Linear-scaling first-principles study of a quasicrystalline molecular material

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Generating optimized Fourier interpolation routines for density function theory using SPIRAL

© 2015 IEEE.Upsampling of a multi-dimensional data-set is an operation with wide application in image processing and quantum mechanical calculations using density functional theory. For small up sampling factors as seen in the quantum chemistry code ONETEP, a time-shift based implementation that shifts samples by a fraction of the original grid spacing to fill in the intermediate values using a frequency domain Fourier property can be a good choice. Readily available highly optimized multidimensional FFT implementations are leveraged at the expense of extra passes through the entire working set. In this paper we present an optimized variant of the time-shift based up sampling. Since ONETEP handles threading, we address the memory hierarchy and SIMD vectorization, and focus on problem dimensions relevant for ONETEP. We present a formalization of this operation within the SPIRAL framework and demonstrate auto-generated and auto-tuned interpolation libraries. We compare the performance of our generated code against the previous best implementations using highly optimized FFT libraries (FFTW and MKL). We demonstrate speed-ups in isolation averaging 3x and within ONETEP of up to 15%

Accurate ionic forces and geometry optimization in linear-scaling density-functional theory with local orbitals

Linear scaling methods for density-functional theory (DFT) simulations are formulated in terms of localized orbitals in real space, rather than the delocalized eigenstates of conventional approaches. In local-orbital methods, relative to conventional DFT, desirable properties can be lost to some extent, such as the translational invariance of the total energy of a system with respect to small displacements and the smoothness of the potential-energy surface. This has repercussions for calculating accurate ionic forces and geometries. In this work we present results from onetep, our linear scaling method based on localized orbitals in real space. The use of psinc functions for the underlying basis set and on-the-fly optimization of the localized orbitals results in smooth potential-energy surfaces that are consistent with ionic forces calculated using the Hellmann-Feynman theorem. This enables accurate geometry optimization to be performed. Results for surface reconstructions in silicon are presented, along with three example systems demonstrating the performance of a quasi-Newton geometry optimization algorithm: an organic zwitterion, a point defect in an ionic crystal, and a semiconductor nanostructure.<br/

Real-space grid representation of momentum and kinetic energy operators for electronic structure calculations

We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis set, the discrete coordinate eigenkets $\vert x_n\rangle$ defined on the uniform grid $x_n=na$. Simple closed form expressions of the matrix elements are obtained starting from integrals involving the canonical commutation rule. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method

Computational prediction of L_{3} EXAFS spectra of gold nanoparticles from classical molecular dynamics simulations

We present a computational approach for the simulation of extended x-ray absorption fine structure (EXAFS) spectra of nanoparticles directly from molecular dynamics simulations without fitting any of the structural parameters of the nanoparticle to experimental data. The calculation consists of two stages. First, a molecular dynamics simulation of the nanoparticle is performed and then the EXAFS spectrum is computed from “snapshots” of structures extracted from the simulation. A probability distribution function approach calculated directly from the molecular dynamics simulations is used to ensure a balanced sampling of photoabsorbing atoms and their surrounding scattering atoms while keeping the number of EXAFS calculations that need to be performed to a manageable level. The average spectrum from all configurations and photoabsorbing atoms is computed as an Au L3-edge EXAFS spectrum with the FEFF 8.4 package, which includes the self-consistent calculation of atomic potentials. We validate and apply this approach in simulations of EXAFS spectra of gold nanoparticles with sizes between 20 and 60 Å. We investigate the effect of size, structural anisotropy, and thermal motion on the gold nanoparticle EXAFS spectra and we find that our simulations closely reproduce the experimentally determined spectra

