Least-squares Plane Research Articles

Oxalic acid–pyridine-4-carbonitrile (1/2)

In the title compound, 2C6H4N2·C2H2O4, the oxalic acid mol­ecule lies about an inversion center. The pyridine ring of the pyridine-4-carbonitrile mol­ecule is almost planar, the largest deviation from the least-squares plane being 0.006 (1) Å; the nitrile N atom deviates from this plane by 0.114 (1) Å. In the crystal, the oxalic acid mol­ecules and the pyridine-4-carbonitrile mol­ecules form stacks. Neighboring mol­ecules within the stacks are related by translation in the a direction, with inter­planar distances of 3.183 (1) and 3.331 (2) Å, respectively. Each oxalic acid mol­ecule forms strong O—H⋯N hydrogen bonds with two mol­ecules of pyridine-4-carbonitrile. Besides this, there are also weak C—H⋯O inter­actions.

Dichlorido(5,10,15,20-tetraphenylporphyrinato-κ4 N)antimony(V) hemi{di-μ-chlorido-bis[trichloridoantimonate(III)]} dichloromethane monosolvate

The asymmetric unit of the title complex, [Sb(C44H28N4)Cl2][Sb2Cl8]0.5·CH2Cl2, is composed of a SbV complex cation wherein the Sb atom is hexa­coordinated by four N atoms of the pyrrole rings of the tetra­phenyl­porphyrinate (TPP) ligands and two chloride ions, a half di-μ-chlorido-bis­[trichloridoanti­monate(III)] counter-anion and a dichloro­methane solvent mol­ecule. In the cation, the average Sb—N distance is 2.066 (2) Å, while the Sb—Cl distances are 2.3410 (11) and 2.3639 (12) Å. The central unit of the cation, SbN4C20, is far from being planar, with deviations of atoms from the least-squares plane ranging from −0.110 (4) to 0.124 (4) Å. The Sb—Cl distances in the anion, which is located about an inversion center, lie in the wide range 2.3715 (13)–2.7489 (13) Å, the longest distances being between the Sb and bridging Cl atoms. The crystal structure is stabilized by inter­molecular C—H⋯Cl inter­actions involving the cations, the anions and the solvent mol­ecules. The solvent mol­ecule is disordered over two orientations in a 0.901 (13):0.099 (13) ratio.

3-(2,4-Dichloro-phen-yl)-5-(4-fluoro-phen-yl)-2-methyl-7-(trifluoro-meth-yl)pyrazolo-[1,5-a]pyrimidine.

In the title compound, C20H11Cl2F4N3, the central pyrazolo­[1,5-a]pyrimidine unit is almost planar [the mean deviation from the best least-square plane through the nine atoms is 0.006 (2) Å]. The fluoro­benzene ring is rotated out of this plane by 10.3 (3)°, whereas the dichloro­benzene ring is rotated by 46.2 (3)°. The crystal packing is dominated by Cl⋯Cl inter­actions of 3.475 (3) Å and van der Waals inter­actions.

Bis(2-aminopyridinium) 2,5-dicarboxybenzene-1,4-dicarboxylate

In the title compound, 2C5H7N2 +·C10H4O8 2−, the 2-amino­pyridinium (2-apyH) cation and 2,5-dicarb­oxy­benzene-1,4-dicarboxyl­ate (btcH2) anion are both nearly planar, with r.m.s. deviations of 0.015 and 0.050 Å, respectively. The angle between the latter least-squares planes is 17.68 (9)°. The overall crystal structure results from the packing of two-dimensional networks, formed by alternating 2-apyH and btcH2 linked by hydrogen bonds, parallel to (100).

2-Amino-4-nitrophenol–1-(2,4,6-trihydroxyphenyl)ethanone (1/1)

In the title compound, C6H6N2O3·C8H8O4, the 2-amino-4-nitro­phenol (ANP) and 1-(2,4,6-trihy­droxy­phen­yl)ethanone (THA) mol­ecules are both nearly planar, with r.m.s. deviations of 0.0630 and 0.0313 Å, respectively. The angle between the least-squares planes of THA and ANP is 48.99 (2)°. In THA, an intra­molecular O—H⋯O hydrogen bond generates an S(6) ring motif. In the crystal, N—H⋯O, O—H⋯O and O—H⋯N hydrogen bonds lead to the formation of a three-dimensional network. There are also inter­molecular π–π inter­actions between the benzene rings of ANP–ANP and of THA–THA mol­ecules, with centroid–centroid distances of 3.5313 (14) and 3.8440 (16) Å, respectively. Weak C—O⋯π and N—O⋯π inter­actions also occur.

