Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session S13: Focus Session: Frontiers in Electronic Structure Theory I |
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Sponsoring Units: DCOMP DCP Chair: Andrew Rappe, University of Pennsylvania Room: Morial Convention Center 204 |
Wednesday, March 12, 2008 2:30PM - 2:42PM |
S13.00001: Total and self-energies beyond LDA and GGA: exact-exchange, {\it GW} and MP2 united by numeric atom-centered orbitals Xinguo Ren, Andrea Sanfilippo, Alexandre Tkatchenko, Patrick Rinke, Volker Blum, Karsten Reuter, Matthias Scheffler Well-known deficiencies of (semi-)local exchange correlation functionals in density functional theory comprise the spurious self-interaction, the absence of long-range correlation, and the absence of the derivative discontinuity with respect to the electron number. Present approaches to overcome these deficiencies (e.g., hybrid functionals, MP2, and {\it GW}) typically involve expensive two-electron Coulomb repulsion integrals. For molecules, the resulting numerical effort usually restricts these methods to Gaussian basis functions. We here show how all these methods can be handled accurately with efficient all-electron numerical atom-centered basis sets [1], by using a second, auxiliary basis for products of basis functions (resolution of the identity). For an extended set of finite systems spanning small molecules (water dimer, benzene), metal clusters (Na$_n$) and biomolecules (polyalanine peptides), we demonstrate that the efficiency of optimized numeric atom-centered basis sets is directly carried over into our new approach. Our approach is then applied to analyze the CO-adsorption problem (CO/Cu(111)). [1] V. Blum {\it et al.}, The FHI-aims project, www.fhi-berlin.mpg.de/aims [Preview Abstract] |
Wednesday, March 12, 2008 2:42PM - 2:54PM |
S13.00002: Order N Implementation of Exact Exchange Xifan Wu, Annabella Selloni, Roberto Car Exact (Hartree Fock) exchange is needed to overcome some of the limitations of local and semilocal approximations of density functional theory (DFT). Moreover exact exchange is a basic ingredient in modern approaches to compute excitation properties, like the GW and the OEP schemes. So far, however, computational cost has limited the use of exact exchange in plane wave calculations for extended systems. We show that this difficulty can be overcome by performing a unitary transformation from Bloch to Maximally Localized Wannier functions in combination with an efficient technique to compute real space Coulomb integrals. The resulting scheme scales linearly with system size and, when used in ab-initio molecular dynamics simulations, requires only a modest increase in computational cost compared to standard DFT implementations. We validate the scheme with representative applications. [Preview Abstract] |
Wednesday, March 12, 2008 2:54PM - 3:06PM |
S13.00003: Accurate and fast DFT calculations with the AM05 functional Ann E. Mattsson The AM05 functional [1] has the same excellent performance for solids as the hybrid density functionals tested in Paier \emph{et.\ al.}\ (J. Chem. Phys {\bf 124}, 154709 (2006); \emph{ibid} {\bf 125}, 249901 (2006)). This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. While hybrid functionals are computationally expensive, preveting them from being used in large systems and/or long molecular dynamics simulations, the AM05 functional is on a regular semi-local GGA form with corresponding computational cost. The performance of AM05 is even superior to an `informed choice' between LDA and PBE. By comparing data from different electronic-structure codes we have determined that the numerical errors in this study are equal to or smaller than corresponding experimental uncertainties. Results for other systems will also be presented. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. \newline [1] R. Armiento and A. E. Mattsson, Phys. Rev. B {\bf 72}, 085108 (2005). [Preview Abstract] |
Wednesday, March 12, 2008 3:06PM - 3:42PM |
S13.00004: Beller Lectureship Talk: Exploring Exact Exchange for collinear and non-collinear magnetism Invited Speaker: In standard density functional theory, one usually describes exchange and correlation effects by approximations on the same footing, where typical examples are the local density approximation (LDA) and different flavours of the generalized gradient approximation (GGA). Only in recent years the exact exchange (EXX) or optimized effective potential (OEP) method has been investigated in more detail, where most of the work has been dedicated to semiconductors [1]. Here we explore the OEP approach for magnetic materials. We provide a general description of the method which comprises the case of non-collinear magnetism. The equations for the effective Kohn-Sham scalar potential and magnetic field are derived within this framework, where the exact exchange energy functional explicitly depends on two-component spinor orbitals. The example of a magnetically frustrated Cr monolayer shows [2] that the resulting magnetization density exhibits much more non-collinear structure compared to LDA. The finding that a time-dependent generalization of the non-collinear OEP method can be a promising approach for an \textit{ab-initio} description of spin dynamics provides an interesting outlook for future work. In the present study, a series of materials is investigated in view of the reliability of the OEP method in terms of their magnetic properties. \newline [1] M. St\"{a}dele, M. Moukara, J. A. Majewski, P. Vogl, and A. G\"{o}rling, Phys. Rev. B 59, 10031 (1999). \newline [2] S. Sharma, J. K. Dewhurst, C. Ambrosch-Draxl, N. Helbig, S. Kurth, S. Shallcross and L. Nordstr\"{o}m, and E. K. U. Gross, Phys. Rev. Lett. 98, 196405 (2007). [Preview Abstract] |
