Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session X13: Density Functional Methods: Applications |
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Sponsoring Units: DCOMP Chair: Samuel Trickey, University of Florida Room: 309 |
Thursday, March 19, 2009 2:30PM - 2:42PM |
X13.00001: System-averaged exchange-correlation holes and self interaction in second-row atoms Antonio C. Cancio Recent work is presented on the theoretical calculation of system-averaged exchange and correlation holes (intracules) for a pseudopotential model of the valence shell for the second row atoms Mg through Ar. Exchange holes are obtained from numerical fourier transform methods and correlation holes from variational quantum Monte Carlo calculations using the method of correlated estimates. We observe scaling behavior in both exchange and correlation, following the known scaling of the valence density across the row, once self-interaction effects are taken into account. The holes are compared to density-functional models including LDA, GGA and related SIC approaches. We note a sizeable error due to self-interaction occurs in the same-spin channel of the correlation hole which persists for the LDA and GGA even after standard self-interaction corrections are applied. The effects of this error and proposed corrections to it on the total exchange-correlation energy will be discussed. [Preview Abstract] |
Thursday, March 19, 2009 2:42PM - 2:54PM |
X13.00002: Constraint-based, Single-point Approximate Kinetic Energy Functionals Frank E. Harris, V. V. Karasiev, R. S. Jones, S. B. Trickey We work toward the development of orbital-free density functionals for the Kohn-Sham kinetic energy $T_s$ of a quality suitable for the computation of quantum-mechanical forces in multi-scale molecular dynamics simulations. The functionals are based on constraints applicable to the Pauli potential $v_\theta=\delta T_\theta/\delta n$, where $T_s=T_w+T_\theta$ and $T_w$ is the von Weizs\"acker kinetic-energy functional. We review our progress to date, and exhibit functionals that do not generate spurious singularities and that produce chemical bonding in semi-quantitative agreement with Kohn-Sham computations and relevant experiments. [Preview Abstract] |
Thursday, March 19, 2009 2:54PM - 3:06PM |
X13.00003: Functional minimization scheme for first-principles electronic structure calculations with bi-orthogonal interpolating wavelets William Garber, Wei Ku, James Davenport, Dmitri Volja A new development of first-principles electronic method will be presented based on direct energy functional minimization and bi-orthogonal wavelet basis set. The employment of bi-orthogonal basis allows systematically controlled accuracy while benefiting from the compact support that allows O(N) algorithms. Furthermore, utilization of the interpolating nature of the wavelet, together with the effectiveness of multi-resolution of wavelet, enables very efficient calculation without compromising accuracy. By avoiding solving eigenvalue equation as in standard Kohn-Sham framework, the method is easily extended to parallel algorithms, and allows simple implementation of various non-local functionals. In case of crystals, our method gives directly solution as Wannier functions, further utilizing their sparseness. This new development is ideal for easy implementation and accurate systematic benchmarking of various modern functionals, and holds the potential to attack very large systems such as nano- materials. [Preview Abstract] |
Thursday, March 19, 2009 3:06PM - 3:18PM |
X13.00004: Quenched Lieb-Oxford Satisfaction and Improved Performance for PBE-type Functionals S.B. Trickey, V. Medel, A. Vela Success for the orbital-free DFT approach to Born-Oppenheimer forces for first-principles molecular dynamics requires progress on orbital-free exchange-correlation (XC) functionals to go along with newly developed orbital-free kinetic energy functionals [V.V. Karasiev \emph{et al}.\, arXiv 0809.4798, J.\ Comput.-Aided Mat.Des.\ \textbf{13}, 111 (2006)]. We report on development and testing of a non-empirical X functional which generalizes PBE X. It satisfies a reduced Lieb-Oxford bound by quenching to homogeneous electron gas behavior for large values of the inhomogeneity $s \propto |\nabla n|/n^{4/3}$ on the grounds that large $s$ often corresponds (counter-intuitively) to small, smooth density. Used with the PBE C functional, our X functional reduces mean absolute errors for small molecules by 20\% or more with respect to conventional PBE XC. Used with LYP C (a semi-empirical combination), the performance also is improved relative to PBE-LYP. [Preview Abstract] |
