturally suggests the truncation of the Coulomb potential on the superlattice Wigner-Seitz cell. We demonstrate that this scheme systematically exhibits the best $k$-point convergence, comparable to that of semi-local functionals, even for low-symmetry and reduced-periodicity systems where previous methods fail. [Preview Abstract] |
Thursday, March 21, 2013 11:39AM - 11:51AM |
U24.00003: Large-scale DFT calculations with the ONETEP program on metallic systems Alvaro Ruiz-Serrano, Chris-Kriton Skylaris We present a direct energy minimization method based on the Kohn-Sham formulation of Mermin's extension of density functional theory (DFT) to finite electronic temperature for large-scale calculations on metallic systems. Our approach employs norm-conserving pseudopotentials for the core electrons, whereas the valence electrons are accurately described using a set of localized orbitals, optimized in-situ in terms of a high-resolution periodic-sinc (psinc) basis set equivalent to plane-waves. The localization constraint results in predictable sparsity patterns that simplify the algebraic operations with matrices, while the description in terms of psinc functions allows near-minimal matrix sizes. As a consequence, the traditional computational bottleneck due to diagonalization of the Hamiltonian matrix is greatly reduced, allowing calculations on larger systems. Additionally, we take advantage of available parallel eigensolvers to enhance the efficiency of the method. We present a number of validation results on metallic systems of increasing complexity and size, including calculations on nanoparticles of more than a thousand atoms. [Preview Abstract] |
Thursday, March 21, 2013 11:51AM - 12:03PM |
U24.00004: On the Generalization of Homogeneous Coordinate Scaling in Density Functional Theory Lazaro Calderin The scaling properties of functionals find direct applications in the design, testing and use of approximated kinetic-energy and exchange-correlation functionals. Methods, such as the so called orbital-free, benefit from approximations to both functionals, while Kohn-Sham Density Functional Theory approximates only the exchange-correlation functional. In this talk we will introduce a generalization of the uniform scaling of coordinates, that not only embodies all previously known scaling and related results, but also leads to new and important properties of functionals. [Preview Abstract] |
Thursday, March 21, 2013 12:03PM - 12:15PM |
U24.00005: Non-linear eigensolver-based alternative to traditional SCF methods Brendan Gavin, Eric Polizzi The self-consistent iterative procedure in Density Functional Theory calculations is revisited using a new, highly efficient and robust algorithm for solving the non-linear eigenvector problem (i.e. H({X})X = EX;) of the Kohn-Sham equations. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm, and provides a fundamental and practical numerical solution for addressing the non-linearity of the Hamiltonian with the occupied eigenvectors. In contrast to SCF techniques, the traditional outer iterations are replaced by subspace iterations that are intrinsic to the FEAST algorithm, while the non-linearity is handled at the level of a projected reduced system which is orders of magnitude smaller than the original one. Using a series of numerical examples, it will be shown that our approach can outperform the traditional SCF mixing techniques such as Pulay-DIIS by providing a high converge rate and by converging to the correct solution regardless of the choice of the initial guess. We also discuss a practical implementation of the technique that can be achieved effectively using the FEAST solver package. [Preview Abstract] |
Thursday, March 21, 2013 12:15PM - 12:27PM |
U24.00006: The pole expansion and selected inversion technique for solving Kohn-Sham density functional theory at large scale Lin Lin, Mohan Chen, Weinan E, Lixin He, Jianfeng Lu, Chao Yang, Lexing Ying The standard diagonalization based method for solving Kohn-Sham density functional theory (KSDFT) requires N eigenvectors for an O(N) * O(N) Kohn-Sham Hamiltonian matrix, with N being the number of electrons in the system. The computational cost for such procedure is expensive and scales as O(N$^3$). We have developed a novel pole expansion plus selected inversion (PEXSI) method, in which KSDFT is solved by evaluating the selected elements of the inverse of a series of sparse symmetric matrices, and the overall algorithm scales at most O(N$^2$) for all materials including metallic and insulating systems without any truncation. The PEXSI method can be used with orthogonal or nonorthogonal basis set, and the electron density, total energy, Helmholtz free energy and atomic force are calculated simultaneously and accurately without using the eigenvalues and eigenvectors. Combined with atomic orbital basis functions, the PEXSI method can be applied to study the electronic structure of boron nitride nanotube and carbon nanotube with more than 10,000 atoms on a single processor. [Preview Abstract] |
