Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session A1: Recent Advances in Density Functional Theory I |
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Sponsoring Units: DCP DCOMP Chair: Weitao Yang, Duke University Room: 103/105 |
Monday, March 3, 2014 8:00AM - 8:36AM |
A1.00001: Strong Correlation in Density-Functional Theory Invited Speaker: Axel Becke What do fractional occupancies mean in Kohn-Sham Density-Functional Theory (KS-DFT)? Can we model configuration mixing in KS-DFT? Can molecular bonds be dissociated using spin-restricted KS orbitals? These questions will be addressed in the context of recent work on a strongly-correlated, exact-exchange based (or Hartree-Fock based) correlation functional of the author. [Preview Abstract] |
Monday, March 3, 2014 8:36AM - 8:48AM |
A1.00002: Strong correlation in Kohn-Sham DFT Francesc Malet Giralt, Andr\'e Mirtschink, Jonas Cremon, Christian Mendl, Klaas Giesbertz, Stephanie Reimann, Paola Gori-Giorgi The knowledge on the strong-interacting limit of density functional theory can be used to construct exchange- correlation functionals able to address strongly-correlated systems without introducing any symmetry breaking. We report calculations on semiconductor nanostructures and one-dimensional models for chemical systems, showing that this approach yields quantitatively good results in both the weakly- and the strongly-correlated regimes, with a numerical cost much lower than the traditional wavefunction methods. [Preview Abstract] |
Monday, March 3, 2014 8:48AM - 9:00AM |
A1.00003: Local Correction to Reduce Delocalization Errors in Approximate Density Functionals Chen Li, Xiao Zheng, Weitao Yang We develop a local correction scheme to reduce delocalization errors in approximate density functionals. A concept of local fractional electron distribution is proposed and corresponding local functions are designed to evaluate its magnitude. Following our previous idea of linearizing each of the nonlinear components in Kohn-Sham density functional, we impose a local linearity condition rather than a global condition. By building our correction functionals in terms of our local functions, we can largely reduce the error in systems that present local fractional electron distribution but no global fractional charge. Our results show that the dissociation curves of diatomic molecules as well as dimer cations can be largely improved. Furthermore, the non-physical ionic product of dissociated molecules by traditional density functionals can be corrected to neutral atoms. We believe the analogous problems in charge transfer systems that are inaccessible for traditional density funcitonals can be correctly handled by our correction functional, and the well-known delocalization error in large extent improved. In addition, our correction scheme maintains the computational efficiency of traditional DFT, enabling it to be applicable to large scale systems. [Preview Abstract] |
Monday, March 3, 2014 9:00AM - 9:12AM |
A1.00004: Density-driven delocalization error for a model solvated electron system Stephen Dale, Alberto Otero-de-la-Roza, Erin Johnson Electrides are a unique class of ionic solids in which the anions are replaced by a lone electron localized within a crystal void. Theoretical modeling of these systems is possible using DFT methods. However, delocalization error inherent in common density-functional approximations increases the complexity of this study. To investigate delocalization error effects, we propose a simplified electride model, known in solvated electron chemistry as the Kevan structure. This model localizes an electron within a void formed by six radially-oriented, octahedrally-arranged water molecules. The Kevan structure is then coupled with atoms of various electronegativities, and the resulting complex is used to test different density functionals. We show that fractional charges caused by delocalization error have a significant impact on the electron density of the Kevan structure. Finally, we use results for the Kevan structure to rationalize the calculated band gaps for the actual electrides. [Preview Abstract] |
Monday, March 3, 2014 9:12AM - 9:48AM |