Wednesday, March 12, 2008 3:42PM - 3:54PM |
S13.00005: A GGA+U approach to realistic modeling of transition-metal complexes Heather Kulik, Nicola Marzari Despite the importance of transition metal centers in a variety of biological and inorganic chemical reactions, density functional theory calculations often fail quantitatively in describing both the stable intermediate electronic structures, splittings, and geometries as well as reaction barriers and geometries of transition states. We have shown$^1$ that augmenting the generalized-gradient approximation (GGA) with a Hubbard U which is obtained from a self-consistent linear response procedure can greatly improve the description of both spin state splittings in the iron dimer as well as reaction barriers in the addition-elimination reaction of hydrogen and methane with FeO$^+$. This fully ab-initio GGA+U approach provides excellent agreement with accurate, correlated-electron quantum chemistry calculations but at a fraction of the cost of these methods. We will further highlight how our method affords substantial improvement in the physical description of hybridization and bonding irrespective of system size. We thus fruitfully employ GGA+U in the study of large-scale complexes which contain hundreds of atoms such as the active site of halogenating enzymes and various porphyrin complexes. \\ \\ $^1$ H. J. Kulik, M. Cococcioni, D. Scherlis and N. Marzari, PRL \textbf{97} 103001, (2006). [Preview Abstract] |
Wednesday, March 12, 2008 3:54PM - 4:06PM |
S13.00006: Accurate description of the bonding of C$_6$H$_6$ at noble metal surfaces, using a local exchange-correlation correction scheme Erik McNellis, Karsten Reuter, Matthias Scheffler The adsorption of benzene (C$_6$H$_6$) at the Cu(111) surface is a much studied model system for the interaction of larger $\pi$-conjugated molecules with solid surfaces. At first glance a simple system, the suspected predominantly van der Waals type bonding at the extended metal surface poses a severe challenge for accurate first-principles calculations. Density-Functional Theory (DFT) with local and semi-local exchange-correlation (xc) functionals is uncertain to properly account for this type of bonding, while the system sizes required to correctly grasp the metallic band structure are computationally untractable with correlated wave function techniques. We overcome these limitations with a recently introduced ``local xc correction'' scheme [1], correcting the adsorption energetics from present-day DFT xc functionals with hybrid functional and M\o ller-Plesset perturbation theory calculations for small clusters. From the obtained convergence of the xc correction with cluster size we can disentangle short-range and dispersion type contributions to the bonding of the molecule at different heights above the surface. This enables us to qualify the role played by the two contributions in determining the binding energetics and geometry. [1] Q.-M. Hu, K. Reuter, and M. Scheffler, PRL {\bf 98}, 176103 (2007) and {\bf 99}, 169903 (2007); C. Tuma and J. Sauer, CPL {\bf 387}, 388 (2004). [Preview Abstract] |
Wednesday, March 12, 2008 4:06PM - 4:18PM |
S13.00007: Transcorrelated method applied to covalent and ionic solids: total energy and band structure calculation Keitaro Sodeyama, Shinji Tsuneyuki, Rei Sakuma To calculate the electronic structures of solids including
electron correlation effects, we have developed the
transcorrelated (TC) method which was first proposed by Boys and
Handy. In the TC method, the wave function is represented by a
correlated wave function $F \Phi$, where $\Phi$ is a single
Slater determinant and $F$ is a Jastrow function,
$F=\exp[-\sum_{i |
Wednesday, March 12, 2008 4:18PM - 4:30PM |
S13.00008: System-averaged exchange and correlation holes in third-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 of third-row atoms. 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 approximate scaling behavior in both exchange and correlation, following the known scaling of the valence density across the row. The holes are compared to density-functional models including LDA, GGA and meta-GGA approaches. Particular attention is paid to self interaction (SI) error; we find that a sizeable error occurs in the same-spin channel of the correlation hole which persists for the LDA and GGA even after standard SI corrections are applied. A simple SI correction that eliminates this error will be discussed. [Preview Abstract] |
Wednesday, March 12, 2008 4:30PM - 4:42PM |