Thursday, March 19, 2009 3:18PM - 3:30PM |
X13.00005: On the performance of Thomas-Fermi in periodic two-dimensional systems Lazaro Calderin, Malcolm J. Stott The largest missing piece of a completely orbital free Density Functional Theory is the kinetic energy functional $T_s[n]$, and approximations for this are of interest. One of these expands $T_s$ in terms of density gradients with the Thomas-Fermi functional as the first term. But in three-dimensions the expansion appears not to converge, and the sixth and higher order corrections diverge for localized systems. In contrast, a number of authors have shown that the density gradient corrections all vanish in two-dimensions, while numerical test revealed that, even when not exact, TF is a very good approximation. That has been shown for the case of an impurity in a otherwise two-dimensional uniform electron gas. In this work we explore the validity of TF and linear response theory for a periodic two-dimensional system, a system that is likely to be more widely applicable. [Preview Abstract] |
Thursday, March 19, 2009 3:30PM - 3:42PM |
X13.00006: Effect of disorder on the electronic properties of strongly correlated systems within the dynamical cluster approximation Unjong Yu, Abdolmajid Nili, Juana Moreno, Mark Jarrell We study the interplay of disorder and strong correlations on the electronic properties of highly correlated systems. We employ the dynamical cluster approximation (DCA) to include the effects of short-range correlations and alloy disorder beyond the coherent potential approximation (CPA). Our study focus on the double exchange model, relevant on the study of dilute magnetic semiconductors, and the periodic Anderson model to study heavy fermion compounds. We present results of several electronic properties as function of disorder strength, alloy concentration, and electron or hole doping. [Preview Abstract] |
Thursday, March 19, 2009 3:42PM - 3:54PM |
X13.00007: Basic Variables in Density Functional Theory in the Presence of a Magnetic Field Viraht Sahni, Xiaoyin Pan We have shown$^{\dag}$ via a unitary or equivalently a gauge transformation that for a system of $N$ electrons in an external field ${\vec{\cal{F}}}^{ext} = - {\vec{\nabla}} v({\vec{r}})$, the wave function $\Psi$ is in general a functional of the ground state density $\rho ({\vec{r}})$ and a gauge function $\alpha ({\vec{R}})$; ${\vec{R}} = {\vec{r}}_{1}, \ldots , {\vec{r}}_{N} $, i.e. $\Psi = \Psi [\rho, \alpha]$. The functions $\alpha ({\vec{R}})$ are arbitrary, the choice $\alpha ({\vec{R}}) = 0$ being equally valid. It is the presence of $\alpha ({\vec{R}})$ that ensures the wave function functional is gauge variant. Similarly, in the presence of a magnetic field ${\vec{B}} ({\vec{r}}) = {\vec{\nabla}} \times {\vec{A}} ({\vec{r}})$, we show that in general the wave function is a functional of the density $\rho ({\vec{r}})$, the physical current density ${\vec{j}}_{\vec{A}} ({\vec{r}})$, and a gauge function $\alpha ({\vec{R}}): \Psi = \Psi[\rho, {\vec{j}}_{\vec{A}}, \alpha]$. Again, the $\alpha ({\vec{R}})$ are arbitrary, the choice $\alpha ({\vec{R}}) = 0$ being valid. Hence, it is possible to construct a theory in which the basic variables are $\rho ({\vec{r}})$ and ${\vec{j}}_{\vec {A}} ({\vec{r}})$. The generalized Hohenberg-Kohn theorems, as well as the equations for the noninteracting fermion Kohn-Sham system that reproduces the $\rho ({\vec{r}})$ and ${\vec{j}}_{\vec{A}} ({\vec{r}})$ of the interacting system of electrons, are derived. \\ $^{\dag}$X.-Y. Pan and V. Sahni, Int. J. Quantum Chem. \textbf {108}, 2756 (2008). [Preview Abstract] |
Thursday, March 19, 2009 3:54PM - 4:06PM |
