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Journal articles on the topic 'Dihedral angles'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Horálek, Vratislav. "Stereology of dihedral angles." Applications of Mathematics 45, no. 6 (2000): 411–17. http://dx.doi.org/10.1023/a:1022329432636.

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2

MITAN, Carmen-Irena, Emerich BARTHA та Petru FILIP. "DISTANCES lHnHn+1[A0] CALCULATED FROM 3-SPHERE DIHEDRAL ANGLES θHnHn+1[deg]". Revue Roumaine de Chimie 69, № 10-12 (2024): 579–84. https://doi.org/10.33224/rrch.2024.69.10-12.07.

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Dihedral angles θHnHn+1[deg] calculated from NMR data with 3-Sphere approach, a method under Hopf fibration and Lie group theories, are angles in close relationship with vicinal angles ϕ[deg], angles result from vicinal coupling constant 3 JHnHn+1[Hz]. The signs of dihedral angles calculated with algebraic equations are demonstrated with A2 root system Lie group. In attempt to find the best model for visualization of the phase angle of the pseudorotation P[deg] the proton-proton distances lHH[A0 ] between two atoms of carbon consecutives are calculated from 3-Sphere dihedral angles θHnHn+1[deg

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3

Sugimoto, Nobuo, and Atsushi Minato. "Retroreflector with acute dihedral angles." Optics Letters 19, no. 20 (1994): 1660. http://dx.doi.org/10.1364/ol.19.001660.

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4

Oldmixon, E. H., J. P. Butler, and F. G. Hoppin. "Dihedral angles between alveolar septa." Journal of Applied Physiology 64, no. 1 (1988): 299–307. http://dx.doi.org/10.1152/jappl.1988.64.1.299.

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To determine the dihedral angle, alpha, at the characteristic three-way septal junctions of lung parenchyma, we examined photomicrographs of sections. The three angles, A, formed where three septal traces meet on section, were measured and found to range between approximately 50 and 170 degrees. Theoretical considerations predicted that the dispersion of alpha is much narrower than that of A. The mean of A and alpha is identically 120 degrees. The standard deviation of alpha was inferred from the cumulative distribution function of A. In lungs inflated to 30 cmH2O (VL30), the standard deviatio

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5

Atavin, E. G., and L. V. Vilkov. "Dihedral Angles in Cyclic Molecules." Journal of Structural Chemistry 44, no. 5 (2003): 846–51. http://dx.doi.org/10.1023/b:jory.0000029823.17159.0b.

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6

Gubernat, Agnieszka, and Ludosław Stobierski. "Dihedral angles in silicon carbide." Ceramics International 29, no. 8 (2003): 961–65. http://dx.doi.org/10.1016/s0272-8842(03)00053-1.

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7

Cho, Eung Chun. "Dihedral angles of n-simplices." Applied Mathematics Letters 5, no. 4 (1992): 55–57. http://dx.doi.org/10.1016/0893-9659(92)90087-p.

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8

-M. Schlenker, J. "Dihedral Angles of Convex Polyhedra." Discrete & Computational Geometry 23, no. 3 (2000): 409–17. http://dx.doi.org/10.1007/pl00009509.

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9

DERYABIN, Igor, Viktor GUZEEV, Alexander KOZLOV, and Dmitrii ARDASHE. "FEATURES OF PROCESSING AND ASSEMBLY OF COMPOSITE PRODUCTS." Machine Science Journal 11, no. 2 (2022): 37–43. http://dx.doi.org/10.61413/iwwe8712.

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The paper examines the assembling of cylindrical products consisting of sector parts with dihedral angles. A crucial issue in the assembly of such parts is the accuracy of dihedral angles during processing. Based on methods of analytical geometry, we proved that in order to achieve gapless assembly of three sectors, the sum of all dihedral angles of the sectors should be less than or equal to 360°. Since it is impossible to ensure the exact equality of the sum of all dihedral angles of 360°, characteristic “flatness deviation” is always formed during assembly. In order t obtain a gapless conne

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10

Suo, Yue, Ling Zhou, Huiling Zhu, and Lucheng Ji. "The influence of two different dihedral angles on diffuser performance based on LES." Journal of Physics: Conference Series 2820, no. 1 (2024): 012100. http://dx.doi.org/10.1088/1742-6596/2820/1/012100.