Effect of interarray elevation differences on infrasound beamforming

SUMMARY The International Monitoring System infrasound network will, upon completion, contain 60 microbarometer arrays with apertures of between 1 and 4 km. These arrays are located within a variety of terrains, leading to large ratios of interelement elevation differences to array aperture for those arrays situated in areas of significant topography. Systematic errors in beamforming estimates caused by neglecting the vertical extent of the arrays, are quantified for both signal backazimuth and apparent velocity. Of the 43 arrays certified as of 2011 January, I14CL on Juan Fernandez Island has the greatest topography across an array, with a least-squares fitted plane through the array elements having an 8.1° slope from the horizontal (compared to a network mean of 1.6°). Beamforming errors (both backazimuth and apparent velocity) are a function of the arrival azimuth and become increasingly large for steeply inclined arrivals, such that systematic errors will be significantly larger for signals returned from the thermosphere compared to those from the stratosphere. At several arrays, azimuthal errors due to array topography are comparable in magnitude to deviations often associated with atmospheric propagation. These findings are illustrated using signals recorded in Greenland at I18DK, where differences between results processed using both full 3-D array geometry and the 2-D (topography neglected) approximation exhibit good correspondence to theoretical predictions.

2-(5-Bromothiophen-2-yl)-5-[5-(10-ethylphenothiazin-3-yl)thiophen-2-yl]-1,3,4-oxadiazole

The mol­ecule of the title compound, C24H16BrN3OS3, contains three approximately planar fragments, viz. an oxadiazole ring plus two adjacent thio­phene groups, and two phenothia­zine benzene rings, with largest deviations from the least-squares planes of 0.051 (3), 0.019 (4) and 0.014 (3) Å, respectively. The phenothia­zine unit adopts a butterfly conformation, with a dihedral angle of 38.06 (15)° between the terminal benzene rings. The dihedral angle between the 2,5-bis­(thio­phen-2-yl)oxadiazole unit and the attached benzene ring is 15.35 (11)°. In the crystal, mol­ecules form stacks along the b-axis direction; neighboring mol­ecules within the stack are related by inversion centers, with shortest inter­centroid separations of 3.741 (2) and 3.767 (2) Å.

Potassium [1-(tert-butoxycarbonyl)-1H-indol-3-yl]trifluoroborate hemihydrate

The asymmetric unit of the title salt, K+·C13H14BF3NO2·0.5H2O, consists of two derivatized indolyltrifluoridoborate anions, two potassium cations and one water mol­ecule. Within the indolyltrifluoro­borate anions, the least-square planes consisting of the carboxyl group and the adjacent quarternary C atom of the tert-butyl groups deviate significantly from coplanarity with the indolyl planes [20.44 (11) and 21.02 (10)°]. The potassium ions are coordinated by six atoms (one K+ ion by two O and four F atoms, and the second K+ ion by one O and five F atoms), however, one of the potassium ions undergoes an additional weak potassium–π inter­action (K⋯centroid = 3.722 Å). The packing is stabilized by sequential O—H⋯O hydrogen bonds along [100] between water mol­ecules and also by O—H⋯F hydrogen bonds.

