Hybrid programming-model strategies for GPU offloading of electronic structure calculation kernels.

To address the challenge of performance portability and facilitate the implementation of electronic structure solvers, we developed the basic matrix library (BML) and Parallel, Rapid O(N), and Graph-based Recursive Electronic Structure Solver (PROGRESS) library. The BML implements linear algebra operations necessary for electronic structure kernels using a unified user interface for various matrix formats (dense and sparse) and architectures (CPUs and GPUs). Focusing on density functional theory and tight-binding models, PROGRESS implements several solvers for computing the single-particle density matrix and relies on BML. In this paper, we describe the general strategies used for these implementations on various computer architectures, using OpenMP target functionalities on GPUs, in conjunction with third-party libraries to handle performance critical numerical kernels. We demonstrate the portability of this approach and its performance in benchmark problems.

On-Surface Carbon Nitride Growth from Polymerization of 2,5,8-Triazido-s-heptazine.

Carbon nitrides have recently come into focus for photo- and thermal catalysis, both as support materials for metal nanoparticles as well as photocatalysts themselves. While many approaches for the synthesis of three-dimensional carbon nitride materials are available, only top-down approaches by exfoliation of powders lead to thin-film flakes of this inherently two-dimensional material. Here, we describe an in situ on-surface synthesis of monolayer 2D carbon nitride films as a first step toward precise combination with other 2D materials. Starting with a single monomer precursor, we show that 2,5,8-triazido-s-heptazine can be evaporated intact, deposited on a single crystalline Au(111) or graphite support, and activated via azide decomposition and subsequent coupling to form a covalent polyheptazine network. We demonstrate that the activation can occur in three pathways, via electrons (X-ray illumination), via photons (UV illumination), and thermally. Our work paves the way to coat materials with extended carbon nitride networks that are, as we show, stable under ambient conditions.

High-resolution magnetization-transfer imaging of post-mortem marmoset brain: Comparisons with relaxometry and histology.

Cell membranes and macromolecules or paramagnetic compounds interact with water proton spins, which modulates magnetic resonance imaging (MRI) contrast providing information on tissue composition. For a further investigation, quantitative magnetization transfer (qMT) parameters (at 3T), including the ratio of the macromolecular and water proton pools, F, and the exchange-rate constant as well as the (observed) longitudinal and the effective transverse relaxation rates (at 3T and 7T), R1obs and R2*, respectively, were measured at high spatial resolution (200 µm) in a slice of fixed marmoset brain and compared to histology results obtained with Gallyas' myelin stain and Perls' iron stain. R1obs and R2* were linearly correlated with the iron content for the entire slice, whereas distinct differences were obtained between gray and white matter for correlations of relaxometry and qMT parameters with myelin content. The combined results suggest that the macromolecular pool interacting with water consists of myelin and (less efficient) non-myelin contributions. Despite strong correlation of F and R1obs, none of these parameters was uniquely specific to myelination. Due to additional sensitivity to iron stores, R1obs and R2* were more sensitive for depicting microstructural differences between cortical layers than F.

Reactive metal-organic interfaces studied with hard x-ray photoelectron spectroscopy: controlled formation of metalloporphyrin interphase layers during metal vapor deposition onto porphyrin films.

Interfaces between organic semiconductors and metallic layers are ubiquitous in organic (opto-) electronic devices and can significantly influence their functionality. Here, we studied in situ prepared metal-organic interfaces, which were obtained by vapor deposition of metals (Co, Fe) onto organic semiconductor films (2H-tetraphenylporphyrin), with hard x-ray photoelectron spectroscopy. In these systems, the interphase zones, which are formed by diffusion and reaction of the metal in the organic material, can be clearly distinguished spectroscopically from the unreacted organic bulk, since they comprise the corresponding metalloporphyrins, CoTPP and FeTPP. In order to gain control over the thickness of the interphase layers, we varied process parameters such as sample temperature and metal-atom flux during interface preparation. We found that the temperature of the organic film during metal deposition was the only parameter that significantly influenced the formation of the interphase layers: their thicknesses were typically ~0.5 nm for deposition at 90 K, compared to ~1 nm at 300 K, irrespective of metal atom flux and chemical nature of the metal atom (Fe versus Co). Notably, these values are significantly smaller than the thicknesses of other metal/organics interphase regions reported in the literature.

Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.

Graph-based linear scaling electronic structure theory.

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Communication: An N-body solution to the problem of Fock exchange.

We report an N-Body approach to computing the Fock exchange matrix with and without permutational symmetry. The method achieves an O(NlgN) computational complexity through an embedded metric-query, allowing hierarchical application of direct SCF criteria. The advantages of permutational symmetry are found to be 4-fold for small systems, but decreasing with increasing system size and/or more permissive neglect criteria. This work sets the stage for: (1) the introduction of range queries in multi-level multipole schemes for rank reduction, and (2) recursive task parallelism.