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Abstract The influence of two different dihedral angles on diffusion capability and flow separation in a diffuser was investigated in this study. Geometric models of straight-walled diffusers with dihedral angles of 90° and 108° were established. The mean and transient flow fields were obtained by using the large eddy simulation (LES) method. The research results show that increasing the dihedral angle enhances the diffusion capability of the diffuser and reduces the volume fraction of the mean separation zones for the diffusers with dihedral angles of 90° and 108°. Besides, hairpin vortexes a

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11

Priestle, John P. "Improved dihedral-angle restraints for protein structure refinement." Journal of Applied Crystallography 36, no. 1 (2003): 34–42. http://dx.doi.org/10.1107/s0021889802018265.

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Because of the relatively low-resolution diffraction of typical protein crystals, structure refinement is usually carried out employing stereochemical restraints to increase the effective number of observations. Well defined values for bond lengths and angles are available from small-molecule crystal structures. Such values do not exist for dihedral angles because of the concern that the strong crystal contacts in small-molecule crystal structures could distort the dihedral angles. This paper examines the dihedral-angle distributions in ultra-high-resolution protein structures (1.2 Å or better

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12

Bottomley, GA. "Dihedral Angles of the Cycloheptane Ring." Australian Journal of Chemistry 41, no. 7 (1988): 1139. http://dx.doi.org/10.1071/ch9881139.

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A method is described for calculating sets of dihedral angles in a seven- membered ring with equal tetrahedral bond angles and equal bond lengths. Representative values are given for the separate chair and boat manifolds of solutions.

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13

Lehane, Ryan L., James A. Golen, Arnold L. Rheingold, and David R. Manke. "Dimethyl 2,2′-dinitrobiphenyl-4,4′-dicarboxylate." Acta Crystallographica Section E Structure Reports Online 70, no. 3 (2014): o305. http://dx.doi.org/10.1107/s1600536814003067.

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The title compound, C16H12N2O8, exhibits two near-planar aromatic ester groups with aryl–ester dihedral angles of 2.1 (2) and 4.2 (3)°. The dihedral angle between the aromatic rings is 58.0 (1)°. The two nitro groups are tilted slightly from the plane of the aromatic rings, making dihedral angles of 14.1 (1) and 8.2 (2)°. In the crystal, molecules are connected by weak C—H...O interactions, forming a three-dimensional network.

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14

Hogervorst, M. A., and R. A. Eagle. "Accurate Recovery of Structure from Motion under Perspective Projection." Perception 26, no. 1_suppl (1997): 176. http://dx.doi.org/10.1068/v970375.

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For small objects rotating over a small angle, the 3-D structure and motion are inseparable. Increasing the angle of rotation helps to define image accelerations while increasing the angular size of the object produces greater perspective effects. Both of these cues could be used by the visual system to disambiguate the structure and motion. In a 2 × 2 design we tested the influence of angular size (8 deg ‘S’ or 32 deg ‘L’) and projection type (perspective ‘P’ or orthographic ‘O’) on the perceived dihedral angle of vertically hinged planes (‘open books’). Stimuli depicted hinged planes with di

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MITAN, Carmen-Irena, Emerich BARTHA, and Petru FILIP. "Relationship between tetrahedral and dihedral on hypersphere coordinates." Revue Roumaine de Chimie 68, no. 5-6 (2023): 261–68. http://dx.doi.org/10.33224/rrch.2023.68.5-6.09.

