Dynamical versus variational symmetries: understanding Noether's first theorem

It is argued that awareness of the distinction between dynamical and variational symmetries is crucial to understanding the significance of Noether's 1918 work. Special attention is paid, by way of a number of striking examples, to Noether's first theorem, which establishes a correlation between dynamical symmetries and conservation principles.     

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.     

Influence of Finite-Time Velocity Correlations on Scaling Properties of the Magnetic Field in the Kazantsev-Kraichnan Model: Two-Loop Renormalization Group Analysis

Theoretical and Mathematical Physics - Using the field theory renormalization group method and the operator product expansion technique in the two-loop approximation, we investigate the influence...     

Passive Advection in a Percolation Process: Two-Loop Approximation

Theoretical and Mathematical Physics - We study an instructive model of the directed percolation process near its second-order phase transition between absorbing and active states. We first express...     

Reversible C=C Bond Activation by an Intramolecularly Coordinated Antimony(I) Compound

The reaction of N,C,N-chelated stibinidene ArSb ( 1 ) (Ar=C₆H₃-2,6-(CH=NtBu)₂) with selected N-alkyl/aryl-maleimides RN(C(O)CH)₂ (R=Me, tBu, Ph) gave the addition products with bridged bicyclic [2.2.1] structure containing an antimony atom at the bridgehead position, fused with a 6-membered benzene and a 5-membered N-alkyl/aryl-pyrrolidine ring. These compounds were completely characterized. More importantly, additional studies showed that these reactions are reversible in solution, thereby representing an unprecedented reversible activation of a C=C bond by an antimony(I) compound.     

Photoinduced dynamics of a cyanine dye: parallel pathways of non-radiative deactivation involving multiple excited-state twisted transients

Cyanine dyes are broadly used for fluorescence imaging and other photonic applications. 3,3′-Diethylthiacyanine (THIA) is a cyanine dye composed of two identical aromatic heterocyclic moieties linked with a single methine, –CH. The torsional degrees of freedom around the methine bonds provide routes for non-radiative decay, responsible for the inherently low fluorescence quantum yields. Using transient absorption spectroscopy, we determined that upon photoexcitation, the excited state relaxes along two parallel pathways producing three excited-state transients that undergo internal conversion to the ground state. The media viscosity impedes the molecular modes of ring rotation and preferentially affects one of the pathways of non-radiative decay, exerting a dominant effect on the emission properties of THIA. Concurrently, the polarity affects the energy of the transients involved in the decay pathways and further modulates the kinetics of non-radiative deactivation.     

Disappearing Polymorphs in Metal–Organic Framework Chemistry: Unexpected Stabilization of a Layered Polymorph over an Interpenetrated Three-Dimensional Structure in Mercury Imidazolate

The “disappearing polymorph” phenomenon is well established in organic solids, and has had a profound effect in pharmaceutical materials science. The first example of this effect in metal-containing systems in general, and in coordination-network solids in particular, is here reported. Specifically, attempts to mechanochemically synthesize a known interpenetrated diamondoid (dia) mercury(II) imidazolate metal–organic framework (MOF) yielded a novel, more stable polymorph based on square-grid (sql) layers. Simultaneously, the dia-form was found to be highly elusive, observed only as a short-lived intermediate in monitoring solvent-free synthesis and not at all from solution. The destabilization of a dense dia-framework relative to a lower dimensionality one is in contrast to the behavior of other imidazolate MOFs, with periodic density functional theory (DFT) calculations showing that it arises from weak interactions, including structure-stabilizing agostic C−H⋅⋅⋅Hg contacts. While providing a new link between MOFs and crystal engineering of organic solids, these findings highlight a possible role for agostic interactions in directing topology and stability of MOF polymorphs.     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.