Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session S32: Electronic Structure |
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Sponsoring Units: DCOMP Chair: Estela Blaisten-Barojas, GMU Room: LACC 507 |
Wednesday, March 23, 2005 2:30PM - 2:42PM |
S32.00001: Nearsightedness of Electronic Matter Emil Prodan, Walter Kohn The concept of ``nearsightedness of electronic matter" (NEM) articulates and quantifies the common, qualitative consensus among chemists and also among many physicists, that static, local electronic properties like the density or energy density at a given point r, of a many-atomic covalent or metallic system depend significantly on the external potential v(r$'$) only for values of r$'$ near r. NEM provides the physical basis for linear scaling [O(N)] electronic structure calculations. We say that a system of electrons is nearsighted at r, if distant potential perturbations w(r$'$) [w(r$'$) vanishing for $\vert $r-r$'\vert <$D] produce insignificant density changes at r. For non-interacting electrons in 1, 2 and 3 dimensions, we have obtained explicit complete asymptotic (D large) functional behaviors and the pre-factors of the density changes generated by distant perturbing potentials. For periodic or non-periodic metals and insulators, these results show that the density changes at r cannot exceed a maximum value regardless of the shape or magnitude of w(r$'$). This allows us to introduce a new concept, the nearsightedness range R, defined as the minimum distance for which the density changes at r, due to any potential w(r$'$) vanishing for $\vert $r-r$'\vert <$R, are less than a desired accuracy. We present here the dependence of the nearsightedness range on the desired accuracy, for gapped and un-gapped electronic systems. We also discuss the implications for O(N) electronic structure calculations. [Preview Abstract] |
Wednesday, March 23, 2005 2:42PM - 2:54PM |
S32.00002: Static Electricity in Sublimated CO2 Gas -- One in a Class of Phenomena Chung Liao Feng The charge state of CO$_{2}$ gas, sublimated from neutral solid, is observed to be positive. This phenomenon will be demonstrated. This discovery is made by testing a hypothesis which expects a group of molecules to become more positive when moving faster. The same hypothesis has also led to other discoveries of a special class of phenomena which include static electric charges being produced by thermal changes during vaporization, condensation and heating of water, as well as charges being produced by mechanical motion of metal discs. These phenomena were reported at the APS meetings of MAR02 (W30 4), MAR03 (J1 206) and MAR04 (Y38 12 - demonstration using toy gyroscopes). All of these phenomena appear to contradict the idea that the fundamental (or elemental) charge is constant. Each of these phenomena shows readings of positive voltage increasing without a decreasing electron count. Calculations show that the deviation from a static value of the fundamental (or elemental) charge may be the source of magnetism. This appears to answer the question why charges can appear to be constant. One of these calculations will be presented briefly. [Preview Abstract] |
Wednesday, March 23, 2005 2:54PM - 3:06PM |
S32.00003: First-Principle Perturbative Computation of Phonon Properties of Insulators in Finite Electric Fields Xinjie Wang, David Vanderbilt The methods of density-functional perturbation theory have been shown to provide a powerful tool for realistic calculations of lattice-vibrational, dielectric, elastic, and other response properties of crystals.\footnote{S. Baroni {\it et al.}, Rev. Mod. Phys. {\bf 73}, 515 (2001).} Recently, a total-energy method for insulators in nonzero electric fields was proposed.\footnote{I. Souza, J. \'I\~niguez, and D. Vanderbilt, Phys. Rev. Lett. {\bf 89}, 117602 (2002).} However, the perturbative computation of phonon properties under a dc bias field has not previously been addressed. Here, we start from a variational total-energy functional with a field coupling term that represents the effect of the electric field on the crystal. The linear response of the field-polarized Bloch functions is obtained by minimizing the second-order derivative of the total-energy functional. Due to the presence of the electric field, the field-polarized Bloch functions at each k-point in the Brillouin zone are weakly coupled to those at the neighboring k-points. We implement the method in the {\tt ABINIT} code and perform illustrative calculations of the phonon frequencies for III-V semicondutors. [Preview Abstract] |