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The wave character of the NMR data (chemical shift ΔδCn[ppm] – vicinal coupling constant 3JHH[Hz]) enable calculation the tandem dihedral-vicinal or tetrahedral-internal angles with 3-sphere approach. Golden ratio, invers of Fibonacci number, and manifold inversion torus to Dupin cyclide under 3-sphere units ensure the calculation of the tetrahedral angles of five membered ring in opposite with dihedral angles sin versus tan functions. The transformation from space/time to space under electric and magnetic rule gives dodecahedron and icosahedron values for calculation tetrahedral angles from p

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16

Mitan, Carmen-Irena, Emeric Bartha, Petru Filip, Constantin Draghici, Miron-Teodor Caproiu, and Robert Moriarty. "Java Script Programs for Calculation of Dihedral Angles with Manifold Equations." Science Journal of Chemistry 12, no. 3 (2024): 42–54. http://dx.doi.org/10.11648/j.sjc.20241203.11.

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Java Script programs for calculation dihedral angles from NMR data with manifold equations of 3-Sphere approach: rectangle, Villarceau circles of cyclide (Torus – Dupin Cyclide), polar equations, Euler-Conic. Manifolds are curves or surface in higher dimension used for calculation of dihedral angles under wave character of NMR data, carbon and/or proton chemical shift δ&lt;sub&gt;Xn&lt;/sub&gt;[ppm] and vicinal coupling constant &lt;sup&gt;3&lt;/sup&gt;&lt;I&gt;J&lt;/I&gt;&lt;sub&gt;HnHn+1&lt;/sub&gt;[Hz]. 3-Sphere approach for ca

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17

Johmoto, Kohei, Takashi Ishida, Akiko Sekine, Hidehiro Uekusa, and Yuji Ohashi. "Relation between photochromic properties and molecular structures in salicylideneaniline crystals." Acta Crystallographica Section B Structural Science 68, no. 3 (2012): 297–304. http://dx.doi.org/10.1107/s0108768112010993.

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The crystal structures of the salicylideneaniline derivatives N-salicylidene-4-tert-butyl-aniline (1), N-3,5-di-tert-butyl-salicylidene-3-methoxyaniline (2), N-3,5-di-tert-butyl-salicylidene-3-bromoaniline (3), N-3,5-di-tert-butyl-salicylidene-3-chloroaniline (4), N-3,5-di-tert-butyl-salicylidene-4-bromoaniline (5), N-3,5-di-tert-butyl-salicylidene-aniline (6), N-3,5-di-tert-butyl-salicylidene-4-carboxyaniline (7) and N-salicylidene-2-chloroaniline (8) were analyzed by X-ray diffraction analysis at ambient temperature to investigate the relationship between their photochromic properties and mo

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18

Subramanian, Raghavendran, and Kazem Kazerounian. "Residue Level Inverse Kinematics of Peptide Chains in the Presence of Observation Inaccuracies and Bond Length Changes." Journal of Mechanical Design 129, no. 3 (2006): 312–19. http://dx.doi.org/10.1115/1.2406102.

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The process of calculating the dihedral angles of a peptide chain from atom coordinates in the chain is called residue level inverse kinematics. The uncertainties and experimental observation inaccuracies in the atoms’ coordinates handicap this otherwise simple and straightforward process. In this paper, we present and analyze three new efficient methodologies to find all the dihedral angles of a peptide chain for a given conformation. Comparison of these results with the dihedral angle values reported in the protein data bank (PDB) indicates significant improvements. While these improvements

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19

Bakare, Oladapo, Candice Thompson, Yakini Brandy, and Ray J. Butcher. "2-Chloro-N-(2-chlorobenzoyl)-N-(2-ethyl-4-oxo-3,4-dihydroquinazolin-3-yl)benzamide." Acta Crystallographica Section E Structure Reports Online 70, no. 4 (2014): o503—o504. http://dx.doi.org/10.1107/s1600536814006035.

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In the title compound, C24H17Cl2N3O3, the quinazolinone ring system is close to planar (r.m.s. deviation = 0.0132 Å), with the imide unit almost perpendicular to it, subtending a dihedral angle of 89.1 (1)°. However, the imide unit itself is not planar, the dihedral angle between the two O=C—N components being 34.6 (1)°. The dihedral angle between the two chlorobenzene rings is 40.50 (7)°, while the angles between these rings and the imide moiety are 54.6 (1) and 58.2 (1)°, respectively. The dihedral angles between the 2-chlorophenyl rings and the quinazolinone ring system are 48.77 (5) and 32

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20

Jahns, Hartmut, Pierre Koch, Dieter Schollmeyer, and Stefan Laufer. "1-[2-(Benzylamino)-4-pyridyl]-2-(4-fluorophenyl)ethane-1,2-dione." Acta Crystallographica Section E Structure Reports Online 65, no. 6 (2009): o1451. http://dx.doi.org/10.1107/s1600536809019801.

