Robust multilevel methods for quadratic finite element anisotropic elliptic problems

This paper discusses a class of multilevel preconditioners based on approximate block factorization for conforming finite element methods employing quadratic trial and test functions. The main focus is on diffusion problems governed by a scalar elliptic partial differential equation with a strongly anisotropic coefficient tensor. The proposed method provides a high robustness with respect to non‐grid‐aligned anisotropy, which is achieved by the interaction of the following components: (i) an additive Schur complement approximation to construct the coarse‐grid operator; (ii) a global block (Jacobi or Gauss–Seidel) smoother complementing the coarse‐grid correction based on (i); and (iii) utilization of an augmented coarse grid, which enhances the efficiency of the interplay between (i) and (ii). The performed analysis indicates the high robustness of the resulting two‐level method. Moreover, numerical tests with a nonlinear algebraic multilevel iteration method demonstrate that the presented two‐level method can be applied successfully in the recursive construction of uniform multilevel preconditioners of optimal or nearly optimal order of computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.     

Structures of Highly Twisted Amides Relevant to Amide N−C Cross‐Coupling: Evidence for Ground‐State Amide Destabilization

Herein, we show that acyclic amides that have recently enabled a series of elusive transition‐metal‐catalyzed N?C activation/cross‐coupling reactions are highly twisted around the N?C(O) axis by a new destabilization mechanism of the amide bond. A unique effect of the N‐glutarimide substituent, leading to uniformly high twist (ca. 90°) irrespective of the steric effect at the carbon side of the amide bond has been found. This represents the first example of a twisted amide that does not bear significant steric hindrance at the α‐carbon atom. The ¹⁵N NMR data show linear correlations between electron density at nitrogen and amide bond twist. This study strongly supports the concept of amide bond ground‐state twist as a blueprint for activation of amides toward N?C bond cleavage. The new mechanism offers considerable opportunities for organic synthesis and biological processes involving non‐planar amide bonds.     

Adhesive fracture of heterogeneous interfaces

We have studied the effect of interface heterogeneity on fracture, at both local and global scales. The single cantilever beam adhesion test was used to investigate interfacial fracture between polycarbonate plates and an elastic/fragile epoxy adhesive. Two surface treatments were applied to a (given) polycarbonate plate giving zones of strong and weak adhesion parallel to the crack direction. Calculated fracture energies differed from those expected from a simple rule-of-mixtures. A perturbation method, proposed by Rice, was used and results compared with crack fronts observed in situ. The technique was applied successfully but the difference in values of stress intensity factor between the zones was found substantially different from the experimental value. In an attempt to explain discrepancies, specimens with discontinuous crack fronts (adhesive and/or plates severed along the strong/weak adhesion frontier) were tested. Good agreement was found with the rule-of-mixtures predictions raising questions about the role of crack front continuity in load transfer.     

Strategies to synthesize a new glyphosate tetrazole analogue

The specific synthesis of a new glyphosate tetrazole analogue with pesticidal properties is reported.     

Experimental and Theoretical Evidence of Spin-Orbit Heavy Atom on the Light Atom 1H NMR Chemical Shifts Induced through H⋅⋅⋅I− Hydrogen Bond

Spin-orbit (SO) heavy-atom on the light-atom (SO-HALA) effect is the largest relativistic effect caused by a heavy atom on its light-atom neighbors, leading, for example, to unexpected NMR chemical shifts of ¹H, ¹³C, and ¹⁵N nuclei. In this study, a combined experimental and theoretical evidence for the SO-HALA effect transmitted through hydrogen bond is presented. Solid-state NMR data for a series of 4-dimethylaminopyridine salts containing I⁻, Br⁻ and Cl⁻ counter ions were obtained experimentally and by theoretical calculations. A comparison of the experimental chemical shifts with those calculated by a standard DFT methodology without the SO contribution to the chemical shifts revealed a remarkable error of the calculated proton chemical shift of a hydrogen atom that is in close contact with the iodide anion. The addition of the relativistic SO correction in the calculations significantly improves overall agreement with the experiment and confirms the propagation of the SO-HALA effect through hydrogen bonds.     

Electrophilicity Scale of Activated Amides: 17O NMR and 15N NMR Chemical Shifts of Acyclic Twisted Amides in N−C(O) Cross-Coupling

The structure and properties of amides are of tremendous interest in organic synthesis and biochemistry. Traditional amides are planar and the carbonyl group non-electrophilic due to n_N→π*_C=O conjugation. In this study, we report electrophilicity scale by exploiting ¹⁷O NMR and ¹⁵N NMR chemical shifts of acyclic twisted and destabilized acyclic amides that have recently received major attention as precursors in N-C(O) cross-coupling by selective oxidative addition as well as precursors in electrophilic activation of N-C(O) bonds. Most crucially, we demonstrate that acyclic twisted amides feature electrophilicity of the carbonyl group that ranges between that of acid anhydrides and acid chlorides. Furthermore, a wide range of electrophilic amides is possible with gradually varying carbonyl electrophilicity by steric and electronic tuning of amide bond properties. Overall, the study quantifies for the first time that steric and electronic destabilization of the amide bond in common acyclic amides renders the amide bond as electrophilic as acid anhydrides and chlorides. These findings should have major implications on the fundamental properties of amide bonds.     

Validating additive correction schemes against gradient-based extrapolations

The use of additive correction schemes to obtain structures and vibrational frequencies of increasingly larger molecules is becoming more common. Such approaches, based on the cubic extrapolation formula applied directly to the quantity of interest, have been successfully validated only at the highest levels of computational accuracy: for coupled cluster methods with comparably large basis sets. Here, a systematic validation of geometries and vibrational frequencies is carried out, including more affordable and relevant levels of theory, such as the Møller-Plesset perturbation theory applied with smaller basis sets. Comparisons of such additive schemes against the more rigorous gradient-based extrapolation are presented. The cbs () routine of the open-source quantum-chemistry package Psi4 has been extended for this purpose. The results confirm that geometries and frequencies of covalently bound species obtained with additive correction schemes are in an excellent agreement with the results of gradient-based extrapolations. However, when applied to systems involving noncovalent interactions, the errors due to such schemes are significantly larger. In general, we propose the application of gradient-based extrapolations, as they incur no extra cost compared to additive schemes.