Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session T24: Electronic Structure Methods IV 
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Sponsoring Units: DCOMP Room: 203AB 
Thursday, March 5, 2015 11:15AM  11:27AM 
T24.00001: Reduced DensityMatrix Functional Theory: correlation and spectroscopy Stefano Di Sabatino, Arjan Berger, Lucia Reining, Pina Romaniello In this work we explore the performance of approximations to electron correlation in reduced densitymatrix functional theory (RDMFT) and of approximations to the observables calculated within this theory\footnote{S. Di Sabatino, J.A. Berger, L. Reining, and P. Romaniello, submitted}. Particular focus is put on the spectral function, which determines, for example, photoemission spectra, and which cannot be obtained in a straightforward way from the density matrix, and on the regime of strong electron correlation, which is difficult to treat by standard methods. Using the simple Hubbard model as test case shines light on the content, successes and limits of current RDMFT approaches. [Preview Abstract] 
(Author Not Attending)

T24.00002: A problem with the stress theorem commonly used in DFT codes Donald Nicholson The change in energy when an affine transformation (strain) is applied to a lattice of ions can be obtained by evaluating the algebraic derivative of the DFT energy (in practice a local or other approximation) of an electron density that has been similarly strained [1]. Because the DFT energy is stationary in the density, it is only required that the strained density reduces to the exact density at zero strain; it does. The algebraic derivatives of the Hartree and exchange energies are straightforward. The derivative with respect to strain of the noninteracting kinetic energy depends on two assumptions: 1) the modulus squared of the strained orbitals equals the strained electron density, and 2) the strained orbitals minimize the noninteracting kinetic energy. The first assumption is correct. I find that the second assumption applies only in special cases. The limitations and possible modifications of the stress theorem are discussed.\\[0pt] [1] Nielsen, O. H. \& Martin, R. M. 1983 FirstPrinciples Calculation of Stress. Physical Review Letters 50, 697.\\[0pt] [2] D. M. Nicholson, Madhusudan Ojha, and T. Egami, Journal of Physics Condensed Matter 10/2013; 25(43):435505. [Preview Abstract] 
Thursday, March 5, 2015 11:39AM  11:51AM 
T24.00003: Predictive DFT$+$U Methods for Small Molecule Binding in MOF74 Gregory Mann, Kyuho Lee, Matteo Cococcioni, Berend Smit, Jeffrey Neaton In order to use density functional theory (DFT) to reliably treat small molecule binding at open metal sites in metalorganic frameworks (MOFs), electron correlation effects associated with the localized dstates present at the metal centers must be accounted for. Incorporation of a Hubbard Ulike term can be an approximate but computationally efficient means, yielding excellent agreement with experiment provided an appropriate value for the parameter U is chosen. To predict adsorption energetics for asyet unsynthesized MOFs, we would need to select U using a systematic, physically motivated approach rather than the ad hoc methods typically employed. Here, we use an \textit{ab initio}linear response approach to calculate U. We show that U values determined with this method reproduce previous results for the binding of carbon dioxide in CoMOF74 and CuMOF74, and we discuss the method's application to other 3d metals in theMOF74 framework; our preliminary results suggest that a wide range of U's above a critical value will produce accurate binding energies. Finally, we present U values calculated for Co2$+$ ions in other systems, probing the environment dependence of this parameter. This work supported by DOE, and computational resources provided by NERSC. [Preview Abstract] 
Thursday, March 5, 2015 11:51AM  12:03PM 
T24.00004: Density versus spindensity functional in DFT+U and DFT+DMFT Hyowon Park, Andrew Millis, Chris Marianetti The construction of multivariable effective action theories such as DFT+U and DFT+DMFT requires the choice of a local subspace of correlated orbitals and an additional variable being either the charge density or spin density. This talk examines the differences between using chargeonly and spindependent exchangecorrelation functionals with the aim of providing guidance for constructing more sophisticated beyonddensity functional theories. The widely used spindependent approximations to the exchangecorrelation functional are found to lead to a large and in some cases unphysical effective exchange coupling within the correlated subspace. Additionally, the differences between Wannier and Projector based definitions of the correlated orbitals are examined, and only small differences are found provided that the orbitals are orthonormal and strongly localized. These results are documented in the context of the rare earth nickelates. [Preview Abstract] 
