Least-squares Plane Research Articles

Mol-ecular and crystal structure, Hirshfeld analysis and DFT investigation of 5-(furan-2-yl-methyl-idene)thia-zolo[3,4-a]benzimidazole-2-thione.

The thia-zolo[3,4-a]benzimidazole fused-ring system in the title compound, C14H8N2OS2, is nearly planar, the r.m.s. deviation being 0.0073 Å. The thia-zolo-benzimidazole-2-thione system is almost in the same plane as the furan-2-yl-methyl-ene moiety, with a dihedral angle of 5.6 (2)° between the two least-squares planes. In the crystal, adjacent mol-ecules are connected by weak inter-molecular inter-actions (C-H⋯N and slipped π-π stacking) into a three-dimensional network. The nature of the inter-molecular inter-actions was also qu-anti-fied by Hirshfeld surface analysis. DFT analysis indicates a good agreement of the experimentally determined and the theoretically calculated mol-ecular structures.

1-Hy-droxy-3,4-dimeth-oxy-10-methyl-acridin-9-one.

There are two independent mol-ecules in the asymmetric unit of the title compound, C16H15NO4, which was isolated from fruits of Zanthoxylum leprieurii. The atoms of the three rings of each mol-ecule are close to coplanar with the largest deviations from the least-squares planes being 0.084 (3) Å and 0.069 (2) Å. Each molecule features an intramolecular O-H⋯·O hydrogen bond. In the crystal, C-H⋯·O hydrogen-bonding inter-actions link the mol-ecules into a three-dimensional network.

Crystal structure and Hirshfeld surface analysis of 1-(2-fluoro-phen-yl)-1H-tetra-zole-5(4H)-thione.

In the crystal of the title compound, C7H5FN4S, the mol-ecules are non-planar, with dihedral angle formed by least-squares planes of tetra-zole and benzene rings of 59.94 (8) °. The crystal packing is formed by N-H⋯S hydrogen bonds, which link the mol-ecules into centrosymmetric dimers with an R 2 2(8) ring motif, and by the offset face-to-face π-π stacking inter-actions between the benzene rings, which join the dimers into layers parallel to (100). The Hirshfeld surface analysis shows that the most important contributions to the surface contacts are from N⋯H/H⋯N (21.9%), S⋯H/H⋯S (21.1%), H⋯H (14.6%), F⋯H/H⋯F (11.8%) and C⋯H/H⋯C (9.5%) inter-actions.

Crystal structure of (1,4-diphenyl-4H-1,2,4-triazol-3-yl)phenyl-amine di-fluoro-phosphate, and a survey of the di-fluoro-phosphate anion (PO2F2 -).

Nitron is the trivial name of (1,4-diphenyl-4H-1,2,4-triazol-3-yl)phenyl-amine (C20H16N4), a triazole derivative used as an analytical reagent for gravimetric analysis of the nitrate anion. The crystal structure of the di-fluoro-phosphate salt of Nitron, 3-anilino-1,4-diphenyl-1H-1,2,4-triazol-4-ium di-fluoro-phosphate, C20H17N4 +·PO2F2 -, is reported here. Within the protonated Nitron mol-ecule, the triazole ring, one of the phenyl rings and the NHPh moiety are virtually co-planar, with the third phenyl ring inclined to the least-squares plane of the other three rings by 56.07 (3)°. Inter-molecular N-H⋯O and C-H⋯O hydrogen bonds between cations and di-fluoro-phosphate anions lead to the formation of a three-dimensional network that is consolidated by additional π-π stacking inter-actions between the triazole ring and one of the phenyl rings. Database surveys on inorganic, metal-organic and organic structures comprising the tetra-hedral PO2F2 group reveal mean bond lengths of P-O = 1.459 (27) Å, P-F = 1.530 (21) Å, and angles of O-P-O = 121.2 (2.9)°, O-P-F = 108.7 (6)°, and F-P-F = 98.5 (2.6)°, using a dataset of 67 independent PO2F2 - anions or PO2F2 entities.

