Least-squares Plane Research Articles

Disk of the Small Magellanic Cloud as traced by Cepheids

The structure and evolution of the disk of the Small Magellanic Cloud (SMC) are traced by studying the Cepheids. We aim to estimate the orientation measurements of the disk, such as the inclination and the position angle of the line of nodes, and the depth of the disk. We used the V and I band photometric data of the fundamental and first-overtone Cepheids from the Optical Gravitational Lensing Experiment survey. The period-luminosity relations were used to estimate the relative distance and reddening of each Cepheid. A weighted least-square plane fitting method was then applied to estimate the structural parameters. The line-of-sight depth and then the orientation corrected depth or thickness of the disk were estimated from the relative distance measurements. The period-age-colour relation of Cepheids were used to derive the age of the Cepheids. A break in the PL relations of the fundamental-mode and first-overtone Cepheids at P ~ 2.95 days and P ~ 1 day are observed. An inclination of 64$^o$.4$\pm$0$^o$.7 and a PA$_{lon}$=155$^o$.3$\pm$6$^o$.3 are obtained from the full sample. A reddening map of the SMC disk is also presented. The orientation-corrected depth or thickness of the SMC disk is found to be 1.76 $\pm$ 0.6 kpc. The scale height is estimated to be 0.82 $\pm$ 0.3 kpc. The age distribution of Cepheids matches the SMC cluster age distribution. The radial variation of the disk parameters mildly indicate structures/disturbances in the inner SMC (0.5 $<$ r $<$ 2.5 degree). Some of the Cepheids found in front of the fitted plane in the eastern regions are possibly the youngest tidally stripped counterpart of the H {{\sc i}} gas of the Magellanic Bridge. The Cepheids behind the fitted plane are most likely the population in the Counter Bridge predicted in recent numerical simulations. Different scenarios for the origin of the extra-planar Cepheids are also discussed.

Crystal structure of desvenlafaxinium 3,5-dinitrobenzoate 3,5-dinitrobenzoic acid monohydrate, C30H35N5O15

In the crystal, a mol. of H2O is present next to 1 addnl. mol. of the non-dissocd. carboxylic acid. While the least-squares planes defined by the atoms of the nitro groups of the deprotonated carboxylic acid enclose angles of 5.8(2) and 9.8(2)° with the plane defined by the C atoms of the arom. system they are bonded to, the least-squares plane defined by the atoms of the carboxylate group intersect with the aromat's plane at an angle of 13.88(14)°. The resp. values for the co-crystd. carboxylic acid are found at 4.9(2) and 7.25( 16)° for the nitro groups and 11.12( 16)° for the least-squares plane defined by the non-H atoms of the carboxylic acid group on the 1 hand and the plane defined by the C atoms of the arom. system they are bonded to on the other hand. According to a puckering anal., the satd. 6-membered ring adopts a 4C1 conformation (C24CC21). In the crystal, H bonds of the N-H···O as well as the O-H···O type are obsd. In total, the different moieties of the title compd. are connected to a 3-dimensional network. The shortest intercentroid distance between two centers of gravity was measured at 4.2942(8) A… and is apparent between the arom. system of the cation as well as the Ph ring of the deprotonated carboxylic acid. Crystallog. data are given.

Abstract 12332: Tethering of Mitral Leaflets Relates to Displacement of Papillary Muscles by Dislocation of Heart During Off-Pump Coronary Artery Bypass Surgery: Assessment of Mitral Valve Complex by Three-Dimensional Echocardiography in Porcine Model

Introduction: It is considered that morphological changes of mitral valve complex and worsening of mitral regurgitation (MR) cause the hemodynamic deterioration during off-pump coronary artery bypass grafting (OPCAB) in ischemic heart disease. Hypothesis: Mitral valve tethering is caused by dislocation of papillary muscle and leads to exacerbation of ischemic MR and hemodynamics. Methods: In 9 healthy swine with median sternotomy, we positioned the beating heart using Starfish heart positioner ® and Octopus 2 ® (Medtronic) as OPCAB model. In 4 positions for CABG, i.e., control, LAD-, RCA-, and LCX- positions, three-dimensional (3D) full volume images by echocardiography were acquired (iE33 ® and X5-1 ® , Phillips Healthcare) to assess mitral valve complex with hemodynamic parameters. We assessed the morphological changes of the mitral valve complex in 4 positions using by Real-view ® (YD Co.) and Cardio-view ® (TomTec). Results: Systolic arterial pressure was significantly lower in LCX position than in control position (LCX 48.9±2.5 vs control 69.8±2.7 mmHg, P&lt;0.001). There were no significant differences in the mitral annular diameters in each position. On the other hand, there were significantly increased in the maximum tenting height (control 2.9±0.5, LAD 2.7± 0.3, RCA 3.7± 0.3, LCX 4.1± 0.3 mm, P&lt;0.01) and the tenting volume (control 0.7±0.1, LAD 0.6±0.1, RCA 0.8±0.1, LCX 1.0±0.1 cm 3 , P&lt;0.05) in LCX position compered to other positions. The angle α, i. e., the angle between the posterior papillary muscle-to-annulus line and the least-squares annular plane, were tended to decrease in LCX position, and there was a significantly relationship between the tenting volume and the angle α (r= -0.643, P&lt;0.001). By the assessment of 3D-coordinates of the papillary muscles, posterior papillary muscle was displaced to medial site in LCX position compered to other positions (P&lt;0.001). Conclusions: In the dislocated and rotated position of the heart, especially in LCX position, the tethering of the mitral valve leaflets was increased, and related to the displacement of posterior papillary muscle. This suggests that mitral valve tethering is caused by dislocation of papillary muscle and leads to exacerbation of ischemic MR and hemodynamics during OPCAB.

