4-Methyl-2-oxo-2,3-dihydro-1-benzopyran-7-yl benzene­sulfonate

The title compound, C16H12O5S, is a derivative of coumarin. The dihedral angle between the coumarin ring system and the phenyl ring is 65.9 (1)°. In the crystal structure, mol­ecules are linked by weak C—H⋯O hydrogen bonding to form molecular ribbons

Diaqua­bis(N,N′-dibenzyl­ethane-1,2-diamine-κ2 N,N′)nickel(II) dichloride N,N-dimethyl­formamide solvate

The asymmetric unit of the title complex, [Ni(C16H20N2)2(H2O)2]Cl2·C3H7NO, consists of two NiII atoms, each lying on an inversion center, two Cl anions, two N,N′-dibenzyl­ethane-1,2-diamine ligands, two coordinated water mol­ecules and one N,N-dimethyl­formamide solvent mol­ecule. Each NiII atom is six-coordinated in a distorted octa­hedral coordination geometry, with the equatorial plane formed by four N atoms and the axial positions occupied by two water mol­ecules. The complex mol­ecules are linked into a chain along [001] by N—H⋯Cl, N—H⋯O and O—H⋯Cl hydrogen bonds. The C atoms and H atoms of the solvent mol­ecule are disordered over two sites in a ratio of 0.52 (2):0.48 (2)

Tetra­kis(μ-naphthalene-1-acetato-1:2κ2 O:O′)bis­(naphthalene-1-acetato)-1κ2 O,O′;2κ2 O,O′-bis­(1,10-phenanthroline)-1κ2 N,N′;2κ2 N,N′-europium(III)samarium(III)

In the title compound, [EuSm(C12H9O2)6(C12H8N2)2], the metal site is statistically occupied (50:50) by Eu and Sm atoms, forming a centrosymmetric complex. The metal site is nine-coordinate, in a distorted monocapped square-anti­prismatic coordination geometry. Mol­ecules are linked into three chains by C—H⋯π interactions and C—H⋯O hydrogen bonds. The combination of these chains generates a three-dimensional framework structure. One of the bridging naphthalene-1-ace­tate ligands was found to be disordered over two sites; the site occupancies for the naphthylmethyl group refined to 0.628 (14) and 0.372 (14)

Poly[(N,N-dimethyl­formamide-κO)tris­(μ-naphthalene-1-acetato)terbium(III)]

In title compound, [Tb(C12H9O2)3(C3H7NO)]n, the Tb atom is nine-coordinated by nine O atoms from three naphthalene-1-acetate and one N,N-dimethyl­formamide ligands. The Tb atoms are linked by three bridging naphthalene-1-acetate ligands into a chain parallel to the b axis. Further stabilization of the structure is accomplished by non-classical C—H⋯O hydrogen bonds and C—H⋯π interactions

Aqua­[N-phenyl-2-(quinolin-8-yl­oxy)acetamide]dinitratozinc(II)

In the title complex, [Zn(NO3)2(C17H14N2O2)(H2O)], the six-coordinated Zn atom is in a distorted octa­hedral geometry, the donor centers being two O atoms and one N atom from the tridentate organic ligand, a water O atom and two O atoms from two monodentate nitrate ions. In the crystal, O—H⋯O hydrogen bonds between the coordinated water mol­ecules and nitrate O atoms and N—H⋯O hydrogen bonds between the main ligand and nitrate O atoms consolidate the three-dimensional network

Power-Law Decay of Standing Waves on the Surface of Topological Insulators

We propose a general theory on the standing waves (quasiparticle interference pattern) caused by the scattering of surface states off step edges in topological insulators, in which the extremal points on the constant energy contour of surface band play the dominant role. Experimentally we image the interference patterns on both Bi$_2$Te$_3$ and Bi$_2$Se$_3$ films by measuring the local density of states using a scanning tunneling microscope. The observed decay indices of the standing waves agree excellently with the theoretical prediction: In Bi$_2$Se$_3$, only a single decay index of -3/2 exists; while in Bi$_2$Te$_3$ with strongly warped surface band, it varies from -3/2 to -1/2 and finally to -1 as the energy increases. The -1/2 decay indicates that the suppression of backscattering due to time-reversal symmetry does not necessarily lead to a spatial decay rate faster than that in the conventional two-dimensional electron system. Our formalism can also explain the characteristic scattering wave vectors of the standing wave caused by non-magnetic impurities on Bi$_2$Te$_3$.Comment: 4 pages, 3 figure

Bis{6,6′-dimeth­oxy-2,2′-[ethane-1,2-diyl­bis(imino­methyl­ene)]diphenolato(1.5−)-κ4 O,N,N′,O′}praeseodymium(III)

The title compound, [Pr(C18H22.5N2O4)2], is isotypic with its Er and Tb analogues. All interatomic distances, angles and the hydrogen bond geometry are very similar for the three structures.

Bis{6,6′-dimeth­oxy-2,2′-[ethane-1,2-diyl­bis(imino­methyl­ene)]diphenolato(1.5−)-κ4 O,N,N′,O′}terbium(III)

The title compound, [Tb(C18H22.5N2O4)2], is isotypic with its Pr and Tb analogues. All interatomic distances, angles and the hydrogen bond geometry are very similar for the three structures