Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session A23: Density Functional Theory I |
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Sponsoring Units: DCOMP Chair: John Perdew, Tulane University Room: C125-C126 |
Monday, March 15, 2010 8:00AM - 8:12AM |
A23.00001: Linear-Scaling Density-Functional Theory with Tens of Thousands of Atoms: Expanding the Scope and Scale of Calculations with ONETEP A.A. Mostofi, N.D.M. Hine, P.D. Haynes ONETEP$^1$ is an {\em ab initio} electronic structure package for total energy calculations within density functional theory (DFT). It combines linear-scaling computational effort with plane-wave accuracy, through use of a systematically-convergable basis equivalent to plane-waves. We present recent progress improving the feasible scope and scale of of calculations with ONETEP. Efficient manipulation of sparse matrices (the Hamiltonian, overlap and density matrix expressed in a localized basis) is crucial to the performance of LS-DFT, and depends strongly on the suitability of the algorithms to a) the physics of the system, and b) efficient parallelization over thousands of processors. We present details of a scheme for matrix algebra employing hierarchical sparsity, optimized for calculations distributed over hundreds to thousands of parallel processors. Implementing this alongside new communications algorithms, we demonstrate a very considerable improvement in speed and parallel efficiency. We are therefore able to make calculations even for dense solid systems of tens of thousands of atoms routine, within comparably modest computational demands. This enables treatment of a range of new systems of technological interest, such as defect formation energies at grain boundaries in Al$_2$O$_3$. \\ $^1$ C-K. Skylaris {\em et al}, J.Chem. Phys. {\bf 122}, 084119 (2005). [Preview Abstract] |
Monday, March 15, 2010 8:12AM - 8:24AM |
A23.00002: Optimised local orbitals from linear-scaling density-functional theory calculations Peter Haynes, Laura Ratcliff, Gareth Conduit, Philip Avraam, Mark Robinson Total energy calculations within density-functional theory can be performed with a computational cost that scales linearly with system-size by employing a density-matrix-based description of the fictitious Kohn-Sham system and exploiting the property of nearsightedness. One class of linear-scaling methods determines the ground-state density-matrix by optimising a set of local orbitals in situ, as for example implemented in the ONETEP code, where they are referred to as ``nonorthogonal generalised Wannier functions''. This work investigates the physical significance of such orbitals and assesses whether the term Wannier function is appropriate. Band structures interpolated from these orbitals are presented and compared with those from traditional methods. It is seen that the occupied valence and low-lying conduction bands are well-described, but that states higher up in energy in the conduction band are poorly described or even absent. Changes in macroscopic polarisation are also calculated using a generalisation of the centre of charge to the nonorthogonal case. [Preview Abstract] |
Monday, March 15, 2010 8:24AM - 8:36AM |
A23.00003: Multidomain decomposition approach to large scale electronic structure calculations Kalman Varga A first-principles electronic structure calculation is presented using a domain decomposition technique. The domain decomposition leads to block tridiagonal Hamiltonian and overlap matrices. With the help of an LDL decomposition the block tridiagonal structure can be exploited and the Kohn-Sham states and/or the electron density can be calculated in an computationally efficient way. The electron density can be calculated from the Green's function or from the eigensolution obtained using subspace iteration. In both cases, the calculation of the density is divided into a series of independent computations that can be done in parallel. This approach allows us to determine tens of thousands of eigenstates with any desired accuracy. If the Kohn-Sham states are not required, the density can be calculated from the Green's function in a linearly scaling fashion. The linear scaling is achieved by using the special structure resulting from the domain decomposition and not by truncation or cutoff. [Preview Abstract] |
Monday, March 15, 2010 8:36AM - 8:48AM |
