Ethyl 4-(4-chlorophenyl)-6-methyl-2-thioxo-1,2,3,4-tetrahydropyrimidine-5-carboxylate

In the title compound, C14H15ClN2O2S, the tetrahydropyrimidine ring adopts a twisted boat conformation with the carbonyl group in an s-trans conformation with respect to the C C double bond of the six-membered tetrahydropyrimidine ring. The molecular conformation is determined by an intramolecular C-H center dot center dot center dot pi interaction. The crystal structure is further stabilized by intermolecular N-H center dot center dot center dot O molecular chains and centrosymmetric N-H center dot center dot center dot S dimers.

Pi-turns in proteins and peptides: Classification, conformation, occurrence, hydration and sequence.

The i + 5-->i hydrogen bonded turn conformation (pi-turn) with the fifth residue adopting alpha L conformation is frequently found at the C-terminus of helices in proteins and hence is speculated to be a "helix termination signal." An analysis of the occurrence of i + 5-->i hydrogen bonded turn conformation at any general position in proteins (not specifically at the helix C-terminus), using coordinates of 228 protein crystal structures determined by X-ray crystallography to better than 2.5 A resolution is reported in this paper. Of 486 detected pi-turn conformations, 367 have the (i + 4)th residue in alpha L conformation, generally occurring at the C-terminus of alpha-helices, consistent with previous observations. However, a significant number (111) of pi-turn conformations occur with (i + 4)th residue in alpha R conformation also, generally occurring in alpha-helices as distortions either at the terminii or at the middle, a novel finding. These two sets of pi-turn conformations are referred to by the names pi alpha L and pi alpha R-turns, respectively, depending upon whether the (i + 4)th residue adopts alpha L or alpha R conformations. Four pi-turns, named pi alpha L'-turns, were noticed to be mirror images of pi alpha L-turns, and four more pi-turns, which have the (i + 4)th residue in beta conformation and denoted as pi beta-turns, occur as a part of hairpin bend connecting twisted beta-strands. Consecutive pi-turns occur, but only with pi alpha R-turns. The preference for amino acid residues is different in pi alpha L and pi alpha R-turns. However, both show a preference for Pro after the C-termini. Hydrophilic residues are preferred at positions i + 1, i + 2, and i + 3 of pi alpha L-turns, whereas positions i and i + 5 prefer hydrophobic residues. Residue i + 4 in pi alpha L-turns is mainly Gly and less often Asn. Although pi alpha R-turns generally occur as distortions in helices, their amino acid preference is different from that of helices. Poor helix formers, such as His, Tyr, and Asn, also were found to be preferred for pi alpha R-turns, whereas good helix former Ala is not preferred. pi-Turns in peptides provide a picture of the pi-turn at atomic resolution. Only nine peptide-based pi-turns are reported so far, and all of them belong to pi alpha L-turn type with an achiral residue in position i + 4. The results are of importance for structure prediction, modeling, and de novo design of proteins.

2-[2-(Cyclohexylcarbonyl)phenyl]-1-phenylethanone

The title diketone, C21H22O2, features a phenylene ring having benzoylmethyl and cyclohexanoyl substituents ortho to each other. The cyclohexyl ring adopts a chair conformation with the ketonic group occupying an equatorial position; the four-atom -C(O)-C ketonic unit is twisted out of the plane of the phenylene ring by 34.9 (1)degrees.

Ethyl 2,6-dichloro-4-phenylquinoline-3-carboxylate

In the title compound,C18H13Cl2NO2,the quinoline ring system is almost planar (r.m.s.deviation 0.009 angstrom), and the phenyl and carboxylate planes are twisted away from it by 59.2 (1)and 65.9 (2)degrees,respectively.

