Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session D37: Focus Session: Fundamental Developments in Density Functional Theory III |
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Sponsoring Units: DCP Chair: Alberto Castro, Free University of Berlin Room: 409 |
Monday, March 16, 2009 2:30PM - 3:06PM |
D37.00001: Bounds on the correlation energy of Coulomb interacting systems: How negative does $E_c$ get, and what does this imply for approximate density functionals? Invited Speaker: The indirect part of the Coulomb interaction energy of a three-dimensional many-fermion system has a lower bound in terms of a power of the particle density, known as the Lieb-Oxford bound. This bound can be reformulated as a bound on the correlation energy, and in this reformulated version is an ingredient in the construction of many modern density functionals. In this talk, I describe several recent investigations and refinements of this bound: (i) an empirical analysis strongly suggesting that the bound can be tightened without loosing its universality [collaboration: Mariana Odashima], (ii) the construction of a particle-number dependent version of the bound and an exploration of its consequences for PBE GGA [collaboration: Mariana Odashima and Sam Trickey], (iii) a simplified scaling derivation of the power law in the bound, and its application to construct similar bounds also for one- and two-dimensional systems [collaborators: C\'{e}sar Proetto, Esa R\"{a}s\"{a}nen and Stefano Pittalis], and (iv) a connection between the Lieb-Oxford bound and common hybrid functionals, providing an alternative rationale for why these functionals work, as well as a possible route for the construction of improved beyond-GGA functionals [collaborator: Mariana Odashima]. [Preview Abstract] |
Monday, March 16, 2009 3:06PM - 3:42PM |
D37.00002: Van der Waals Interactions in Density-Functional Theory. Invited Speaker: The application of conventional GGA, and meta-GGA, density functionals to van der Waals complexes is fraught with difficulties. Conventional functionals do not contain the physics of the dispersion interaction. To make matters worse, the exchange part alone can yield anything from severe over-binding to severe over-repulsion depending on the choice of functional. We rectify these problems by - adding a dispersion term with nonempirical C6, C8, and C10 dispersion coefficients (the Becke-Johnson dispersion model), and - selecting a GGA exchange functional (PW86, also nonempirical) that gives excellent agreement with exact Hartree-Fock repulsion curves. The result is a simple GGA+dispersion theory giving excellent noble-gas pair interaction energies for He through Kr with only two adjustable parameters in the dispersion cutoff. [Preview Abstract] |
Monday, March 16, 2009 3:42PM - 4:18PM |
D37.00003: Van der Waals interactions in density functional theory Invited Speaker: The van der Waals density functional which we introduced half a decade ago\footnote{M. Dion et al.\ Phys.\ Rev.\ Lett. \textbf{92}, 246401 (2004).} and its self-consistent generalization\footnote{T. Thonhauser et al., Phys.\ Rev.\ B \textbf{76}, 125112 (2007).} will be briefly reviewed. There are many collaborators in the application review that will follow, not only those who worked in the physics department at Rutgers% \footnote{Maxime Dion, Aaron Puzder, T. Thonhauser, Valentino R. Cooper, Shen Li, Eamonn Murray, Lingzhu Kong, and Kyuho Lee.} and at Chalmers,% \footnote{Henrik Rydberg, Svetla Chakarova-K{\"a}ck, Jesper Kleis, Elsebeth Schr{\"o}der, Per Hyldgaard, and Bengt I. Lundqvist.} but also at Denmarks Technical University,% \footnote{Andrei Kelkkanen, Poul G. Moses, Jesper Kleis, and Bengt I. Lundqvist.} the chemistry department at Rutgers,% \footnote{Konhoa Li, Jing Li, Yves Chabal, and Wilma K. Olson.} and most recently at the University of Texas at Dallas.% \footnote{Nour Nijem and Yves Chabal.} I will expand on our recent review article,\footnote{D. C. Langreth et al., J. Phys.\ Cond.\ Mat.\ (in press).} which hopefully will be published before the present talk, and include applications by other groups not listed below. If possible, I will also review results from a more recent collaboration to study nucleosomal DNA and beyond. [Preview Abstract] |
Monday, March 16, 2009 4:18PM - 4:30PM |
D37.00004: Accurate van-der-Waals interactions from (semi)-local density functional theory Alexandre Tkatchenko, Matthias Scheffler Non-covalent forces, such as hydrogen bonding and van der Waals (vdW) interactions, are crucial for the formation, stability and function of molecules and materials. At present, vdW interactions can only be satisfactorily accounted for by high-level quantum-chemical wave function or by the Quantum Monte Carlo (QMC) method. In contrast, (semi)-local DFT and Hartree-Fock approximation fail for the description of vdW forces. We present a parameter-free method for describing the long-range vdW interaction in (semi)-local DFT. The leading $C_6$ coefficients are derived from the electron density of a molecule/solid and accurate reference values for the free atoms. The mean absolute error in the $C_6$ coefficients is 5.5\% when compared to accurate experimental values for 1225 intermolecular pairs. We show that the $C_6$ coefficients depend strongly on the bonding type and geometry of molecules/solids. Finally, we analyze the vdW radii and the damping function in the $C_6R^{-6}$ correction method for DFT calculations. [Preview Abstract] |
Monday, March 16, 2009 4:30PM - 4:42PM |