Crystal structure of (E)-3-(5-bromo-2-hydroxy-phen-yl)acryl-aldehyde.

The title compound, C9H7BrO2, displays a trans configuration with respect to the C=C double bond and is essentially planar [maximum deviation from the least-squares plane through all non-H atoms = 0.056 (4) Å]. The vinyl­aldehyde group adopts an extended conformation wih a C—C—C—C torsion angle of 179.7 (4)°. In the crystal, mol­ecules are linked by classical O—H⋯O and weak C—H⋯O hydrogen bonds into a three-dimensional supra­molecular network.

Crystal structure of di-chlorido-(2,2':6',2''-terpyridine-κ(3) N,N',N'')zinc: a redeter-min-ation.

The crystal structure of the title compound, [ZnCl2(C15H11N3)], was redetermined based on modern CCD data. In comparison with the previous determination from photographic film data [Corbridge & Cox (1956 ▶). J. Chem. Soc. 159, 594–603; Einstein & Penfold (1966 ▶). Acta Cryst. 20, 924–926], all non-H atoms were refined with anisotropic displacement parameters, leading to a much higher precision in terms of bond lengths and angles [e.g. Zn—Cl = 2.2684 (8) and 2.2883 (11) compared to 2.25 (1) and 2.27 (1) Å]. In the title mol­ecule, the ZnII atom is five-coordinated in a distorted square-pyramidal mode by two Cl atoms and by the three N atoms from the 2,2′:6′,2′′-terpyridine ligand. The latter is not planar and shows dihedral angles between the least-squares planes of the central pyridine ring and the terminal rings of 3.18 (8) and 6.36 (9)°. The mol­ecules in the crystal structure pack with π–π inter­actions [centroid–centroid distance = 3.655 (2) Å] between pyridine rings of neighbouring terpyridine moieties. These, together with inter­molecular C—H⋯Cl inter­actions, stablize the three-dimensional structure.

Crystal structure of bis-[2-tert-but-oxy-6-fluoro-3-(pyridin-2-yl-κN)pyridin-4-yl-κC (4)](pentane-2,4-dionato-κ(2) O,O')iridium(III).

The title mol-ecule, [Ir(C14H14FN2O)2(C5H7O2)], is located on a twofold rotation axis, which passes through the Ir(III) atom and the central C atom of the pentane-2,4-dionate anion. The Ir(III) atom adopts a distorted octa-hedral coordination geometry, being C,N-chelated by two 2-tert-but-oxy-6-fluoro-3-(pyridin-2-yl)pyridin-4-yl ligands and O,O'-chelated by the pentane-2,4-dionato ligand. The bipyridinate ligands, which are perpendicular to each other [dihedral angle between the two least-squares planes = 89.95 (5)°], are arranged in a cis-C,C' and trans-N,N' fashion relative to the central metal cation. Intra-molecular C-H⋯O and C-H⋯N hydrogen bonds and inter-molecular C-H⋯F hydrogen bonds as well as π-π inter-actions between neighbouring pyridine rings [centroid-centroid distance 3.680 (1) Å] contribute to the stabilization of the mol-ecular and crystal structure, respectively.

Crystal structure of 4-methyl-2-oxo-2H-chromen-7-yl ferrocene-carboxyl-ate.

The title mol­ecule, [Fe(C5H5)(C16H11O4)], consists of a ferrocenyl moiety and a 4-methyl­coumarin group linked through an ester unit to one of the cyclo­penta­dienyl (Cp) rings. The two Cp rings are virually parallel, with an angle between the two least-squares planes of 0.74 (16)°. The distances between the FeII atom and the centroids of the two Cp rings are 1.639 (2) and 1.652 (2) Å. The conformation of the ferrocenyl moiety is slightly away from eclipsed. The dihedral angle between the coumarin ring system and the ferrocenyl ester moiety is 69.17 (19)°. π–π stacking inter­actions involving the benzene rings of neighbouring coumarin moieties, with centroid–centroid distances of 3.739 (2) Å, consolidate the crystal packing.