Molecular Magnetism of M6Hexagon Ring inD3dSymmetric [(MCl)6(XW9O33)2]12–(M = CuIIand MnII, X = SbIIIand AsIII)

Ferromagnetic [n-BuNH(3)](12)[(CuCl)(6)(SbW(9)O(33))(2)]·6H(2)O (1) and antiferromagnetic [n-BuNH(3)](12)[(MnCl)(6)(AsW(9)O(33))(2)]·6H(2)O (4) have been synthesized and structurally and magnetically characterized. Two complexes are structural analogues of [n-BuNH(3)](12)[(CuCl)(6)(AsW(9)O(33))(2)]·6H(2)O (2) and [n-BuNH(3)](12)[(MnCl)(6)(SbW(9)O(33))(2)]·6H(2)O (3) with their ferromagnetic interactions, first reported by us in 2006. (1) When variable temperature (T) direct current (dc) magnetic susceptibility (χ(M)) data are analyzed with the isotropic exchange Hamiltonian for the magnetic exchange interactions, χ(M)T vs T curves fitted by a full matrix diagonalization (for 1) and by the Kambe vector coupling method/Van Vleck's approximation (for 4) yield J = +29.5 and -0.09 cm(-1) and g = 2.3 and 1.9, respectively. These J values were significantly distinguished from +61.0 and +0.14 cm(-1) for 2 and 3, respectively. The magnetization under the pulsed field (up to 10(3) T/s) at 0.5 K exhibits hysteresis loops in the adiabatic process, and the differential magnetization (dM/dB) plots against the pulsed field display peaks characteristic of resonant quantum tunneling of magnetization (QTM) at Zeeman crossed fields, indicating single-molecule magnets for 1-3. High-frequency ESR (HFESR) spectroscopy on polycrystalline samples provides g(∥) = 2.30, g(⊥) = 2.19, and D = -0.147 cm(-1) for 1 (S = 3 ground state), g(∥) = 2.29, g(⊥) = 2.20, and D = -0.145 cm(-1) for 2 (S = 3), and g(∥) = 2.03 and D = -0.007 cm(-1) for 3 (S = 15). An attempt to rationalize the magnetostructural correlation among 1-4, the structurally and magnetically modified D(3d)-symmetric M (=Cu(II) and Mn(II))(6) hexagons sandwiched by two diamagnetic α-B-[XW(9)O(33)](9-) (X = Sb(III) and As(III)) ligands through M-(μ(3)-O)-W linkages, is made. The strongest ferromagnetic coupling for the Cu(6) hexagon of 2, the structure of which approximately provides the Cu(6)(μ(3)-O)(12) cylindrical geometry, is demonstrated by the polarization mechanism based on the point-dipole approximation, which provides a decrease of the ferromagnetic interaction due to the out-of-cylinder deviation of the Cu atoms for 1. The different nature of the magnetic exchange interaction in 3 and 4 is understood by the combined effect of the out-of plane deviation (the largest for 4) of the Mn atoms from the Mn(μ(3)-O)(2)Mn least-squares plane and the antiferromagnetic contribution arising from the large Mn-O-Mn bond angle. The primary contribution to D is discussed in terms of the magnetic dipole-dipole interaction between the electrons located on the magnetic sites in the M(6) hexagon.

2,7-Bis(2-nitrophenyl)-9-octyl-9H-carbazole

The title compound, C32H31N3O4, was obtained in a Suzuki coupling of carbazole diboronic acid and bromo­nitro­benzene. In the crystal, the mol­ecule adopts a non-symmetric conformation. The carbazole ring system is approximately planar [maximum deviation from the least-squares plane = 0.039 (2) Å]. The planes of the carbazole unit and the benzene rings subtend dihedral angles of 48.42 (7) and 41.81 (6)°. The dihedral angles between the planes of the nitro­phenyl rings and the nitro groups are 44.34 (19) and 61.64 (15)°. The crystal is built from two strands of parallel mol­ecules with inter­digitated octyl chains. These strands are symmetry related by a twofold screw axis.

Bis(azido-κN)(di-2-pyridylamine-κ2N2,N2′)palladium(II)

In the title complex, [Pd(N3)2(C10H9N3)], the PdII ion is in a slightly distorted square-planar coordination environment. The ligator atoms comprise the two pyridine N atoms of the chelating di-2-pyridyl­amine (dpa) ligand and two N atoms from two azide anions. The dpa ligand coordinates the Pd atom in a boat conformation, the dihedral angle between the pyridine rings being 24.4 (1)°. The pyridine rings are somewhat inclined to the least-squares plane of the PdN4 unit, making dihedral angles of 29.02 (9) and 26.47 (9)°. The azide ligands are slightly bent, with N—N—N angles of 173.0 (4) and 174.2 (4)°. In the crystal, mol­ecules are connected by N—H⋯N and C—H⋯N hydrogen bonds, forming chains along the c axis. When viewed down the b axis, successive chains are stacked in opposite directions. Intra­molecular C—H⋯N hydrogen bonds are also observed.

