On the long‐range relativistic effects in the 15N NMR chemical shifts of halogenated azines

Long‐range β‐ and γ‐relativistic effects of halogens in ¹⁵N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines) are shown to be unessential for fluoro‐, chloro‐, and bromo‐derivatives (1–2 ppm in average). However, for iodocontaining compounds, β‐ and γ‐relativistic effects are important contributors to the accuracy of the ¹⁵N calculation. Taking into account long‐range relativistic effects slightly improves the agreement of calculation with experiment. Thus, mean average errors (MAE) of ¹⁵N NMR chemical shifts of the title compounds calculated at the non‐relativistic and full 4‐component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the polarizable continuum model scheme marginally improves agreement of computational results with experiment decreasing MAEs from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non‐relativistic and relativistic levels, respectively. The best result (MAE: 5.3 ppm) is achieved at the 4‐component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z with taking into account solvent effects within the polarizable continuum solvation model. The long‐range relativistic effects play a major role (of up to dozen of parts per million) in ¹⁵N NMR chemical shifts of halogenated nitrogen‐containing heterocycles, which is especially crucial for iodine derivatives. This effect should apparently be taken into account for practical purposes.     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

Physical Dimensions/Units and Universal Constants: Their Invariance in Special and General Relativity

The theory of physical dimensions and units in physics is outlined. This includes a discussion of the universal applicability and superiority of quantity equations. The International System of Units (SI) is one example thereof. By analyzing mechanics and electrodynamics, it naturally leads one, besides the dimensions of length and time, to the fundamental units of action $\mathfrak{h}$, electric charge q, and magnetic flux ?. Also, $q\times ?=\text{action}$ and $q/?=1/\text{resistance}$ are known. These results of classical physics suggests to look into the corresponding quantum aspects of q and ? (and also of $\mathfrak{h}$): The electric charge occurs exclusively in elementary charges e, whereas the magnetic flux can have any value; in specific situations, however, in superconductors of type II at very low temperatures, ? appears quantized in the form of fluxons (Abrikosov vortices). And $\mathfrak{h}$ leads, of course, to the Planck quantum h. Thus, one is directed to superconductivity and, because of the resistance, to the quantum Hall effect. In this way, the Josephson and the quantum Hall effects come into focus quite naturally. One goal is to determine the behavior of the fundamental constants in special and in general relativity.     

Defects within the landau theory: A perturbation approach

We discuss the continuum medium theory that enables us to find the defect contribution to phase transition anomalies with the use of only a few phenomenological parameters. The theory is invalid in the immediate vicinity of the phase transition temperature and for high concentration of defects. The possibilities of interpretation of experimental data on the basis of the theory are also discussed.     

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.     

Uniqueness of Solution to Systems of Elliptic Operators and Application to Asymptotic Synchronization of Linear Dissipative Systems II: Case of Multiple Feedback Dampings

In this paper, the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback dampings. They ?rst show that under the observability of a scalar equation, Kalman’s rank condition is su?cient for the uniqueness of solution to a complex system of elliptic equations with mixedobservations. The authors then establish a general theory on the asymptotic stability and the asymptotic synchronization for the corresponding evolutional system subjected to mixed dampings of various natures. Some classic models are presented to illustrate the ?eld of applications of the abstract theory.     

Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity

In our previous two works, we studied the blow-up and lifespan estimates for damped wave equations with a power nonlinearity of the solution or its derivative, with scattering damping independently. In this work, we are devoted to establishing a similar result for a combined nonlinearity. Comparing to the result of wave equation without damping, one can say that the scattering damping has no influence.     

How computational methods and relativistic effects influence the study of chemical reactions involving Ru‐NO complexes?

Two treatments of relativistic effects, namely effective core potentials (ECP) and all‐electron scalar relativistic effects (DKH2), are used to obtain geometries and chemical reaction energies for a series of ruthenium complexes in B3LYP/def2‐TZVP calculations. Specifically, the reaction energies of reduction ( A ‐ F ), isomerization ( G‐I ), and Cl⁻ negative trans influence in relation to NH₃ ( J ‐ L ) are considered. The ECP and DKH2 approaches provided geometric parameters close to experimental data and the same ordering for energy changes of reactions A ‐ L . From geometries optimized with ECP, the electronic energies are also determined by means of the same ECP and basis set combined with the computational methods: MP2, M06, BP86, and its derivatives, so as B2PLYP, LC‐wPBE, and CCSD(T) (reference method). For reactions A ‐ I , B2PLYP provides the best agreement with CCSD(T) results. Additionally, B3LYP gave the smallest error for the energies of reactions J ‐ L . © 2017 Wiley Periodicals, Inc.     

Rational design of thermoelastic damping in microresonators with phase-lagging heat conduction law

The design of thermoelastic damping (TED) affected by the phase-lagging non-Fourier heat conduction effects becomes significant but challenging for enlarging the quality factor of widely-used microresonators operating in extreme situations, including ultra-high excitation frequency and ultra-low working temperature. However, there does not exist a rational method for designing the TED in the framework of non-Fourier heat conduction law. This work, therefore, proposes a design framework to achieve low thermoelastic dissipation of microresonators governed by the phase-lagging heat conduction law. The equation of motion and the heat conduction equation for phase-lagging TED microresonators are derived first, and then the non-Fourier TED design problem is proposed. A topology optimization-based rational design method is used to resolve the design problem. What is more, a two-dimensional (2D) plain-strain-based finite element method (FEM) is developed as a solver for the topology optimization process. Based on the suggested rational design technique, numerical instances with various phase lags are investigated. The results show that the proposed design method can remarkably reduce the dissipation of microresonators by tailoring their substructures.