Characteristic Numbers of Matrix Lie Algebras

A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.     

The multicomponent discrete equation hierarchy with variable spectral parameters and a new integrable coupling system

This Letter reports on a study of the multicomponent discrete integrable equation hierarchy with variable spectral parameters. An instance of new multicomponent lattice equation is obtained. Correspondingly, a feasible way to construct the integrable couplings is presented. It indicates that the study of integrable couplings using the block matrix-form of Lie algebra is an important and effective method.     

Influence of stereoelectronic effects on the 1JC─F spin–spin coupling constant in fluorinated heterocyclic compounds

The Perlin effect and its analog for fluorinated compounds (the fluorine Perlin-like effect) manifest on one-bond C─H (C─F for the fluorine Perlin-like effect) spin–spin coupling constants (SSCCs) in six-membered rings. These effects can be useful to probe the stereochemistry (axial or equatorial) of the C─H and C─F bonds, respectively. The origin of these effects has been debatable in the literature as being due to hyperconjugative interactions, dipolar effects, and induced current density. Accordingly, a variety of model compounds has been used to probe such effects since the cyclohexanone carbonyl group and the endocyclic heteroatom lone pairs play different roles on the above-mentioned effects. Thus, the ¹J_C─F SSCC in fluorinated lactams and lactones were theoretically studied to gain further insight on the nature of the fluorine Perlin-like effect. In addition, because the intramolecular α-effect has recently gained attention for its importance in the reactivity and stereoelectronic interactions in peroxide compounds, some fluorinated 1,2-dioxanes and 1,2-dithianes were studied to evaluate the role of the α-effect on the behavior of ¹J_C─F SSCCs. Differently from fluorinated ketones and ethers, the fluorine Perlin-like effect in the amides and esters cannot be explained by hyperconjugative or dipolar interactions alone, because the resonance in these groups affect the ¹J_C─F values. The O─O and S─S-containing systems exhibit a strong fluorine Perlin-like effect, but unlike the α-effect, this behavior cannot be explained neither by hyperconjugation nor by dipolar interactions alone; the spatial proximity of the C─F and O─O/S─S bonds is proposed to affect the magnitude of the ¹J_C─F SSCC.     

Asymmetric Total Synthesis of (−)‐Englerin A through Catalytic Diastereo‐ and Enantioselective Carbonyl Ylide Cycloaddition

An asymmetric total synthesis of the guaiane sesquiterpene (?)‐englerin A, a potent and selective inhibitor of the growth of renal cancer cell lines, was accomplished. The basis of the approach is a highly diastereo‐ and enantioselective carbonyl ylide cycloaddition with an ethyl vinyl ether dipolarophile under catalysis by dirhodium(II) tetrakis[N‐tetrachlorophthaloyl‐(S)‐tert‐leucinate], [Rh₂(S‐TCPTTL)₄], to construct the oxabicyclo[3.2.1]octane framework with concomitant introduction of the oxygen substituent at C9 on the exo‐face. Another notable feature of the synthesis is ruthenium tetraoxide‐catalyzed chemoselective oxidative conversion of C9 ethyl ether to C9 acetate.     

Synthesis of μ2-Oxo-Bridged Iron(III) Tetraphenylporphyrin–Spacer–Nitroxide Dimers and their Structural and Dynamics Characterization by using EPR and MD Simulations

Iron(III) porphyrins have the propensity to form μ₂-oxo-dimers, the structures of which resemble two wheels on an axle. Whereas their crystal structure is known, their solution structure and internal dynamics is not. In the present work, the structure and dynamics of such dimers were studied by means of electron paramagnetic resonance (EPR) spectroscopy and quantum chemistry based molecular dynamics (MD) simulations by using the semiempirical tight-binding method (GFN-xTB). To enable EPR investigation of the dimers, a nitroxide was attached to each of the tetraphenylporphyrin cores through a linear and a bent linker. The inter-nitroxide distance distributions within the dimers were determined by continuous-wave (cw)-EPR and pulsed electron–electron double resonance (PELDOR or DEER) experiments and, with the help of MD, interpreted in terms of the rotation of the porphyrin planes with respect to each other around the Fe–O–Fe axis. It was found that such rotation is restricted to the four registers defined by the phenyl substituents. Within the registers, the rotation angle swings between 30° and 60° in the proximal and between 125° and 145° in the distal register. With EPR, all four angles were found to be equally populated, whereas the 30° and 145° angles are strongly favored to the expense of the 60° and 125° angles in the MD simulation. In either case, the internal dynamics of these dimers thus resemble the motion of a step motor.     