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The crystal structure of the title compound, C20H15FN2O2, contains two crystallographically independent molecules, which are related by a pseudo-inversion center and linked into dimersviaintermolecular N—H...N hydrogen bonds. The 4-fluorophenyl ring of moleculeAmakes dihedral angles of 17.17 (16) and 62.25 (15)°, respectively, with the phenyl and pyridine rings. The 4-fluorophenyl ring of moleculeBmakes dihedral angles of 8.50 (16) and 64.59 (15)°, respectively, with the phenyl and pyridine rings. The dihedral angle between the pyridine ring and the phenyl ring of moleculeA[60.97 (15)°] is big

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21

Kim, Sung-Gon. "N-(2-Formylphenyl)-4-methyl-N-[(4-methylphenyl)sulfonyl]benzenesulfonamide." Acta Crystallographica Section E Structure Reports Online 70, no. 6 (2014): o660. http://dx.doi.org/10.1107/s1600536814010666.

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In the title compound, C21H19NO5S2, the dihedral angles between the formylphenyl ring and the two methylphenyl rings are 29.3 (3) and 28.9 (3)°, respectively; the dihedral angle between the methylphenyl rings is 48.4 (2)°. The C—N—S—C torsion angles are −74.1 (2) and −105.4 (2)°. In the crystal, molecules are linked by pairs of C—H...O hydrogen bonds, forming inversion dimers.

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22

Zhang, W., P. Sachenko, and J. H. Schneibel. "Kinetics of Thermal Grain Boundary Grooving for Changing Dihedral Angles." Journal of Materials Research 17, no. 6 (2002): 1495–501. http://dx.doi.org/10.1557/jmr.2002.0222.

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In his classic paper on thermal grain boundary grooving Mullins [W.W. Mullins, J. Appl. Physics 28, 333 (1957)] assumes that the dihedral angle at the groove root remains constant and predicts that the groove width and depth grow αt0.25. Here, we derive models describing groove growth while the dihedral angle changes. In our grooving experiments with tungsten at 1350 °C in which the dihedral angle decreased, the growth exponent for the groove depth reached values as high as 0.44 while the growth exponent for the width decreased slightly from Mullins' value of 0.25. Hence groove width data alon

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23

Cao, Chen, Lincong Wang, Xiaoyang Chen, Shuxue Zou, Guishen Wang, and Shutan Xu. "Amino Acids in Nine Ligand-Prefer Ramachandran Regions." BioMed Research International 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/757495.

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Several secondary structures, such asπ-helix and left-handed helix, have been frequently identified at protein ligand-binding sites. A secondary structure is considered to be constrained to a specific region of dihedral angles. However, a comprehensive analysis of the correlation between main chain dihedral angles and ligand-binding sites has not been performed. We undertook an extensive analysis of the relationship between dihedral angles in proteins and their distance to ligand-binding sites, frequency of occurrence, molecular potential energy, amino acid composition, van der Waals contacts,

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24

Zukerman-Schpector, Julio, I. Caracelli, Hélio A. Stefani, Amna N. Khan, and Edward R. T. Tiekink. "Crystal structure of ethyl 2-[(4-bromophenyl)amino]-3,4-dimethylpent-3-enoate." Acta Crystallographica Section E Structure Reports Online 70, no. 10 (2014): o1122—o1123. http://dx.doi.org/10.1107/s1600536814020832.

