Least-squares Plane Research Articles

Little change but great effect: varying supramolecular interactions in 2,5-dimethoxyterephthalic acid and 2,5-diethoxyterephthalic acid

The title terephthalic acid derivatives, namely 2,5-dimethoxyterephthalic acid, C(10)H(10)O(6), (I), and 2,5-diethoxyterephthalic acid, C(12)H(14)O(6), (II), exhibit nearly planar molecular structures, with maximum deviations from the least-squares planes calculated for all non-H atoms of 0.0418 (6) and 0.0902 (10) Å for (I) and (II), respectively. The molecules of both title compounds contain an inversion centre and thus the asymmetric unit of both crystal structures consists of only half a molecule. It is a remarkable fact that a comparatively small change in the substitution of the terephthalic acid [dimethoxy in (I) versus diethoxy in (II)] causes major differences in the dominating supramolecular interactions. While in (II) the packing structure is stabilized by typical intermolecular hydrogen-bonded carboxylic acid dimer interactions, the carboxyl group in (I) forms an unusual intramolecular hydrogen bond with the O atom of the neighbouring methoxy group.

21-Hydroxypregna-1,4-diene-3,20-dione

The title compound, C21H28O3, is a fungal transformed metabolite of decoxycorticosterone acetate, consisting of four fused rings A, B, C and D. Ring A is nearly planar, with a maximum deviation of 0.010 (3) Å from the least-squares plane, while the trans-fused rings B and C adopt chair conformations. The five-membered ring D is in an envelope conformation. The orientation of the side chain is stabilized by an intramolecular O—H⋯O hydrogen bond. In the crystal, adjecent mol­ecules are linked by C—H⋯O hydrogen bonds into extended zigzag chains along the a axis.

{N′-[(E)-1-(5-Bromo-2-oxidophenyl)ethylidene-κO]-4-methylbenzohydrazidato-κ2N′,O}(pyridine-κN)nickel(II)

The central NiII atom in the title complex, [Ni(C16H13BrN2O2)(C5H5N)], is in a square-planar trans-N2O2 environment defined by the NO2 donor atoms of the tridentate hydrazone ligand and the monodentate pyridine ligand. The pyridine mol­ecule forms a dihedral angle of 9.99 (11)° with the least-squares plane through the NiN2O2 atoms.

(2,3,7,8,12,13,17,18-Octaethyl-5-phenylporphyrinato)platinum(II)

The title compound, [Pt(C42H48N4)], was obtained through metallation of the corresponding free base with PtCl2, followed by crystallization from methyl­ene chloride/methanol. The mol­ecule exhibits an almost planar macrocycle with an average deviation of the 24 macrocyclic atoms from their least-squares plane (Δ24) of 0.04 Å and an average Pt—N bond length of 2.022 Å. Despite the unsymmetrical substitution pattern, there is no significant difference between distortion of the geometry at the phenyl substituted meso position and those of unsubstituted meso positions.

2-Cyano-N′-(5-hydroxy-2-nitrobenzylidene)acetohydrazide monohydrate

The title compound, C10H8N4O4·H2O, was obtained by the reaction of 5-hy­droxy-2-nitro­benzaldehyde with cyano­acetohydrazide in methanol. The non-H atoms of the hydrazone molecule are approximately coplanar, with a mean deviation from the least-squares plane of 0.056 Å. In the crystal, mol­ecules are linked by N—H⋯O, O—H⋯N and O—H⋯O hydrogen bonds, generating a three-dimensional network.

1-(Benzyloxy)naphthalene

In the title compound, C17H14O, the dihedral angle between the naphthyl ring system and the benzyl group is 83.22 (4)°. Both of these moieties are planar, with mean deviations from their least-squares planes, defined by the naphthyl ring C atoms and the O atom, and the phenyl ring C atoms and the benzyl α-C atom, of 0.0176 (1) and 0.0024 (13) Å, respectively. The crystal structure is stabilized by C—H⋯π and π–π inter­actions [centroid–centroid distance = 3.7817 (10) Å].

Methyl (2Z)-2-(2-fluoro-4-methoxybenzylidene)-5-(4-methoxyphenyl)-7-methyl-3-oxo-2,3-dihydro-5H-[1,3]thiazolo[3,2-a]pyrimidine-6-carboxylate

The asymmetric unit of the title compound, C24H21FN2O5S, consists of two crystallographically independent mol­ecules. In each mol­ecule, the central dihydro­pyrimidine ring is significantly puckered and adopts a conformation which is best described as an inter­mediate between a boat and a screw boat. The least-squares planes of the dihydro­pyrimidine rings are almost coplanar with the fluoro-substituted benzene rings, making dihedral angles of 9.04 (7) and 6.68 (7)°, and almost perpendicular to the meth­oxy-substituted benzene rings with dihedral angles of 89.23 (7) and 88.30 (7)°. In the mol­ecular structure, S(6) ring motifs are formed by C—H⋯O and C—H⋯S hydrogen bonds. In the crystal, mol­ecules are linked into a three-dimensional network by inter­molecular C—H⋯O and C—H⋯F hydrogen bonds. The crystal structure is further stabilized by a C—H⋯π inter­action.

