Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session W24: Density Functional Theory I |
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Sponsoring Units: DCOMP Chair: Alexey Zayak, Lawrence Berkeley National Laboratory Room: D167 |
Thursday, March 24, 2011 11:15AM - 11:27AM |
W24.00001: A conventional, massively parallel eigensolver for electronic structure theory V. Blum, M. Scheffler, R. Johanni, H. Lederer, Th. Auckenthaler, Th. Huckle, H.-J. Bungartz, L. Kr\"amer, P. Willems, B. Lang, V. Havu We demonstrate a robust large-scale, massively parallel conventional eigensolver for first-principles theory of molecules and materials. Despite much research into $O(N)$ methods, standard approaches (Kohn-Sham or Hartree-Fock theory and excited-state formalisms) must still rely on conventional but robust $O(N^3)$ solvers for many system classes, most notably metals. Our eigensolver overcomes especially parallel scalability limitations, where standard implementations of certain steps (reduction to tridiagonal form, solution of reduced tridiagonal eigenproblem) can be a serious bottleneck already for a few hundred CPUs. We demonstrate scalable implementations of these and all other steps of the full generalized eigenvalue problem. Our largest example is a production run with 1046 Pt (heavy-metal) atoms [1] with converged all-electron accuracy in the numeric atom-centered orbital code FHI-aims,[2] but the implementation is generic and should easily be portable to other codes. [1] P. Havu \emph{et al.}, Phys. Rev. B \textbf{82}, 161418 (2010). [2] V. Blum \emph{et al.}, Comp. Phys. Comm. \textbf{180}, 2175 (2009). [Preview Abstract] |
Thursday, March 24, 2011 11:27AM - 11:39AM |
W24.00002: GPAW on Blue Gene/P Nichols Romero, Jussi Enkovaara, Marcin Dulak, Christian Glinsvad, Ask Larsen, Jens Mortensen, Sameer Shende, Vitali Morozov, Jeffrey Greeley Density function theory (DFT) is the most widely employed electronic structure method due to its favorable scaling with system size and accuracy for a broad range of molecular and condensed-phase systems. The advent of massively parallel supercomputers have enhanced the scientific community's ability to study larger system sizes. Ground state DFT calculations of systems with $O(10^3)$ valence electrons can be routinely performed on present-day supercomputers. The performance of these massively parallel DFT codes at the scale of 1 - 10K execution threads are not well understood; even experienced DFT users are unaware of Amdahl's Law and the non-trivial scaling bottlenecks that are present in standard $O(N^3)$ DFT algorithms. The GPAW code was ported an optimized for the Blue Gene/P. We present our algorithmic parallelization strategy and interpret the results for a number of benchmark tests cases. Lastly, I will describe opportunities for computer allocations at the Argonne Leadership Computing Facility. [Preview Abstract] |
Thursday, March 24, 2011 11:39AM - 11:51AM |
W24.00003: Application of partition density-functional theory to model systems Larry Boyer, Michael Mehl Elliott et al.\footnote{P. Elliott, K. Burke. M. H. Cohen and A. Wasserman, Phys. Rev. A {\bf 82}, 024501 (2010)} have introduced a method called partition density-functional theory (PDFT) for expressing the Kohn-Sham charge density as a sum of overlapping fragment densities, which promises accuracy and efficiency along with a framework for developing and testing useful approximations for kinetic-energy functionals, T[n]. They illustrate their method using results obtained for non-interacting electrons in a one-dimensional model potential. Following their approach, we apply PDFT to similar models which examine its usefulness in developing approximations for T. We also discuss how PDFT compares with the self-consistent atomic deformation\footnote{L. L. Boyer, H. T. Stokes, M. M. Ossowski and M. J. Mehl, Phys. Rev. B {\bf 78}, 045121 (2008)} method. [Preview Abstract] |
Thursday, March 24, 2011 11:51AM - 12:03PM |