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In the title compound, C15H20BrNO2, there are two independent molecules (AandB) comprising the asymmetric unit and these adopt very similar conformations. InA, the dihedral angle between the CO2and MeC=CMe2groups is 80.7 (3)°, and these make dihedral angles of 3.5 (3) and 84.09 (16)°, respectively, with the bromobenzene ring. The equivalent dihedral angles for moleculeBare 78.4 (3), 2.1 (3) and 78.37 (12)°, respectively. The most prominent interactions in the crystal packing are amine-N—H...O(carbonyl) hydrogen bonds between the two independent molecules, resulting in non-centrosymmetric ten-m

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25

Reeds, James A., and James P. Butler. "Stereology of Dihedral Angles II: Distribution Function." SIAM Journal on Applied Mathematics 47, no. 3 (1987): 678–87. http://dx.doi.org/10.1137/0147046.

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26

Wood, Matthew J., and Jonathan D. Hirst. "Protein secondary structure prediction with dihedral angles." Proteins: Structure, Function, and Bioinformatics 59, no. 3 (2005): 476–81. http://dx.doi.org/10.1002/prot.20435.

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27

Tan, Meltem, İshak Bildirici, and Nurettin Mengeş. "Determination of the enol form of asymmetric 1,3-dicarbonyl compounds: 2D HMBC NMR data and DFT calculations." Journal of the Serbian Chemical Society 83, no. 9 (2018): 953–68. http://dx.doi.org/10.2298/jsc010318053t.

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In this study, a series of asymmetric aryl 1,3-dicarbonyl compounds were synthesized and their enol forms were observed via experimental data and theoretical calculations. According to the 1H- and 13C-NMR results, all the investigated compounds were found as a single enol form in CDCl3 solution. Moreover, their HMBC spectra were applied to identify the observed enol forms and correlations between certain protons and carbon atoms were considered. The dihedral angles of the asymmetric compounds that have aryl units on both sides were calculated by DFT to understand the reason for the observed en

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28

Butler, J. P., E. H. Oldmixon, and F. G. Hoppin. "Dihedral angles of septal “bend” structures in lung parenchyma." Journal of Applied Physiology 81, no. 4 (1996): 1800–1806. http://dx.doi.org/10.1152/jappl.1996.81.4.1800.

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Butler, J. P., E. H. Oldmixon, and F. G. Hoppin, Jr.Dihedral angles of septal “bend” structures in lung parenchyma. J. Appl. Physiol. 81: 1800–1806, 1996.—Alveolar parenchyma comprises two interacting tensile systems: the cable system (a network of linear condensations of connective tissue) and the membrane system (a network of quasiplanar alveolar septa). Inferences can be drawn about the mechanics of this structure from its configuration. We reported earlier (E. H. Oldmixon, J. P. Butler, and F. G. Hoppin, Jr. J. Appl. Physiol. 64: 299–307, 1988) that the angles between alveolar septa at the

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29

Reddy, M. Sivasankar, Y. Sarala, M. Jagadeesh, Samar K. Das, and Varada Reddy Ammireddy. "5-Hydroxy-2-nitrobenzaldehyde thiosemicarbazone (HNBATSC)." Acta Crystallographica Section E Structure Reports Online 70, no. 8 (2014): o846. http://dx.doi.org/10.1107/s1600536814015098.

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The asymmetric unit of the title compound, C8H8N4O3S, consists of two independent molecules. Each molecule is approximately planar with dihedral angles of 8.71 (3) and 1.50 (2)° between the aromatic ring and the thiosemicarbazide moiety while the NO2group makes dihedral angles of 29.27 (3) and 17.78 (3)° with the benzene ring. In the crystal, the molecules are linked by N—H...S, O—H...O and N—H...O hydrogen bonds, forming two-dimensional networks parallel to (100).

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30

Trigunait, Ankur, Kannan Damodharan, Bakthadoss Manickam, and Gunasekaran Krishnasamy. "Crystal structure of methyl (2Z)-2-{[N-(2-formylphenyl)-4-methylbenzenesulfonamido]methyl}-3-(4-methoxyphenyl)prop-2-enoate." Acta Crystallographica Section E Crystallographic Communications 71, no. 12 (2015): o1088—o1089. http://dx.doi.org/10.1107/s2056989015024172.

