Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session R24: Focus Session: Recent Developments in Density Functional Theory I |
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Sponsoring Units: DCOMP Chair: David Vanderbilt, Rutgers University Room: 326 |
Wednesday, March 20, 2013 2:30PM - 3:06PM |
R24.00001: Density-functional theory: time to move up? Invited Speaker: Nicola Marzari Materials' simulations based on density-functional theory (DFT) have become an extremely powerful and widely used tool for scientific discovery and technological advancement. Still, in the current approximations, they remain an imperfect tool for predicting materials' properties, with open and urgent challenges in the quest towards qualitative and quantitative accuracy. Several of these challenges stem from the remnants of self-interaction in the electronic-structure framework, leading to qualitative failures in describing some of the fundamental processes involved e.g. in energy applications - from charge-transfer excitations to photoemission spectra to the structure and reactivity of transition-metal complexes. I'll discuss these challenges in realistic case studies, and present a brief overview of some of our suggestions for possible solutions - including constrained DFT, DFT + onsite and intersite Hubbard terms, and Koopmans' compliant energy functionals. In particular, I'll highlight how Koopmans' compliant functionals point to a beyond-DFT formulation where both total energies and spectroscopic properties can be accounted for. Such framework will be illustrated with applications to real systems and with simplified models that can be solved exactly. [Preview Abstract] |
Wednesday, March 20, 2013 3:06PM - 3:18PM |
R24.00002: Self-Consistent Density Functional Including Long-Range van der Waals Interactions Nicola Ferri, Robert A. DiStasio Jr., Roberto Car, Matthias Scheffler, Alexandre Tkatchenko Van der Waals (vdW) interactions are significant for a wide variety of systems, from noble-gas dimers to organic/inorganic interfaces. The long-range vdW energy is a tiny fraction (0.001\%) of the total energy, hence it is typically assumed not to change electronic properties. Although the vdW-DF functional includes the effect of vdW energy on electronic structure [1], the influence of ``true'' long-range vdW interactions is difficult to assess since a significant part of vdW-DF energy arises from short distances. Here, we present a self-consistent (SC) implementation of the long-range Tkatchenko-Scheffler (TS) functional [2], including its extension to surfaces [3]. The analysis of self-consistency for rare-gas dimers allows us to reconcile two different views on vdW interactions: (i) Feynman's view that claims changes in the electron density and (ii) atoms separated by infinite barrier. In agreement with previous work [1], we find negligible contribution from self-consistency in the structure and stability of vdW-bound complexes. However, a closer look at organic/inorganic interfaces reveals notable modification of energy levels when using the SC-TS vdW density functional. [1] Thonhauser et al., PRB (2007). [2] Tkatchenko and Scheffler, PRL (2009). [3] Ruiz et al., PRL (2012). [Preview Abstract] |
Wednesday, March 20, 2013 3:18PM - 3:30PM |
R24.00003: Efficient Oscillator-Based Approach for Polarizability and van der Waals Interactions Vivekanand Gobre, Robert A. Distasio, Jr., Roberto Car, Matthias Scheffler, Alexandre Tkatchenko The dynamic polarizability measures the response to an applied time-dependent electric field, and its accurate determination is crucial for van der Waals (vdW) interactions and other response properties. First-principles calculations of polarizabilities in principle require a computationally expensive explicit treatment of many-electron excitations, and are only applicable in practice to systems with less than about 100 atoms. In this work, we present an efficient parameter-free approach for calculating accurate frequency dependent polarizabilities for molecules with thousands of atoms, as well as periodic materials. This is achieved by the synergistic coupling of the Tkatchenko-Scheffler method [1], which accurately treats short-range hybridization effects, with the self-consistent screening equation from classical electrodynamics [2,3]. Using only the electron density and free atom reference, we obtain an accuracy of 7\% for both static polarizabilities and vdW coefficients for an extensive database of gas-phase molecules and crystals. We analyze the interplay of hybridization and long-range electrostatic screening effects on the polarizability. [1] Tkatchenko and Scheffler, PRL (2009), [2] Felderhof, Physica (1974), [3] Tkatchenko, DiStasio, Car, and Scheffler, PRL (2012). [Preview Abstract] |
Wednesday, March 20, 2013 3:30PM - 3:42PM |
