Plane Wave Electronic Structure Calculations Research Articles

Practical Error Bounds for Properties in Plane-Wave Electronic Structure Calculations

We propose accurate computable error bounds for quantities of interest in plane-wave electronic structure calculations, in particular ground-state density matrices and energies, and interatomic forces. These bounds are based on an estimation of the error in terms of the residual of the solved equations, which is then efficiently approximated with computable terms. After providing coarse bounds based on an analysis of the inverse Jacobian, we improve on these bounds by solving a linear problem in a small dimension that involves a Schur complement. We numerically show how accurate these bounds are on a few representative materials, namely silicon, gallium arsenide and titanium dioxide.

Speeding up plane-wave electronic-structure calculations using graphics-processing units

We report on a source-code modification of the density-functional program suite VASP which benefits from the use of graphics-processing units (GPUs). For the electronic minimization needed to achieve the ground state using an implementation of the blocked Davidson iteration scheme (EDDAV), speed-ups of up to 3.39 on S1070 devices or 6.97 on a C2050 device were observed when calculating an ion–conductor system of actual research interest. Concerning the GPU specialty – memory throughput – the low double-precision performance forms the bottleneck on the S1070, whereas on Fermi cards the code reaches 61.7% efficiency while not suffering from any accuracy losses compared to well-established calculations performed on a central processing unit (CPU). The algorithmic bottleneck was found to be the multiplication of rectangular matrices. An initial idea to solve this problem is given.

New eigensolvers for large-scale nanoscience simulations

We present results for applications to nanosystems of state-of-the-art iterative eigensolvers based on conjugate gradients and variants of Davidson in the context of semi-empirical plane wave electronic structure calculations. We are concerned with the computation of electronic and optical properties of nanosystems using the Energy SCAN method to compute interior eigenstates around the band gap that determine their properties. Numerically, this interior Hermitian eigenvalue problem poses several challenges, with respect to both accuracy and efficiency. All the iterative eigensolvers are seeking the minimal eigenvalues of the folded operator with reference shift in the band-gap. The tested methods include standard conjugate-gradient (CG)-based Rayleigh quotient minimization, Locally optimal block-preconditioned CG (LOBPCG) and two variants of the (Jacobi-)Davidson method: JDQMR and GD+1. Our experimental results indicated that Davidson-type methods are often the fastest.

An efficient 3-dim FFT for plane wave electronic structure calculations on massively parallel machines composed of multiprocessor nodes

Three-dimensional Fast Fourier Transforms (FFTs) are the main computational task in plane wave electronic structure calculations. Obtaining a high performance on a large numbers of processors is non-trivial on the latest generation of parallel computers that consist of nodes made up of a shared memory multiprocessors. A non-dogmatic method for obtaining high performance for such 3-dim FFTs in a combined MPI/OpenMP programming paradigm will be presented. Exploiting the peculiarities of plane wave electronic structure calculations, speedups of up to 160 and speeds of up to 130 Gflops were obtained on 256 processors.

Ab initio calculation of electron affinities of diamond surfaces

Diamond surfaces combine chemical inertness with, in some cases, a negative electron affinity. Such surfaces have great potential for use on cold cathodes in flat displays. We present ab initio plane wave electronic structure calculations which enable us to predict the electron affinities of many different diamond surfaces with various terminations and reconstructions. Such calculations give good accuracy and enable the study of perfect surfaces with a range of terminating species so that the effect of the passifying layer can be readily seen. Results for the (1 0 0) and (1 1 1) surfaces will be presented, giving a range of surfaces more comprehensive than previously published. We find that the electron affinity varies by over 5.5 V between oxygen and hydrogen coverings, and that this magnitude of variation can be understood as simply a rising from surface dipoles as polarised covalent bonds would be expected to produce. A brief discussion of some of the technical points of performing such a calculation is given, which combines ab initio LDA work with experimental results for the band gap for diamond in order to estimate accurately the position of the unoccupied levels.

Population analysis in plane wave electronic structure calculations

Plane wave basis sets are widely used in ab initio electronic structure calculations even though such an expansion in terms of extended states does not provide a natural way of quantifying local atomic properties. To overcome this deficiency we have implemented a scheme for projection of plane wave states onto a localised basis set. This approach is used to calculate atomic charges and bond populations, and is illustrated by application to a selection of small molecules. Finally, we calculate the changes in these quantities induced by adsorption of a molecule onto a zeolite substrate. Thus, using the procedure described in this paper, plane wave calculations can yield the same information as traditional quantum chemical methods.