Thursday, March 5, 2015 12:03PM  12:15PM 
T24.00005: The Hubbard Dimer: A Complete DFT Solution to a ManyBody Problem Justin Smith, Diego Carrascal, Jaime Ferrer, Kieron Burke In this work we explain the relationship between density functional theory and strongly correlated models using the simplest possible example, the twosite asymmetric Hubbard model. We discuss the connection between the lattice and realspace and how this is a simple model for stretched H$_2$. We can solve this elementary example analytically, and with that we can illuminate the underlying logic and aims of DFT. While the manybody solution is analytic, the density functional is given only implicitly. We overcome this difficulty by creating a highly accurate parameterization of the exact function. We use this parameterization to perform benchmark calculations of correlation kinetic energy, the adiabatic connection, etc. We also test HartreeFock and the Bethe Ansatz Local Density Approximation. We also discuss and illustrate the derivative discontinuity in the exchangecorrelation energy and the infamous gap problem in DFT. [Preview Abstract] 
Thursday, March 5, 2015 12:15PM  12:27PM 
T24.00006: Development of a DFT$+$DMFT method using multiorbital impurity solver Mancheon Han, Hyungju Oh, Choongki Lee, Hyoung Joon Choi The density functional theory (DFT), often performed with the local density approximation or the generalized gradient approximation, is very successful for ab initio calculations of various materials. However, it has limited accuracy for strongly correlated materials. The dynamical mean field theory (DMFT), which maps a correlated lattice system to an interacting impurity site in a noninteracting bath, may describe local correlation effects. Combination of above methods, DFT$+$DMFT, can be an adequate approach for investigation of strongly correlated materials. We have implemented a DFT$+$DMFT method based on the abinitio pseudopotential method of the SIESTA code, where electronic wavefunctions are expanded with pseudoatomic orbitals. An exact diagonalization method is used in our DFT$+$DMFT method to obtain the local Green function of the impurity site with multiple orbitals. We apply our DFT$+$DMFT method to the electronic structure of LaFeAsO and compare the results with those from DFT and experiments. This work is supported by the NRF of Korea (Grant No.20110018306). Computational resources have been provided by KISTI Supercomputing Center (Project No. KSC2013C3062). [Preview Abstract] 
Thursday, March 5, 2015 12:27PM  12:39PM 
T24.00007: Nonorthogonal generalized hybrid Wannier functions for linear scaling DFT simulations of surfaces and interfaces Andrea Greco, Arash Mostofi, John Freeland Semiconductorbased thinfilms have applications in microelectronics, from transistors to nanocapacitors. Many of their properties depend on phenomena at multiple length scales, but their complexity makes it difficult to obtain a detailed understanding of their behavior from experiment alone. Firstprinciples simulations based on densityfunctional theory (DFT) are invaluable for providing insight into materials' properties including for the study of thin films. In particular, hybrid Wannier functions (WFs), fully extended in the surface plane, but localized along the direction normal to the surface, have been successfully used to explore the properties of systems layered along a given direction. The large length scales associated with structures and processes in more realistic surfaces, however, are beyond the scope of such calculations, because they rely on first performing a traditional cubicscaling DFT calculation. To overcome this limitation we extend the concept of hybrid WFs to nonorthogonal orbitals that are directly optimized in situ in the electronic structure calculation. We show that this method, implemented in the ONETEP linear scaling DFT code, enables the study of largescale surfaces and interfaces with planewave accuracy but at reduced computational expense. [Preview Abstract] 
Thursday, March 5, 2015 12:39PM  12:51PM 
