Linear-scaling DFT-pseudopotential calculations on parallel computers

Goringe, C. M.; Hernández, Eduardo; Gillan, M. J.; Bush, Ian J.

doi:10.1016/s0010-4655(97)00029-5

Cited by 64 publications

(71 citation statements)

References 38 publications

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“…onetep belongs to the category of methods that aim for high accuracy by optimising self-consistently the energy not only with respect to K but also with respect to the NGWFs 15,16,17,18,19,20 . In onetep the NGWFs are expanded in a basis set of periodic cardinal sine (psinc) functions 13,21 , also known as Dirichlet or Fourier Lagrange-mesh functions 22,23 .…”

Section: Overview Of Theorymentioning

confidence: 99%

Using ONETEP for accurate and efficient density functional calculations

Skylaris¹,

Haynes²,

Mostofi³

et al. 2005

J. Phys.: Condens. Matter

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We present a detailed comparison between onetep, our linear-scaling density functional method, and the conventional pseudopotential plane wave approach in order to demonstrate its high accuracy. Further comparison with all-electron calculations shows that only the largest available Gaussian basis sets can match the accuracy of routine onetep calculations. Results indicate that our minimisation procedure is not ill-conditioned and that convergence to self-consistency is achieved efficiently. Finally we present calculations with onetep, on systems of about 1000 atoms, of electronic, structural and chemical properties of a wide variety of materials such as metallic and semiconducting carbon nanotubes, crystalline silicon and a protein complex.

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Section: Overview Of Theorymentioning

confidence: 99%

Using ONETEP for accurate and efficient density functional calculations

Skylaris¹,

Haynes²,

Mostofi³

et al. 2005

J. Phys.: Condens. Matter

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“…In the CONQUEST code used here (for technical details, see refs. [15][16][17][18], the DFT ground state is found by minimizing the total energy with respect to ðr; r 0 Þ, subject to being idempotent and yielding the correct electron number. The density matrix is assumed to be separable, so that ðr; r 0 Þ ¼ P i; j i ðrÞK i; j j ðr 0 Þ, where LETTERS i ðrÞ are localized orbitals (th orbital on ith atom), confined within spherical regions of radius R reg centred on the atoms (positions R i ).…”

mentioning

confidence: 99%

The Energetics of Hut-Cluster Self-Assembly in Ge/Si(001) from Linear-Scaling DFT Calculations

et al. 2008

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Density functional theory (DFT) in a linear-scaling implementation is used to study the energetics of three-dimensional (3D) Ge islands (hut clusters) grown on Si(001) surface. DFT calculations on the fully relaxed energies of a series of hut clusters of increasing size are reported, finding a 2D to 3D cross-over near three monolayers; the number of atoms in the largest simulated system is over 20,000. A variety of technical issues which are important in addressing the accuracy and validity of the calculations are described and assessed. The results suggest that energetics alone is responsible for the initial transition from 2D to 3D growth. Self-assembly is one of the major routes to the formation of surface nanostructures (quantum dots, nanowires, etc.), but our understanding of the underlying processes is limited. In the initial stages of growth, structures which are metastable and whose formation is dominated by kinetic effects can often form before the energetically stable structure; 1) this is particularly true on semiconductor surfaces where the interplay between strain and electronic energies compete to give a rich variety of one-dimensional 2) and two-dimensional (2D) structures.3) Atomistic modeling based on electronic structure theory has a key role to play in this area, but progress depends on addressing a number of issues, including accuracy, the scaling of computer effort with system size, the control of computational artefacts, and the sampling of energetically competing geometries. The much studied system of self-assembled Ge hut clusters on Si (001) 4,5) serves as a paradigm where modeling encounters all these issues. We describe here how we have used OðNÞ (linear-scaling) density-functional theory (DFT) to tackle these questions.Ge hut clusters, which have a pyramid-like shape, are formed when Ge is deposited epitaxially on Si(001): the first few monolayers (ML) grow two-dimensionally, forming a 2 Â N missing-dimer reconstruction which relieves the strain from the 4.2% lattice mismatch between Ge and Si. Subsequently, three-dimensional (3D) islands form, 6) their edges lying along the elastically soft (100) and (010) directions. The coverage at which huts appear depends on substrate temperature, deposition rate and the presence or absence of hydrogen, because these affect the diffusion rates on the surface as well as the amount of Ge/Si alloying. The lowest coverage at which huts appear is $3 ML. STM measurements show that the hut clusters have four (105) facets; details of the Ge(105) surface reconstruction have been elucidated by combining STM measurements and DFT calculations. 7,8) However, the mechanisms underlying hut formation are not understood; in particular, the energetic balance between strain, surface energy and the energies of edges between facets is subtle, and may be subject to kinetic effects. Such balances are important even for simple surface reconstructions, and will be crucial for small sizes of hut cluster.Attempts have been made to model semiconductor nanostructures using e...

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“…This form of sparse blocked matrix is common to many linear-scaling electronic structure implementations. [21][22][23] Note that the number of row elements may differ from the number of column elements for a given atom to allow treatment of nonsquare matrices such as the overlap matrix between NGWFs and projectors.…”

Section: B Parallel Distribution Of Sparse Matrix Algebramentioning

confidence: 99%

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra

Hine

Haynes

Mostofi

et al. 2010

The Journal of Chemical Physics

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We present calculations of formation energies of defects in an ionic solid ͑Al 2 O 3 ͒ extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.

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Linear-scaling DFT-pseudopotential calculations on parallel computers

Cited by 64 publications

References 38 publications

Using ONETEP for accurate and efficient density functional calculations

Using ONETEP for accurate and efficient density functional calculations

The Energetics of Hut-Cluster Self-Assembly in Ge/Si(001) from Linear-Scaling DFT Calculations

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra

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