Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations

We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are $i)$ valid in the pre-asymptotic regime; $ii)$ solely depend on the geometry and the polynomial order; and $iii)$ are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order ($p = 1, 2, 3, 4$) hierarchic $H(\mathrm{curl})$-conforming polynomial basis functions

Estimating DNA coverage and abundance in metagenomes using a gamma approximation

Motivation: Shotgun sequencing generates large numbers of short DNA reads from either an isolated organism or, in the case of metagenomics projects, from the aggregate genome of a microbial community. These reads are then assembled based on overlapping sequences into larger, contiguous sequences (contigs). The feasibility of assembly and the coverage achieved (reads per nucleotide or distinct sequence of nucleotides) depend on several factors: the number of reads sequenced, the read length and the relative abundances of their source genomes in the microbial community. A low coverage suggests that most of the genomic DNA in the sample has not been sequenced, but it is often difficult to estimate either the extent of the uncaptured diversity or the amount of additional sequencing that would be most efficacious. In this work, we regard a metagenome as a population of DNA fragments (bins), each of which may be covered by one or more reads. We employ a gamma distribution to model this bin population due to its flexibility and ease of use. When a gamma approximation can be found that adequately fits the data, we may estimate the number of bins that were not sequenced and that could potentially be revealed by additional sequencing. We evaluated the performance of this model using simulated metagenomes and demonstrate its applicability on three recent metagenomic datasets

Accurate Treatment of Large Supramolecular Complexes by Double-Hybrid Density Functionals Coupled with Nonlocal van der Waals Corrections

In this work, we present a thorough assessment of the performance of some representative double-hybrid density functionals (revPBE0-DH-NL and B2PLYP-NL) as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly interacting molecular systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogeneous set of reference interaction energies was computed for the supramolecular complexes constituting the L7 and S12L data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (for the S12L set) have been crucial for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the density functionals evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate association energies very close to the chemical accuracy. Overall, the NL van der Waals approach combined with proper density functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly bonded supramolecular systems.Financial support by the “Ministerio de Economía y Competitividad” (MINECO) of Spain and European FEDER funds through projects CTQ2011-27253 and CTQ2012-31914 is acknowledged. The support of the Generalitat Valenciana (Prometeo/2012/053) is also acknowledged. J.A. thanks the EU for the FP7-PEOPLE-2012-IEF-329513 grant. J.C. acknowledges the “Ministerio de Educación, Cultura y Deporte” (MECD) of Spain for a predoctoral FPU grant

Preparation and Characterization of 1-(5-Azido-1H-1,2,4-triazol-3-yl)tetrazole

This study presents the preparation of 1-(5-azido-1H-1,2,4-triazol-3yl)tetrazole (5) from commercially available chemicals in a five step synthesis. The energetic title compound was comprehensively characterized by various means, including vibrational (IR, Raman) and multinuclear (1H, 13C, 14N, 15N) NMR spectroscopy, mass spectrometry and differential scanning calorimetry. The sensitivities towards various outer stimuli (impact, friction) were determined according to BAM standards. The enthalpy of formation was calculated at the CBS-4M level of theory

Systematic High-Accuracy Prediction of Electron Affinities for Biological Quinones

Quinones play vital roles as electron carriers in fundamental biological processes; therefore, the ability to accurately predict their electron affinities is crucial for understanding their properties and function. The increasing availability of cost‐effective implementations of correlated wave function methods for both closed‐shell and open‐shell systems offers an alternative to density functional theory approaches that have traditionally dominated the field despite their shortcomings. Here, we define a benchmark set of quinones with experimentally available electron affinities and evaluate a range of electronic structure methods, setting a target accuracy of 0.1 eV. Among wave function methods, we test various implementations of coupled cluster (CC) theory, including local pair natural orbital (LPNO) approaches to canonical and parameterized CCSD, the domain‐based DLPNO approximation, and the equations‐of‐motion approach for electron affinities, EA‐EOM‐CCSD. In addition, several variants of canonical, spin‐component‐scaled, orbital‐optimized, and explicitly correlated (F12) Møller–Plesset perturbation theory are benchmarked. Achieving systematically the target level of accuracy is challenging and a composite scheme that combines canonical CCSD(T) with large basis set LPNO‐based extrapolation of correlation energy proves to be the most accurate approach. Methods that offer comparable performance are the parameterized LPNO‐pCCSD, the DLPNO‐CCSD(T0), and the orbital optimized OO‐SCS‐MP2. Among DFT methods, viable practical alternatives are only the M06 and the double hybrids, but the latter should be employed with caution because of significant basis set sensitivity. A highly accurate yet cost‐effective DLPNO‐based coupled cluster approach is used to investigate the methoxy conformation effect on the electron affinities of ubiquinones found in photosynthetic bacterial reaction centers. © 2018 Wiley Periodicals, Inc

High-order accurate discontinuous Galerkin method for the indefinite time-harmonic Maxwell equations

We introduce a high-order accurate discontinuous Galerkin (DG) method for the indefinite frequency-domain Maxwell equations in three spatial dimensions. The novelty of the method lies in the way the numerical flux is computed. Instead of using the more popular local discontinuous Galerkin (LDG) or interior-penalty discontinuous Galerkin (IP-DG) numerical fluxes, we opt for a formulation which makes use of the local lifting operator. This allows us to choose a penalty parameter that is independent of the mesh size and the polynomial order. Moreover, we use a hierarchic construction of $H$(curl)-conforming basis functions, the first-order version of which correspond to the second family of Nédélec elements. We also provide a priori error bounds for our formulation, and carry out three-dimensional numerical experiments to validate the theoretical results