Integrable Couplings of the Coupled Burgers Hierarchy

In this letter, a new loop algebra G is constructed, from which a new isospectral problem is established. It follows that integrable couplings of the well-known coupled Burgers hierarchy are obtained.     

N Chemical Shift Tensor Magnitude and Orientation in the Molecular Frame of Uracil Determined via MAS NMR

The potential of heteronuclear MAS NMR spectroscopy for the characterization of ¹⁵N chemical shift (CS) tensors in multiply labeled systems has been illustrated, in one of the first studies of this type, by a measurement of the chemical shift tensor magnitude and orientation in the molecular frame for the two ¹⁵N sites of uracil. Employing polycrystalline samples of ¹⁵N₂ and 2-¹³C,¹⁵N₂-labeled uracil, we have measured, via ¹⁵N–¹³C REDOR and ¹⁵N–¹H dipolar-shift experiments, the polar and azimuthal angles (θ, ψ) of orientation of the ¹⁵N–¹³C and ¹⁵N–¹H dipolar vectors in the ¹⁵N CS tensor frame. The (θ_NC, ψ_NC) angles are determined to be (92 ± 10°, 100 ± 5°) and (132 ± 3°, 88 ± 10°) for the N1 and N3 sites, respectively. Similarly, (θ_NH, ψ_NH) are found to be (15 ± 5°, −80 ± 10°) and (15 ± 5°, 90 ± 10°) for the N1 and N3 sites, respectively. These results obtained based only on MAS NMR measurements have been compared with the data reported in the literature.     

Effect of anomalous tbW vertex on decay-lepton distributions in e + e − → tt and CP-violating asymmetries

We obtain analytic expressions for the energy and polar-angle double differential distributions of a secondary lepton l ⁺ (l ⁻) arising from the decay of t(t) in e ⁺ e ⁻ → tt with an anomalous tbW decay vertex. We also obtain analytic expressions for the various differential cross-sections with the lepton energy integrated over. In this case, we find that the angular distributions of the secondary lepton do not depend on the anomalous coupling in the decay, regardless of possible anomalous couplings occurring in the production amplitude for e ⁺ e ⁻ → tt. Our study includes the effect of longitudinal e ⁻ and e ⁺ beam polarization. We also study the lepton energy and beam polarization dependence of certain CP-violating lepton angular asymmetries arising from an anomalous tbW decay vertex and compare them with the asymmetries arising due to CP-violation in the production process due to the top electric or weak dipole moment.     

A Path Integral Molecular Dynamics Simulation of a Harpoon-Type Redox Reaction in a Helium Nanodroplet

We present path integral molecular dynamics (PIMD) calculations of an electron transfer from a heliophobic Cs2 dimer in its (3Σu) state, located on the surface of a He droplet, to a heliophilic, fully immersed C60 molecule. Supported by electron ionization mass spectroscopy measurements (Renzler et al., J. Chem. Phys. 2016, 145, 181101), this spatially quenched reaction was characterized as a harpoon-type or long-range electron transfer in a previous high-level ab initio study (de Lara-Castells et al., J. Phys. Chem. Lett. 2017, 8, 4284). To go beyond the static approach, classical and quantum PIMD simulations are performed at 2 K, slightly below the critical temperature for helium superfluidity (2.172 K). Calculations are executed in the NVT ensemble as well as the NVE ensemble to provide insights into real-time dynamics. A droplet size of 2090 atoms is assumed to study the impact of spatial hindrance on reactivity. By changing the number of beads in the PIMD simulations, the impact of quantization can be studied in greater detail and without an implicit assumption of superfluidity. We find that the reaction probability increases with higher levels of quantization. Our findings confirm earlier, static predictions of a rotational motion of the Cs2 dimer upon reacting with the fullerene, involving a substantial displacement of helium. However, it also raises the new question of whether the interacting species are driven out-of-equilibrium after impurity uptake, since reactivity is strongly quenched if a full thermal equilibration is assumed. More generally, our work points towards a novel mechanism for long-range electron transfer through an interplay between nuclear quantum delocalization within the confining medium and delocalized electronic dispersion forces acting on the two reactants.     

Measurements of Long-Range Homonuclear Coupling Constants

Coupling constants in proton systems provide access to useful structural information. Several methods have been proposed to measure these constants in high-resolution spectra, but many of them are not well suited when the coupling constants are comparable to the spectral linewidth. In such a case the measurement of the apparent splitting, obtained from conventional NMR or from two-dimensional correlation spectroscopy (COSY), can cause a miscalculation of the true coupling constant value. In this work, data processing for extracting small coupling constants is described. Signals are obtained from spin-echo experiments and analysed in the time domain in such a way that couplings are apparently multiplied by n+1, where n is positive. Small coupling constants in 4-methyl-1,3-dioxane were obtained by this method. © 1997 John Wiley & Sons, Ltd.     

Influence of the Thiophene Ring on the Molecular Order of Structurally Simple π-Conjugated Smectogens: 13C NMR Study

Structurally simple rod-like π-conjugated mesogens with thiophene directly connected to phenyl, biphenyl, and fluorenone rings with terminal chains are synthesized respectively. The occurrence of smectic A/smectic C phases is concurred by a hot-stage optical polarising microscope (HOPM), differential scanning calorimetry (DSC), and X-ray diffraction (XRD). The static 1D and 2D ¹³C nuclear magnetic resonance (NMR) studies in the liquid crystalline phase are carried out to find the alignment-induced chemical shifts (AIS) and ¹³C−¹H dipolar couplings. The orientational order parameters of the mesogens determined from ¹³C−¹H dipolar couplings disclose that the long axis is not only collinear to the C3−C4 bond of the thiophene ring but also for the local axes of phenyl and biphenyl rings. For fluorenone-based mesogen, the molecular biaxiality is found to be high owing to the increased breadth of the molecule. The study unveils that the orientation of thiophene and the phenyl rings is similar in the current mesogens in stark contrast to mesogens, where thiophene is connected to phenyl rings through linking groups.