Wednesday, March 23, 2005 3:06PM - 3:18PM |
S32.00004: Relativistic correction to the single-particle kinetic energy term Mark Pederson, Tunna Baruah Evaluation of the relativistic kinetic energy, given by $ \sqrt{(p^2c^2+m^2c^4)}$, is one strategy that may be promising from the standpoint of approximate scalar relativistic treatments. However the square root makes it cumbersome in quantum mechanical operator form. Chandra et al. [P. Chandra et al., Chem. Phys.{\bf 84}, 1 (1984)] have shown that it is possible to derive a simplified method for evaluating the relativistic kinetic energy within a single-particle framework. In this method a finite basis set of the $p^2$ operator is used to evaluate the expectation values of the $p^2$ dependent operators. In our formulation, we use a complete basis set of the $p^2$ operator to determine a variational expression for the above operator that is useful for Gaussian-orbital-based calculations. We compare the results of the corrections to the kinetic energy obtained by our formulation with other methods such as the expansion of the kinetic energy operator method and an incomplete $p^2$ basis method. Comparison to the full Dirac equation is made for simple atoms and the importance of the Darwin term will also be discussed. [Preview Abstract] |
Wednesday, March 23, 2005 3:18PM - 3:30PM |
S32.00005: Calculation of Raman and infrared spectra by coherent-phonon stimulation Jonathan Yates, Ivo Souza We propose a novel method for the efficient first principles prediction of Infra-Red and non-resonant Raman spectra. The method is inspired by the experimental technique of impulsive- stimulated Raman scattering. We apply initial impulsive forces to the ions in the system. For IR spectroscopy these forces correspond to the first order forces induced by a static electric field; for Raman spectroscopy they are the second order forces. We show how the corresponding vibrational spectrum can be obtained from the ensuing short-time dynamics of the system. The method has better scaling with system size than existing techniques. We present applications of the method to various clusters and molecules. [Preview Abstract] |
Wednesday, March 23, 2005 3:30PM - 3:42PM |
S32.00006: Exponentially localized quasi-free-particle generalized Wannier functions Bradley A. Foreman A new class of localized basis functions is proposed as a generalization of the Wannier functions for a free particle. The basis is orthonormal and its Fourier transform is given in explicit analytical form. For large values of the coordinate ($x \rightarrow \infty$), the wave functions are localized as $\exp (-C x^{\gamma})$, where $C > 0$ and $\frac12 \le \gamma < 1$ are fixed constants (with the same value for each state in a given basis). In contrast, ordinary free-particle Wannier functions are localized only as $1/x$, while the Wannier functions for a crystal behave as $\exp (-C_n x)$, where $C_n$ vanishes as the band index $n \rightarrow \infty$. Potential applications of the theory are discussed. [Preview Abstract] |
Wednesday, March 23, 2005 3:42PM - 3:54PM |
S32.00007: Ab initio electronic structure calculations of metals by the finite element method John E. Pask, Philip A. Sterne The finite-element (FE) method is a general approach for the solution of partial differential equations. Like the planewave (PW) method, the FE method is a systematically improvable expansion approach. Unlike the PW method, however, its basis functions are strictly local in real space, which allows for variable resolution in real space and facilitates massively parallel implementation. We discuss the application of the FE method to \textit{ab initio} electronic-structure calculations of metals. In particular, we discuss the use of nonlocal pseudopotentials in crystalline calculations, the handling of long-range interactions in the construction of the Kohn-Sham effective potential and total energy, and the synthesis of the metallic charge density. We show that the total energy converges variationally and at the optimal theoretical rate consistent with the cubic completeness of the basis. [Preview Abstract] |
Wednesday, March 23, 2005 3:54PM - 4:06PM |