Crystal structure of (E)-1(anthracen-9-ylmethylidene)[2-(morpholin-4-yl)eth-yl]amine.

The title compound, C21H22N2O, crystallizes with two independent mol­ecules in the asymmetric unit. In both mol­ecules, the anthracene ring systems are almost planar, with maximum deviations of 0.071 (8) and 0.028 (7) Å, and make dihedral angles of 73.4 (2) and 73.3 (2)° with the least-squares planes formed by the four C atoms of the morpholine rings, which adopt a chair conformation. An intra­molecular C—H⋯π inter­action occurs. In the crystal, the packing is stabilized by weak C—H⋯O hydrogen bonds, which connect pairs of molecules into parallel to the c axis, and C—H⋯π inter­actions.

Crystal structure of 3-[4-(1-methyl-eth-yl)phen-yl]-1-(naphthalen-2-yl)prop-2-en-1-one.

The title compound, C22H20O, was synthesized by reacting 4-iso­propyl­benzaldehyde with 2-acetonaphtone by aldolic condensation under Claisen–Schmidt conditions. The mol­ecule consists of a naphthalene group and a benzene ring with a pendant isopropyl moiety, both rings bound by a propenone linker. The naphthalene ring system is almost planar [maximum deviation from the least-squares plane = 0.026 (10) Å] and subtends a dihedral angle of 52.31 (4)° with the benzene ring. The propenone linker, in turn, deviates slightly more from planarity [maximum deviation = 0.125 (18) Å] and has its least-squares plane oriented midway the former two, at 25.62 (6) and 28.02 (5)° from the naphthalene ring system and the benzene ring, respectively. Finally, the isopropyl group presents its CC2 plane almost perpendicular to the benzene ring, at 85.30 (4)°. No significant hydrogen bonding or π–π stacking inter­actions are found in the crystal structure.

Crystal structure of ethyl (E)-4-(4-chlorophen-yl)-4-meth-oxy-2-oxobut-3-enoate.

In the title compound, C13H13ClO4, the dihedral angle between the chloro­benezene ring and the least-squares plane through the 4-meth­oxy-2-oxobut-3-enoate ethyl ester residue (r.m.s. deviation = 0.0975 Å) is 54.10 (5)°. In the crystal, mol­ecules are connected by meth­oxy–ketone and benzene–carboxyl­ate carbonyl C—H⋯O inter­actions, generating a supra­molecular layer in the ac plane.

Crystal structure of 7-bromo-4-oxo-4H-chromene-3-carbaldehyde.

In the title compound, C10H5BrO3, a brominated 3-formyl­chromone derivative, all atoms are essentially coplanar (r.m.s. = 0.0631 Å for the non-H atoms), with the largest deviation from the least-squares plane [0.215 (3) Å] being for the formyl O atom. In the crystal, mol­ecules are linked into tapes through C—H⋯O hydrogen bonds and these tapes are assembled by stacking inter­actions [centroid–centroid distance between the pyran rings = 3.858 (3) Å] to form supra­molecular layers that stack along the c axis.

Crystal structure of (E)-N-(3,4-di-meth-oxy-benzyl-idene)morpholin-4-amine.

In the title compound, C13H18N2O3, the benzene ring makes a dihedral angle of 17.19 (11)° with the least-squares plane formed by the four C atoms of the morpholine ring, which adopts a chair conformation. In the crystal, C—H⋯N hydrogen bonds link the mol­ecules into supramolecular chains running along a 21 screw axis parallel to the b-axis direction. Weak C—H⋯π inter­actions are also observed.

7-Chloro-4-oxo-4H-chromene-3-carbaldehyde.

In the title compound, C10H5ClO3, a chlorinated 3-formyl­chromone derivative, all atoms are essentially coplanar (r.m.s. deviation = 0.0592 Å for all non-H atoms), with the largest deviation from the least-squares plane [0.1792 (19) Å] being for the chromone-ring carbonyl O atom. In the crystal, mol­ecules are linked through C—H⋯O hydrogen bonds to form tetrads, which are assembled by stacking inter­actions [centroid–centroid distance between the pyran rings = 3.823 (3) Å] and van der Waals contacts between the Cl atoms [Cl⋯Cl = 3.4483 (16) Å and C—Cl⋯Cl = 171.73 (7)°] into a three-dimensional architecture.

6-Chloro-7-fluoro-4-oxo-4H-chromene-3-carbaldehyde.

