Literatur

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Topological charge quantization via path integration: An application of the Kustaanheimo-Stiefel transformation

The unified treatment of the Dirac monopole, the Schwinger monopole, and the Aharonov-Bohm problem by Barut and Wilson is revisited via a path integral approach. The Kustaanheimo-Stiefel transformation of space and time is utilized to calculate the path integral for a charged particle in the singular vector potential. In the process of dimensional reduction, a topological charge quantization rule is derived, which contains Dirac's quantization condition as a special case.

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On the Scope of a Prins‐Type Cyclization of Oxonium Ions

The Prins cyclization of an aldehyde 1 with a homoallylic alcohol 2 , affording tetrahydro‐2H‐pyrans 4 via the oxonium ion 3 as central intermediate, was conceptually transferred to (alk‐3‐enyloxy)acrylates 6 , which form a related oxonium ion 7 upon treatment with acids (Scheme 1). The scope and utility of this modification of the Prins‐type cyclization of oxonium ions is discussed exemplarily by means of the syntheses of ten tetrahydro‐2H‐pyran and tetrahydrofuran derivatives, featuring diverse substitution patterns as well as different degrees of molecular complexity. These target structures include (±)‐ethyl (2RS)‐2‐[(2RS,4SR,6RS)‐ and (2SR,4RS,6SR)‐2‐tetahydro‐4‐hydroxy‐6‐methylpyran‐2‐yl]propanoate ( 23 ), (±)‐ethyl [(2RS, 3RS)‐tetrahydro‐3‐isopropenylfuran‐2‐yl]acetate ( 32 ), (±)‐ethyl (2Z)‐3‐(tetrahydro‐2,2‐dimethylfuran‐3‐yl)acrylate ( 37 ), (±)‐(3aRS,6RS, 7aRS)‐octahydro‐7a‐methylbenzofuran‐6‐yl formate ( 42 ), (±)‐ethyl (2RS,3RS,4aRS,8SR,8aRS)‐hexahydro‐2,5,5,8‐tetramethyl‐7‐oxo‐2H,5H‐pyrano[4,3‐b]pyran‐3‐carboxylate ( 48 ), and (±)‐ethyl (2RS,3RS,6SR)‐tetrahydro‐6‐(2‐methoxy‐2‐oxoethyl)‐3‐methyl‐2H‐pyran‐2‐carboxylate ( 53 ) (see Schemes 3 and 5–8). Besides the stereochemistry and mechanistic details of this versatile oxonium‐ion cyclization, the synthesis of suitable starting materials is also described.     

Controlling dimensionality of silver(I) coordination networks with rigid aliphatic amino ligands: from a 2D to a 3D network of unprecedented topology comprising helical channels

Ligand-directed 2D and 3D Ag(I) coordination networks are self-assembled from the rigid, topologically related tri-amino ligands cis-3,5-diaminopiperidine (cis-dapi) and cis,trans-1,3,5-triaminocyclohexane (trans-tach), yielding two networks of differing dimensionality including a 3D network of unprecedented topology comprising helical channels.     

Two-photon spectroscopy of dipole-forbidden transitions

We have investigated the applicability of CNDO/S-type methods for the calculation of optical spectra of molecules with the special implication that the calculations should not only describe the intense, dipole-allowed transitions which dominate the one-photon absorption spectrum but also those transitions which are one-photon forbidden in first-order approximation. We show that such a method is well suited to predict dipole allowed and dipole forbidden transitions at a similar level of accuracy if double excited configurations are taken into account. In spite of the lack of perfect pairing in NDO methods there are still two types of states which exhibit a different sensitivity towards correlation effects. Therefore, the approximation by which we describe the R-dependence of the Coulomb repulsion gains much more importance than in cases where mainly dipole allowed transitions are of interest. These findings confirm results obtained earlier from theories for which the pairing theorem is valid. The calculated data show an excellent stability with respect to further increase of the number of configurations if at least about 200 energy selected configurations are taken into account.     

One-pot multi-step synthesis: a challenge spawning innovation

Creating one-pot synthetic routes is a challenge that is already spawning new chemistry, enzymes, materials, and mechanistic insight. Through one-pot reactions, the chemical products that add value to our lives can be produced with less waste and greater economic benefits. Within this Emerging Area, we describe models for designing one-pot reactions as well as advanced catalysts created to facilitate their realization.     

On the structure of non-superconducting YBa2Cu3O6+ɛ

The crystal structure of non-superconducting, tetragonal YBa₂Cu₃O₆₊ ( close to 0) (s.g.P4/mmm) was studied at room temperature by means of single crystal X-ray diffraction, electron microscopy and electron diffraction. Crystals may easily be obtained by heating YBa₂Cu₃O₇ samples under vacuum. For 0, the tetragonal single crystals are chemically and crystallographically homogeneous — without any twin domains. The only defects immediately apparent are stacking faults alongc. The structure is very closely related to that of the high-T _c superconductor YBa₂Cu₃O₇. The most important difference is, that the oxygen on theb-axis (O(1)), which together with Cu(1) forms Cu–O–Cu–O-chains alongb in YBa₂Cu₃O₇, is vacant in YBa₂Cu₃O₆. Some crystals show a superstructure with superstructure reflections which are sharp in thea ^*–a ^*-plane but form diffuse streaks alongc ^*. We propose a model which relates these superstructure reflections to a 2-dimensional ordering of residual oxygen atoms on the O(1) site (corresponding to >0 in the chemical formula YBa₂Cu₃O₆₊).