Control of Intramolecular π–π Stacking Interaction in Cationic Iridium Complexes via Fluorination of Pendant Phenyl Rings

Intramolecular π-π stacking interaction in one kind of phosphorescent cationic iridium complexes has been controlled through fluorination of the pendant phenyl rings on the ancillary ligands. Two blue-green-emitting cationic iridium complexes, [Ir(ppy)(2)(F2phpzpy)]PF(6) (2) and [Ir(ppy)(2)(F5phpzpy)]PF(6) (3), with the pendant phenyl rings on the ancillary ligands substituted with two and five fluorine atoms, respectively, have been synthesized and compared to the parent complex, [Ir(ppy)(2)(phpzpy)]PF(6) (1). Here Hppy is 2-phenylpyridine, F2phpzpy is 2-(1-(3,5-difluorophenyl)-1H-pyrazol-3-yl)pyridine, F5phpzpy is 2-(1-pentafluorophenyl-1H-pyrazol-3-yl)-pyridine, and phpzpy is 2-(1-phenyl-1H-pyrazol-3-yl)pyridine. Single crystal structures reveal that the pendant phenyl rings on the ancillary ligands stack to the phenyl rings of the ppy ligands, with dihedral angles of 21°, 18°, and 5.0° between least-squares planes for complexes 1, 2, and 3, respectively, and centroid-centroid distances of 3.75, 3.65, and 3.52 Å for complexes 1, 2, and 3, respectively, indicating progressively reinforced intramolecular π-π stacking interactions from complexes 1 to 2 and 3. Compared to complex 1, complex 3 with a significantly reinforced intramolecular face-to-face π-π stacking interaction exhibits a significantly enhanced (by 1 order of magnitude) photoluminescent efficiency in solution. Theoretical calculations reveal that in complex 3 it is unfavorable in energy for the pentafluorophenyl ring to swing by a large degree and the intramolecular π-π stacking interaction remains on the lowest triplet state.

4-[2-(Benzyl-amino)-phen-yl]-2,6-dimethyl-quinoline N-oxide.

The title compound, C24H22N2O, was obtained in a two-step procedure from the corresponding 4-(2-iodo­phen­yl)quinoline. The quinoline system is approximately planar [maximum deviation from the least-squares plane = 0.021 (2) Å]. The planes of the quinoline system and the phenyl ring subtend a dihedral angle of 78.08 (8)°. In the crystal, pairs of mol­ecules are connected via a center of symmetry and linked by a pair of angular N—H⋯O hydrogen bond. These dimers form columns oriented along the c axis.

N′-(3,5-Dichloro-2-hydroxybenzylidene)-4-(dimethylamino)benzohydrazide methanol monosolvate

The title compound, C16H15Cl2N3O2·CH3OH, a Schiff base molecule, is prepared by the reaction of 3,5-dichloro­salicyl­aldehyde with 4-dimethyl­amino­benzohydrazide in methanol. The Schiff base mol­ecule is approximately planar, with a mean deviation from the least-squares plane defined by the non-H atoms of 0.0452 (3) Å, and with a dihedral angle between the benzene rings of 4.2 (3)°. This planarity is assisted by the formation of an intra­molecular O—H⋯N hydrogen bond. In the crystal, adjacent Schiff base mol­ecules are linked by two methanol mol­ecules through N—H⋯O and O—H⋯O hydrogen bonds, forming dimers.

Poly[[μ10-4,4′-(ethane-1,2-diyldioxy)dibenzoato]dipotassium

The title salt, [K2(C16H12O6)]n, was obtained by the reaction of 1,2-bis­[4-(ethyl-carbox­yl)-phenox­yl]ethane with KOH in water. The anion lies on a crystallographic inversion center, which is located at the mid-point of the central C—C bond. The K+ cation is coordinated by six O atoms, two from the chelating carboxyl­ate group of the anion and four from four neighboring and monodentately binding anions, giving rise to an irregular [KO6] coordination polyhedron. The coordination mode of the cation leads to the formation of K/O layers parallel to (100). These layers are linked by the nearly coplanar anions (r.m.s. deviation of 0.064 Å of the carboxyl, aryl and O—CH2 groups from the least-squares plane) into a three-dimentional network.

