Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session A37: Focus Session: Fundamental Developments in Density Functional Theory I |
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Sponsoring Units: DCP Chair: Adam Wasserman, Purdue University Room: 409 |
Monday, March 16, 2009 8:00AM - 8:36AM |
A37.00001: Insights and Progress in Density Functional Theory. Invited Speaker: Weitao Yang Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, there are spectacular failures for many predicted properties, which can be traced to the delocalization error and static correlation error of commonly used approximations. These errors include underestimation of the barriers of chemical reactions, the band gaps of materials, the energies of dissociating molecular ions and charge transfer excitation energies. Typical DFT calculations also fail to describe degenerate or near degenerate systems, as arise in the breaking of chemical bonds, and strongly correlated materials. These can all be characterized and understood through the perspective of fractional charges and fractional spins introduced recently. Understanding the errors of functionals in the simplest way possible --- as violations of exact conditions for fractional charges and fractional spins -- opens the path forward for reduction of the errors and for applications of density functional theory in new frontiers. [P.~Mori-Sanchez, A.~J. Cohen, and W.~T. Yang, \textit{Phys. Rev. Lett. }100:146401(2008); \textit{Phys. Rev. B},77:115123(2008)\textit{; J. Chem. Phys.} 129:121104(2008); \textit{Science}, 321:792(2008)] [Preview Abstract] |
Monday, March 16, 2009 8:36AM - 9:12AM |
A37.00002: Semiclassical origins of density functional theory Invited Speaker: Kieron Burke Until the seminal work of Hohenberg, Kohn, and Sham of the mid 60's, most density functional theory (DFT) was derived from semiclassical approximations. This non-empirical approach shows an intrinsic difference between solids (for which DFT was originally developed) and molecules, and explains many of its more mysterious manifestations. For example, the success of DFT for molecules has nothing to do with the uniform gas. Results include [1] a derivation of the empirical parameter in the B88 exchange functional, [2] PBEsol, a new GGA that restores the exchange gradient expansion and improves lattice constants in solids, [3] a novel approach to ``orbital-free'' DFT that, in preliminary tests, is 40 times more accurate than its DFT counterpart. The talk is aimed at a general theoretical audience. Detailed technical knowledge of DFT is neither needed, nor desirable. \\[4pt] [1] J.P. Perdew, L.A. Constantin, E. Sagvolden, and KB, Phys. Rev. Lett. 97, 223002 (2006). \\[0pt] [2] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, and KB, Phys. Rev. Lett. 100, 136406 (2008). \\[0pt] [3] Peter Elliott, Donghyung Lee, Attila Cangi, KB, Phys. Rev. Lett. 100, 256406 (2008). [Preview Abstract] |
Monday, March 16, 2009 9:12AM - 9:24AM |
A37.00003: Semiclassics in Density Functional Theory Donghyung Lee, Attila Cangi, Peter Elliott, Kieron Burke Recently, we published an article [1] about the semiclassical origin of density functional theory. We showed that the density and the kinetic energy density of one dimensional finite systems with hard walls can be expressed in terms of the external potential using the semiclassical Green's function method. Here, we show a uniformization scheme for the semiclassical density and the kinetic energy density for turning-point problems.\newline \newline [1] P. Elliott, D. Lee, A. Cangi, and K. Burke, Phys. Rev. Lett. 100, 256406 (2008). [Preview Abstract] |
Monday, March 16, 2009 9:24AM - 9:36AM |
A37.00004: Correlated Thomas-Fermi: Semiclassical ground-state energies of many-electron systems Brian Landry, Adam Wasserman, Eric Heller A new semiclassical method is proposed to obtain accurate ground-state energies for many-electron systems. The method borrows its semiclassical character from Thomas Fermi theory (TF), but improves upon it by including correlation effects, at least approximately. We illustrate our method (CTF) on simple models of 1D-interacting electrons, showing that it yields dramatic improvements over TF, particularly in the strongly-correlated regime. [Preview Abstract] |
Monday, March 16, 2009 9:36AM - 9:48AM |
A37.00005: Dimensional crossover of the exchange-correlation energy at the semilocal level Lucian Constantin Commonly used semilocal density functional approximations for the exchange-correlation energy fail badly when the true two dimensional limit is approached. We show, using a quasi-two-dimensional uniform electron gas in the infinite barrier model, that the semilocal level can correctly recover the exchange-correlation energy of the two-dimensional uniform electron gas. We derive new exact constraints at the semilocal level for the dimensional crossover of the exchange-correlation energy and we propose a method to incorporate them in any exchange-correlation density functional approximation. [Preview Abstract] |
Monday, March 16, 2009 9:48AM - 10:00AM |