Collection of NMR Scalar and Residual Dipolar Couplings Using a Single Experiment

A new DMSO‐compatible aligning gel based on cross‐linked poly(2‐hydroxylethyl methacrylate) (poly‐HEMA) has been developed. Due to a significant difference in bulk magnetic susceptibility between the DMSO inside and outside the gel, it is possible to simultaneously collect isotropic and anisotropic NMR data, such as residual dipolar couplings (RDC), in the same NMR tube. RDC‐assisted structural analysis of menthol and the alkaloid retrorsine is reported as proof of concept.     

Two Histidines in an α‐Helix: A Rigid Co2+‐Binding Motif for PCS Measurements by NMR Spectroscopy

Pseudocontact shifts (PCS) generated by paramagnetic metal ions present valuable long‐range information in the study of protein structural biology by nuclear magnetic resonance (NMR) spectroscopy. Faithful interpretation of PCSs, however, requires complete immobilization of the metal ion relative to the protein, which is difficult to achieve with synthetic metal tags. We show that two histidine residues in sequential turns of an α‐helix provide a binding site for a Co²⁺ ion, which positions the metal ion in a uniquely well‐defined and predictable location. Exchange between the bound and free cobalt is slow on the timescale defined by chemical shifts, but the NMR resonance assignments are nonetheless readily transferred from the diamagnetic to the paramagnetic NMR spectrum by an I_zS_z‐exchange experiment. The double‐histidine‐Co²⁺ motif offers a straightforward, inexpensive, and convenient way of generating precision PCSs in proteins.     

Stereoselective Total Synthesis of Hetisine‐type C20‐Diterpenoid Alkaloids: Spirasine IV and XI

The first total synthesis of the architecturally complex hetisine‐type heptacyclic C₂₀‐diterpenoid alkaloids (±)‐spirasine IV and XI is reported. The A/F/G/C tetracyclic skeleton with the challenging N?C6 and C14?C20 linkages was efficiently constructed by an intramolecular azomethine‐ylide‐based 1,3‐dipolar cycloaddition with unusual regioselectivity. SmI₂‐mediated free‐radical addition to the arene moiety without prior dearomatization and a stereoselective intramolecular aldol reaction further enabled rapid access to the hetisine core, providing a bicyclo[2.2.2]octane ring with a new oxygen substitution pattern.     

High‐Temperature and High‐Energy‐Density Dipolar Glass Polymers Based on Sulfonylated Poly(2,6‐dimethyl‐1,4‐phenylene oxide)

A new class of high‐temperature dipolar polymers based on sulfonylated poly(2,6‐dimethyl‐1,4‐phenylene oxide) (SO₂‐PPO) was synthesized by post‐polymer functionalization. Owing to the efficient rotation of highly polar methylsulfonyl side groups below the glass transition temperature (T_g≈220 °C), the dipolar polarization of these SO₂‐PPOs was enhanced, and thus the dielectric constant was high. Consequently, the discharge energy density reached up to 22 J cm^?3. Owing to its high T_g , the SO₂‐PPO₂₅ sample also exhibited a low dielectric loss. For example, the dissipation factor (tan δ) was 0.003, and the discharge efficiency at 800 MV m^?1 was 92 %. Therefore, these dipolar glass polymers are promising for high‐temperature, high‐energy‐density, and low‐loss electrical energy storage applications.