W24.00004: Simple Impurity Embedded in a Spherical Jellium: Approximations of Density Functional Theory compared to Quantum Monte Carlo Benchmarks Michal Bajdich, Jeognim Kim, Paul R.C. Kent, Fernando A. Reboredo We study the electronic structure of a simple Gaussian impurity embedded in a spherical jellium in order to mimic the localization effects present in $d$- and $f$-electron compounds. We use quantum Monte Carlo benchmarks to validate approximations of density functional theory (DFT), such as local density approximation (LDA) and generalized gradient approximation (GGA) as well as the Hartree--Fock (HF) method. We identify distinct transitions between delocalized and localized states in the phase space of realistic densities ($1 \le r_s\le 5$) and moderate depths of the Gaussian impurity. We also extend the previous fixed-node diffusion Monte Carlo calculations of impurity-free jellium spheres and extract very accurate jellium surface exchange-correlation energies. Computer resources supported by DOE, Office of Science under contract DE-AC05-00OR22725 (NCCS). Research sponsored by DOE, BES, Materials Sciences and Engineering Division (FAR) and LDRD program (MB) and DOE SUF, CNMS (PRCK). [Preview Abstract] |
Thursday, March 24, 2011 12:03PM - 12:15PM |
W24.00005: Periodic Density Functional Theory Solver using Multiresolution Analysis with MADNESS Robert Harrison, William Thornton We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for nuclear potential, and an implementation for Hartree Fock exchange. [Preview Abstract] |
Thursday, March 24, 2011 12:15PM - 12:27PM |
W24.00006: A Robust Spectrum Slicing Method Applied to the Kohn-Sham Equation for the Liquid/Solid Silicon Interface Grady Schofield, James Chelikowsky A difficult aspect of solving the Kohn Sham equation is the super-linear scaling of eigensolvers with the number of valence orbitals desired. We present a robust spectrum slicing technique that calculates the valence orbitals in a divide and conquer fashion through the use of smooth Chebyshev-Jackson filters. This algorithm allows for a ``parallel'' implementation of the eigensolver. Our calculations are done in the real-space density functional framework implemented in the program PARSEC. We apply this method to examine the liquid-solid silicon interface. [Preview Abstract] |
Thursday, March 24, 2011 12:27PM - 12:39PM |
W24.00007: Beyond the LDA in density functional theory: empirical Laplacian-based models for the exchange-correlation energy Antonio C. Cancio, Christopher E. Wagner We report recent work in developing a GGA-level density functional theory using primarily the Laplacian of the density $\nabla^2 n$ as an input beyond the LDA. Our starting point and motivation is a model fit to the exchange-correlation energy density of the valence shell of the Si crystal and other systems, as calculated by quantum Monte Carlo simulations, which show a strong, roughly linear dependence of this quantity on the Laplacian. The model respects the Lieb-Oxford bound for large positive Laplacian but suffers from a pole at negative values. A better treatment of $\nabla^2 n$ in this limit can be used to construct an all-electron extension of our model, and as an added benefit, avoid the singularity in the Kohn-Sham potential that gradient-based models suffer due to the cusp in electron density at the nucleus. Using an expansion in $1/\nabla^2 n$ we fit exchange energy densities in the cusp region accurately; obtaining reasonable potentials is a harder task but made easier by keeping the gradient of the density. [Preview Abstract] |
Thursday, March 24, 2011 12:39PM - 12:51PM |
W24.00008: Better GGA and meta-GGA Functionals: VT{84}, meta-VMT, meta-VT{84} Alberto Vela, J. Martin del Campo, J.L. Gazquez, S.B. Trickey The goal of fast DFT calculations on large families of highly complicated systems (e.g.\ large clusters, biomolecules) implicitly conflicts with the heavy emphasis of recent years on inclusion of exact exchange. In response we have worked on improving non-empirical GGA X functionals. Here we report extension of our VMT GGA functional (J.\ Chem.\ Phys.\ \textbf{130} 244103 (2009)) to satisfy a relevant asymptotic constraint, yielding the VT\{84\} X functional. With the PBE C functional, VT\{84\} gives about 10\% improvement over VMT in energetics on the G3 223 molecule set. At the meta-GGA level of complexity, we have both meta-VMT and meta-\{84\}. The former is about 10\% better on the G3 set than the TPSS meta-GGA, while meta-VT\{84\} gives roughly 10\% further improvement over meta-VMT. Details of these assessments, including improvements in chemical shifts, will be presented. [Preview Abstract] |