A1.00005: Gedanken Densities and Lower Bounds in Density Functional Theory Invited Speaker: John P. Perdew A gedanken density is not a real one but one imagined in the construction of density functional approximations. The uniform electron gas is the original gedanken density, but we will be concerned here with two others: (1) the ground-state density of one electron in the presence of a nonuniform periodic potential , in which the reduced density gradient $s=\left| {\nabla n} \right|/[2(3\pi^{2})^{1/3}n^{4/3}$diverges almost everywhere as the volume tends to infinity. This density was used in the construction [1] of a generalized gradient approximation (GGA): To satisfy the general Lieb-Oxford lower bound [2] on the exchange-correlation energy for all possible densities, the exchange enhancement factor $F_{x} \equiv \varepsilon _{x}^{approx} /\varepsilon_{x}^{unif} $ in the large-$s$ limit for a spin-unpolarized density must be less than or equal to 1.804. (2) a two-electron spherical ground-state density in which $s$ takes the same arbitrary positive value wherever the density is non-zero [3]. This density can be used to show that, to satisfy the tight Lieb-Oxford bound on the exchange energy of a two-electron density for every possible such density, $F_{x} $ for such a density (and probably for every density) must be less than 1.174. The local spin density approximation (LSDA) for exchange ($F_{x} =1)$ satisfies this tight bound, but standard GGA's and meta-GGA's do not. A talk by Jianwei Sun will present what may be the first beyond-LSDA approximation to satisfy this strong new constraint. \\[4pt] [1] J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. \textit{77,} 3815 (1996).\\[0pt] [2] E.H. Lieb and S. Oxford, Int. J. Quantum Chem. \textit{19}, 427 (1981).\\[0pt] [3] J.P. Perdew, J. Sun, A. Ruzsinszky, and K. Burke, in preparation. [Preview Abstract] |
Monday, March 3, 2014 9:48AM - 10:00AM |
A1.00006: First beyond-LSDA density functional satisfying a tight lower bound for exchange Jianwei Sun, John Perdew, Adrienn Ruzsinszky Universal constraints of density functional theory (DFT) play major roles in approximating its exchange-correlation energy ($E_{\mbox{xc}} )$. One of the prominent constraints is the Lieb-Oxford bound: $E_{xc}^{exact} [N]\ge \lambda_{xc} [N]E_{x}^{LDA} [N]$, where LDA stands for local density approximation, N is the electron number of systems, and $\lambda_{xc} [N]$ increases with N with an upper bound of 2.275. For ground-state 1-e systems, the above inequality reduces to $E_{x}^{exact} [N\mbox{=1}]\ge \lambda_{xc} [N\mbox{=1}]E_{x}^{LDA} [N\mbox{=1}]$ with a tight bound $\lambda_{xc} [N\mbox{=1}]=$1.48, shedding light on the exchange energy. Our recent study (John P. Perdew's talk) shows that, to avoid violating the tight bound for any possible 1-e densities, a semilocal functional should respect it locally. We further conjecture for exchange energies that $E_{x}^{exact} [N]\ge \gamma_{x} [N]E_{x}^{L\mbox{S}DA} [N]$ with$\gamma_{x} [N]$ decreasing with N and $\gamma_{x} [N=1]=\gamma_{x} [N=2]=\lambda _{xc} [N\mbox{=1}]$/2$^{1/3} =$1.174. Here, local spin density approximation (LSDA) is used as the reference since the exchange has a well-defined spin-scaling relation. Based on the tight Lieb-Oxford bound and the conjecture, we present a simple meta-generalized gradient approximation (MGGA) for exchange that interpolates different LSDAs for N$=$1 and uniform electron gas (N $\to$ infinity), respectively, and delivers excellent exchange energies for atoms. When combined with a modified PBE correlation, the MGGA yields good binding energies for molecules and lattice constants for solids. [Preview Abstract] |
Monday, March 3, 2014 10:00AM - 10:12AM |
A1.00007: Band gaps with approximate density functionals: the derivative discontinuity revealed from ensemble considerations Eli Kraisler, Leeor Kronik The band gap is a central property of solids. Unfortunately, this quantity is not generally equal to the Kohn-Sham band gap of density functional theory (DFT), even in principle. The two band gaps differ precisely by the derivative discontinuity. Popular approximate functionals are thought to be devoid of a derivative discontinuity, thereby eliminating their usefulness for gap prediction. Here we show that all exchange-correlation functionals possess a derivative discontinuity, which arises naturally from the application of ensemble considerations within DFT. The approach requires no empiricism and involves no approximations beyond the choice of the exchange-correlation functional. Furthermore, the derivative discontinuity can be expressed in closed form using quantities obtained in the course of a standard DFT calculation of the neutral system, allowing for band gap calculations in periodic systems. The approach is demonstrated by calculations of the band gap for eleven representative insulators and semiconductors, using the ensemble approach with the local density approximation. We find that the derivative discontinuity revealed by this approach accounts for a significant part of the overall band gap and its inclusion reduces the error in band gap prediction from 50\% to 10\%. [Preview Abstract] |
