Methyl rotational tunneling dynamics of p-xylene confined in a crystalline zeolite host

The methyl rotational tunneling spectrum of p-xylene confined in nanoporous zeolite crystals has been measured by inelastic neutron scattering (INS) and proton nuclear magnetic resonance (NMR), and analyzed to extract the rotational potential energy surfaces characteristic of the methyl groups in the host-guest complex. The number and relative intensities of the tunneling peaks observed by INS indicate the presence of methyl-methyl coupling interactions in addition to the methyl-zeolite interactions. The INS tunneling spectra from the crystals (space group P2(1)2(1)2(1) with four crystallographically inequivalent methyl rotors) are quantitatively interpreted as a combination of transitions involving two coupled methyl rotors as well as a transition involving single-particle tunneling of a third inequivalent rotor, in a manner consistent with the observed tunneling energies and relative intensities. Together, the crystal structure and the absence of additional peaks in the INS spectra suggest that the tunneling of the fourth inequivalent rotor is strongly hindered and inaccessible to INS measurements. This is verified by proton NMR measurements of the spin-lattice relaxation time which reveal the tunneling characteristics of the fourth inequivalent rotor.     

Synthese und Struktur hochfunktionalisierter 2, 3‐Dihydro‐1H‐1, 3, 2‐diazaborole

Synthesis and Structure of Highly Functionalized 2, 3‐Dihydro‐1H‐1, 3, 2‐diazaboroles A series of differently substituted 2, 3‐dihydro‐1H‐1, 3, 2‐diazaboroles has been prepared by various methods. 1, 3‐Di‐tert‐butyl‐2‐trimethylsilylmethyl‐1H‐1, 3, 2‐diazaborole ( 7 ), 2‐isobutyl‐1, 3‐bis(1‐cyclohexylethyl)‐1H‐1, 3, 2‐diazaborole ( 8 ), 1, 3‐bis‐(1‐cyclohexylethyl)‐2‐trimethylsilylmethyl‐1H‐1, 3, 2‐diazaborole ( 9 ) 1, 3‐bis(1‐methyl‐1‐phenyl‐propyl)‐2‐trimethylsilylmethyl‐1H‐1, 3, 2diazaborole ( 10 ) and 2‐bromo‐1, 3‐bis(1‐methyl‐1‐phenyl‐propyl)‐1H‐1, 3, 2‐diazaborole ( 11 ) were formed by reaction of the corresponding 1, 4‐diazabutadienes with the boranes Me₃SiCH₂BBr₂, iBuBBr₂ and BBr₃ followed by reduction of the resulting borolium salts [R¹ = tBu, Me(cHex)CH, [Me(Et)Ph]C; R² = Me₃SiCH₂, iBu, Br] with sodium amalgam. Treatment of 11 and 12 with silver cyanide afforded the 2‐cyano‐1, 3, 2‐diazaboroles 13 and 14 . An alternative route to compound 8 is based on the alkylation of 2‐bromo‐1, 3, 2‐diazaborole 12 with isobutyllithium. Equimolar amounts of 13 and isobutyllithium give rise to the formation of 15 . The new compounds were characterized by ¹H‐, ¹³C‐, ¹¹B‐NMR, IR and mass spectra. The molecular structures of 7 and meso ‐10 were confirmed by x‐ray structural analysis.     

Theorems of Stein-Rosenberg type. III. The singular case

In the theory of iterative methods, the classical Stein-Rosenberg theorem can be viewed as giving the simultaneous convergence (or divergence) of the extrapolated Jacobi (JOR) matrix J_ω and the successive overrelaxation (SOR) matrix

, in the case when the Jacobi matrix J₁ is nonnegative. As has been established recently by Buoni and Varga, necessary and sufficient conditions for the simultaneous convergence (or divergence) of J_ω and

have been established which do not depend on the assumption that J₁ is nonnegative. Our aim here is to extend these results to the singular case, using the notion of semiconvergence. In particular, for a real singular matrix A with nonpositive off-diagonal entries, we find conditions (Theorem 3.4) which imply that J_ω and

simultaneously semiconverge for all ω in the real interval [0,1).