Ethyl 6-chloro-2-oxo-4-phenyl-1,2-dihydroquinoline-3-carboxylate

In the title compound,C18H14ClNO3,the dihydroquinolin-2-one ring system is almost planar (r.m.s.deviation = 0.033 angstrom).The carboxylate plane and the phenyl group are twisted away from the dihydroquinolin-2-one ring system by 50.3(1) and 64.9(1)degrees,respectively.In the crystal structure, inversion-related molecules form R-2(2)(8)dimers via pairs of N-H center dot center dot center dot O hydrogen bonds.

Harmonic Analysis On Heisenberg Nilmanifolds

In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Gammakslash}H-n. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L-2 (Gammakslash}H-n) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and characterise the image of L-2 (GammakslashH-n) in terms of twisted Bergman and Hermite Bergman spaces.

5-Phenyl-3-(2-thienyl)-1,2,4-triazolo[3,4-a]isoquinoline

In the title molecule, C20H13N3S, the triazoloisoquinoline ring system is approximately planar, with an r.m.s. deviation of 0.045 angstrom and a maximum deviation of 0.090 (2) angstrom from the mean plane for the triazole ring C atom which is bonded to the thiophene ring. The phenyl ring is twisted by 52.0 (1)degrees with respect to the mean plane of the triazoloisoquinoline ring system. The thiophene ring is rotationally disordered by approximately 180 degrees over two sites, the ratio of refined occupancies being 0.73 (1): 0.27 (1).

Adducts of bis(acetylacetonato)zinc(II) with 1,10-phenanthroline and 2,2'-bipyridine

In each of the zinc(II) complexes bis(acetylacetonato-kappa(2)O,O')(1,10-phenanthroline-kappa(2)N,N')zinc(II), [Zn(C(5)H(7)O(2))(2)(C(12)H(8)N(2))], (I), and bis(acetylacetonato-kappa(2)O,O')(2,2'-bipyridine-kappa(2)N,N')zinc(II), [Zn(C(5)H(7)O(2))(2)(C(10)H(8)N(2))], (II), the metal center has a distorted octahedral coordination geometry. Compound (I) has crystallographically imposed twofold symmetry, with Z' = 0.5. The presence of a rigid phenanthroline group precludes intramolecular hydrogen bonding, whereas the rather flexible bipyridyl ligand is twisted to form an intramolecular C-H...O interaction [the chelated bipyridyl ligand is nonplanar, with the pyridyl rings inclined at an angle of 13.4 (1) degrees]. The two metal complexes are linked by dissimilar C-H...O interactions into one-dimensional chains. The present study demonstrates the distinct effects of two commonly used ligands, viz. 1,10-phenanthroline and 2,2'-bipyridine, on the structures of metal complexes and their assembly.

Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle

Via a computer search, Altshuler and Steinberg found that there are 1296+1 combinatorial 3-manifolds on nine vertices, of which only one is non-sphere. This exceptional 3-manifold View the MathML source triangulates the twisted S2-bundle over S1. It was first constructed by Walkup. In this paper, we present a computer-free proof of the uniqueness of this non-sphere combinatorial 3-manifold. As opposed to the computer-generated proof, ours does not require wading through all the 9-vertex 3-spheres. As a preliminary result, we also show that any 9-vertex combinatorial 3-manifold is equivalent by proper bistellar moves to a 9-vertex neighbourly 3-manifold.

4-(5-Phenyl-1,2,4-triazolo[3,4-a]isoquinolin--yl)benzonitrile

In the title molecule, C23H14N4, the triazoloisoquinoline ring system is nearly planar, with an r.m.s. deviation of 0.038 (2) angstrom and a maximum deviation of -0.030 (2) angstrom from the mean plane of the triazole ring C atom which is bonded to the benzene ring. The benzene and phenyl rings are twisted by 57.65 (8) and 53.60 (9)degrees, respectively, with respect to the mean plane of the triazoloisoquinoline ring system. In the crystal structure, molecules are linked by weak aromatic pi-pi interactions [centroid-centroid distance = 3.8074 (12) angstrom]. In addition, the crystal structure exhibits a nonclassical intermolecular C-H center dot center dot center dot N hydrogen bond.