A23.00004: Acceleration of DFT calculations with dual parallel method Hidekazu Tomono, Masaru Aoki, Kazuo Tsumuraya We accelerate an \textit{ab initio} periodic DFT (Density Functional Theory) calculation using both the MPI (Message Passing Interface) and GPGPU\@. The acceleration of the calculation has been achieved by the sequence of scalar, vector, parallel, and multi-core parallel processings. This sequence has requested the modifications of computation algorithms of the \textit{ab initio} codes. For instance, periodic methods have invoked the MPI parallelization for each $k$-point calculation. Next we implement a heterogeneous multi-core processing, GPGPU (General Purpose computing on Graphics Processing Units), into a planewave based pseudopotential code. In this paper, we propose a new algorithm to implement the processing into MPI\@. We will discuss the extent of the acceleration using the two parallel methods. This talk is the extension of the earlier application of the GPGPU to a single CPU code at APS March Meeting 2009 Y13.00002. [Preview Abstract] |
Monday, March 15, 2010 8:48AM - 9:00AM |
A23.00005: Bloch-state-based interpolation -- an efficient generalization of the Shirley approach to interpolating electronic structure David Prendergast, Steven G. Louie We present an efficient generalization of the k-space interpolation scheme for electronic structure presented by E. L. Shirley, Phys. Rev. B \textbf{54}, 16464 (1996), which permits the construction of a compact k-dependent Hamiltonian using a numerically optimal basis derived from a coarse-grained set of density functional theory calculations. We provide some generalizations of the initial approach which reduce the number of required initial electronic structure calculations, enabling accurate interpolation over the entire Brillouin zone based on calculations at the zone-center only for large systems. We also generalize the representation of non-local Hamiltonians, leading to a more efficient implementation which permits the use of both norm-conserving and ultrasoft pseudopotentials in the input calculations. Numerically interpolated electronic eigenvalues with accuracy that is within 0.01 eV can be produced at very little computational cost. The approach is also applicable to other theoretical frameworks such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter equation for optical responses. [Preview Abstract] |
Monday, March 15, 2010 9:00AM - 9:12AM |
A23.00006: All-electron Hybrid Functional Treatment of Oxides using the FLAPW Method Markus Betzinger, Martin Schlipf, Christoph Friedrich, Marjana Le\v{z}ai\'c, Stefan Bl\"ugel Hybrid functionals are a practical approximation for the exchange-correlation (xc) functional of density-functional theory. They combine a local or semi-local xc functional with nonlocal Hartree-Fock (HF) exchange and improve the band gap for semiconductors and insulators as well as the description of localized states. So far, most implementations for periodic systems employ a pseudopotential planewave approach. We present an efficient all-electron implementation in the context of the FLAPW methodology realized in the {\tt FLEUR} (www.flapw.de) code. We report on the implementation of the PBE0 and HSE functionals where an auxiliary basis is constructed from products of LAPW basis functions and used to calculate the HF potential. The Coulomb matrix$^1$ then has a sparse form. Spatial and time-reversal symmetry is exploited in restricting the Brillouin zone sum in the nonlocal potential to an irreducible wedge. We give account on the efficiency of our concept and of the convergence of the self-consistency cycle. Finally we present results for a variety of oxides and compare those to results obtained with functionals based on the generalized gradient approximation. [1]\emph{ Comput. Phys. Comm. }{\bf 180}, 347 (2009) [Preview Abstract] |
Monday, March 15, 2010 9:12AM - 9:24AM |
A23.00007: Gaussian-type orbitals in \emph{ab-initio} calculations for periodic systems: Solving the so-called ``linear-dependence'' problem with efficient dual space summation Cristian Diaconu, Joachim Paier, Gustavo Scuseria Expanding single-particle wave functions in a local basis set using Gaussian-type orbitals (GTO) is well established. All-electron GTO basis sets of so-called multi-$\zeta$ quality are available for a large number of elements. However, the application of GTOs in \emph{ab-initio} calculations for periodic systems is not straightforward. Diffuse \emph{i.e.}~low-exponent basis functions are necessary for an accurate treatment of metals and small-gap semiconductors, but their use leads to the well documented problem of so-called ``linear dependence.'' However, we found out that the problem is not due to linear dependence, but rather to the vanishingly small norms of some of the Bloch functions. The present work introduces Poisson summation for alleviating this problem. Moreover, this approach will lead to a much more efficient calculation of Hamiltonian matrix elements. Exploiting the dual properties of real and momentum space, computations involving tight, \emph{i.e.}~high-exponent basis functions, are carried out in real space, whereas calculations using diffuse basis functions are carried out in Fourier space. This is what we mean with ``dual space summation''. Roughly speaking, exploiting ``the best of both worlds'', \emph{i.e.}~real as well as momentum space, can solve the technical problems incurred by the so-called ``linear-dependence'' of crystal orbitals. [Preview Abstract] |