X13.00008: Projector Augmented Wave database with automatic parameter optimization R.J. Snow, A.F. Wright, C.Y. Fong Projector Augmented Wave (PAW) parameter sets, similar to pseudopotential parameters, can be constructed in many ways. Due to a non-local expansion of projectors, the PAW method can include parameters for each angular momentum channel separately. While this gives the flexibility to optimize projectors individually, it also creates an unfathomable parameter space for searching for good parameter sets. To automatically search for good PAW sets, logarithmic derivatives were analyzed numerically for matching with AE logarithmic derivatives. Logarithmic derivative matching, total energy convergence, and scf convergence were used as scores for automatic optimization of the accuracy and speed of PAW parameter sets using a genetic algorithm within an optimization code. The Dakota [1] program was used for the parameter optimization, while the atompaw program was used for PAW generation. A new database of PAW functions will be introduced and a number of examples discussed. [1] Sand Report Sand 2001-3514, (2002) [2] N.A.W. Holzwrth, A.R. Tackett, and G.E. Matthews, Computer Physics Communications 135, 329 (2001) [Preview Abstract] |
Thursday, March 19, 2009 4:06PM - 4:18PM |
X13.00009: A Projector Augmented Wave Formulation of the Optimized Effective Potential Formalism Xiao Xu, N.A.W. Holzwarth The optimized effective potential (OEP) or exact exchange (EXX) formalism has recently received renewed attention\footnote{ S. K\"{u}mmel and L. Kronik, RMP {\bf{80}}, 3 (2008).} as a method which can improve the accuracy of density functional calculations by representing orbital-dependent functionals and avoiding self-interaction errors found in density functionals. Since the Projector Augmented Wave (PAW) formalism\footnote{ P. Bl\"{o}chl, PRB {\bf{50}}, 17953 (1994); N. A. W. Holzwarth {\em{et al}}, PRB {\bf{55}}, 2005 (1997).} ensures accurate evaluation of interaction integrals by controlling the multipole moments,\footnote{ J. Paier {\em{et al}}, JCP {\bf{122}}, 234102 (2005).} it is a natural choice for implementing OEP within an efficient pseudopotential-like scheme. We developed a frozen core approximation scheme for the atomic all-electron OEP formalism, partitioning the exchange potential into core and valence contributions. The corresponding valence exchange pseudopotential for PAW, $\widetilde{V}_x^{\rm{vale}}({\bf{r}})$, can be derived in a similar way so that for $r > R_c$, $\widetilde{V}_x^{\rm{vale}}({\bf{r}})= {V}_x^{\rm{vale}}({\bf{r}})$. We have investigated the behavior of PAW-OEP basis, projector, and pseudopotential functions for several elements throughout the periodic table. [Preview Abstract] |
Thursday, March 19, 2009 4:18PM - 4:30PM |
X13.00010: Density functional study of CO adsorption on d-metal surface using TPSS functional Jianwei Sun, John Perdew Feibelman \textit{et al}$^{[1]}$ presented the puzzle of CO at the Pt(111) surface, showing that the LDA and Perdew-type GGA put the molecule at the wrong, high-coordination site. However, a recent study $^{[2]}$ showed that the BLYP yielded very satisfactory adsorption energies and the correct adsorption sites for CO adsorption on late 4d and 5d transition metal (111) surfaces, although at the price of large errors in the volume of the d metals. Since PBE and BLYP have similar accuracy, it seems the probable reason for the wrong adsorption site is due to the fact that the LDA and Perdew-type GGA's are ``jellium derived'' and hence prefer a more delocalized bonding, rather than that the LDA and GGA inaccurately describe the CO molecule's chemical bond. TPSS meta-GGA is also ``jellium derived'', but improves accuracy for molecules$^{[3]}$. Therefore, as a possible candidate to identify the major reason for the wrong adsorption site, TPSS is used to calculate the adsorption energies and sites of CO on the d-metal surface in the more accurate geometric structure obtained by PBEsol$^{[4]}$. [1] P.J. Feibelman \textit{et al}, J. Phys. Chem. \textbf{105}, 4018(2001). [2] A. Stroppa and G. Kresse, New Journal of Physics \textbf{10}, 063020(2008). [3] V.N. Staroverov\textit{ et al}, J. Chem. Phys., \textbf{119}, 12129(2003). [4] J.P. Perdew\textit{ et al}, Phys. Rev. Lett., \textbf{100}, 136406(2008). [Preview Abstract] |
Thursday, March 19, 2009 4:30PM - 4:42PM |