3-(4-Chlorophenyl)-5-phenyl-1,2,4-triazolo[3,4-a]isoquinoline

In the title molecule, C22H14ClN3, the triazoloisoquinoline ring system is approximately planar, with an r.m.s. deviation of 0.033 (2) angstrom and a maximum departure from the mean plane of 0.062 (1) angstrom for the triazole ring C atom, bonded to the benzene ring. The benzene and phenyl rings are twisted by 57.02 (6) and 62.16 (6)degrees, respectively, to the mean plane of the triazoloisoquinoline ring system. The molecule is stabilized by a weak intramolecular pi-pi interaction [centroid-centroid distance = 3.7089 (10) angstrom] between the benzene and phenyl rings. In the crystal structure, weak intermolecular C-H center dot center dot center dot N hydrogen bonds and C-H center dot center dot center dot pi interactions link the molecules.

5-(4-Chlorophenyl)-3-(2,4-dimethylthiazol-5-yl)-1,2,4-triazolo[3,4-a]isoquinoline

In the title molecule, C21H15ClN4S, the triazoloisoquinoline ring system is approximately planar, with an r.m.s. deviation of 0.054 (2) angstrom and a maximum deviation of 0.098 (2) angstrom from the mean plane for the triazole ring C atom that is bonded to the thiazole ring. The thiazole and benzene rings are twisted by 66.36 (7) and 56.32 (7)degrees respectively, with respect to the mean plane of the triazoloisoquinoline ring system. In the crystal structure, molecules are linked by intermolecular C-H center dot center dot center dot N interactions along the a axis. The molecular conformation is stabilized by a weak intramolecular pi-pi interaction involving the thiazole and benzene rings, with a centroid-centroid distance of 3.6546 (11) angstrom . In addition, two other intermolecular pi-pi stacking interactions are observed, between the triazole and benzene rings and between the dihydropyridine and benzene rings [centroid-centroid distances = 3.6489 (11) and 3.5967 (10) angstrom, respectively].

Fate of the superconducting ground state on the Moyal plane

It is known that Berry curvature of the band structure of certain crystals can lead to effective noncommutativity between spatial coordinates. Using the techniques of twisted quantum field theory, we investigate the question of the formation of a paired state of twisted fermions in such a system. We find that to leading order in the noncommutativity parameter, the gap between the non-interacting ground state and the paired state is smaller compared to its commutative counterpart. This suggests that BCS type superconductivity, if present in such systems, is more fragile and easier to disrupt. (C) 2010 Elsevier B.V. All rights reserved.

1-(3,5-Diethyl-1H-pyrazol-1-yl)-3-phenylisoquinoline

In the title molecule, C22H21N3, the isoquinoline ring is almost planar maximum deviation = 0.046 (1) A] and makes dihedral angles of 52.01 (4) and 14.61 (4)degrees with the pyrazole and phenyl rings, respectively. The phenyl ring and the pyrazole ring are twisted by 44.20 (6)degrees with respect to each other. The terminal C atoms of both of the ethyl groups attached to the pyrazole ring are disordered over two sites with occupancy ratios of 0.164 (7):0.836 (7) and 0.447 (16):0.553 (16). A weak intramolecular C-H...N contact may influence the molecular conformation. The crystal structure is stabilized by C-H...pi contacts involving the phenyl and pyrazole rings, and by pi-pi stacking interactions involving the pyridine and benzene rings centroid-centroid distance = 3.5972 (10) A].

Liquid-crystal display as a spectral selector for visible spectrometers

The polarization properties of a twisted nematic liquid crystal display (TNLCD) are studied experimentally with the aim of using it as a wavelength selector. The output of a white LED is split into its constituent wavelengths with a resolution of 2-5 nm in proportion to a voltage applied to the TNLCD. The feasibility of employing the display as a wavelength selector in visible spectrometers is demonstrated. A simple inexpensive design of a spectrometer built around an LED and a TNLCD is suggested.