R24.00004: Range-separated approach to the RPA correlation applied to van der Waals bond and to diffusion of defects Fabien Bruneval The Random Phase Approximation (RPA) is a promising approximation to the exchange-correlation energy of Density Functional Theory (DFT), since it contains the van der Waals (vdW) interaction and yields a potential with the correct band gap. However, its calculation is computationally very demanding. We apply a range separation concept [1] to RPA and demonstrate how it drastically speeds up the calculations without loss of accuracy. The scheme is succesfully applied to a layered system subjected to weak vdW attraction and to address the controversy of the self-diffusion in silicon [2]. We calculate the formation and migration energies of self-interstitials and vacancies taking into account atomic relaxations. The obtained activation energies deviate significantly from the earlier calculations that were affected by the band gap problem and challenge some of the experimental interpretations [3]: the diffusion of vacancies and interstitials have almost the same activation energy.\\[4pt] [1] J. Toulouse, F. Colonna, and A. Savin, Phys. Rev. A \textbf{70}, 062505 (2004).\\[0pt] [2] F. Bruneval, Phys. Rev. Lett. \textbf{108}, 256403 (2012).\\[0pt] [3] H. Bracht, E. E. Haller, and R. Clark-Phelps, Phys. Rev. Lett. \textbf{81}, 393 (1998). [Preview Abstract] |
Wednesday, March 20, 2013 3:42PM - 3:54PM |
R24.00005: Performance of Common Density Functional Methods for the N-Body Interaction Energies of Water Clusters Kenneth Jordan, Fangfang Wang Using an isomer of (H$_2$O)$_{16}$, which has been the subject of several earlier studies, we demonstrate that, in contrast to the commonly held view, the N-body expansion of the interaction energy evaluated at the MP2 level does not converge monotonically with increasing N. Moreover, comparison of the results of HF and MP2 calculations reveals that this unexpected behavior is primarily due to electron correlation effects. The results of various common density functionals are considered, and the implications of our results for various procedures for correcting DFT for dispersion will be discussed. [Preview Abstract] |
Wednesday, March 20, 2013 3:54PM - 4:06PM |
R24.00006: Chemi- and Physisorption Together from a Semilocal Density Functional: Graphene on Ni (111) Jianwei Sun, Bing Xiao, Adrienn Ruzsinszky, John Perdew Conventional semilocal approximations of density functional theory at the level of local spin density approximation (LSDA) and generalized gradient approximations (GGA) are thought to lack the ability to describe weak interactions. This is well illustrated by the system of a graphene adsorbed on a Ni (111) surface, in which the graphene can adsorb on the Ni (111) surface chemically or physically at different distances. LSDA, the standard Perdew-Burke-Ernzerhof (PBE) GGA, and its variant designed for solids, PBEsol, miss the physisorption. We show improved descriptions for weak interactions from a newly-developed semilocal meta-GGA (MGGA)---that performs equally well for molecules, surfaces, and solids---by demonstrating its ability to capture both the chemisorption and the physisorption. [Preview Abstract] |
Wednesday, March 20, 2013 4:06PM - 4:18PM |
R24.00007: A generalized gradient approximation for the Coulomb energy Alberto Vela, Jorge Luis Rosas-Trigueros, Samuel B. Trickey, Jos\'e L. Gazquez In this contribution we generate, implement and fully test expressions for the Coulomb energy without explicit dependence of the electron density at two points in space. These approximate expressions depend solely on the density and its derivatives. The starting point is the implementation and testing of the gradient expansions suggested by Bartolotti and Parr that, to the authors' knowledge, have never been tried in molecules. One of the drawbacks of this approach is that its functional derivative diverges in finite systems. To circumvent this deficiency we will show results for a gradient expansion that incorporates several restrictions, among them to have a finite first functional derivative. Since the functionals are derived imposing some restrictions we call these functionals generalized gradient approximations to the Coulomb energy. [Preview Abstract] |
Wednesday, March 20, 2013 4:18PM - 4:30PM |
R24.00008: Analysis of the large reduced density gradient limit for the exchange energy Jose Gazquez, Jorge M. del Campo, Juan Pacheco-Kato, Sam Trickey, Alberto Vela Electronic structure calculations have become very important for the analysis, at the microscopic level, of a wide variety of systems in physics, chemistry and biology. The Kohn-Sham version of density functional theory has played a fundamental role in such development. In particular, the generalized gradient approximation (GGA) has proven to be a very useful tool in electronic structure studies of complex systems, because it leads to a reasonable description of many properties, at a moderate computational effort. However, it is desirable to improve beyond the actual limits of accuracy. In this work we will present an analysis of the GGA in the regions of small and large values of the reduced density gradient. Then, taking as starting point the PBE and RPBE functionals, the large reduced density gradient limit will be incorporated, in order to show that it induces small, but subtle changes that lead to a better description of several molecular properties. [Preview Abstract] |
Wednesday, March 20, 2013 4:30PM - 4:42PM |
