Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session J19: Frontiers in Electronic Structure Theory I |
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Sponsoring Units: DCP DCOMP Chair: Martin Head-Gordon, University of California, Berkeley Room: Colorado Convention Center 104 |
Tuesday, March 6, 2007 11:15AM - 11:51AM |
J19.00001: Post-Hartree-Fock Correlation Models Invited Speaker: We have developed post-Hartree-Fock correlation models for all of dynamical, nondynamical, and dispersion correlations, based on real-space modelling of the correlation hole. Many of the outstanding problems in the density-functional theory of atomic, molecular, and condensed matter systems arise from local exchange approximations. Our post-Hartree-Fock approach circumvents these. The latest developments will be reported, [Preview Abstract] |
Tuesday, March 6, 2007 11:51AM - 12:27PM |
J19.00002: Resolutions of the Coulomb Operator Invited Speaker: The ``Resolution of the Identity Operator'' \begin{equation} \hat{I} \equiv | \chi_n \rangle \langle \chi_n | \end{equation} is a mathematical device that can be used to decouple the bra and ket in an overlap matrix element \begin{equation} \label{eq:RI} \langle f | g \rangle = \langle f | \chi_n \rangle \langle \chi_n | g \rangle \end{equation} through the introduction of an infinite complete expansion basis $\{\chi_n\}$. In practical implementations, where the basis set is finite and incomplete, (2) yields systematic approximations to difficult overlap integrals and is widely used in quantum physics and chemistry. We will present an analogous ``Resolution of the Coulomb Operator'' \begin{equation} r_{12}^{-1} \equiv | \phi_n \rangle \langle \phi_n | \end{equation} which allows one to expand Coulomb matrix elements \begin{equation} \label{eq:RC} \langle f | r_{12}^{-1} | g \rangle = \langle f | \phi_n \rangle \langle \phi_n | g \rangle \end{equation} and we will discuss the potential utility of (4) in the efficient treatment of the matrix elements that arise in quantum chemistry and elsewhere. [Preview Abstract] |
Tuesday, March 6, 2007 12:27PM - 12:39PM |
J19.00003: Spin Polarization Resolved Energetics of a Quasi One Dimensional Electron Gas Luke Shulenburger, Michele Casula, Richard M. Martin, Gaetano Senatore This work extends that of Casula et. al.$^1$ by using Quantum Monte Carlo to calculate the exact energy of a quasi one dimensional electron gas at nonzero polarizations. We present a parameterization of the correlation energy suitable for LSDA density functional calculations$^2$. The energy of the momentum resolved spin and charge excitations is also calculated via the intermediate scattering function$^3$. At low densities, correlation opens a gap for charge excitations near $2 k_f$ for each spin species. The modes with periodicity close to the mean interparticle spacing are softened due to the formation of a quasi Wigner crystal. These effects disappear as the density increases and correlation becomes less important. The calculated excitation spectrum agrees with the long wavelength behavior predicted by Luttinger liquid theory. \begin{itemize} \item[{[1]}] M. Casula, S. Sorella and G. Senatore, cond-mat/0607130 (2006) \item[{[2]}] Abedinpour, Polini, Xianlong and Tosi, private communication. \item[{[3]}] S. Yamamoto, Physical Review Letters, {\bf 75}, 3349 (1995) \end{itemize} [Preview Abstract] |
Tuesday, March 6, 2007 12:39PM - 12:51PM |
J19.00004: Electronic Counting Rules for the Stability of Metal-Silicon Clusters Jose Ulises Reveles, Shiv N. Khanna Theoretical investigations of the ground state geometries, electronic structure, spin magnetic moment and the stability of the metal encapsulated neutral, cationic, and anionic MSi$_{16}$ ( M= Sc, Ti, V) clusters have been carried out within a gradient corrected density functional formalism. ScSi$_{16}^{-}$, TiSi$_{16}$, and VSi$_{16}^{+}$ are found to be particularly stable in agreement with recent experiments. It is shown that the enhanced stability can be reconciled within a model where each Si atom coordinated to the metal contributes one electron to the valence pool. We propose the use of the bond critical points (BCP) from the topological analysis of the electronic density, in order to identify the Si sites that are bonded to the metal atom. Clusters where the total number of valence electrons obtained by summing one electron from each Si site coordinated to metal atom and the valence electrons of the metal attain 20 are found to be particularly stable. Combined with the earlier reported stability at 18 electrons, it is proposed that such valence pools might be looked upon as a nearly free electron gas inside a silicon cage. [Preview Abstract] |