6-[(tert-Butyl-dimethyl-sil-yl)-oxy]-3-ethenyl-7-meth-oxy-4-[(tri-methyl-sil-yl)ethyn-yl]naphtho-[2,3-c]furan-1(3H)-one.

The tricyclic core in the title compound, C26H34O4Si2, shows disorder of the furan ring and deviates slightly from planarity, with the largest displacement from the least-squares plane [0.166 (2) Å] for the major disordered part of the methine C atom. To this C atom the likewise disordered vinyl group is attached, lying nearly perpendicular to the tricyclic core. In the crystal, mutual C-H⋯π inter-actions between the methine group of the furan ring and the central ring of the tricyclic core of an adjacent mol-ecule lead to inversion-related dimers.

Synthesis, Characterization and Crystal Structure of 1-(2-benzamidophenyl)-3-benzoylthiourea Hemihydrate

The dissymmetric compound C₂₁H₁₇N₃O₂S.0.5H₂O obtained by a reaction of 1,2-diaminobenzene, potassium thiocyanate and benzoyl chloride in 1/1/2 ratio is characterized by elemental analyses, IR, and NMR spectroscopies. The structure is elucidated by X-ray diffraction technic. The compound crystallizes in the monoclinic system with a space group of <i>I2</i>. The asymmetric unit contains one hemihydrate organic molecule. The title thiourea derivative, features an almost planar, C₂N₂S (S1/N1/N2/C7/C8) moiety, with a maximum deviation from the least-squares plane of 0.0422 (3) Å. This moiety is flanked by a disubstituted and a monosubstituted phenyl rings. The dihedral angles between the thiourea and the monosubstituted phenyl ring and the thiourea and the central disubstituted phenyl ring are respectively 10.418 (7)° and 60.292 (2)°, indicating twist in the molecule. On the other arm, a phenyl ring supported by an amide function, which is linked to the central ring through the nitrogen atom, is present. The dihedral angle between this phenyl group and the central disubstituted phenyl is 76.862 (7)° showing that their mean planes are not coplanar. Intramolecular S(thiono)—H…O(water) hydrogen bonds which close in <i>S</i> (6) and <i>S</i> (7) rings consolidate the conformation. Intermolecular N(amido)—H…O(carbonyl) which form layers parallel to the <i>ac</i> plane stabilized the structure.

Synthesis and structure of 2,4,6-tri-cyclo-butyl-1,3,5-trioxane.

The synthesis and structure of 2,4,6,-tri-cyclo-butyl-1,3,5-trioxane, C15H24O3 1, is described. It was formed in 39% yield during the work-up of the Swern oxidation of cyclo-butyl-methanol and may serve as a stable precursor of the cyclo-butane carbaldehyde. The mol-ecule of 1 occupies a special position (3.m) located at the center of its 1,3,5-trioxane ring. The latter is in a chair conformation, with the symmetry-independent O and C atoms deviating by 0.651 (4) Å from the least-squares plane of the other atoms of the trioxane ring. All three cyclo-butane substituents, which have a butterfly conformation with an angle between the two planes of 25.7 (3)°, are in the cis conformation relative to the 1,3,5-trioxane ring. Inter-molecular C-H⋯O inter-actions between the 1,3,5-trioxane rings consolidate the crystal structure, forming stacks along the c-axis direction. The crystal studied was refined a as a racemic twin.

3D scene reconstruction of landslide topography based on data fusion between laser point cloud and UAV image

The main topic of this research was to propose an optimizing modeling method of landslide topography. This method fuses high-resolution imagery from an unmanned aerial vehicle (UAV) with laser point cloud. Due to the relatively high efficiency and large coverage area, the UAV system is suitable for emergency investigation of landslide. Based on the UAV images and laser point cloud, the use of partial differential equation (PDE) combines the hole repair technology with non-uniform rational B-splines (NURBS) method to rapidly reconstruct a three-dimensional (3D) scene. The mean square error (MSE) determined by comparison with measured data from the laser scanner technology is 16.1274 mm. And the error of plane calculated by the NURBS surface fitting is smallest by comparing with the least-squares plane fitting, Delaunay triangulation and polygon mesh method. In addition, the realistic 3D landslide model is obtained by texture mapping. The XiaPa landslide in Liangshan District, Xichang City, Sichuan Province China, was selected as a case study, in which the accuracy is evaluated to prove that the model has higher precision than traditional methods. The experiment results show that the integrated approach in this paper could be implemented in qualitative and quantitative risk assessment procedures pertaining to landslides.