X13.00011: Fully numerical all-electron solutions of the optimized effective potential equation for diatomic molecules Adi Makmal, Stephan Kummel, Leeor Kronik We present an approach for fully numerical, all-electron solutions of the optimized effective potential equation within Kohn-Sham density functional theory for diatomic molecules. The approach is based on a real-space, prolate-spherical-coordinate grid for solving the all-electron Kohn-Sham equations and an iterative scheme for solving the optimized effective potential equation. The accuracy of this method is demonstrated by comparison with previously reported calculations and new benchmark fully numerical results for selected dimers are provided. [Preview Abstract] |
Thursday, March 19, 2009 4:42PM - 4:54PM |
X13.00012: Exchange Energy Density Functionals that reproduce the Linear Response Function of the Free Electron Gas David Garc\'Ia-Aldea, J.E. Alvarellos We present several nonlocal exchange energy density functionals that reproduce the linear response function of the free electron gas. These nonlocal functionals are constructed following a similar procedure used previously for nonlocal kinetic energy density functionals by Chac\'{o}n-Alvarellos-Tarazona, Garc\'ia-Gonz\'{a}lez et al., Wang-Govind-Carter and Garc\'ia-Aldea-Alvarellos. The exchange response function is not known but we have used the approximate response function developed by Utsumi and Ichimaru, even we must remark that the same \emph{ansatz} can be used to reproduce any other response function with the same scaling properties. We have developed two families of new nonlocal functionals: one is constructed with a mathematical structure based on the LDA approximation -- the Dirac functional for the exchange - and for the second one the structure of the second order gradient expansion approximation is took as a model. The functionals are constructed is such a way that they can be used in localized systems (using real space calculations) and in extended systems (using the momentum space, and achieving a quasilinear scaling with the system size if a constant reference electron density is defined). [Preview Abstract] |
Thursday, March 19, 2009 4:54PM - 5:06PM |
X13.00013: Non-local exchange-correlation term implemented into the density functional theory Youky Ono, Koichi Kusakabe, Takashi Nakayama The local density approximation (LDA) has serious limitation that this approximation cannot estimate the long-ranged (non-local) exchange-correlation interaction, as typified by the van der Waals (vdW) interaction. In this study we develop a method to calculate the vdW interaction based on the LDA together within the plasmon-pole approximation [1]. The computation code is developed as one of a module program of an existing first principle calculation package. Usefulness and efficiency of the method are confirmed by calculating the interaction energy of simple periodic systems. This method never relies on external parameters and/or on asymptotic model functions, and thus being applicable to any isolated 3 dimensional structures. [1] PRL \textbf{96}, 073201 (2006), PRB \textbf{62}, 6997 (2000), PRL \textbf{92}, 246401 (2004). [Preview Abstract] |
Thursday, March 19, 2009 5:06PM - 5:18PM |
X13.00014: A series expansion of the Coulomb operator for optimization scheme of the multi-reference density functional theory Koichi Kusakabe, Isao Maruyama A quadratic form of the Coulomb operator for the many-electron system is derived.[1] This form of the electron-electron interaction is a sum of quadratic form pairs, which can be redefined in a self-consistent calculation of the multi-reference density functional theory. By virtue of this finding, the extended Kohn-Sham scheme[2] is shown to possess an optimization scheme of the effective electron model, which converges on the exact Coulomb system. For a defined accuracy of computation with given numerical technique, we can provide an algorithm to have an optimized electron model. The present procedure provides also an exact derivation of effective negative interactions in charge fluctuation channels. Relevance to the high-temperature superconductors is discussed. [1] K. Kusakabe, to appear in J. Phys.: Condens. Matter. [2] K. Kusakabe, J. Phys. Soc. Jpn. 70, 2038 (2001). [Preview Abstract] |
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