Fitting EXAFS data using molecular dynamics outputs and a histogram approach

The estimation of metal nanoparticle diameter by analysis of extended x-ray absorption fine structure (EXAFS) data from coordination numbers is nontrivial, particularly for particles &lt;5 nm in diameter, for which the undercoordination of surface atoms becomes an increasingly significant contribution to the average coordination number. These undercoordinated atoms have increased degrees of freedom over those within the core of the particle, which results in an increase in the degree of structural disorder with decreasing particle size. This increase in disorder, however, is not accounted for by the standard means of EXAFS analysis, where each coordination shell is fitted with a single bond length and disorder term. In addition, the surface atoms of nanoparticles have been observed to undergo a greater contraction than those in the core, further increasing the range of bond distances. Failure to account for this structural change results in an increased disorder being measured, and therefore, a lower apparent coordination number and corresponding particle size are found. Here, we employ molecular dynamics (MD) simulations for a range of nanoparticle sizes to determine each of the nearest neighbor bond lengths, which were then binned into a histogram to construct a radial distribution function (RDF). Each bin from the histogram was considered to be a single scattering path and subsequently used in fitting the EXAFS data obtained for a series of carbon-supported platinum nanoparticles. These MD-based fits are compared with those obtained using a standard fitting model using Artemis and the standard model with the inclusion of higher cumulants, which has previously been used to account for the non-Gaussian distribution of neighboring atoms around the absorber. The results from all three fitting methods were converted to particle sizes and compared with those obtained from transmission electron microscopy (TEM) and x-ray diffraction (XRD) measurements. We find that the use of molecular dynamics simulations resulted in an improved fit over both the standard and cumulant models, in terms of both quality of fit and correlation with the known average particle size

Library Reader Issue 04: The eBook Edge

Library resource awareness poster covering electronic books, Kill A Wat energy meters, and Staff Pick Rome.https://dune.une.edu/libraryreader/1003/thumbnail.jp

Linear-scaling density-functional theory with tens of thousands of atoms: Expanding the scope and scale of calculations with ONETEP

ONETEP is an ab initio electronic structure package for total energy calculations within density-functional theory. It combines ‘linear scaling’, in that the total computational effort scales only linearly with system size, with ‘plane-wave’ accuracy, in that the convergence of the total energy is systematically improvable in the manner typical of conventional plane-wave pseudopotential methods. We present recent progress on improving the performance, and thus in effect the feasible scope and scale, of calculations with ONETEP on parallel computers comprising large clusters of commodity servers. Our recent improvements make calculations of tens of thousands of atoms feasible, even on fewer than 100 cores. Efficient scaling with number of atoms and number of cores is demonstrated up to 32,768 atoms on 64 cores.<br/

Pulay forces from localized orbitals optimized in situ using a psinc basis set

In situoptimization of a set of localized orbitals with respect to a systematically improvable basis set independent of the position of the atoms, such as psinc functions, would theoretically eliminate the correction due to Pulay forces from the total ionic forces. We demonstrate that for strict localization constraints, especially with small localization regions, there can be non-negligible Pulay forces that must be calculated as a correction to the Hellmann-Feynman forces in the ground state. Geometry optimization calculations, which rely heavily upon accurate evaluation of the total ionic forces, show much better convergence when Pulay forces are included. The more conventional case, where the local orbitals remain fixed to pseudo-atomic orbital multiple-ζ basis sets, also benefits from this implementation. We have validated the method on several test cases, including a DNA fragment with 1045 atoms

Preconditioned iterative minimization for linear-scaling electronic structure calculations

Linear-scaling electronic structure methods are essential for calculations on large systems. Some of these approaches use a systematic basis set, the completeness of which may be tuned with an adjustable parameter similar to the energy cut-off of plane-wave techniques. The search for the electronic ground state in such methods suffers from an ill-conditioning which is related to the kinetic contribution to the total energy and which results in unacceptably slow convergence. We present a general preconditioning scheme to overcome this ill-conditioning and implement it within our own first-principles linear-scaling density functional theory method. The scheme may be applied in either real space or reciprocal space with equal success. The rate of convergence is improved by an order of magnitude and is found to be almost independent of the size of the basis