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In the title compound, C26H25NO6S, the S atom shows a distorted tetrahedral geometry, with O—S—O [119.46 (9)°] and N—S—C [107.16 (7)°] angles deviating from ideal tetrahedral values, a fact attributed to the Thorpe–Ingold effect. The sulfonyl-bound phenyl ring forms dihedral angles of 41.1 (1) and 83.3 (1)°, respectively, with the formylphenyl and phenyl rings. The dihedral angle between formylphenyl and phenyl rings is 47.6 (1)°. The crystal packing features C—H...O hydrogen-bond interactions.

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31

Guo, Y. Z., J. G. Liu, and S. Y. Yang. "5-(2,5-Dioxooxolan-3-yl)-8-methyl-3,3a,4,5-tetrahydro-1H-naphtho[1,2-c]furan-1,3-dione." Acta Crystallographica Section E Structure Reports Online 69, no. 2 (2013): o226. http://dx.doi.org/10.1107/s1600536813000482.

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In the title compound, C17H14O6, the dihedral angle between the two anhydride rings is 76.01 (8)°while the dihedral angles between the benzene and anhydride rings are 42.60 (7) and 68.94 (7)°. The cyclohexene ring of the tetrahydronaphthalene unit exhibits an envelope conformation.

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32

Prasath, R., P. Bhavana, Seik Weng Ng та Edward R. T. Tiekink. "[meso-5,10,15,20-Tetrakis(5-bromothiophen-2-yl)porphyrinato-κ4N,N′,N′′,N′′′]nickel(II)". Acta Crystallographica Section E Structure Reports Online 68, № 4 (2012): m471—m472. http://dx.doi.org/10.1107/s1600536812011671.

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The NiIIatom in the title porphyrin complex, [Ni(C36H16Br4N4S4)], is in a square-planar geometry defined by four pyrrole N atoms. There is considerable buckling in the porphyrin ring with the dihedral angles between the N4donor set and the pyrrole rings being in the range 17.0 (3)–18.8 (3)°. Each of the six-membered chelate rings is twisted about an Ni—N bond and the dihedral angles between diagonally opposite chelate rings are 13.08 (15) and 13.45 (11)°; each pair of rings is orientated in opposite directions. The bromothienyl rings are twisted out of the plane of the central N4core with dihe

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Prasath, R., P. Bhavana, Sushil K. Gupta та Ray J. Butcher. "[meso-5,10,15,20-Tetrakis(3-methylthiophen-2-yl)porphyrinato-κ4N,N′,N′′,N′′′]nickel(II) benzene hemisolvate". Acta Crystallographica Section E Structure Reports Online 69, № 12 (2013): m652—m653. http://dx.doi.org/10.1107/s1600536813030468.

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In the title compound, [Ni(C40H28N4S4)]·0.5C6H6, the NiIIatom is in a square-planar geometry defined by four pyrrole N atoms. There is considerable buckling in the porphyrin ring with the dihedral angles between the N4donor set and the pyrrole rings being in the range 16.24 (5)–22.47 (5)°. Each of the six-membered chelate rings is twisted about an Ni—N bond and the dihedral angles between diagonally opposite chelate rings are 21.36 (4) and 23.87 (4)°; each pair of rings is oriented in opposite directions. The methylthienyl rings are twisted out of the plane of the central N4core with dihedral

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34

Jackson, Michael, and Henry H. Mantsch. "Protein secondary structure from FT-IR spectroscopy: correlation with dihedral angles from three-dimensional Ramachandran plots." Canadian Journal of Chemistry 69, no. 11 (1991): 1639–42. http://dx.doi.org/10.1139/v91-240.

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The frequency of the so-called "amide I" band (amide C=O stretching vibration, vC=O) of proteins is discussed in terms of the dihedral angles of the various secondary structures present within proteins. We propose that in the case of intra- or intermolecular hydrogen-bonded amide carbonyl groups the frequency of this absorption can be directly related to the [Formula: see text], ψ angles of the amide moieties for the major secondary structures. Amide I bands at frequencies above those found for non-hydrogen bonded amide carbonyl groups are rationalized in terms of a change in the third dihedra

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35

Fun, Hoong-Kun, Tze Shyang Chia, Mashooq A. Bhat, Mohamed A. Al-Omar, and Hatem A. Abdel-Aziz. "(E)-2-(2,3-Dimethylanilino)-N′-(thiophen-2-ylmethylidene)benzohydrazide." Acta Crystallographica Section E Structure Reports Online 68, no. 8 (2012): o2524—o2525. http://dx.doi.org/10.1107/s160053681203259x.