Thursday, March 24, 2011 12:51PM - 1:03PM |
W24.00009: All-Electron and Pseudopotential Orbital-Free Density Functional Calculations Valentin Karasiev, T. Sjostrom, S.B. Trickey Generalized gradient approximation (GGA) and modified-conjoint GGA kinetic energy functionals, proposed recently, have been implemented in an all-electron diatomic molecule code and in a periodic boundary condition code which uses local pseudopotentials. Self-consistent OF-DFT calculations confirm earlier non-self-consistent results. The GGA KE functionals give qualitatively incorrect total energy surfaces in the attractive region (isolated molecule) and the equilibrium crystalline cell volume is strongly expanded. In contrast, the mcGGA functional predicts a qualitatively correct energy surface for isolated systems, and the equilibrium geometry for pseudopotential calculations is in agreement with the Kohn-Sham results. We show the closeness in behavior between GGA-based functionals and simpler approximations defined by mixing of the Thomas-Fermi and the von Weizs\"acker KE functionals. Effects of the pseudopotential in OF-DFT calculations also are discussed. [Preview Abstract] |
Thursday, March 24, 2011 1:03PM - 1:15PM |
W24.00010: Contributions to the Non-interacting Free Energy Density Functional S.B. Trickey, James Dufty, T. Sjostrom Phenomenological models for the T=0 non-interacting kinetic energy density functional often use a linear combination of the von Weizs\"acker (vW) and Thomas-Fermi (TF) functionals. A more systemmatic approach, for any temperature follows from extracting the vW functional from the exact free energy density functional, and analyzing the remainder in a local density approximation. We show that the vW functional is a lower bound for the free energy functional, extending a well-known T=0 result and indicating its priority in the decomposition. The exact remainder involves gradients of the off-diagonal one-body Fermi density matrix, for which a local density approximation is ambiguous. We discuss the extent to which a TF contribution can be extracted. Extension of the original vW phenomenological approach gives complementary insight. Modeling the orbitals as modulated plane waves, with coefficients identified in terms of the density and its gradients leads to vW and TF functionals plus higher-order gradient and temperature corrections. [Preview Abstract] |
Thursday, March 24, 2011 1:15PM - 1:27PM |
W24.00011: Finite-size correction in many-body electronic structure calculations of spin polarized systems Fengjie Ma, Shiwei Zhang, Henry Krakauer We extend the post-processing finite-size (FS) correction method, developed by Kwee, Zhang, and Krakauer\footnote{H.~Kwee, S.~Zhang, and H.~Krakauer, Phys. Rev. Lett. {\bf 100}, 126404 (2008)}, to spin polarized systems. The method estimates the FS effects in many-body (MB) electronic structure calculations by a modified density functional theory (DFT) calculation, without having to repeat expensive MB simulations. We construct a unified FS DFT exchange-correlation functional for spin unpolarized and fully spin polarized systems, and then interpolate the results to arbitrary spin polarizations using the formula of Perdew and Wang\footnote{J.~P.~Perdew and Y.~Wang, Phys. Rev. B {\bf 45}, 13244 (1992)} or that of Perdew and Zunger.\footnote{J.~P.~Perdew and A.~Zunger, Phys. Rev. B {\bf 23}, 5048 (1981)} The application of this FS correction method to several typical magnetic systems with varying supercell sizes demonstrates that it consistently removes most of the FS errors, leading to rapid convergence of the MB results to the infinite size limit. [Preview Abstract] |
Thursday, March 24, 2011 1:27PM - 1:39PM |
