Recent progress in linear-scaling density functional calculations with plane waves and pseudopotentials: the ONETEP code

Structural properties of silicon-germanium and germanium-silicon core-shell nanowires

Core-shell nanowires made of Si and Ge can be grown experimentally with excellent control for different sizes of both core and shell. We have studied the structural properties of Si/Ge and Ge/Si core-shell nanowires aligned along the [Formula: see text] direction, with diameters up to 10.2 nm and varying core to shell ratios, using linear scaling density functional theory. We show that Vegard's law, which is often used to predict the axial lattice constant, can lead to an error of up to 1%, underlining the need for a detailed ab initio atomistic treatment of the nanowire structure. We analyse the character of the intrinsic strain distribution and show that, regardless of the composition or bond direction, the Si core or shell always expands. In contrast, the strain patterns in the Ge shell or core are highly sensitive to the location, composition and bond direction. The highest strains are found at heterojunction interfaces and the surfaces of the nanowires. This detailed understanding of the atomistic structure and strain paves the way for studies of the electronic properties of core-shell nanowires and investigations of doping and structure defects.

Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

O(N) methods in electronic structure calculations

Linear-scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high-performance computers. The linear-scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas are then discussed. The applications of linear-scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear-scaling methods are discussed.

Systematically improvable optimized atomic basis sets for ab initio calculations

We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the spillage of the wavefunctions between the atomic orbital calculations and the converged plane wave results for dimer systems. The quality of the bases can be systematically improved by increasing the size of the bases within the same framework. We show that the spillage can describe the convergency of the total energy very well and the cutoff radii of the atomic orbitals are extremely important for the quality of the atomic orbitals. The scheme is easy to implement and very flexible. We have performed extensive tests of this scheme for a wide variety of systems, including semiconductors, oxides, metals, clusters, etc. The results show that the obtained atomic bases are very satisfactory for both accuracy and transferability.

Large-scale first principles and tight-binding density functional theory calculations on hydrogen-passivated silicon nanorods

We present a computational study by density functional theory (DFT) of entire silicon nanorods with up to 1648 atoms without any periodicity or symmetry imposed. The nanorods have been selected to have varying aspect ratios and levels of surface passivation with hydrogen. The structures of the nanorods have been optimized using a density functional tight-binding approach, while energies and electronic properties have been computed using linear-scaling DFT with plane-wave accuracy with the ONETEP (Skylaris et al 2005 J. Chem. Phys. 122 084119) program. The aspect ratio and surface passivation (1×1 and 2×1 reconstructions) along with the size of the nanorods which leads to quantum confinement along all three dimensions, significantly affect their electronic properties. The structures of the nanorods also show interesting behaviour as, depending on their characteristics, they can in certain areas retain the structure of bulk silicon while in other parts significantly deviate from it.

Simulating functional magnetic materials on supercomputers

The recent passing of the petaflop per second landmark by the Roadrunner project at the Los Alamos National Laboratory marks a preliminary peak of an impressive world-wide development in the high-performance scientific computing sector. Also, purely academic state-of-the-art supercomputers such as the IBM Blue Gene/P at Forschungszentrum Jülich allow us nowadays to investigate large systems of the order of 10(3) spin polarized transition metal atoms by means of density functional theory. Three applications will be presented where large-scale ab initio calculations contribute to the understanding of key properties emerging from a close interrelation between structure and magnetism. The first two examples discuss the size dependent evolution of equilibrium structural motifs in elementary iron and binary Fe-Pt and Co-Pt transition metal nanoparticles, which are currently discussed as promising candidates for ultra-high-density magnetic data storage media. However, the preference for multiply twinned morphologies at smaller cluster sizes counteracts the formation of a single-crystalline L1(0) phase, which alone provides the required hard magnetic properties. The third application is concerned with the magnetic shape memory effect in the Ni-Mn-Ga Heusler alloy, which is a technologically relevant candidate for magnetomechanical actuators and sensors. In this material strains of up to 10% can be induced by external magnetic fields due to the field induced shifting of martensitic twin boundaries, requiring an extremely high mobility of the martensitic twin boundaries, but also the selection of the appropriate martensitic structure from the rich phase diagram.

Including dispersion interactions in the ONETEP program for linear-scaling density functional theory calculations

While density functional theory (DFT) allows accurate quantum mechanical simulations from first principles in molecules and solids, commonly used exchange-correlation density functionals provide a very incomplete description of dispersion interactions. One way to include such interactions is to augment the DFT energy expression by damped London energy expressions. Several variants of this have been developed for this task, which we discuss and compare in this paper. We have implemented these schemes in the ONETEP program, which is capable of DFT calculations with computational cost that increases linearly with the number of atoms. We have optimized all the parameters involved in our implementation of the dispersion correction, with the aim of simulating biomolecular systems. Our tests show that in cases where dispersion interactions are important this approach produces binding energies and molecular structures of a quality comparable with high-level wavefunction-based approaches.