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In the title compound, C20H19N3OS, the central benzene ring makes dihedral angles of 45.36 (9) and 55.33 (9)° with the thiophene ring and the dimethyl-substituted benzene ring, respectively. The dihedral angle between the thiophene ring and dimethyl-substituted benzene ring is 83.60 (9)°. The thiophene ring and the benzene ring are twisted from the mean plane of the C(=O)—N—N=C bridge [maximum deviation = 0.0860 (13) Å], with dihedral angles of 23.86 (9) and 24.77 (8)°, respectively. An intramolecular N—H...O hydrogen bond generates anS(6) ring. In the crystal, molecules are linked by N—H...O

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36

Rodríguez, Alan J., J. Martin E. Quirke, and Aida O. Diouf. "Crystal structure of methylN-ferrocenylcarbamate." Acta Crystallographica Section E Crystallographic Communications 71, no. 2 (2015): m30. http://dx.doi.org/10.1107/s2056989015000043.

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The asymmetric unit of the title compound, [Fe(C5H5)(C7H8NO2)], contains two independent molecules consisting of a ferrocenyl moiety and a nitrogen-bound methyl carbamate. These units are almost perpendicular to each other, making dihedral angles of 87.74 (9) and 87.32 (8)°. In each independent molecule, the cyclopentadienyl rings deviate slightly from an eclipsed conformation and lie virtually parallel [dihedral angles = 1.42 (15) and 0.49 (13)°]. In the crystal, molecules are linked by N—H...O hydrogen bonds into chains along thea-axis direction.

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37

Förster, Sebastian, Wilhelm Seichter, and Edwin Weber. "Crystal structure of 1,3-bis{[4-(acetylsulfanyl)phenyl]ethynyl}azulene." Acta Crystallographica Section E Crystallographic Communications 71, no. 12 (2015): o1099—o1100. http://dx.doi.org/10.1107/s2056989016000323.

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In the title compound, C30H20O2S2, the dihedral angles between the central azulene ring system (r.m.s. deviation = 0.039 Å) and the pendant benzene rings are 28.96 (7) and 55.15 (7)°. The dihedral angles between the benzene rings and their attached acetylsulfanyl groups are 59.60 (10) and 84.79 (10)°. The expected π–π stacking interactions are not observed in the crystal structure; instead, the packing features C—H...O hydrogen bonds, which link the molecules intoC(12) [010] chains, which are supported by weak C—H...π contacts.

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38

Peng, Xin-Mei, Ben-Tao Yin, and Cheng-He Zhou. "(Z)-3-(4-Chlorophenyl)-1-(2,4-difluorophenyl)-2-(1H-1,2,4-triazol-1-yl)prop-2-en-1-one." Acta Crystallographica Section E Structure Reports Online 68, no. 6 (2012): o1828. http://dx.doi.org/10.1107/s1600536812022118.

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The asymmetric unit of the title compound, C17H10ClF2N3O, contains three independent molecules. In each molecule, the C=C bond has a cis conformation with respect to the triazole and chlorophenyl groups. The dihedral angles formed by the triazole ring with the diflurophenyl and chlorophenyl benzene rings, respectively, are 20.10 (14) and 73.22 (15), 25.31 (15) and 84.44 (15), and 16.44 (13) and 61.72 (14)° in the three molecules while the dihedral angles between the benzene rings are 66.54 (13), 85.82 (12) and 58.37 (12)°.

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39

RUVINSKY, ANATOLY M., TATSIANA KIRYS, ALEXANDER V. TUZIKOV, and ILYA A. VAKSER. "STRUCTURE FLUCTUATIONS AND CONFORMATIONAL CHANGES IN PROTEIN BINDING." Journal of Bioinformatics and Computational Biology 10, no. 02 (2012): 1241002. http://dx.doi.org/10.1142/s0219720012410028.