T24.00008: Performance and Accuracy of Recursive Subspace Bisection for Hybrid DFT Calculations William Dawson, Francois Gygi The high cost of computing the HartreeFock exchange has resulted in limited use of Hybrid Functionals in DFT calculations. Approximations based on transformation to localized orbitals provide one way to reduce this cost. One such method is the recursive subspace bisection method (RSB)[1]. Such localization methods involve truncation of localized orbitals, which introduces an additional approximation. We take advantage of our ability to systematically reduce the error in RSB calculations through a single parameter to study this approximation. We present the errors in ground state energy, forces, and relative energy differences between configurations for a variety of systems, including tungsten oxide, a siliconwater interface, and liquid water including the calculation of empty states. \\{} [1] F.Gygi, Phys. Rev. Lett. 102, 166406 (2009). \\{} [2] Qbox code, http://eslab.ucdavis.edu/software/qbox/ \\{} [Preview Abstract] 
Thursday, March 5, 2015 12:51PM  1:03PM 
T24.00009: Speeding up DFT: A faster method for integrating band energy in SCF cycles Matthew M. Burbidge, Jeremy J. Jorgensen, Conrad W. Rosenbrock, Derek C. Thomas, Bret C. Hess, Rodney W. Forcade, Stefano Curtarolo, Gus L. W. Hart Typically in SCF cycles, a ``rectangle rule'' is used on uniformly spaced points (Monk Pack meshes)$^{1}$ to integrate the band energy. The use of rectangles is motivated by their fast convergence when used on the fully occupied bands of semiconductors. Unfortunately integration with rectangles is extremely inefficient for metals. This motivates the use of gauss quadrature (or other higher order methods) for integrating the band energy. As we show, however, even in the case of semiconductors where the rectangle convergence is extremely efficient, higher order methods are still {\em more} efficient. The savings in semiconductors alone are sufficient to motivate the implementation of a higher order method in current DFT codes. Even though higher order quadrature methods were discussed immediately following the original Monkhorst and Pack$^{1}$ paper, we revisit the issue in light of modern DFT calculations. [1] H.J. Monkhorst and J.D. Pack, Phys. Rev. B 13, 5188 (1976). [Preview Abstract] 
Thursday, March 5, 2015 1:03PM  1:15PM 
T24.00010: Efficient parameterfree calculation of absorption spectra for insulators, semiconductors and metals from timedependent current DFT Arjan Berger In this work we show that with a simple dynamical kernel we can obtain good absorption spectra from timedependent currentdensity functional theory (TDCDFT) for insulators, semiconductors and metals. Our approach is fully parameter free since no artificial broadening parameter is used to match calculated and measured spectra. The cost of a calculation is equal to an RPA calculation. Moreover, our TDCDFT approach scales better with system size than standard TDDFT implementations. [Preview Abstract] 
Thursday, March 5, 2015 1:15PM  1:27PM 
T24.00011: Gauge invariant calculation of magnetic properties from timedependent current DFT Nathaniel Raimbault, Paul L. de Boeij, Pina Romaniello, Arjan Berger We present a method to calculate magnetic properties from the current density that does not depend on the gauge choice for the vector potential when a finite basis set is used [1]. To obtain this we put paramagnetic and diamagnetic contributions to the current on equal footing by making use of a sum rule [1]. Our method is general. Here we use it to calculate static and dynamical magnetizabilities of molecules within TimeDependent CurrentDensityFunctional Theory. \\[4pt] [1] N. Raimbault, P.L. de Boeij, P. Romaniello, and J.A. Berger, submitted [Preview Abstract] 
Thursday, March 5, 2015 1:27PM  1:39PM 
T24.00012: Accurate Energies and Orbital Description in SemiLocal KohnSham DFT Alexander Lindmaa, Stephan Kuemmel, Rickard Armiento We present our progress on a scheme in semilocal KohnSham densityfunctional theory (KSDFT) for improving the orbital description while still retaining the level of accuracy of the usual semilocal exchangecorrelation (xc) functionals. DFT is a widely used tool for firstprinciples calculations of properties of materials. A given task normally requires a balance of accuracy and computational cost, which is well achieved with semilocal DFT. However, commonly used semilocal xc functionals have important shortcomings which often can be attributed to features of the corresponding xc potential. One shortcoming is an overly delocalized representation of localized orbitals. Recently a semilocal GGAtype xc functional was constructed to address these issues [1], however, it has the tradeoff of lower accuracy of the total energy. We discuss the source of this error in terms of a surplus energy contribution in the functional that needs to be accounted for, and offer a remedy for this issue which formally stays within KSDFT, and, which does not harshly increase the computational effort. The end result is a scheme that combines accurate total energies (e.g., relaxed geometries) with an improved orbital description (e.g., improved band structure). [1] PRL 111, 036402 (2013) [Preview Abstract] 