Monday, March 15, 2010 9:24AM - 9:36AM |
A23.00008: PAW Calculations for Core Edge Specroscopy Micah Prange, Weidong Luo, Sokrates Pantelides The projector augmented wave (PAW) method is the tool of choice for density-functional calculations for bulk materials. Meanwhile, core loss spectroscopies like EELS, XAS, NRIXS, etc. are powerful experimental tools for probing the physical properties of bulk materials. Yet, despite the fact that PAW yields the all-electron Kohn-Sham wave functions, theoretical predictions of core edge fine structure within the PAW method have been limited to projected densities of states (and hence the dipole approximation). We present PAW calculations of full matrix elements of $e^{i \vec q \cdot \vec r}$ based on extensions to the VASP code. This strategy provides full-potential near-edge structure at arbitrary momentum transfer. The capability to go beyond the dipole approximation allows applications to spectroscopies for which the signal comes from large $\vec q$, like NRIXS and EELS in STEM geometry or with an off-axis detector. We compare our results to measurements as well as traditional theoretical approaches. [Preview Abstract] |
Monday, March 15, 2010 9:36AM - 9:48AM |
A23.00009: Exact conditions and scaling relations in finite temperature density functional theory Stefano Pittalis, C. R. Proetto, A. Floris, A. Sanna, C. Bersier, E. K. U. Gross Density functional theory is in principle an exact theory of electronic structure, but in practical applications the corresponding functionals need to be approximated. Accurate and efficient approximations may be developed if exact and relevant properties of the density functionals are known and taken into consideration as constraints. In this work, we present rigorous derivations of exact properties, scaling relations and virial theorems for the main quantities of finite temperature density functional theory. The scaling transformation at finite temperature is introduced and its physical meaning and consequences are elucidated. [Preview Abstract] |
Monday, March 15, 2010 9:48AM - 10:00AM |
A23.00010: DFPT approach to the temperature dependence of electronic band energies Paul Boulanger, Michel Cote, Xavier Gonze The energy bands of semiconductors exhibit significant shifts and broadening with temperature at constant volume. This is an effect of the direct renormalization of band energies due to electron-phonon interactions. In search of an efficient linear response DFT approach to this effect, beyond semi-empirical approximation or frozen- phonon DFT, we have implemented formulas derived by Allen and Heine [J. Phys. C \textbf{9}, 2305 (1976)] inside the ABINIT package. We have found that such formulas need a great number of bands, O(1000), to properly converge the thermal corrections of deep potential well atoms, i.e. elements of the first row. This leads to heavy computational costs even for simple systems like diamond. The DFPT formalism can be used to circumvent entirely the need for conduction bands by computing the first-order wave-functions using the self-consistent Sternheimer equation. We will compare the results of both formalism demonstrating that the DFPT approach reproduces the correct converged results of the formulas of Allen and Heine. [Preview Abstract] |
Monday, March 15, 2010 10:00AM - 10:12AM |
A23.00011: 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 a first-principles electronic method will be presented based on direct energy functional minimization and a bi-orthogonal wavelet basis set. The employment of a bi-orthogonal basis allows systematically controlled accuracy while benefiting from compact support that allows O(N) algorithms. Furthermore, utilization of the interpolating nature of wavelets, together with the effectiveness of the multi-resolution of wavelets enables very efficient calculation without compromising accuracy. By avoiding solving an eigenvalue equation as in the standard Kohn-Sham framework, the method is easily extended to parallel algorithms, and allows simple implementation of various non-local functionals. In the case of crystals, our method gives the solution directly as a set of 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] |
