Discrete symmetry transformations on non-abelian gauge fields

All gauge bosons of a non-abelian gauge theory do not transform the same way under the discrete transformations of time-reversal and charge-conjugation. Moreover, the transformations rules depend on how the generators are chosen. We show how well-defined rules pertain only to specific choices of generators, and then show how unified rules can be constructed, using matrix forms of the gauge bosons, which are completely independent of the choice of generators.Comment: 10 pages, no figure, LaTe

5,11,17,23-Tetra-tert-butyl-25,26,27,28-tetra­kis[2-(2-chloro­ethoxy)eth­oxy]-2,8,14,20-tetra­sulfonyl­calix[4]arene

Mol­ecules of the title compound, C56H76Cl4O16S4, have crystallographic C 2 symmetry and adopt a 1,3-alternate conformation where the four –OCH2CH2OCH2CH2Cl groups are located alternately above and below the virtual plane (R) defined by the four bridging S atoms. The dihedral angles between the plane (R) and the phenolic rings are 72.85 (7) and 74.57 (7)°. An unusual 24-membered macrocyclic ring is formed in the crystal structure with an array of eight intra­molecular C—H⋯O hydrogen bonds between the ether arm H atoms and the sulfonyl O atoms. In the supra­molecular structure, the mol­ecular components are linked into infinite zigzag one-dimensional chains by a combination of four inter­molecular C—H⋯O hydrogen bonds, forming R 2 2(13), R 2 2(16), R 2 2(21) and R 2 2(26) ring motifs. These chains are augmented into a wave-like two-dimensional network by weak C⋯O inter­actions. One tert-butyl group shows rotational disorder, and one CH2CH2Cl group is disordered over two orientations; the site-occupation factors are 0.756 (6) and 0.244 (6) for the two tert-butyl groups, and 0.808 (3) and 0.192 (3) for the two CH2CH2Cl units

5,11,17,23-Tetra­bromo-25,26,27,28-tetra­kis(4-tolyl­sulfon­yloxy)-2,8,14,20-tetra­thia­calix[4]arene dichloro­methane solvate

In the crystal structure of the title compound, C52H36Br4O12S8·CH2Cl2, the thia­calix[4]arene unit adopts a 1,3-alternate conformation with an intra­molecular C—H⋯O hydrogen bond and four C—H⋯π inter­actions, with the four 4-MeC6H4SO3 groups located alternately above and below the virtual plane (R) defined by the four bridging S atoms. The benzene ring of each 4-MeC6H4SO3 unit is nearly perpendicular to one of the two neighboring phenol rings with inter­planar angles varying from 72.97 (13) to 78.70 (13)°, while the dihedral angles between the plane (R) and the phenol rings range from 83.04 (7) to 84.30 (9)°. In the supra­molecular structure, a solvent-bridged dimer composed of two main mol­ecules is formed by four inter­molecular C—H⋯O hydrogen bonds and locally creates an R 4 4(26) motif. Such dimers associate further into chains by inter­dimer C—Cl⋯O short contacts [Cl⋯O 3.182 (5) Å]. Finally, these chains are linked into a two-dimensional network by a combination of inter­chain C—Br⋯O inter­actions [Br⋯O = 3.183 (3) and 2.966 (4) Å] as well as C—H⋯O hydrogen bonds

Intramolecular co-operative hydrogen bond in calix[n]arenes (n = 4, 6, 8) bearing bulky substituents

Based on the Fourier transform IR spectroscopy together with the published NMR and X-ray data, it was shown that cyclic co-operative intramolecular hydrogen bond in calix[n]arene (n = 4, 6, 8) molecules is mainly responsible for their conformational state irrespective of the presence or absence of bulky substituents at the upper rim of the molecules. In accordance with the size of a macrocycle (n = 4, 6, 8), the stable conformation, secured by such a hydrogen bond, constitutes a cone, a pinched cone, and a pleated loop, respectively. The new, potentially competing system of hydrogen bonds in calix[6]arenes with 3-carboxymethyl-1-adamantyl substituents does not affect the conformational state of the macrocycle and its H-bonding. Six carboxy groups at the upper rim form in pairs three cyclic dimers, which does not disturb the hydrogen bonds of the hydroxy groups and the conformation of the macrocycle. In addition, the cavity of the molecule is considerably enlarged. The removal or rearrangement of the guest molecules in the solid calixarene by heating up to 180 °C only slightly affects the conformational state of macrocycles bearing bulky substituents, whereas in calixarenes devoid of such substituents, the similar procedure leads to somewhat of a distortion of the macrocycles (judging from the IR spectral indications of hydrogen bonding). © 2007 Springer Science+Business Media, Inc

Synthesis and evaluation of a novel pyrenyl-appended triazole-based thiacalix[4]arene as a fluorescent sensor for Ag+ ion

New fluorescent chemosensors 1,3-alternate-1 and 2 with pyrenyl-appended triazole-based on thiacalix[4]arene were synthesized. The fluorescence spectra changes suggested that chemosensors 1 and 2 are highly selective for Ag+ over other metal ions by enhancing the monomer emission of pyrene in neutral solution. However, other heavy metal ions, such as Cu2+, and Hg2+ quench both the monomer and excimer emission of pyrene acutely. The 1H NMR results indicated that Ag+ can be selectively recognized by the triazole moieties on the receptors 1 and 2 together with the ionophoricity cavity formed by the two inverted benzene rings and sulfur atoms of the thiacalix[4]arene