Thursday, March 21, 2013 12:27PM - 12:39PM |
U24.00007: Density Functional Theory of Thermoelectric Phenomena Giovanni Vignale, Florian Eich, Massimiliano Di Ventra We introduce a non-equilibrium density functional theory of local temperatures and associated heat currents that is particularly suited for the study of thermoelectric phenomena. This theory rests on a local temperature field coupled to the energy density operator. We prove the basic theorems of the theory and discuss the construction of approximate functionals. [Preview Abstract] |
Thursday, March 21, 2013 12:39PM - 12:51PM |
U24.00008: Simulated non-contact atomic force microscopy based on real space pseudopotentials and density functional theory Minjung Kim, James Chelikowsky Non-contact atomic force microscopy (nc-AFM) is a commonly used technique in surface and nano science owing to its high-resolution and ease of implementation. Theoretical simulations of nc-AFM have been able to facilitate the interpretation of experimental images. However, first-principles AFM simulations can be computationally intensive and problematic if the morphology of the AFM tip is unknown. We introduce an efficient simulation method that does not include an explicit morphology for the tip as suggested by Chan and coworkers.\footnote{T. -L. Chan, C. Z. Wang, K. M. Ho, and James R. Chelikowsky, \textit{Phys. Rev. Lett.} \textbf{102}, 176101 (2009)} Our method is based on a real space implementation of pseudopotentials constructed using density functional theory. We illustrate the method by simulating nc-AFM images for binary semiconducting materials, {\it e.g.}, the GaAs(110) surface, and compare our results to previously performed first principles simulations as well as experimental data. [Preview Abstract] |
Thursday, March 21, 2013 12:51PM - 1:03PM |
U24.00009: Dynamical Steps in the Time-Dependent Exchange-Correlation Potential Kai Luo, Neepa Maitra, Peter Elliott, Johanna Fuks, Angel Rubio It was recently demonstrated that the exact correlation potential of time-dependent density functional theory (TDDFT) generically develops step and peak features that have a density-dependence that is non-local in space and time [arXiv:589981]. Usual adiabatic functional approximations fail to capture these steps, yet these same functionals work quite well for excitation spectra. We investigate the role of the steps in the linear response regime. [Preview Abstract] |
Thursday, March 21, 2013 1:03PM - 1:15PM |
U24.00010: Time-Dependent Spin-Density Functional Theory for strongly correlated systems Volodymyr Turkowski, Talat S. Rahman We present a formulation of the basic principles for a time-dependent spin-density functional theory (TDSDFT) capable of describing the main properties of strongly correlated systems. Electron-electron correlations are contained in the correlation part of the exchange-correlation (XC) kernel, which we construct using some exact results for the Hubbard model of strongly correlated electrons. The principal feature of the theory is nonadiabaticity of the XC kernel, which corresponds to a local time-resolved (oscillating in time) electron-electron interaction. As in dynamical mean-field theory, in TDSDFT such interaction defines the main properties of correlated systems, including satellite Hubbard peaks in the electronic spectrum. We demonstrate that the corresponding nonadiabatic XC kernel reproduces main features of the spectrum of the Hubbard dimer and infinite-dimensional Hubbard model, some of which are impossible to obtain within the adiabatic approach. We test the theory by applying it to several strongly correlated materials, including calculation of nonequilibrium response of these systems. [Preview Abstract] |
Thursday, March 21, 2013 1:15PM - 1:27PM |
U24.00011: Time-dependent density functional theory of extreme environments Rudolph Magyar, Luke Shulenburger, Michael Desjarlais We describe the challenges involved when using time-dependent density functional theory (TDDFT) to describe warm dense matter (WDM) within a plane-wave, real-time formulation. WDM occurs under conditions of temperature and pressure (over 1000 K and 1 Mbar) where plasma physics meets condensed matter physics. TDDFT is especially important in this regime as it can describe ions and electrons strongly out of equilibrium. Several theoretical challenges must be overcome including assignment of initial state orbitals, choice of time-propogation scheme, treatment of PAW potentials, and inclusion of non-adiabatic effects in the potential energy surfaces. The results of these simulations are critical in several applications. For example, we will explain how the TDDFT calculation can resolve modeling inconsistencies in X-ray Thompson cross-sections, thereby improving an important temperature diagnostic in experiments. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [Preview Abstract] |