A37.00006: Towards a semiclassical theory of electronic structure Attila Cangi, Donghyung Lee, Peter Elliott, Kieron Burke Modern density functional theory (DFT) -formulated in the context of the Kohn-Sham scheme- evolved from ``old'' Thomas-Fermi theory to an accurate theory for predicting various properties of molecules and solids. We discuss the interrelation of semiclassical physics[1] with the fundamental gradient approximation, which is the basis of all functional construction. We speculate that applying semiclassical methods in the context of a DFT-like theory is a path towards more accurate and efficient approximations to electronic properties of condensed systems.[2]\newline \newline [1] M. V. Berry and K. E. Mount, Reports of Progress in Physics 35, 315 (1972). \newline [2] P. Elliott, D. Lee, A. Cangi, and K. Burke, Phys. Rev. Lett. 100, 256406 (2008). [Preview Abstract] |
Monday, March 16, 2009 10:00AM - 10:12AM |
A37.00007: Spin-Current-Density Functional Theory with $SU(2)$ Potentials: the Local Approximation Saeed H. Abedinpour, Giovanni Vignale In order to study spin-orbit coupled systems, spin-transfer torque devices, or even systems with pseudospin coupling like graphene, non-Abelian vector potentials and their conjugate variables, the spin-current densities, should be incorporated in the density functional theory. The general formalism for doing this has been known for some time [K. Bencheikh, J. Phys. A: Math. Gen. {\bf 36} 11929 (2003)], but explicit functionals of the spin currents are not known. Here we identify the most general form of an exchange-correlation (xc) functional of the spin-currents, which satisfies the $SU(2)$ gauge invariance and construct the local density approximation (LDA) for it. As an illustration we present the LDA functional for a two-dimensional (2D) electronic system, using as reference system a homogeneous 2D electron gas subjected to isotropic $SU(2)$ vector potentials (\emph{i.e.}, linear spin-orbit coupling). The numerical results for the xc energy of this reference system will be presented. [Preview Abstract] |
Monday, March 16, 2009 10:12AM - 10:24AM |
A37.00008: Coupling of electrons to the electromagnetic field in a localized basis Roland Allen A simple formula is obtained for coupling electrons in a complex system to the electromagnetic field. It includes the effect of intra-atomic excitations and nuclear motion, and can be applied in, e.g., first-principles-based simulations of the coupled dynamics of electrons and nuclei in materials and molecules responding to ultrashort laser pulses. Some additional aspects of nonadiabatic dynamical simulations are also discussed, including the potential of reduced Ehrenfest simulations for treating problems where standard Ehrenfest simulations will fail. [Preview Abstract] |
Monday, March 16, 2009 10:24AM - 10:36AM |
A37.00009: Density-Functional Partition Theory for Order-N Electonic-Structure and Quantum-Dynamic Computations Morrel Cohen, Roberto Car Large Complex Systems pose a challenge to first-principles electronic-structure and quantum-dynamics computations. Most widely used codes scale as N$^{3}$, where N measures the size of the system. In this talk we describe a new order-N scheme based on a new conceptual structure, density-functional partition theory. In partition theory, the system is broken up into mono- or multinuclear parts and its electron density exactly decomposed into contributions from each part. A common partition potential and partition forces acting on each part carry the influence of the rest of the system to that part. A novel functional for the partition potential and a new iteration scheme achieve linear scaling. The scheme will integrate smoothly into the current widely-used Car-Parrinello electronic- and atomic-structure and quantum-dynamics codes. [Preview Abstract] |
Monday, March 16, 2009 10:36AM - 10:48AM |
A37.00010: Performance of Long-Range Corrected Functionals Mary Rohrdanz, John Herbert Popular generalized gradient approximations (GGA) to the exchange-correlation functional are accurate and useful in many different physical systems. However they have several well-documented shortcomings, including the incorrect asymptotic behavior. One manifestation of this is that linear response time-dependent density functional calculations of vertical excitation energies with GGA functionals sharply underestimate charge-transfer excitations in large systems. Consequently, such functionals are not reliable for calculations in such situations, for example, biomolecules in solution. To circumvent this problem, a number of long-range-corrected functionals (based on GGAs) have recently been developed, which posses the correct asymptotic form by construction. We analyze the performance of some of these functionals through a battery of tests, and demostrate that there exists a functional form and parameter set that provide reasonable results for both ground-state properties and vertical excitation energies. We find these functionals suitable for general use in large condensed-phase systems. [Preview Abstract] |
Monday, March 16, 2009 10:48AM - 11:00AM |
A37.00011: Density Functional with Full Exact Exchange, Balanced Nonlocality of Correlation, and Constraint Satisfaction John P. Perdew, Viktor N. Staroverov, Jianmin Tao, Gustavo E. Scuseria We construct a nonlocal density functional with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a ``normal region'', the exact exchange-correlation hole around an electron is semilocal because its range is reduced by correlation and because it integrates over a narrow range to -1. ``Abnormal'' regions, where nonlocality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high density, and rapidly-varying limits), and those open systems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a local hybrid mixing exact and semilocal exchange locally. [Preview Abstract] |
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