In the title compound, C10H4ClFO3, a chlorinated and fluorinated 3-formyl­chromone derivative, all atoms are essentially coplanar (r.m.s. = 0.0336 Å for the non-H atoms), with the largest deviation from the least-squares plane [0.062 (2) Å] being for a benzene-ring C atom. In the crystal, mol­ecules are linked through stacking inter­actions [centroid–centroid distance between the benzene and pyran rings = 3.958 (3) Å and inter­planar distance = 3.259 (3) Å], C—H⋯O hydrogen bonds, and short C⋯O contacts [2.879 (3) Å]. Unsymmetrical halogen–halogen inter­actions between the Cl and F atoms [Cl⋯F = 3.049 (3) Å, C—Cl⋯F = 148.10 (9)° and C—F⋯Cl = 162.06 (13)°] are also formed, giving a meandering two-dimensional network along the a axis.

6-Chloro-7-methyl-4-oxo-4H-chromene-3-carbaldehyde.

In the title compound, C11H7ClO3, a chlorinated and methyl­ated 3-formyl­chromone derivative, the non-H atoms are essentially coplanar (r.m.s. deviation = 0.0670 Å), with the largest deviation from the least-squares plane [0.2349 (17) Å] being for the pyran carbonyl O atom. In the crystal, mol­ecules are linked through π–π stacking inter­actions along the a axis [centroid–centroid distance between the pyran rings = 3.824 (6) Å] and two stacks are connected by type I halogen–halogen inter­actions between the Cl atoms [Cl⋯Cl = 3.397 (3) Å].

1-(Morpholin-4-yl)-4-(2-nitro-phen-yl)spiro-[azetidine-3,9'-xanthen]-2-one.

In the title compound, C22H21N3O5, the β-lactam (azetidin-2-one) ring is nearly planar [maximum deviation = 0.010 (1) Å] and makes dihedral angles of 69.22 (5), 55.32 (5) and 89.42 (4)° with the least-squares planes formed by the four C atoms of the morpholine ring, which adopts a chair conformation, the benzene ring and the xanthene ring system, respectively. In the crystal, C—H⋯O hydrogen-bond contacts connect neighbouring mol­ecules into infinite zigzag chains running parallel to the b axis.

8-Chloro-4-oxo-4H-chromene-3-carbaldehyde.

In the title compound, C10H5ClO3, a chlorinated 3-formyl­chromone derivative, all atoms are essentially coplanar (r.m.s. deviation = 0.032 Å for the non-H atoms), with the largest deviation from the least-squares plane [0.0598 (14) Å] being for a pyran-ring C atom. In the crystal, mol­ecules are linked through stacking inter­actions along the b axis [shortest centroid–centroid distance between the pyran and benzene rings = 3.566 (2) Å].

6-Iodo-4-oxo-4H-chromene-3-carbaldehyde.

In the title compound, C10H5IO3, an iodinated 3-formyl­chromone derivative, the non-H atoms are essentially coplanar (r.m.s. deviation = 0.0259 Å), with the largest deviation from the least-squares plane [0.056 (5) Å] being found for the formyl O atom. In the crystal, mol­ecules are linked through I⋯O halogen bonds [I⋯O = 3.245 (4) Å, C—I⋯O = 165.95 (13) and C=O⋯I = 169.7 (4)°] along [101]. The supra­molecular chains are assembled into layers via π–π stacking inter­actions along the b axis [shortest centroid–centroid distance between the pyran and benzene rings = 3.558 (3) Å].

Crystal structure of cis-diiodidobis(quinoline-κN)platinum(II), C18H14I2N2Pt

Abstract C18H14I2N2Pt, monoclinic, C2/c (no. 15), a = 18.803(1) Å, b = 9.1761(5) Å, c = 11.6537(7) Å, β = 112.260(1)°, V = 1860.9 Å3, Z = 4, Rgt(F) = 0.0307, wRref(F2) = 0.0685, T = 200 K.

(2E)-2-Benzyl-idene-N-phenyl-hydrazinecarboxamide.

The mol­ecule of the title compound, C14H13N3O, adopts an E conformation with respect to the azomethine C=N bond, and is roughly planar, with an r.m.s. deviation of the non-H atoms from the least-squares plane of 0.100 (2) Å and a dihedral angle between the terminal benzene rings of 5.74 (12)°. An intramolecular N—H⋯N hydrogen bond closes an S(6) ring. In the crystal, mol­ecules are linked by the pairs of N—H⋯O hydrogen bonds into centrosymmetric dimers. Dimers related by translation along [010] form slanted stacks, the shortest C⋯C inter­molecular distance within the stack being 3.283 (3) Å. Weak C—H⋯π inter­actions link the stacks into a three-dimensional structure.