Thursday, March 21, 2013 1:27PM - 1:39PM |
U24.00012: Direct calculation of exciton binding energies with time-dependent density-functional theory Zenghui Yang, Carsten Ullrich Excitons are coupled electron-hole pairs below the band gap in bulk semiconductors. They are vital to photovoltaics, but they are hard to obtain in a TDDFT calculation, due to usually employed exchange-correlation kernels lacking the long-range part. Another difficulty comes from the usual method of applying TDDFT on bulk materials which calculate the spectrum - though suitable for continuum excitations, this approach does not upfront yield the binding energy of the discrete excitonic excitations. We develop a method in analog with the Casida equation formalism, in which exciton binding energies are obtained directly. We calculate exciton binding energies for both small- and large-gap semiconductors with this method. We study the recently published 'bootstrap' exchange-kernel within our method, and we extend the formalism to treat triplet excitons. [Preview Abstract] |
Thursday, March 21, 2013 1:39PM - 1:51PM |
U24.00013: Nonlocal formulation of spin Coulomb drag in nanostructures: implications for time-dependent current-density-functional theory Carsten A. Ullrich, Irene D'Amico The spin Coulomb drag (SCD) effect occurs in materials and devices where charged carriers with different spins exchange momentum via Coulomb scattering. This causes frictional forces between spin-dependent currents that lead to dissipation and limit spin mobilities. We consider the role of the SCD in the damping of intersubband spin plasmons in semiconductor quantum wells, and show that a local density approximation leads to overdamping. A nonlocal formulation of the SCD is developed which agrees with experimental observations of spin plasmon linewidths. General consequences for using density-functional approaches to describe electronic many-body effects in nanostructures are discussed. [Preview Abstract] |
Thursday, March 21, 2013 1:51PM - 2:03PM |
U24.00014: Alternative time-dependent optimized effective potential Vladimir Nazarov The OEP is known as a single-particle potential minimizing the expectation value of a many-body Hamiltonian on the set of eigen-functions of a single-particle Hamiltonian [1]. The time-dependent (TD) OEP can be constructed with the TD quantum stationary-action principle [2]. Very useful conceptually in DFT and TDDFT, both OEPs are not practicable due to the complexity of their implementations. Here we report a TDOEP by minimizing the difference of LHS and RHS of the TD Schr\"{o}dinger equation [3]. If the orbitals are varied, then the TD Hartree-Fock equations are reproduced. Similarly, we now find the OEP. New OMP does not involve the inversion of the density-response function $\chi_s$, which greatly facilitates implementations. Accordingly, the exchange-correlation kernel $f_{xc}$ involves of $\chi^{-1}_s$ only, not its quadratic counterpart. To show the power of this method, we work out the $f^h_{xc}(q,\omega)$ of the homogeneous electron gas to be used with the nearly-free electrons theory, where $f^h_{xc}$ is the main input [4].\\[4pt] [1]. J. D. Talman et al. Phys. Rev. A 14, 36 (1976).\\[0pt] [2]. C. A. Ullrich et al. Phys. Rev. Lett. 74, 872 (1995).\\[0pt] [3]. V. U. Nazarov, Math. Proc. Cambridge Phil. Soc. 98, 373 (1985).\\[0pt] [4]. V. U. Nazarov et al. Phys. Rev. Lett. 102, 113001 (2009). [Preview Abstract] |
Thursday, March 21, 2013 2:03PM - 2:15PM |
U24.00015: Dynamical Hyperpolarizabilities from Real-Time Density Functional Theory Vladimir Goncharov, Kalman Varga The explicitly time dependent wave function obtained in the framework of Real-Space, Time-Dependent Density Functional Theory captures the essential physics and allows a non-perturbative calculations of important observables. We generalize finite-difference method typically used to calculate static hyperpolarizabilities to the dynamical case \footnote{V. A. Goncharov and K. Varga, \emph{J. Chem. Phys.}, 2012, 137, 094111} and compute nonlinear optical response functions to the third order inclusively. The method is simple and free of errors associated with basis function based methods. Comparison with experimental results for a range of molecules including $C_{60}$ is presented. [Preview Abstract] |
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