S13.00009: RPA Correlation Energy in ACFD Formalism with Thomas-Fermi-von Weizs\"{a}cker Approximation Viet Huy Nguyen, Stefano de Gironcoli It is well known that LDA or GGAs approximations in DFT do not describe correctly systems where long range correlations are important. In the Adiabatic Connection Fluctuation-Dissipation (ACFD) formalism correlation energy can be computed accurately from Kohn-Sham and interacting linear response functions. Although computationally very demanding, this formalism has shown to describe correctly systems where standart DFT fails qualitatively by combining RPA xc-kernel with short-range local-density corrections (RPA+). On the other hand, Thomas-Fermi-von Weizs\"acker approximate kinetic response function can capture reasonably well asymptotic long range interactions via van der Waals coefficients, and has the computationally desirable feature that it only involves a single auxiliary wavefunction regardless of the number of electrons in the system. Here, we show how to use this approach to calculate approximate RPA correlation energies. Numerical results for atoms show that this approach gives approximate RPA correlation energies closer to the experimental values than those obtained by full RPA and, when combined with a short-range local-density correction, it gives results at least as good as those of full RPA+. The possibility is therefore open to address large systems where correlations need to be treated beyond LDA and GGAs. [Preview Abstract] |
Wednesday, March 12, 2008 4:42PM - 4:54PM |
S13.00010: Generalized density functional theory for effective potentials in many-body electronic structure F. A. Reboredo, P. R. C. Kent We demonstrate the existence of different density functionals that retain selected properties of the many-body ground state in the non-interacting density functional solution. We focus on diffusion Monte Carlo applications that require trial wave functions with Fermion optimal nodes. The theory can be extended and used to understand current practices in several electronic structure methods [GW-BSE,CI,EPM] within a generalized density functional framework. The theory justifies and stimulates the search of optimal empirical density functionals and effective potentials but also cautions on the limits of their applicability. The theoretical concepts are tested against a near-analytic model that can be solved to numerical precision. Research performed at the Materials Science and Technology Division and the Center of Nanophase Material Sciences at Oak Ridge National Laboratory sponsored the Division of Materials Sciences and the Division of Scientific User Facilities U.S. Department of Energy. [Preview Abstract] |
Wednesday, March 12, 2008 4:54PM - 5:06PM |
S13.00011: Towards QMC benchmarks for large scale dispersive interactions Jonathan L DuBois, Randolph Q. Hood, Sebastien Hamel, Eric R. Schwegler Fixed-node quantum Monte-Carlo (QMC) methods are becoming an increasingly attractive approach for the study of large scale problems in electronic structure. Current challenges lie in efficient application of QMC to large (thousands of electrons) systems and removal or amelioration of the uncontrolled approximations inherent in most practical applications of the method. I will present recent progress and address some of the particular challenges associated with the development of exact potential energy surfaces for weakly interacting closed shell carbon complexes within the fixed-node QMC ansatz. In particular, the efficacy / necessity of backflow corrections and multi-determinant expansions as a method for optimizing the nodal surface in these systems will be discussed. [Preview Abstract] |
Wednesday, March 12, 2008 5:06PM - 5:18PM |
S13.00012: Real or artifactual symmetry breaking in BNB: A fixed-node diffusion Monte Carlo study Wissam A. Al-Saidi, Cyrus Umrigar The linear BNB molecule represents one of the most challenging examples of symmetry-breaking effects because of its susceptibility to a second-order Jahn-Teller distortion along the antisymmetric stretching mode. This real symmetry breaking could be confused in calculations with an artifactual one caused by the approximate nature of the theoretical approach. Thus the debate of whether the ground state of BNB is symmetric in the positions of the boron atoms with respect to nitrogen or if this symmetry is broken. Our preliminary investigations with diffusion Monte Carlo shows that the symmetric and the broken symmetry geometries are nearly degenerate, which would suggest a highly floppy quasi-symmetric BNB ground state. [Preview Abstract] |
Wednesday, March 12, 2008 5:18PM - 5:30PM |
S13.00013: Potential Energy Curves and Excited States of the C$_2$ Molecule by Auxiliary-Field Quantum Monte Carlo (AFQMC) Wirawan Purwanto, Henry Krakauer, Shiwei Zhang, Wissam Al-Saidi The accurate determination of potential energy curves (PECs) and excited states represents two difficult problems in electronic structure calculations. We present AFQMC PECs of the challenging C$_2$ molecule, focusing on the ground state and two singlet low-lying excited states. AFQMC calculates a target many-body wave function (WF) by means of random walks in the space of Slater determinants. We employ truncated complete active space (CAS) trial WFs ($\Psi_T$) to guide the AFQMC projection to obtain the desired state. With the phase-free constraint,\footnote{S. Zhang and H. Krakauer, Phys. Rev. Lett. \textbf{90}, 136401 (2003)} the CAS $\Psi_T$ is effective in controlling the sign/phase problem, and filtering in the desired excited state. The AFQMC results are in very good agreement with exact results. Comparison with experimental spectroscopic constants will also be presented. [Preview Abstract] |
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