2,4-Dichloro-N-(2,5-dioxopyrrolidin-1-yl)benzamide

In the title compound, C11H8Cl2N2O3, the plane of the pyrrolidine ring (r.m.s. deviation = 0.065 Å) makes a dihedral angle of 52.9 (2)° with the plane of the benzene ring. The least-squares plane of the central amide fragment makes dihedral angles of 49.3 (7) and 77.9 (7)° with those of the benzene and pyrrolidine rings, respectively. In the crystal, molecules are linked via N—H...O hydrogen bonds, forming chains along the b-axis direction. π–π interactions link these chains into a two-dimensional network parallel to (100).

Digital stone rubbing from 3D models

Abstract Stone rubbing is a traditional method to record surface features of a stone on paper. It has a long history and is still used by Chinese archaeologists and artists up to now. However, stone rubbing can cause permanent damage to precious cultural heritage due to abrasion. We propose a new method to create digital stone rubbing from 3D digital models. We assume the surface of a stone is flat locally and fit a least-squares plane to each point's neighbors individually. To prevent the local plane from being fitted across sharp edges or corners of the model, we make use of the smoothed point normals in the selection of local surface region. The height of a point is defined as the signed distance between the point and its local approximation plane. The estimated height of each point is then mapped to its grey value by a nonlinear transformation function. Finally, we render the 3D model into a rubbing image using orthogonal projection. We demonstrate the effectiveness of the method on real experimental dataset in archaeology.

Crystal, molecular and electronic structure of (5S,11R,11aS)-11-hydroxy-5-methyl-1,2,3,4,5,6,11,11a-octahydropyrido[1,2-b]isoquinolin-5-ium iodide

Abstract The title compound, C14H20INO, is a molecule with three stereogenic centres. It absolute configuration was derived from the synthesis and confirmed by structure determination (AD, Flack (Parsons’) parameter: 0.031 (8)). The expected stereochemistry of atoms N1 was confirmed to be S, C5 was confirmed to S, C6 was confirmed to R. The central N-heterocyclic ring is not planar and adopts a half-chair conformation. A calculation of least-squares planes showed that these rings are puckered in such a manner that the five atoms: C5, C6, C7, C12 and C13 (the second ring: C1, C2, C3, C4, C5 and N1) are planar, while atom N1 is displaced from these plane with the out-of-plane displacement of −0.694 (4) and −0.670 (5) Å in the second ring, respectively. Dihedral angle between the planes of the central N-heterocyclic rings is 23.4 (2)°. Crystal structure is also stabilized by C—H···O hydrogen interactions.

5-Methyl-1-(4-methylphenyl)-N′-[1-(1H-pyrrol-2-yl)ethylidene]-1H-1,2,3-triazole-4-carbohydrazide monohydrate

In the title hydrate, C17H18N6O·H2O, the twist angles between the least-squares planes of the pyrolyl/methyltriazolyl/tolyl groups are 11.4 (2) and 7.9 (1)°, respectively. In the crystal, centrosymmetric tetramers (two organic molecules and two water molecules) are linked by N—H...O and O—H...O hydrogen bonds. Weak aromatic π–π stacking interactions between the triazolyl rings [centroid–centroid separation = 3.6422 (10) Å] link the tetramers.

Crystal structure and luminescent properties of bis-[2,6-dimethyl-3-(pyridin-2-yl-κN)pyridin-4-yl-κC4](2,2,6,6-tetra-methylhepta-ne-3,5-dionato-κ2O,O')iridium(III) ethyl acetate monosolvate.