Monday, March 3, 2014 10:12AM - 10:24AM |
A1.00008: Gap renormalization of molecular crystals from density-functional theory Sivan Refaely-Abramson, Sahar Sharifzadeh, Manish Jain, Roi Baer, Jeffrey B. Neaton, Leeor Kronik Fundamental gap renormalization due to electronic polarization is a basic phenomenon in molecular crystals. Despite its ubiquity and importance, all conventional approaches within density-functional theory completely fail to capture it, even qualitatively. Here, we present a new screened range-separated hybrid functional, which, through judicious introduction of the scalar dielectric constant, quantitatively captures polarization-induced gap renormalization, as demonstrated on the prototypical organic molecular crystals of benzene, pentacene, and C60. This functional is predictive, as it contains system-specific adjustable parameters that are determined from first principles, rather than from empirical considerations [Phys. Rev. B 88, 081204(R) (2013)]. [Preview Abstract] |
Monday, March 3, 2014 10:24AM - 10:36AM |
A1.00009: Local Density Approximation Exchange-correlation Free-energy Functional Valentin Karasiev, Travis Sjostrom, James Dufty, S.B. Trickey Restricted path integral Monte-Carlo (RPIMC) simulation data for the homogeneous electron gas at finite temperatures [1] are used to fit the exchange-correlation free energy as a function of the density and temperature. Together with a new finite-$T$ spin-polarization interpolation, this provides the local spin density approximation (LSDA) for the exchange-correlation free-energy functional required by finite-$T$ density functional theory. We discuss and compare different methods of fitting to the RPIMC data. The new function reproduces the RPIMC data in the fitting range of Wigner-Seitz radius and temperature, satisfies correct high-density, low- and high-$T$ asymptotic limits and is applicable beyond the range of fitting data.\\[4pt] [1] Phys. Rev. Lett. \textbf{110}, 146405 (2013). [Preview Abstract] |
Monday, March 3, 2014 10:36AM - 10:48AM |
A1.00010: Constrained Parmeterization of Reduced Density Approximation of Kinetic Energy Functionals Debajit Chakraborty, Samuel Trickey, Valentin Karasiev Evaluation of forces in ab initio MD is greatly accelerated by orbital-free DFT, especially at finite temperature [1]. The recent achievement of a fully non-empirical constraint-based generalized gradient (GGA) functional for the Kohn-Sham KE $T_s[n]$ [2] brings to light the inherent limitations of GGAs. This motivates inclusion of higher-order derivatives in the form of reduced derivative approximation (RDA)[3] functionals. That, in turn, requires new functional forms and design criteria. RDA functionals are constrained further to produce a positive-definite, non-singular Pauli potential. We focus on designing a non-empirical constraint-based meta-GGA[3-5] functional with certain combinations of higher-order derivatives which avoid nuclear-site singularities to a specified order of gradient expansion. Here we report progress on this agenda.\\[4pt] [1] Phys.\ Rev.\ B \textbf{86}, 115101 (2012);\\[0pt] [2] Phys.\ Rev.\ B \textbf{88}, 161108(R) (2013);\\[0pt] [3] Phys.\ Rev.\ B \textbf{80}, 245120 (2009);\\[0pt] [4] Phys.\ Rev.\ B \textbf{75}, 155109 (2007);\\[0pt] [5] Nuc.\ Phys.\ A \textbf{445} 263 (1985) [Preview Abstract] |
Monday, March 3, 2014 10:48AM - 11:00AM |
A1.00011: Modeling Electron Correlation Using Geminal Hybrid Methods Brett Cagg, Vitaly Rassolov Two approaches to dynamic correlation correction for a variationally optimized, spin-unrestricted, multireference wavefunction based on strongly orthogonal, two electron geminals are presented. The first is a simple density functional based approach using standard correlation functionals rescaled empirically to reduce the correlation double counting error (DCE) inherent in all multireference DFT approaches. The second uses a two electron correlation operator to correlate only intergeminal, mean-field type, interactions within the wavefunction and effectively eliminates DCE. The performance of each is examined by geometric optimization and dissociation energy prediction of 38 diatomic molecules at two different basis sets. [Preview Abstract] |
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