Tuesday, March 6, 2007 12:51PM - 1:03PM |
J19.00005: Compact Representations of Kohn-Sham Invariant Subspaces Francois Gygi We present an algorithm for the computation of reduced numerical representations of the solutions of the Kohn-Sham equations. The method allows for {\em a priori} control of the error caused by the reduction process. When applied to Kohn-Sham wavefunctions expanded on a plane-wave basis, this approach leads to a substantial reduction of the size of the datasets used to restart first-principles simulations, with controlled loss of accuracy. Examples of applications to jellium, liquid water and carbon nanotubes will be presented. A comparison with representations in terms of maximally localized Wannier functions will also be discussed. [Preview Abstract] |
Tuesday, March 6, 2007 1:03PM - 1:15PM |
J19.00006: Density Functional Theory in Transition Metal Chemistry: A Self-Consistent Hubbard U approach Heather Kulik, Matteo Cococcioni, Nicola Marzari Transition metals ions are reactive centers for a broad variety of biological and inorganic chemical reactions. Despite this central importance, density functional theory calculations based on local density or generalized gradient approximations (GGA) often fail qualitatively and quantitatively to describe multiplet splittings, relaxed structures, and reaction barriers for these systems. We have recently proposed$^{1}$ augmenting the GGA functional with a Hubbard U which is obtained from a self-consistent linear response procedure. This fully ab initio GGA+U approach provides excellent agreement with accurate, correlated-electron quantum chemistry calculations for paradigmatic cases that include the ground state of the iron dimer and addition-elimination reactions on bare FeO$^+$. We also show how a GGA+U approach may be applied to large-scale biological systems by preserving the favorable scaling of traditional density functional approaches with improved accuracy. 1) H. J. Kulik, M. Cococcioni, D. Scherlis and N. Marzari, PRL (2006). [Preview Abstract] |
Tuesday, March 6, 2007 1:15PM - 1:27PM |
J19.00007: Linear Scaling First-Principles DFT Calculations with Grid-based Adaptive Orbitals Jean-Luc Fattebert As an alternative to the Plane Waves approach for accurate and unbiased Density Functional Theory (DFT) simulations, we have developed a real-space approach which completely avoids use of Fourier transforms. An effective O(N) complexity is achieved by representing the electronic structure as a set of localized nonorthogonal orbitals. The efficiency of the approach has been demonstrated recently for molecular dynamics simulations in the microcanonical ensemble [J.-L. Fattebert and F. Gygi, Phys. Rev. B 73, 115124 (2006)]. Adapting the position of the localization regions on the fly is a key feature to enable accurate MD simulations. In this talk, we will report recent developments in adapting the size of localization regions to improve efficiency and address very general electronic structure problems. [Preview Abstract] |
Tuesday, March 6, 2007 1:27PM - 1:39PM |
J19.00008: How localized is ``local?'' Efficiency vs. accuracy of $O(N)$ domain decomposition in local orbital based all-electron electronic structure theory Vile Havu, Volker Blum, Matthias Scheffler Numeric atom-centered local orbitals (NAO) are efficient basis sets for all-electron electronic structure theory. The locality of NAO's can be exploited to render (in principle) all operations of the self-consistency cycle $O(N)$. This is straightforward for 3D integrals using domain decomposition into spatially close subsets of integration points, enabling critical computational savings that are effective from $\sim$tens of atoms (no significant overhead for smaller systems) and make large systems (100s of atoms) computationally feasible. Using a new all-electron NAO-based code,$^1$ we investigate the quantitative impact of exploiting this locality on two distinct classes of systems: Large light-element molecules [Alanine-based polypeptide chains (Ala)$_n$], and compact transition metal clusters. Strict NAO locality is achieved by imposing a cutoff potential with an onset radius $r_c$, and exploited by appropriately shaped integration domains (subsets of integration points). Conventional tight $r_c\le$~3{\AA} have no measurable accuracy impact in (Ala)$_n$, but introduce inaccuracies of 20-30 meV/atom in Cu$_n$. The domain shape impacts the computational effort by only 10-20~\% for reasonable $r_c$. \newline $^1$ V. Blum, R. Gehrke, P. Havu, V. Havu, M. Scheffler, \emph{The FHI Ab Initio Molecular Simulations (aims) Project}, Fritz-Haber-Institut, Berlin (2006). [Preview Abstract] |
Tuesday, March 6, 2007 1:39PM - 1:51PM |
J19.00009: Bonding in elemental boron: a view from electronic structure calculations using maximally localized Wannier functions Tadashi Ogitsu, Francois Gygi, John Reed, Eric Schwegler, Giulia Galli Boron exhibits the most complex structure of all elemental solids, with more than 300 atoms per unit cell arranged in interconnecting icosahedra, and some crystallographic positions occupied with a probability of less than one. The precise determination of the ground state geometry of boron---the so-called $\beta $-boron structure--has been elusive and its electronic and bonding properties have been difficult to rationalize. Using lattice model Monte Carlo optimization techniques and \textit{ab-initio} simulations, we have shown that a defective, quasi-ordered $\beta $ solid is the most stable structure \textit{at zero} as well as finite T. In the absence of partially occupied sites (POS), the perfect $\beta $-boron crystal is unstable; the presence of POS lower its internal energy below that of an ordered $\alpha $-phase,\textit{ not mere an entropic effect}. We present a picture of the intricate and unique bonding in boron based on maximally localized Wannier (MLWF) functions, which indicates that the presence of POS provides a subtle, yet essential spatial balance between electron deficient and fully saturated bonds. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/ LLNL under contract no. W-7405-Eng-48. [Preview Abstract] |
Tuesday, March 6, 2007 1:51PM - 2:03PM |
J19.00010: Structural distortions in AlF$_3$ derived using density functional methods L. L. Boyer, M. J. Mehl, Dan Finkenstadt The crystal structure of AlF$_3$ at high temperatures has a simple cubic lattice. Below $\sim 730$K the structure transforms to a rhombohedral ($\alpha$-phase) structure with R$\overline{3}$c symmetry, due to an unstable $R_5^-$ phonon. Density-functional based methods, from the least accurate rigid-ion model to highly-accurate all-electron Kohn-Sham models, yield the triply degenerate $R_5^-$ phonon that becomes unstable with decreasing volume at some critical volume $V_c$. Significant variations for $V_c$ and the equilibrium volume $V_0$ among the models lead to large uncertainties for the energy differences between the cubic and rhombohedral structures, indicating that present density functional models are not reliable for accurate quantitative results in this case. [Preview Abstract] |
Tuesday, March 6, 2007 2:03PM - 2:15PM |
J19.00011: Quantum Monte Carlo studies of transition metal atoms and molecules Ryo Maezono, Lucas K. Wagner, Michal Bajdich, Jindrich Kolorenc, Lubos Mitas We study electron correlation in selected transition metal atoms and molecules from the 3d series by variational and fixed-node diffusion Monte Carlo methods. We test several types of orbitals such as RHF, UHF, B3LYP and atomic natural orbitals in building the Slater determinants. We explore also several types of wave functions based on single determinant, GVB, limited CI expansions with both unoptimized and reoptimized weights. The aim of this study is to estimate the accuracy of various wave functions with regard to fixed-node biases and to provide benchmarks for high accuracy calculations with these types of atoms. [Preview Abstract] |
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