In the solvated title compound, [Ir(C12H11N2)2(C11H19O2)]·CH3CO2C2H5, the IrIII ion adopts a distorted octa-hedral coordination environment resulting from its coordination by two C,N-chelating 2,6-dimethyl-3-(pyridin-2-yl)pyridin-4-yl ligands and one O,O'-chelating 2,2,6,6-tetra-methylhepta-ne-3,5-dionate ligand. The C,N-chelating ligands are perpendicular to each other [dihedral angle between the least-squares planes = 87.86 (5)°] and are arranged in a cis-C,C' and trans-N,N' fashion. In the crystal, pairwise C-H⋯π inter-actions between inversion-related IrIII complexes are present, forming a dimeric structure. The title complex shows bright bluish-green emission with good quantum efficiency in solution at room temperature.

5-Acetyl-6-methyl-4-phenyl-1-(prop-2-ynyl)-3,4-dihydropyrimidin-2(1H)-one

The 4-dihydropyrimidin-2(1H)-one moiety of the title molecule, C16H16N2O2, displays a half-chair conformation. The least-squares mean plane through this heterocycle is almost perpendicular to the aromatic ring [dihedral angle = 89.52 (8)°] and to the prop-2-ynyl chain [C—C—N—C torsion angle of −73.2 (2)°]. The mean plane through the acetyl group makes a dihedral angle of 30.93 (10)° with the mean plane of the heterocycle. There is an intramolecular C—H...O hydrogen bond forming anS(6) ring motif. In the crystal, molecules are linked by pairs of N—H...O hydrogen bonds forming inversion dimers.

2-Sulfanylidene-1,3-dithiolo[4,5-b]pyrazine-5,6-dicarbonitrile

In the title compound, C7N4S3, the molecular entity consisting of a 1,3-dithiole-2-thione with a fused pyrazine ring is planar, with an r.m.s. deviation of 0.042 (3) Å from the least-squares plane. In the crystal, molecules are linked via short intermolecular S...N contacts [3.251 (4) and 3.308 (3) Å] between the S atom of the thiocarbonyl group and N atoms of the cyano groups.

Alkyne-Bridged Multi[Copper(II) Porphyrin] Structures: Nuances of Orbital Symmetry in Long-Range, Through-Bond Mediated, Isotropic Spin Exchange Interactions.

Spin and conformational dynamics in symmetric alkyne-bridged multi[copper(II) porphyrin] structures have been studied in toluene solution at variable temperature using steady-state electron paramagnetic resonance (EPR) spectroscopy. Comparison of the dimer EPR spectra to those of Cu porphyrin monomers shows evidence of an isotropic exchange interaction (Javg) in these biradicaloid structures, manifested by a significant line broadening in the dimer spectra. The extent line broadening depends on molecular structure and temperature, suggesting Javg is modulated by conformational dynamics that impact the torsional angle distribution between the porphyrin-porphyrin least-squares planes. Computational simulation of the experimental EPR spectra, using a developed algorithm for J modulation in flexible organic biradicals, supports this hypothesis. Comparison of ethyne and butadiyne alkyne bridges reveals remarkable sensitivity to orbital interactions between the spacer and the metal, reflected in measurements of Javg as a function of temperature. The results suggest orbital symmetry relationships may be more important than recognized in design of optimized molecular spintronic devices.

Synthesis and crystal structure of di-chlorido-(1,10-phenanthroline-κ2N,N')gold(III) hexa-fluorido-phosphate.

A gold(III) salt of composition [AuCl2(C12H8N2)]PF6 was prepared and characterized by elemental and mass spectrometric analysis (ESI(+)-QTOF-MS), 1H nuclear magnetic resonance measurements and by single-crystal X-ray diffraction. The square-planar coordination sphere of AuIII comprises the bidentate 1,10-phenanthroline ligand and two chloride ions, with the AuIII ion only slightly shifted from the least-squares plane of the ligating atoms (r.m.s. = 0.018 Å). In contrast to two other previously reported AuIII-phenantroline structures that are stabilized by inter-actions involving the chlorido ligands, the packing of the title compound does not present these features. Instead, the hexa-fluorido-phosphate counter-ion gives rise to anion⋯π inter-actions that are a crucial factor for the crystal packing.