S32.00008: Electronic structure of Cu$_2$O within GW approximation Fabien Bruneval, Nathalie Vast, Lucia Reining It is known that density functional theory fails to predict a gap in various insulating oxides like CuO. Cu$_2$O is a good starting point to address the fundamental issue of {\it 3d} electrons of metals in oxides. This semiconductor material has indeed a cubic structure, a closed {\it d} shell, and is non-magnetic. We calculated its band structure within Density Functional Theory and GW approximation [1]. We studied the role of semicore states (3{\it s}$^2$3{\it p}$^6$) and stated that their influence is slight on the Kohn-Sham band structure, but drastic on the GW one. Even a GW calculation including semicore states largely fails with the quasiparticle gap. Further approximations are usually used to perform a ``standard" GW calculation. We extensively discuss the reliability of these technical approximations, and find that they perform well. The most dubious approximation is the equality between GW and LDA wavefunctions. Therefore, we obtained self-consistent quasiparticle wavefunctions within the static COHSEX approximation to the GW scheme. We show that subtle changes in the wavefunctions may have large effects on the different contributions to the band gap. [1] L. Hedin, Phys. Rev. {\bf 139}, A796 (1965). [Preview Abstract] |
Wednesday, March 23, 2005 4:06PM - 4:18PM |
S32.00009: Compact representation of the Green function of an infinite periodic system Jonathan E. Moussa, Marvin L. Cohen The single particle Green function of a periodic system is typically constructed by first calculating the band structure of the system and then summing up wavefunctions and energy denominators in the usual way. To construct an accurate Green function, many unoccupied bands must be included and k-points have to be sampled carefully, making use of both symmetries and approximate integration techniques. An alternate form of the Green function is presented, not based on band structures but rather local coordinate transformations. This method makes no use of Bloch's Theorem and instead exploits periodicity using renormalization-like scaling ideas. Calculations are performed with a localized basis set and the cost is demonstrated to be proportional to the log of the number of included unit cells and linearly scaling with unit cell size. \newline \newline This work was supported by National Science Foundation Grant No. DMR04-39768 and by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, U.S. Department of Energy under Contract No. DE- AC03-76SF00098. [Preview Abstract] |
Wednesday, March 23, 2005 4:18PM - 4:30PM |
S32.00010: Combining quasiparticle energy calculations with exact-exchange density-functional theory Patrick Rinke, Christoph Freysoldt, Matthias Scheffler, Abdallah Qteish, J\"org Neugebauer We present a systematic {\it ab initio} study of the electronic structure for selected II-VI compounds and group III nitrides in the zinc-blende structure with special emphasis on analysing the role played by the semicore $d$-electrons. We show that applying density-functional theory (DFT) in the exact-exchange (EXX) approach [1] leads to an improved description of the $d$-electron hybridisation compared to the local-density approximation (LDA). Moreover we find that it is essential to use the newly developed EXX pseudopotentials [2] in order to treat core-valence exchange consistenly. In combination with quasiparticle energy calculations in the $GW$ approximation we achieve very good agreement with available photoemission data. Since the DFT energies and wavefunctions serve as input for the $GW$ calculation we conclude that for these materials EXX constitutes the better starting groundstate.\\ $[$1$]$ M. St\"adele {\it et al}, Phys.\ Rev.\ Lett. {\bf 79} 2089 (1997) \\ $[$2$]$ M. Moukara {\it et al}, J.\ Phys.: Condens.\ Matter {\bf 12} 6783 (2000) [Preview Abstract] |
Wednesday, March 23, 2005 4:30PM - 4:42PM |
