1H-1,3-Diazepines, 5H-1,3-diazepines, 1,3-diazepinones, and 2,4-diazabicyclo[3.2.0]heptenes

Tetrazolo[1,5-a] pyridines/ 2-azidopyridines 1 undergo photochemical nitrogen elimination and ring expansion to 1,3-diazacyclohepta-1,2,4,6-tetraenes 3, which react with alcohols to afford 2-alkoxy-1H-1,3-diazepines 4 (5), with secondary amines to 2-dialkylamino-5H-1,3-diazepines 16, sometimes via isolable 2-dialkylamino-1H-1,3-diazepines 15, and with water to 1,3-diazepin-2-ones 19. The latter are also obtained by elimination of isobutene or propene from 2-tert-butoxy- or 2-isopropoxy-1H-1,3-diazepines 4 or 5. 1,3-Diazepin-2-one 22B and 1,3-diazepin-4-one 24 were obtained from hydrolysis of the corresponding 4-chlorodiazepines. Diazepinones 19 undergo photochemical ring closure to diazabicycloheptenones 25 in high yields. The 2-alkoxy-1H-1,3-diazepines 4 and 5 interconvert by rapid proton exchange between positions N1 and N3. The free energies of activation for the proton exchange were measured by the Forsen - Hoffman method as DeltaGdouble dagger(298) = 16.2 +/- 0.6 kcal mol(-1) as an average for 4a - c in CD2Cl2, acetone-d(6), and methanol-d(4), and 14.1 +/- 0.6 kcal mol(-1) for 4c in acetone/D2O. The structures of 2-methoxy-5,6-bis( trifluoromethyl)-1H-1,3-diazepine 4k, 1,2-dihydro-4-diethylamino-5H-1,3-diazepin-2-one 22bB, and diazabicycloheptanone 26 were determined by X-ray crystallography. The former represents the first reported X-ray crystal structure of any monocyclic N-unsubstituted 1H-azepine.

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping 6 away from half-filling, finite-system density-matrix renormalizationgroup (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k(F) and 4k(F) for the currents and densities, where 2k(F) = pi(1 - delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities. (c) 2005 Elsevier Inc. All rights reserved.