4,9,12,15-Tetraoxa-3,5,8,10,14,16-hexaazatetracyclo[11.3.0.02,6.07,11]hexadeca-1(16),2,5,7,10,13-hexaen-3-ium-3-olate monohydrate

The organic mol­ecule in the title monohydrate, C6N6O5·H2O, presents an almost planar configuration, the greatest deviation from the least-squares plane through the atoms being 0.061 (1) Å for the O atom within the seven-membered ring. Each water H atom is bifurcated, one forming two O—H⋯N hydrogen bonds and the other forming O—H⋯N,O hydrogen bonds. The result of the hydrogen bonding is the formation of supra­molecular layers with a zigzag topology that stack along [001].

(E)-6-Methyl-3-(2-methylbenzylidene)chroman-2-one

In the title compound, C18H16O2, the heterocyclic ring of the chroman-2-one system adopts a slightly distorted screw-boat conformation. The dihedral angle between the least-squares planes of the coumarin ring system and the benzene ring is 67.5 (1)°. The crystal packing features C—H⋯O hydrogen bonds, which link the mol­ecules into centrosymmetric R22(8) dimers, and C—H⋯π inter­actions.

12-{[4-(2-Fluorophenyl)piperazin-1-yl]methyl}-9α-hydroxy-4,8-dimethyl-3,14-dioxatricyclo[9.3.0.02,4]tetradec-7-en-13-one

The title compound, C25H33FN2O4, was synthesized from 9α-hy­droxy­parthenolide (9α-hy­droxy-4,8-dimethyl-12-methyl­ene-3,14-dioxatricyclo­[9.3.0.02,4]tetra­dec-7-en-13-one), which was isolated from the chloro­form extract of the aerial parts of Anvillea radiata. The asymmetric unit contains two independent mol­ecules. In each mol­ecule, the ten-membered ring displays an approximative chair–chair conformation. Each of the piperazine rings adopts a perfect chair conformation, while both lactone rings show an envelope conformation, one with the C atom bearing the piperazin-1-ylmethyl group as the flap, the other with the junction C atom not attached to the ring O atom as the flap. The dihedral angles between the least-squares planes through the ten- and five-membered rings in the two mol­ecules are similar [19.1 (3) and 16.2 (3)°]. An intra­molecular O—H⋯N hydrogen bond stabilizes the mol­ecular conformation. The crystal packing is stabilized by C—H⋯O hydrogen bonds.

(E)-5-(2-Chlorophenyl)-7-ethyl-2-oxo-2,3-dihydro-1H-thieno[2,3-e][1,4]diazepin-4-ium 2,4,6-trinitrophenolate

In the title molecular salt, C15H14ClN2OS+·C6H2N3O7 −, protonation occurred on the double-bonded N atom. One of the nitro groups shows slight disorder over two orientations, with an occupancy ratio of 0.91:0.09. In the crystal, classical N—H⋯O hydrogen bonds, as well as C—H⋯O contacts connect the components into a three-dimensional network. The seven-membered ring adopts a boat-like conformation. The least-squares plane defined by its non-H atoms encloses an angle of 38.99 (6)° with the benzene ring bonded to it.

Diethyl 2-{[2-(trifluoromethyl)anilino]methylidene}propanedioate

The title compound, C15H16F3NO4, is an N-substituted derivative of ortho-trifluoro­methyl­aniline featuring a twofold Michael system. The least-squares planes defined by the atoms of the phenyl ring and the atoms of the Michael system enclose an angle of 15.52 (5)°. Apart from classical intra­molecular N—H⋯O and N—H⋯F hydrogen bonds, inter­molecular C—H⋯O contacts are observed, the latter connecting the mol­ecules into chains along [110]. The shortest inter­centroid distance between two aromatic systems is 3.6875 (9) Å.