M. C. Payne

First-principles simulation: ideas, illustrations and the CASTEP code

First-principles simulation, meaning density-functional theory calculations with plane waves and pseudopotentials, has become a prized technique in condensed-matter theory. Here I look at the basics of the suject, give a brief review of the theory, examining the strengths and weaknesses of its implementation, and illustrating some of the ways simulators approach problems through a small case study. I also discuss why and how modern software design methods have been used in writing a completely new modular version of the CASTEP code.

First principles methods using CASTEP

Abstract The CASTEP code for first principles electronic structure calculations will be described. A brief, non-technical overview will be given and some of the features and capabilities highlighted. Some features which are unique to CASTEP will be described and near-future development plans outlined.

Electronic structure, properties, and phase stability of inorganic crystals: A pseudopotential plane‐wave study

Recent developments in density functional theory (DFT) methods applicable to studies of large periodic systems are outlined. During the past three decades, DFT has become an essential part of computational materials science, addressing problems in materials design and processing. The theory allows us to interpret experimental data and to generate property data (such as binding energies of molecules on surfaces) for known materials, and also serves as an aid in the search for and design of novel materials and processes. A number of algorithmic implementations are currently being used, including ultrasoft pseudopotentials, efficient iterative schemes for solving the one-electron DFT equations, and computationally efficient codes for massively parallel computers. The first part of this article provides an overview of plane-wave pseudopotential DFT methods. Their capabilities are subsequently illustrated by examples including the prediction of crystal structures, the study of the compressibility of minerals, and applications to pressure-induced phase transitions. Future theoretical and computational developments are expected to lead to improved accuracy and to treatment of larger systems with a higher computational efficiency. c 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 895-910, 2000

Thermal contraction and disordering of the Al(110) surface

Al(110) has been studied for temperatures up to 900 K via ensemble density-functional molecular dynamics. The strong anharmonicity displayed by this surface results in a negative coefficient of thermal expansion, where the first interlayer distance decreases with increasing temperature. Very shallow channels of oscillation for the second-layer atoms in the direction perpendicular to the surface support this anomalous contraction, and provide a novel mechanism for the formation of adatom-vacancy pairs, preliminary to the disordering and premelting transition. Such characteristic behaviour originates in the free-electron-gas bonding at a loosely packed surface. [S0031-9007(99)08925-5].

Introducing ONETEP: Linear-scaling density functional simulations on parallel computers

We present ONETEP (order-N electronic total energy package), a density functional program for parallel computers whose computational cost scales linearly with the number of atoms and the number of processors. ONETEP is based on our reformulation of the plane wave pseudopotential method which exploits the electronic localization that is inherent in systems with a nonvanishing band gap. We summarize the theoretical developments that enable the direct optimization of strictly localized quantities expressed in terms of a delocalized plane wave basis. These same localized quantities lead us to a physical way of dividing the computational effort among many processors to allow calculations to be performed efficiently on parallel supercomputers. We show with examples that ONETEP achieves excellent speedups with increasing numbers of processors and confirm that the time taken by ONETEP as a function of increasing number of atoms for a given number of processors is indeed linear. What distinguishes our approach is that the localization is achieved in a controlled and mathematically consistent manner so that ONETEP obtains the same accuracy as conventional cubic-scaling plane wave approaches and offers fast and stable convergence. We expect that calculations with ONETEP have the potential to provide quantitative theoretical predictions for problems involving thousands of atoms such as those often encountered in nanoscience and biophysics.

Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons

We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, as derived from quantum mechanical calculations. The models do not have a fixed functional form and hence are capable of modeling complex potential energy landscapes. They are systematically improvable with more data. We apply the method to bulk crystals, and test it by calculating properties at high temperatures. Using the interatomic potential to generate the long molecular dynamics trajectories required for such calculations saves orders of magnitude in computational cost.

Finite basis set corrections to total energy pseudopotential calculations

A means of correcting total energy pseudopotential calculations performed using a fixed cut-off energy for the plane waves in the basis set is presented. The use of a finite set of special k-points in such a calculation will introduce errors in the total energies which decrease only slowly with increasing cut-off energy. In particular, total energy differences are not accurate unless the cut-off energy used is sufficiently large that the total energies are themselves converged. This would not be the case if a truly constant cut-off energy could be used. Unfortunately this can only be achieved by using an infinite k-point set. We have derived a correction which will explicitly eliminate these errors to give total energies which can correspond to a strictly constant cut-off energy. In this way, total energy differences and hence many physical properties can be accurately calculated using cut-off energies significantly lower than otherwise possible, with substantial savings in computational time. Total energy pseudopotential calculations can be used to determine a wide variety of physical properties of materials. Calculations are performed on periodic supercells thereby allowing the electronic wavefunctions to be expanded in terms of a discrete set of plane waves at each of an infinite set of k-points in the Brillouin zone. This in turn allows the application of the following two approximations. Firstly, a small number of carefully chosen k-points can be used to accurately represent the wavefunction at all k- points (Chadi and Cohen 1973, Monkhorst and Pack 1976), and secondly, by truncating the basis set the wavefunctions at each k-point can be expanded in terms of a finite basis set. In principle by increasing the number of k-points and the size of the basis set it is possible to achieve absolute energy convergence. However, even in the case of very small systems, this proves to be extremely computationally expensive. In order to perform calculations on larger, more complex systems it is necessary to be able to use smaller plane wave basis sets at each k-point without reducing the accuracy of the calculation. It is known that differences in the total energies of systems of the same size can be accurately calculated for numbers of plane waves and of k-points very much smaller than those required to ensure convergence of the absolute energies provided that identical basis sets are used for each calculation (Cheng et a1 1988). However, when computing energy differences between systems of varying size it is impossible to use identical plane wave basis sets unless an infinite number of k-points are used in the calculation. We must choose instead either to use a constant number of plane waves in

Chemically active substitutional nitrogen impurity in carbon nanotubes.

We investigate the nitrogen substitutional impurity in semiconducting zigzag and metallic armchair single-wall carbon nanotubes using ab initio density functional theory. At low concentrations (less than 1 at. %), the defect state in a semiconducting tube becomes spatially localized and develops a flat energy level in the band gap. Such a localized state makes the impurity site chemically and electronically active. We find that if two neighboring tubes have their impurities facing one another, an intertube covalent bond forms. This finding opens an intriguing possibility for tunnel junctions, as well as the functionalization of suitably doped carbon nanotubes by selectively forming chemical bonds with ligands at the impurity site. If the intertube bond density is high enough, a highly packed bundle of interlinked single-wall nanotubes can form.

WATER CHEMISORPTION AND RECONSTRUCTION OF THE MGO SURFACE

Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE(December 6, 1994)The observed reactivity of MgO with water is in apparent conflict with theoretical calculationswhich show that molecular dissociation does not occur on a perfect (001) surface. We have per-formed ab-initio total energy calculations which show that a chemisorption reaction involving areconstruction to form a (111) hydroxyl surface is strongly preferred with ∆E = −90.2 kJ mol

Large-scale ab initio total energy calculations on parallel computers

Abstract An implementation of a set of total energy plane-wave pseudopotential codes on a parallel computer is described which allows calculations to be performed for systems containing many hundreds of atoms in the unit cell. Possible parallelisation strategies are discussed and it is shown that assigning parts of real and Fourier space across the processors is the least restricted approach. The performance of our parallel codes is demonstrated by timing tests carried out on several i860-based parallel machines and these are compared with tests performed on conventional sequential supercomputers. Ab initio computations on systems which are beyond the power of conventional supercomputers as well as ew perspectives for first-principles molecular dynamics are discussed.