S32.00011: QuasiParticle Self-Consistent, $GW$ Theory Takao Kotani, Mark van Schilfgaarde, Sergey Faleev A formal justification for a new kind self-consistent {\em GW} approximation is developed. In this Landau-Silin picture the $GW$ approximation is based on the ansatz of the existence of bare quasiparticles generated from a noninteracting Hamiltonian $H_0$ and corresponding Green's function $G_0$. In this picture, electrons and holes should have real meaning; $W$ is computed from the time-dependent Hartree approximation; $\Sigma=iG_0W$ means ``exchange effect'' + electrons and holes interacting. A key issue is how to construct the optimum $H_0$. The true Green's function $G$ should have corresponding one-particle excitations, and $H_0$ should approximate the corresponding energies and eigenfunctions as well as possible. We present a prescription for $H_0$ that approximately minimizes the difference between $G^{-1}$ and $G_0^{-1}$. The theory is applied to $sp$ bonded materials, simple and transition metals, transition-metal oxides, some magnetic compounds such as MnAs and some $f$ systems (e.g. CeO$_2$, and Gd). We compare to a variety of experimental data for these different materials classes. The errors are quite small and highly systematic in $sp$ systems, they are somewhat larger but still systematic in transition-metal oxides, and are largest for Gd. Some analysis of the origin of the errors will be presented. [Preview Abstract] |
Wednesday, March 23, 2005 4:42PM - 4:54PM |
S32.00012: Band structure of wurtzite quantum dots with cylindrical symmetry Lok Lew Yan Voon, Calin Galeriu, Benny Lassen, Morten Willatzen, Roderick Melnik A six-band ${\bf k \cdot p}$ theory for wurtzite semiconductor nanostructures with cylindrical symmetry will be presented. Our work extends the formulation of Vahala and Sercel [{\it Phys. Rev. Lett.} {\bf 65}, 239 (1990)] to the Rashba-Sheka-Pikus Hamiltonian for wurtzite semiconductors, without the need for the axial approximation. Results comparing this new formulation for studying the electronic structure of wurzite GaN and CdS cylindrical quantum dots with the conventional formulation will be shown; our formulation is computationally superior. An application to the search for level crossing in the valence band of cylindrical quantum rods as a function of aspect ratio will be given. \\ \\Supported by NSF CAREER award. [Preview Abstract] |
Wednesday, March 23, 2005 4:54PM - 5:06PM |
S32.00013: Electronic Properties of Small Virtual Clusters of Ga and In with As and P atoms Liudmila Pozhar, Alan Yeates, Frank Szmulowicz, William Mitchel The electronic energy level structure (ELS) of several virtually (i.e., fundamental theory-based, computationally) pre-designed stable clusters of Ga, In, As and P atoms is investigated by means of the Hartree-Fock method and compared to that of the corresponding virtual clusters grown in vacuum. The results obtained in the course of this study confirm that the ELS and the direct optical transition energy (OTE) of the clusters are sensitive to manipulations with the covalent radii and cluster composition. Thus, a small displacement (in the range of several hundredths of Angstrom) of atoms in stable pre-designed clusters from their respective positions in vacuum clusters leads to a significant decrease in the OTE and formation of the valence and conduction bands. In agreement with previous results, the OTE for such clusters is in the range of several electron Volts and can be manipulated up to 100{\%} by manipulations with cluster parameters. [Preview Abstract] |
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S32.00014: Superbox method for order-N electronic structure calculations for very large systems Kalman Varga, S.T. Pantelides We have developed a superbox method for ab initio electronic structure calculations for very large systems. The method is applicable to density-fucntional or Hartree-Fock-based calculations. In this approach a molecule, a cluster, or a large supercell of a crystal is divided into a number of boxes. Self-consistent calculations are then carried out in parallel for each box, treating it either as a supercell or as a free unit. The wave function or the Green's function of the total system is then constructed by connecting the solutions obtained in the individual boxes by a rigorous and formally exact procedure that yields a self- consistent solution for the entire system. The method has been implemented by using the recently introduced Lagrange-function basis [1]. Examples will be presented using density functional theory to demonstrate the linear scaling of the approach with respect to the number of atoms in the system. [1] K. Varga, Z. Zhang, and S. T. Pantelides, Phys. Rev. Lett. 93, 176403 (2004). [Preview Abstract] |
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