Thursday, March 5, 2015 1:39PM  1:51PM 
T24.00013: Understanding Density Functional Theory (DFT) and Completing it in Practice Diola Bagayoko A brief review of the seminal article by Hohenberg and Kohn leads to two conditions that have to be met by electronic structure calculations in order for their results to represent the physics content of DFT. One of these conditions is often the verifiable attainment of the absolute minima of the occupied energies. \textit{Using the second Hohenberg Kohn theorem, we show that results of calculations that do not meet this condition, when it applies, do not necessarily represent DFT findings}. We illustrate this fact with over 100 calculated band gaps that are much smaller than corresponding, measured ones; in contrast, we list calculations that strictly adhered to the aforementioned conditions and whose results are in excellent agreement with experiment. \textit{We describe two crucial steps in the latter calculations that add to or complete DFT in practice.} Some implications of our findings for academia, industry, and program package developers will be discussed. Acknowledgments: This work was funded in part by the National Science Foundation (NSF) and the Louisiana Board of Regents, through LASiGMA [Award Nos. EPS 1003897, NSF (201015)RIISUBR] and NSF HRD1002541, the US Department of Energy  National, Nuclear Security Administration (NNSA) (Award Nos. DENA0001861 and DE NA0002630), LaSPACE, and LONISUBR. [Preview Abstract] 
Thursday, March 5, 2015 1:51PM  2:03PM 
T24.00014: Elimination of the fractional dissociation problem in KohnSham DFT using the ensemblegeneralization approach Eli Kraisler, Leeor Kronik Many approximations within densityfunctional theory (DFT) spuriously predict that a manyelectron system can dissociate into fractionally charged fragments. Here, we revisit the case of infinitely separated diatomic molecules, known to exhibit this problem when studied within standard approximations, including the local spindensity approximation (LSDA). We apply the recently suggested ensemblegeneralization to LSDA (eLSDA) [1,2] and find that fractional dissociation is eliminated in all systems examined. The eLSDA KohnSham potential develops a spatial step, associated with the emergence of the derivative discontinuity in the exchangecorrelation energy functional. This step, predicted in the past for the exact KohnSham potential and observed in some of its more advanced approximate forms, is a desired feature that prevents any fractional charge transfer between the system's fragments. Our findings show that, if appropriately generalized for fractional electron densities, even the most simple approximate functionals correctly predict integer dissociation [3]. [1] E. Kraisler, L. Kronik, Phys. Rev. Lett. 110, 126403 (2013) [2] E. Kraisler, L. Kronik, J. Chem. Phys. 140, 18A540 (2014) [3] E. Kraisler, L. Kronik, submitted. [Preview Abstract] 
Thursday, March 5, 2015 2:03PM  2:15PM 
T24.00015: Representability of Bloch states on Projectoraugmentedwave (PAW) basis sets Luis Agapito, Andrea Ferretti, Stefano Curtarolo, Marco Buongiorno Nardelli Design of small, yet `complete', localized basis sets is necessary for an efficient dual representation of Bloch states on both planewave and localized basis\footnote{Agapito, Ferretti, Calzolari, Curtarolo and Buongiorno Nardelli, PRB {\bf 88}, 165127 (2013).}. Such simultaneous dual representation permits the development of faster more accurate (beyond DFT) electronicstructure methods for atomistic materials (e.g. the ACBN0 method\footnote{Agapito, Curtarolo and Buongiorno Nardelli, \texttt{arXiv:1406.3259 [condmat.strel]}}.) by benefiting from algorithms (real and reciprocal space) and hardware acceleration (e.g. GPUs) used in the quantumchemistry and solidstate communities. Finding a `complete' atomicorbital basis (partial waves) is also a requirement in the generation of robust and transferable PAW pseudopotentials. We have employed the atomicorbital basis from available PAW data sets, which extends through most of the periodic table, and tested the representability of Bloch states on such basis. Our results show that PAW data sets allow systematic and accurate representability of the PAW Bloch states, better than with traditional quantumchemistry doublezeta and doublezetapolarizedquality basis sets. [Preview Abstract] 
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