Monday, March 15, 2010 10:12AM - 10:24AM |
A23.00012: Electron-pair-density based approach to density functional theory Markus Daene, Donald Nicholson We propose a nonlocal density functional approximation motivated by consideration of the electron-pair-density. The fully interacting exchange correlation hole is approximated from the Slater electron-pair-density by utilizing coupling constant integration and the pair density as a function of coupling constant in the homogeneous electron gas. The electron-pair-density evaluated for closed shell configurations of spherical external potentials will be compared to exact results and approximate results from local density approximations. The electron-pair-density leads straightforwardly by integration to a density and its corresponding interaction energy. These quantities as a function of coupling constant allow us to discuss the quality of our approximation to the Hohenberg-Kohn functional at series of test densities drawn from spherical systems. [Preview Abstract] |
Monday, March 15, 2010 10:24AM - 10:36AM |
A23.00013: Towards the calculation of experimental spectra using linear-scaling density-functional theory Laura Ratcliff, Peter Haynes The theoretical calculation of spectra is highly useful both in understanding experimental results and making predictions about new materials. This work will combine the power of spectroscopy with the ability of linear-scaling density-functional theory (DFT) to study much larger systems than previously possible. A necessary first step involves finding a method to calculate conduction states and implementing it in \textsc{onetep}, a linear-scaling DFT code, which is currently limited to the calculation of valence states. These can then be used to calculate spectra using perturbation theory. A ``toy model'' has been created with a one-dimensional Kronig-Penney potential and a localised basis set of B-splines, which solves the generalized Schr\"odinger equation using a preconditioned conjugate gradient energy minimisation scheme, analogous to that of \textsc{onetep}. This program has been used to test the possible methods for calculating excited states before implementing in \textsc{onetep}. \\[4pt] [1] C.-K. Skylaris, P. D. Haynes, A. A. Mostofi, and M. C. Payne, J. Chem. Phys. {\bf 122}, 084119 (2005). [Preview Abstract] |
Monday, March 15, 2010 10:36AM - 10:48AM |
A23.00014: Transferability of Fragments in Partition Density Functional Theory Yu Zhang, Adam Wasserman Partition Density Functional Theory (PDFT) is a method for calculating molecular properties from Kohn-Sham calculations on isolated fragments [P. Elliott, K. Burke, M.H. Cohen, and A. Wasserman, arXiv:0901.0942]. For a given choice of fragmentation, PDFT outputs the (in principle exact) molecular energy and density, as well as fragment densities that add up to the correct molecular density. Using a simple one-dimensional model system, we investigate the transferability of the resulting fragment densities by examining how their shape and dipole are preserved as the environment changes. Our results show that the PDFT fragment densities are in general more transferable than those arising from other popular density-partitioning schemes. [Preview Abstract] |
Monday, March 15, 2010 10:48AM - 11:00AM |
A23.00015: Subsystem functional for confinement physics Feng Hao, Ann Mattsson, Rickard Armiento Recent success of the AM05 [1,2] functional shows that the subsystem functional scheme is a practical framework to construct well-performing functionals in density functional theory (DFT). The idea is to divide the real material system into regions with different characteristic physics that can be described by model systems. In AM05, subsystem functionals based on a surface model system and a uniform electron gas model system are combined to include both the edge and interior physics. By studying a harmonic oscillator model system restricted in one dimension, we are aiming to build a subsystem functional that can include ``confinement physics'' into the scheme. The new model system may help in constructing a more generally accurate functional working for both solid-state and chemical systems. 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. [1] R. Armiento, A.E. Mattsson, PRB 72, 085108 (2005), [2] A.E. Mattsson et al. JCP 128, 084714 (2008). [Preview Abstract] |
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