W24.00012: Generalization of the Hohenberg-Kohn theorem to the case of the presence of a magnetic field Viraht Sahni, Xiaoyin Pan We generalize the HK theorem for the nondegenerate ground state of electrons in an external electrostatic field ${\bf{E}}({\bf{r}}) = -$ {\boldmath $\nabla$} $v ({\bf{r}})$ to the presence of an additional external magnetostatic field ${\bf{B}} ({\bf{r}}) =$ {\boldmath $\nabla$} $\times {\bf{A}} ({\bf{r}})$. We prove that the nondegenerate ground state wave function $\Psi$ is a functional of the ground state density $\rho ({\bf{r}})$, the physical current density ${\bf{j}} ({\bf{r}})$, and a gauge function $\alpha ({\bf{R}})$, with ${\bf{R}} = \{{\bf{r}} \}$. In other words, the basic variables, viz. those that uniquely determine the external potentials $ \{v ({\bf{r}}), {\bf{A}} ({\bf{r}}) \}$, are $\{ \rho ({\bf{r}}), {\bf{j}} ({\bf{r}}) \}$. As the choice of $\alpha ({\bf{R}})$ is arbitrary, it is possible to construct a $\{ \rho ({\bf{r}}), {\bf{j}} ({\bf{r}}) \}$ functional theory, as well as the corresponding Kohn-Sham and quantal density functional theories. [Preview Abstract] |
Thursday, March 24, 2011 1:39PM - 1:51PM |
W24.00013: Quantal density functional theory (QDFT) in the presence of a magnetic field Xiaoyin Pan, Tao Yang, Viraht Sahni We present the QDFT of electrons in an external electrostatic ${\bf{E}}({\bf{r}}) = -$ {\boldmath $\nabla$} $v({\bf{r}})$ and magnetostatic ${\bf{B}}({\bf{r}}) =$ {\boldmath $\nabla$} $\times {\bf{A}} ({\bf{r}})$ field. This is the mapping from the interacting system of electrons to one of noninteracting fermions with the same density $\rho ({\bf{r}})$ and physical current density ${\bf{j}} ({\bf{r}})$. The mapping, based on the `quantal Newtonian' first law, is in terms of `classical' fields and quantal sources, the fields being separately representative of electron correlations due to the Pauli exclusion principle and Coulomb repulsion, and correlation-kinetic and correlation-magnetic effects. The theory is valid for ground and excited states. It is explicated by application to a ground state of the exactly solvable Hooke's atom in the presence of a magnetic field. [Preview Abstract] |
Thursday, March 24, 2011 1:51PM - 2:03PM |
W24.00014: Quantum Continuum Mechanics for Many-Electron Systems in a Strong Magnetic Field Stefano Pittalis, I.V. Tokatly, G. Vignale A quantum continuum mechanics approach for the determination of the excitation energies of many-electron systems in strong magnetic field is introduced by means of linear response theory (LRT) and time-dependent deformation-functional theory (TD-DefT). In the high-frequency (anti-adiabatic) limit the collective modes of the system appear as the small oscillations of an elastic body in the presence of non-inertial forces reminiscent of the Coriolis and centrifugal forces. Interestingly, the complexity of the problem does not increase significantly with the particle number and only ground state properties are needed as an input. Further results, together with elementary and illustrative examples, may be presented as well. [Preview Abstract] |
Thursday, March 24, 2011 2:03PM - 2:15PM |
W24.00015: First principles finite temperature magnetism of defects in Fe using Wang-Landau method Aurelian Rusanu, D.M. Nicholson, Kh. Odbadrakh, Gregory Brown, Markus Eisenbach Magnetic structure of materials with defects presents a strong dependence on local atomic arrangements. This dependence affects mechanical, magneto-caloric, and magnetization properties. Insights into thermodynamic and magnetic fluctuations at defects in Fe are obtained from first principle analysis by deploying the first principle local self consistent multiple scattering method(LSMS) and Wang-Landau statistical method. The computation of thermodynamic properties requires the sampling of a large number of configurations. To reduce the computational effort a Heisenberg model will be used to speed the configuration sampling procedures. The approach will be demonstrated for Fe systems and will address the magnetic structure of defects. [Preview Abstract] |
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