R24.00009: Laplacian-based generalized gradient approximations for the exchange energy A.C. Cancio, Chris E. Wagner It is well known that in the gradient expansion approximation to density functional theory (DFT) the gradient and Laplacian of the density make interchangeable contributions to the exchange-correlation (XC) energy. This is an arbitrary ``gauge freedom'' for building DFT models, normally used to eliminate the Laplacian from the generalized gradient approximation (GGA) level of DFT development. We explore the implications of keeping the Laplacian at this level of DFT, in order to develop a model that fits the known behavior of the XC hole, which can only be described as a system average in a conventional GGA. We generate a family of exchange models that obey the same constraints as conventional GGA's, but which in addition have a finite-valued potential at the atomic nucleus unlike GGA's. These are tested against exact densities and exchange potentials for small atoms and finite jellium drops, and for constraints chosen to reproduce the PBEsol and the APBE variants of the GGA. We find that exchange energies of atoms can be reliably reproduced, by breaking the local (but not global) Lieb-Oxford bound. [Preview Abstract] |
Wednesday, March 20, 2013 4:42PM - 4:54PM |
R24.00010: An Exchange Energy Functional with a Derivative Discontinuity Rickard Armiento, Stephan Kuemmel We explore a way to impose a derivative discontinuity onto a semi-local energy functional in density functional theory, rather than a model potential. The derivative discontinuity is a property of exact exchange that states that the exchange potential may have a uniform discontinuous shift as the particle number passes through an integer. The lack of this property is a known major deficiency of current approximate semi-local exchange functionals. We obtain a closed form expression with a number of attractive properties that can be related to an improved description of charge transfer, overdelocalized orbital states, and band gaps, i.e., deficiencies that are commonly seen in applied use of DFT. Various tests of the construction are presented that clarify the relationship between these issues and the derivative discontinuity. [Preview Abstract] |
Wednesday, March 20, 2013 4:54PM - 5:06PM |
R24.00011: A Kinetic Energy Functional From the Airy Gas Model Alexander Lindmaa, Ann Mattsson, Rickard Armiento We present a density functional for the kinetic energy derived from the Airy gas model, which is a model system for an edge electron gas. Electronic edges are the regions in a system where the electronic density changes to become exponentially decaying, and the electron physics requires special consideration. The Airy model describes an electron gas around the classical turning point, where the electrons interact with a uniform forcefield, i.e., an effective linear potential along one of the spatial coordinates. A formally exact energy density is derived in terms of Airy functions and is parametrized to behave correctly in the Thomas-Fermi and von Weizs\"acker limits. In contrast to already existing kinetic energy functionals derived from the Airy gas, starting from a closed-form expression yields greater freedom in the choice of parametrization. Comparative tests between our and previous functionals are presented. Improved kinetic energy functionals are highly relevant in the context of orbital-free DFT (OF-DFT) as well as for applications at very high temperature. [Preview Abstract] |
Wednesday, March 20, 2013 5:06PM - 5:18PM |
R24.00012: Constraint-based, Non-empirical Parameterization of Generalized Gradient Approximation Kinetic Energy Functionals Debajit Chakraborty, Samuel Trickey, Valentin Karasiev Though we have developed constraint-based ``modified conjoint'' generalized gradient approximation forms for the orbital-free Kohn-Sham kinetic energy $T_s[n]$, strategies for parameterizing them without use of small training sets have remained elusive[1]. Here we discuss one possible way to eliminate that empiricism. We take the reparameterized Perdew-Burke-Ernzerhof exchange functional PBEmol [2], which is self-interaction free for the Hydrogen atom density $n_1$. We then constrain the Pauli-term kinetic energy ($T_\theta$ in $T_s=T_W + T_\theta$, with $T_W$ the von Weizs\"acker KE) to cancel the remaining spurious correlation energy $T_\theta[n_1] +E_{c,PBEmol}[n_1] =0$.We bound the functional by $T_W + T_{TF}$, with $T_{TF}$ the Thomas-Fermi KE and retain the original constraint that $T_\theta >0$. We report numerical results and findings for this procedure.\\[4pt] [1] Phys.\ Rev. B \textbf{80}, 245120 (2009);\\[0pt] [2] J.\ Chem.\ Phys.\ \textbf{136}, 104108 (2012) [Preview Abstract] |
Wednesday, March 20, 2013 5:18PM - 5:30PM |
R24.00013: Revised Thomas-Fermi Functional for Singular Potentials James Dufty, Samuel Trickey Approximations to the non-interacting free energy density functional that include the Thomas-Fermi (TF) functional, or a local density approximation, lead to singular densities for singular external potentials (e.g. Coulomb). We address this limitation of the TF approximation by a formal map of the exact functional for a given external potential onto a fictitious TF functional for an effective external potential. The latter functional is found to be a ``regularized'' version of the external singular potential, tempered by convolution with the finite temperature Lindhard response function. The result is a Thomas-Fermi approximation but with the singularity removed. Applications at high and low temperatures are described, including comparison with the Parr-Ghosh cusp-condition procedure for a non-singular TF density at zero temperature. [Preview Abstract] |
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