Population analysis in plane wave electronic structure calculations

Plane wave basis sets are widely used in ab initio electronic structure calculations even though such an expansion in terms of extended states does not provide a natural way of quantifying local atomic properties. To overcome this deficiency we have implemented a scheme for projection of plane wave states onto a localised basis set. This approach is used to calculate atomic charges and bond populations, and is illustrated by application to a selection of small molecules. Finally, we calculate the changes in these quantities induced by adsorption of a molecule onto a zeolite substrate. Thus, using the procedure described in this paper, plane wave calculations can yield the same information as traditional quantum chemical methods.

Plane-wave electronic-structure calculations on a parallel supercomputer.

The development of iterative solutions of Schrodinger`s equation in a plane-wave (pw) basis over the last several years has coincided with great advances in the computational power available for performing the calculations. These dual developments have enabled many new and interesting condensed matter phenomena to be studied from a first-principles approach. The authors present a detailed description of the implementation on a parallel supercomputer (hypercube) of the first-order equation-of-motion solution to Schrodinger`s equation, using plane-wave basis functions and ab initio separable pseudopotentials. By distributing the plane-waves across the processors of the hypercube many of the computations can be performed in parallel, resulting in decreases in the overall computation time relative to conventional vector supercomputers. This partitioning also provides ample memory for large Fast Fourier Transform (FFT) meshes and the storage of plane-wave coefficients for many hundreds of energy bands. The usefulness of the parallel techniques is demonstrated by benchmark timings for both the FFT`s and iterations of the self-consistent solution of Schrodinger`s equation for different sized Si unit cells of up to 512 atoms.

Correction [to “Linearized augmented plane wave electronic structure calculations for MgO and CaO” by M. J. Mehl, R. E. Cohen, and H. Krakauer

Correction [to “Linearized augmented plane wave electronic structure calculations for MgO and CaO” by M. J. Mehl, R. E. Cohen, and H. Krakauer

Linearized augmented plane wave electronic structure calculations for MgO and CaO

We present full‐potential self‐consistent linearized augmented plane wave (LAPW) calculations for the electronic structure and total energy of MgO and CaO, within the local density approximation. Calculated equilibrium properties are in good agreement with experiment. We also consider the transition from the low‐pressure sodium chloride (B1) structure to the high‐pressure cesium chloride (B2) structure for MgO and CaO and the transition to the NiAs (B8) structures for MgO. In calcium oxide we find that the B1‐B2 transition occurs at 54 GPa, in agreement with the experiment. In magnesium oxide a transition from B1 to B2 is found at 510 GPa. This is a factor of 2 lower than found by a previous pseudopotential calculation. We find no transition to the B8 structure at any pressure. The calculated charge densities of MgO and CaO are very close to the charge densities calculated from the overlap of spherical ions used in the potential induced breathing (PIB) model at zero pressure. More significant deviations from overlapping ions are found at extreme pressures. Near equilibrium, the error in the PIB model (compared to the LAPW calculation) is of the same order as the error in the LAPW calculation (compared to the experiment).

Electronic properties of BaO on W(001)

In order to better understand the mechanisms responsible for the lowering of the work function that is observed when surface layers containing barium and oxygen are adsorbed on refractory metals such as tungsten, we have initiated a series of full-potential linearized augmented plane wave electronic structure calculations on well-defined model systems representing the Ba–O/W interface. We report here our initial results for a model in which c(2×2) overlayers of upright BaO molecules have been positioned on both sides of a five-layer W(001) film. Three independent self-consistent calculations were performed involving two different Ba–O separations and two different distances between planes of Ba and surface W atoms. We find that the work function of the clean five-layer tungsten slab (4.65 eV) is lowered by ∼1.8–2 eV by the adsorption of the Ba–O surface layer in this geometry, and that this result is relatively insensitive to the Ba–O separation in the overlayer. The most important factor determining the value of the work function seems to be the position of the barium plane above the W substrate. We find evidence of significant bonding between the d-like surface states of the tungsten substrate and both the Ba d and the oxygen 2p adsorbate levels. As a result, multiple dipoles are formed at the interface and the competition between these polarized charge distributions leads to a net lowering of the work function.