(5E)-5-(4-Meth-oxy-benzyl-idene)-2-(piperidin-1-yl)-1,3-thia-zol-4(5H)-one.

In the title compound, C16H18N2O2S, the piperidine ring adopts a chair conformation. The central 4-thia­zolidinone ring makes dihedral angles of 12.01 (7) and 51.42 (9)°, respectively, with the benzene ring and the least-squares plane of the piperidine ring. An intra­molecular C—H⋯S hydrogen bond stabilizes the mol­ecular structure and generates an S(6) ring motif. In the crystal, mol­ecules are linked into a tape along the c axis by inter­molecular C—H⋯O hydrogen bonds.

Bis(2-hydroxyphenyl)methanone

In the title compound, C13H10O3, a benzophenone derivative, the least-squares planes defined by the C atoms of the 2-hy­droxy­phenyl rings inter­sect at an angle of 45.49 (3)°. The substituents on the aromatic systems are both orientated towards the central O atom. Intra- as well as inter­molecular O—H⋯O hydrogen bonds are observed, the latter giving rise to the formation of centrosymmetric dimers. The closest centroid–centroid distance between two π-systems is 3.7934 (7) Å.

Estimating surface roughness of terrestrial laser scan data using orthogonal distance regression

AbstractWith the increasing accessibility of terrestrial light detection and ranging scanners (LiDAR), generating tools to elicit meaningful information from high-density point cloud data has become of paramount importance. Surface roughness is one metric that has gained popularity, largely due to the accuracy and density of LiDAR-derived point cloud data. Surface roughness is typically defined as a spread of point distances from a reference datum, the standard deviation of point distances from a model surface being a commonly employed model. Unfortunately, a recent literature review has found that existing surface roughness models are far from standardized and may be prone to error resulting from underlying surface topography. In the research presented here, we develop a surface roughness model that is robust to underlying topographic variability by segmenting the point cloud with a three-dimensional regular grid, establishing local (grid cell) reference planes by orthogonal distance regression, and estimating the surface roughness of each grid cell as the standard deviation of orthogonal point-to-plane distances. This surface roughness model is employed to identify fracture and rubble zone distributions within a terrestrial LiDAR scan from a basalt outcrop in southeast Idaho, and the results are compared to a more common model based on ordinary least-squares plane fitting. Results indicate that the orthogonal regression model is robust to outcrop orientation and that the ordinary least-squares model systematically overestimates surface roughness by contaminating estimates with spatially correlated errors that increase with decreasing grid size.

5-Aminopentan-1-ol

The title compound, C5H13NO, is an aliphatic amino­alcohol with both functional groups residing on terminal C atoms. Apart from the hy­droxy group, all non-H atoms are nearly co-planar, the maximum deviation of an atom taking part in the least-squares plane defined by the mentioned non-H atoms being 0.029 (1) Å. In the crystal, O—H⋯N and N—H⋯O hydrogen bonds connect the mol­ecules, forming a three-dimensional network.

Methyl 4-hydroxy-2-isopropyl-1,1-dioxo-2H-1,2-benzothiazine-3-carboxylate

In the crystal structure of the title mol­ecule, C13H15NO5S, the S and N atoms of the thia­zine ring exihibit the maximum deviations from the least-squares plane of 0.3008 (6) and 0.3280 (7) Å, respectively. The ring therefore adopts a half chair conformation. The thia­zine ring is twisted by an angle of 13.29 (7)° with respect to the aromatic ring. The isopropyl substituent is oriented at a dihedral angle of 53.2 (12)° with respect to the thia­zine ring. An intra­molecular O—H⋯O hydrogen bond occurs. Inter­molecular hydrogen bonding is observed in the crystal structure.

1-(3-Fluorophenyl)-4,4,6-trimethyl-3,4-dihydropyrimidine-2(1H)-thione

In the title compound, C13H15FN2S, the dihydro­pyrimidine ring is essentially planar, with a maximum deviation of 0.086 (3) Å from the mean plane of the rest of the ring for the dimethyl­ated C atom. The benzene ring is almost perpendicular to the dihydro­pyrimidine ring, with a dihedral angle of 83.97 (14)°. The crystal packing is characterized by centrosymmetric dimers resulting from pairs of inter­molecular N—H⋯S hydrogen bonds. There are also C—H⋯π inter­actions.