D37.00005: Efficient van der Waals density functional interactions Jose M. Soler, Guillermo Roman-Perez The LDA and GGA functionals are the non empirical methods of choice for large system calculations, but they cannot describe nonlocal dispersion forces. This limits severly their application to many systems of large interest, like molecular solids and liquids, physisorbed molecules, and interactions between biological molecules. Several schemes have been proposed to add ad-hoc atom-atom or atom-electron potentials. But dispersion is an electron-electron correlation effect, that must be described by an appropriate electron density functional, such as that proposed by Dion et al (PRL 92, 246401 (2004)). It is a true universal and general-purpose DFT functional that describes semiquantitatively the week dispersion interactions, without compromising the accuracy of the best GGA functionals for stronger bonds. Its direct evaluation for large molecular systems is very expensive, however, because it requires a double integral in real space. We present a new implementation that avoids this $N^2$ scaling by applying Fourier convolution techniques to an accurately interpolated kernel. The resulting method scales as $N\log N$ and it allows to perform vdW-DFT simulations of essentially any system that can be simulated with GGA. [Preview Abstract] |
Monday, March 16, 2009 4:42PM - 4:54PM |
D37.00006: The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems Paula Mori-Sanchez, Aron Cohen, Weitao Yang Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading to static correlation error. These two conditions are now unified for states with both fractional charge and fractional spin: the exact energy functional is a plane, linear along the fractional charge coordinate and constant along the fractional spin coordinate with a line of discontinuity at the integer. This sheds light on the nature of the derivative discontinuity and calls for explicitly discontinuous functionals of the density or orbitals that go beyond currently used smooth approximations. This is key to understand the physics of strongly correlated systems within DFT, for example the band-gap of Mott insulators. [arXiv:0809.5108] [Preview Abstract] |
Monday, March 16, 2009 4:54PM - 5:06PM |
D37.00007: Advances in Local Hybrid Functionals Alexey Arbuznikov, Martin Kaupp, Hilke Bahmann Local hybrids\footnote{ Jaramillo, J; Scuseria, G. E.; Ernzerhof, M. \textit{J. Chem. Phys.} \textbf{2003}, $118$, 1068} provide a promising new generation of exchange-correlation functionals for the simultaneous accurate description of various properties (atomization energies, reaction barrier heights,\footnote{ Kaupp, M.; Bahmann, H.; Arbuznikov, A. V. \textit{J. Chem. Phys.}, \textbf{2007}, $127$, 194102} NMR chemical shifts,\footnote{ Arbuznikov, A. V.; Kaupp, M. \textit{Chem. Phys. Lett.} \textbf{2007}, $442$, 496} energetics of transition-metal systems, etc.) Compared to traditional (global) hybrids (e.g., B3LYP), instead of a constant exact-exchange admixture, local hybrids employ a position-dependent one. The latter is governed by a so-called \textit{local mixing function} (LMF), and this is the crucial quantity controlling the performance of local hybrids. Here we present and compare new results obtained with LMFs derived both in a semiempirical way and using \textit{ab initio} considerations, e.g., the adiabatic connection formalism.\footnote{ Arbuznikov, A. V.; Kaupp, M. \textit{J. Chem. Phys.} \textbf{2008}, $128$, 214107} The former approach yields better results, while the latter brings valuable insights into the performance and limits of local hybrids. [Preview Abstract] |
Monday, March 16, 2009 5:06PM - 5:18PM |
D37.00008: Calculation of functional derivatives with respect to the external potential Nick Sablon, Tim Fievez, Frank De Proft, Paul W. Ayers, Paul Geerlings Apart from its many computational advantages, density functional theory (DFT) presents a conceptual framework for the reactivity and stability interpretation of chemical systems. The central idea is to identify chemical concepts with first and higher order (functional) derivatives of the electronic energy with respect to the number of electrons N and the external potential $v\left( r \right)$. The local interpretation of chemical reactivtiy is generally done with the Fukui function and the dual descriptor. These reactivity indices are usually calculated by a finite difference approach, which is enitrely justified in an exact theory. Practical DFT calculations make however use of approximate exchange-correlation functionals for which the DFT concepts can only correctly be obained by an effective evaluation of the electronic energy derivatives. A recent methodology for the calculation of functional derivatives with respect to $v\left( r \right)$ is presented.\footnote{P.W. Ayers, F. De Proft, A. Borgoo and P. Geerlings, J. Chem. Phys. 126, 224107 (2007).}$^,$\footnote{T. Fievez, N. Sablon, F. De Proft, P.W. Ayers and P. Geerlings, J. Chem. Theory Comput. 4, 1065 (2008).} Results are shown for a wide range of molecules among which substituted benzenes. A reactivity description of the alkaline earth oxides' (100) surface is expounded on as well. [Preview Abstract] |
Monday, March 16, 2009 5:18PM - 5:30PM |
D37.00009: Simple Illustration of Partition Theory Adam Wasserman, Morrel Cohen, Kieron Burke, Roberto Car In Partition Theory (PT) [M.H. Cohen and A. Wasserman, J.Phys. Chem. A 2007, 111, 2229], the density of a system is decomposed exactly into a superposition of the densities of its parts through the introduction of a common \textit{partition potential} acting on each of the parts as if they were isolated. In this talk we illustrate PT on a simple one-dimensional model of a heteronuclear diatomic molecule. We show that a sharp definition for the charge of the fragments emerges from PT, and that the ensuing population analysis can be used to study how charge redistributes during dissociation. By studying the preservation of the shapes of the parts as different parameters of the model are varied, we address the issue of transferability of the parts. We find good transferability within the chemically meaningful parameter regime, raising hopes that PT will prove useful in chemical applications. [Preview Abstract] |
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