Crystal structures of two platinum(II) complexes containing ethyl eugenoxyacetate and 2-aminopyridine

In the title complexes, trans-(2-amino-pyridine-κN)di-chlorido-{4-eth-oxy-carbonyl-meth-oxy-3-meth-oxy-1-[(2,3-η)-prop-2-en-1-yl]benzene}-platinum(II), [PtCl2(C5H6N2)(C14H18O4)], (I), and (2-amino-pyridine-κN)chlorido{5-eth-oxy-car-bon-yl-meth-oxy-4-meth-oxy-1-[(2,3-η)-prop-2-en-1-yl]phenyl-κC1}-platinum(II), [Pt(C14H17O4)Cl(C5H6N2)], (II), the central PtII metal atom displays a distorted square-planar coordination, with the PtII atom coordinated by the pyridine N atom, the C=C double bond of the eugenol ligand and two Cl atoms for (I) or one Cl atom and a C atom of the phenyl ring for (II). The allyl fragment in (I) is disordered, with population parameters 0.614 (14) and 0.386 (14) for the two positions of the central C atom. The least-squares planes through the two aromatic ring systems make a dihedral angle of 51.10 (13)° for (I) and 78.5 (2)° for (II). Intra-molecular N-H⋯O and N-H⋯π inter-actions occur in (I). In (I), inversion dimers formed by C-H⋯Cl inter-actions are further linked into chains parallel to the b axis by C-H⋯O hydrogen bonds. Both aromatic rings are involved in π-π inter-actions, with centroid-to-centroid distances of 3.508 (3) and 3.791 (3) Å. In (II), inversion dimers form chains parallel to the b axis by C-H⋯O inter-actions.

Redetermination of the crystal structure of di-methyl-bis-[2,4-penta-nedionato(1-)-κ2O2,O4]tin(IV).

The redetermination of the title compound, [Sn(CH3)2(C5H7O2)2] or SnMe2(acac)2, from CCD data recorded at 100 K basically confirms the previous study based on integrated film data recorded at room temperature [Miller & Schlemper (1972 ▸). Inorg. Chem.12, 677-681], but reveals a remarkable shrinkage of the a axis [7.12 (1) > 6.7694 (4) Å]. The mol-ecule belongs to point group Ci with the SnIV atom on a centre of inversion. The SnIV atom shows a slightly distorted octa-hedral coordination sphere with the methyl groups in trans positions and a Sn-C bond length of 2.115 (2) Å which may serve as a standard value for an Sn-CH3 bond of an octa-hedrally coordinated SnIV atom. The Sn-O bonds involving the two carbonyl groups of the acetyl-acetonate ligand are of equal length [2.180 (1) and 2.183 (1) Å], as are the C=O [1.273 (1) and 1.274 (1) Å] and C-C bond lengths [1.393 (2) and 1.400 (2) Å]. The acetyl-acetonate ligand deviates considerably from planarity, with a dihedral angle of 5.57 (9)° between the least-squares planes of the two acetone moieties. The four O atoms of the two symmetry-related acetyl-acetonate ligands are arranged in a nearly quadratic rectangle. Weak C-H⋯O inter-actions consolidate the crystal packing.

Crystal structure of N-(7-di-bromo-methyl-5-methyl-1,8-naphthyridin-2-yl)benzamide-pyrrolidine-2,5-dione (1/1).

The title compound, C17H13Br2N3O·C4H5NO2, is a co-crystal of N-(7-di-bromo-methyl-5-methyl-1,8-naphthyridin-2-yl)benzamide and pyrrolidine-2,5-dione (succinimide). The benzamide mol-ecule exhibits pseudo-mirror symmetry, with an r.m.s. deviation of the non-H atoms of 0.09 Å (except for the two Br atoms). The angle between the least-squares planes of the two mol-ecules is 26.2 (2)°. In the crystal, the two mol-ecules are mutually linked by N-H⋯O and N-H⋯N hydrogen bonds. The packing is consolidated by C-H⋯(O,N) hydrogen bonds and π-π stacking inter-actions.