3,3′-Dihydroxy-3,3′-bis(pyridin-3-yl-κN)-1,1′-(pyridine-2,6-diyl)dipropan-1-one](nitrato-κ2O,O′)silver(I)

In the title compound, a new macrocyclic metal complex, [Ag(NO3)(C21H15N3O4)], all non-H atoms are in a close-to-planar geometry (except for the nitrate anion), with a maximum out-of-plane deviation of 0.327 (6) Å for a pyridine C atom. The dihedral angle between the least-squares plane through the [3,3′-dihy­droxy-3,3′-bis­(pyridin-3-yl)-1,1′-(pyridine-2,6-di­yl)dipropan-1-one]silver(I) fragment and the nitrate anion is 31.29 (13)°. The mol­ecular structure is stabilized by several inter- and intra­molecular O—H⋯O and C—H⋯O hydrogen bonds. The AgI atom is coordinated by two pyridine N atoms and two O atoms of the nitrate anion in a geometry intermediate between tetrahedral and square-planar.

Ethyl 1-[2-(1H-benzotriazol-1-yl)acetyl]-4-hydroxy-2,6-diphenyl-1,2,5,6-tetrahydropyridine-3-carboxylate

In the title compound, C28H26N4O4, the tetra­hydro­pyridine ring adopts a boat conformation. The two phenyl rings form dihedral angles of 88.64 (8) and 59.28 (10)° with the best plane through the tetra­hydro­pyridine ring. The dihedral angle between the two phenyl rings is 82.55 (10)°. The benzotriazole ring system is essentially planar, with a maximum deviation of 0.009 (1) Å from the least-squares plane. The mol­ecular conformation is stabilized by an intra­molecular O—H⋯O hydrogen bond, generating an S(6) motif.

Methyl 4'-benzyl-2,2'-dimethyl-1,3-dioxo-2,3-dihydro-1H,4'H-spiro-[iso-quinoline-4,5'-oxazole]-4'-carboxyl-ate.

In the isoquinoline ring system of the title mol­ecule, C22H20N2O5, the N-heterocyclic ring is in a half-boat conformation. The least-squares plane of the dioxa-2-aza­spiro ring [maximum deviation = 0.076 (1) Å] and forms a dihedral angle of 14.54 (4)° with the phenyl ring. In the crystal, mol­ecules are linked via inter­molecular C—H⋯O hydrogen bonds into layers parallel to (100).

Diethyl 4-[2-(4-methoxyphenyl)-1H-pyrazol-3-yl]-2,6-dimethyl-1,4-dihydropyridine-3,5-dicarboxylate

In the title compound, C23H27N3O5, the pyrazole ring is inclined at dihedral angles of 38.16 (6) and 80.80 (6)°, respectively, to the least-squares planes of the benzene and dihydro­pyridine rings. In the crystal, adjacent mol­ecules are linked via a pair of N—H⋯N hydrogen bonds, forming an inversion dimer. The dimers are stacked in a column along the a axis through N—H⋯O hydrogen bonds. Intra- and inter­molecular C—H⋯N and C—H⋯O hydrogen bonds are also observed.

12-Anilinomethyl-9α-hy-droxy-4,8-dimethyl-3,14-dioxatricyclo-[9.3.0.0]tetra-dec-7-en-13-one.

The title compound, C21H27NO4, was synthesized from 9α-hy­droxy­parthenolide, which was isolated from the chloro­form extract of the aerial parts of Anvillea radiata. The asymmetric unit contains two independent mol­ecules. In each, the ten-membered ring displays an approximative chair-chair conformation. Each of the five-membered rings adopts a flattened envelope conformation, the C(H)—C—C(H) atoms representing the flap lie out of the mean plane through the remaining four atoms by 0.443 (2) and 0.553 (2) Å. The dihedral angle between the least-squares planes through the ten- and five-membered rings in the two mol­ecules are similar [22.54 (17) and 23.39 (14)°]. In the crystal, mol­ecules are linked by O—H⋯O, O—H⋯N and N—H⋯O hydrogen bonds.

Phenyl(3-methyl-1-phenylsulfonyl-1H-indol-2-yl)methanone

In the title compound, C22H17NO3S, the N atom of the indole ring system deviates by 0.031 (3) Å from a least-squares plane fitted through all nine non-H ring atoms. The geometry around the S atom can be described as distorted tetra­hedral. As a result of the electron-withdrawing character of the phenyl­sulfonyl groups, the N—Csp 2 bond lengths are longer than the typical mean value for N atoms with a planar configuration.

(2E)-2-[2-(Cyclohexylcarbamothioyl)hydrazinylidene]propanoic acid

In the title thio­urea derivative, C10H17N3O2S, the carboxyl group and the least-squares plane through the cyclo­hexyl ring are twisted out of the plane through the central CN3S residue; the respective dihedral angles are 7.18 (8) and 62.29 (4)°. The conformation about the azomethine bond [1.275 (2) Å] is E. The NH groups are anti, with one forming an intra­molecular N—H⋯N hydrogen bond. The main feature of the crystal structure is the formation of linear supra­molecular chains along [110] mediated by alternating pairs of O—H⋯O and pairs of N—H⋯S hydrogen bonds.