Extended Lagrangian free energy molecular dynamics.

Extended free energy Lagrangians are proposed for first principles molecular dynamics simulations at finite electronic temperatures for plane-wave pseudopotential and local orbital density matrix-based calculations. Thanks to the extended Lagrangian description, the electronic degrees of freedom can be integrated by stable geometric schemes that conserve the free energy. For the local orbital representations both the nuclear and electronic forces have simple and numerically efficient expressions that are well suited for reduced complexity calculations. A rapidly converging recursive Fermi operator expansion method that does not require the calculation of eigenvalues and eigenfunctions for the construction of the fractionally occupied density matrix is discussed. An efficient expression for the Pulay force that is valid also for density matrices with fractional occupation occurring at finite electronic temperatures is also demonstrated.

Extended Lagrangian Born-Oppenheimer molecular dynamics with dissipation.

Stability and dissipation in the propagation of the electronic degrees of freedom in time-reversible extended Lagrangian Born-Oppenheimer molecular dynamics [Niklasson et al., Phys. Rev. Lett. 97, 123001 (2006); Phys. Rev. Lett. 100, 123004 (2008)] are analyzed. Because of the time-reversible propagation the dynamics of the extended electronic degrees of freedom is lossless with no dissipation of numerical errors. For long simulation times under "noisy" conditions, numerical errors may therefore accumulate to large fluctuations. We solve this problem by including a dissipative external electronic force that removes noise while keeping the energy stable. The approach corresponds to a Langevin-like dynamics for the electronic degrees of freedom with internal numerical error fluctuations and external, approximately energy conserving, dissipative forces. By tuning the dissipation to balance the numerical fluctuations the external perturbation can be kept to a minimum.

Improved model for the transit entropy of monatomic liquids.

In the original formulation of vibration-transit (V-T) theory for monatomic liquid dynamics, the transit contribution to entropy was taken to be a universal constant, calibrated to the constant-volume entropy of melting. This model suffers two deficiencies: (a) it does not account for experimental entropy differences of +/-2% among elemental liquids and (b) it implies a value of zero for the transit contribution to internal energy. The purpose of this paper is to correct these deficiencies. To this end, the V-T equation for entropy is fitted to an overall accuracy of +/-0.1% to the available experimental high-temperature entropy data for elemental liquids. The theory contains two nuclear motion contributions: (a) the dominant vibrational contribution S_{vib}(T/theta_{0}) , where T is temperature and theta_{0} is the vibrational characteristic temperature, and (b) the transit contribution S_{tr}(T/theta_{tr}) , where theta_{tr} is a scaling temperature for each liquid. The appearance of a common functional form of S_{tr} for all the liquids studied is a property of the experimental data, when analyzed via the V-T formula. The resulting S_{tr} implies the correct transit contribution to internal energy. The theoretical entropy of melting is derived in a single formula applying to normal and anomalous melting alike. An ab initio calculation of theta_{0} , based on density-functional theory, is reported for liquid Na and Cu. Comparison of these calculations with the above analysis of experimental entropy data provides verification of V-T theory. In view of the present results, techniques currently being applied in ab initio simulations of liquid properties can be employed to advantage in the further testing and development of V-T theory.

Higher-order symplectic integration in Born-Oppenheimer molecular dynamics.

The extended Lagrangian formulation of time-reversible Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, C. J. Tymczak, and M. Challacombe, Phys. Rev. Lett. 100, 123004 (2008); Phys. Rev. Lett. 97, 123001 (2006)] enables the use of geometric integrators in the propagation of both the nuclear and the electronic degrees of freedom on the Born-Oppenheimer potential energy surface. Different symplectic integrators up to the sixth order have been adapted and optimized in the framework of ab initio self-consistent-field theory. It is shown how the accuracy can be significantly improved compared to a conventional Verlet integration at the same level of computational cost, in particular, for the case of very high accuracy requirements.

Recursive inverse factorization.

A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.

Dimensionality crossover in the induced magnetization of Pd layers.

The magnetic ordering of a series of samples consisting of ultrathin Fe layers embedded in Pd was investigated using the magneto-optical Kerr effect. The samples consisted of a single Fe layer with nominal thickness 0.2≤d(Fe)≤1.6 monolayers sandwiched between two 20 monolayer Pd layers. A dimensionality crossover from two dimensions to three dimensions occurs as d(Fe) is increased from 0.4 to 1.0 monolayers. First-principles calculations were performed in order to determine the magnetic profile, and we used a spin-wave quantum well model for obtaining a qualitative description of the dimensionality crossover. The results clearly prove the existence of a dimensionality crossover in the induced magnetization, opening new routes for addressing the influence of extension on order.