Visualisation of an entangled channel spin-1 system

Co-variance matrix formalism gives powerful entanglement criteria for continuous as well as finite dimensional systems. We use this formalism to study a mixed channel spin-1 system which is well known in nuclear reactions. A spin-j state can be visualized as being made up of 2j spinors which are represented by a constellation of 2j points on a Bloch sphere using Majorana construction. We extend this formalism to visualize an entangled mixed spin-1 system.Comment: 4 pages,4 figure

4-Eth­oxy­phenyl 4-[(meth­oxy­carbon­yl)­oxy]benzoate

In the title compound, C17H16O6, the two benzene rings form a dihedral angle of 54.95 (10)°. Only weak inter­molecular inter­actions are present in the crystal structure, viz. C—H⋯O hydrogen bonds and C—H⋯π inter­actions involving one of the benzene rings

3-Ethyl-6-(4-fluoro­phen­yl)-7H-1,2,4-triazolo[3,4-b][1,3,4]thia­diazine

In the title compound, C12H11FN4S, the thia­diazine ring adopts a twist-boat conformation. The dihedral angle between the triazolothia­diazine system and the benzene ring is 10.54 (9)°. The crystal structure is characterized by C—H⋯N hydrogen bonds. The crystal packing also exhibits π–π inter­actions, with a centroid–centroid distance of 3.6348 (15) Å

1-Chloro-4-(3,4-dichloro­phen­yl)-3,4-dihydro­naphthalene-2-carbaldehyde

The title compound, C17H11Cl3O, was synthesized via the Vilsmeier–Haack reaction. The dihydro­naphthalene ring system is non-planar, the dihedral angle between the two fused rings being 10.87 (13)°; it forms a dihedral angle of 81.45 (10)° with the dichloro­phenyl ring. The crystal structure features inter­molecular C—H⋯O hydrogen bonds

1-(1-Benzofuran-2-yl)-3-(4-chloro­phen­yl)prop-2-en-1-one

In the title compound, C17H11ClO2, the benzofuran ring system is almost planar (r.m.s. deviation = 0.011 Å) and forms a dihedral angle of 10.53 (6)° with the chloro­phenyl ring. No significant inter­molecular inter­actions are observed

2-{[(E)-2-Hy­droxy­benzyl­idene]amino}-1H-isoindole-1,3(2H)-dione

In the title compound, C15H10N2O3, the isoindoline ring system is almost planar [maximum deviation = 0.020 (2) Å] and makes a dihedral angle of 1.57 (7)° with the benzene ring. Intra­molecular O—H⋯N and C—H⋯O hydrogen bonds are observed

Ethyl 2-(4-benzoyl-2,5-dimethyl­phen­oxy)acetate

The title compound, C19H20O4, was synthesized via a Fries rearrangement of hydr­oxy benzophenone. The dihedral angle between the least-squares planes of the two benzene rings is 69.04 (11)°. The mol­ecular structure displays an intra­molecular non-classical C—H⋯O hydrogen bond

(5,7-Dimethyl-2-oxo-2H-chromen-4-yl)methyl diethyl­dithio­carbamate

In the title compound, C17H21NO2S2, the coumarin ring system is nearly planar, with a maximum deviation of 0.080 (2) Å from the mean plane. An intra­molecular C—H⋯S hydrogen bond occurs. The crystal structure features C—H⋯S hydrogen bonds and weak π–π inter­actions with a centroid–centroid distance of 3.679 (1) Å

1,3-Bis(hydroxy­meth­yl)benzimidazolin-2-one

The title compound, C9H10N2O3, crystallizes with one and a half mol­ecules in the asymmetric unit, one lying on a general position and the other on a twofold rotation axis. The dihedral angle between the two independent benzimidazole ring systems is 18.96 (5)°. In the crystal, mol­ecules are linked into a three-dimensional network by O—H⋯O hydrogen bonding involving N-hydroxy­methyl and carbonyl groups, and C—H⋯O hydrogen bonds

(5,7-Dimethyl-2-oxo-2H-chromen-4-yl)methyl pyrrolidine-1-carbodithio­ate

In the title compound, C17H19NO2S2, the 2H-chromene ring system is almost planar, with a maximum deviation of 0.044 (2) Å, and the pyrrolidine ring adopts an envelope conformation. The dihedral angle between the 2H-chromene system and the planar part of the pyrrolidine ring is 83.65 (8)°. A weak intra­molecular C—H⋯S hydrogen bond occurs. The crystal structure features C—H⋯O hydrogen bonds and π–π inter­actions, with a centroid–centroid distance of 3.5728 (16) Å