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Structure fluctuations and conformational changes accompany all biological processes involving macromolecules. The paper presents a classification of protein residues based on the normalized equilibrium fluctuations of the residue centers of mass in proteins and a statistical analysis of conformation changes in the side-chains upon binding. Normal mode analysis and an elastic network model were applied to a set of protein complexes to calculate the residue fluctuations and develop the residue classification. Comparison with a classification based on normalized B-factors suggests that the B-fac

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40

El Fal, Mohammed, Youssef Ramli, El Mokhtar Essassi, Mohamed Saadi, and Lahcen El Ammari. "Crystal structure of 1,5-diethyl-3′,5′-diphenyl-1,5-dihydro-3′H-spiro[pyrazolo[3,4-d]pyrimidine-4,2′-[1,3,4]thiadiazole]." Acta Crystallographica Section E Crystallographic Communications 71, no. 10 (2015): o769—o770. http://dx.doi.org/10.1107/s2056989015017405.

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In the title compound, C22H22N6S, the pyrazolo[3,4-d]pyrimidine rings system is almost planar, with the r.m.s. deviation for the fitted atoms being 0.011 Å. The two phenyl groups linked to the thiadiazole ring are nearly perpendicular to the fused-ring system as indicated by the dihedral angles of 86.93 (10) and 83.35 (11)°. However, the phenyl rings are almost coplanar with the thiadiazole ring (r.m.s. deviation = 0.015 Å), forming dihedral angles of 10.44 (11) and 10.06 (12)°. In the crystal, molecules are connected into a supramolecular layer in theacplaneviaC—H...π interactions.

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41

Afzal, Sadaf, Zareen Akhter, and M. Nawaz Tahir. "4-[(E)-({4-[(4-Aminophenyl)sulfonyl]phenyl}imino)methyl]phenol ethanol monosolvate." Acta Crystallographica Section E Structure Reports Online 68, no. 6 (2012): o1789. http://dx.doi.org/10.1107/s1600536812021563.

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In the title compound, C19H16N2O3S·C2H6O, the 4-hydroxybenzylidene group is oriented at dihedral angles of 73.17 (7) and 77.06 (7)° with respect to the aniline groups. The sulfonyl group make dihedral angles of 44.89 (13) and 59.16 (12)° with the adjacent aniline groups. In the crystal, a two-dimensional polymeric network parallel to (010) is formed by N—H...O, O—H...N and O—H...O hydrogen bonds. There also exist π–π interactions with a distance of 3.5976 (18) Å between the centroids of hydroxyphenyl rings.

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42

Wang, Guo-Xi, and Heng-Yun Ye. "5-(4′-Methylbiphenyl-2-yl)-2-triphenylmethyl-2H-tetrazole." Acta Crystallographica Section E Structure Reports Online 63, no. 11 (2007): o4410. http://dx.doi.org/10.1107/s1600536807051537.

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The title compound, C33H26N4, was synthesized in two steps from 2-phenylbenzonitrile. Geometric parameters are in the usual ranges. The tetrazole ring encloses dihedral angles of 45.76 (9), 71.44 (8) and 72.38 (6)° with the three phenyl rings of the triphenylmethyl group. The dihedral angle between the tetrazole ring and the benzene ring directly attached to it is 49.13 (8)° and the dihedral angle between the aromatic rings of the biphenyl group is 54.29 (8)°.

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43

Vieira, Vanessa C. M., James A. Golen, Arnold L. Rheingold, and David R. Manke. "Dimethyl 2-nitrobiphenyl-4,4′-dicarboxylate." Acta Crystallographica Section E Structure Reports Online 70, no. 3 (2014): o371. http://dx.doi.org/10.1107/s1600536814004218.

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The title compound, C16H13NO6, exhibits a biphenyl unit with a dihedral angle between the two aryl rings of 56.01 (5)°. The two ester groups vary slightly from planarity, with aryl–ester dihedral angles of 4.57 (5) and 16.73 (5)°. The nitro group is turned from the aromatic unit with an aryl–nitro dihedral angle of 48.66 (4)°. In the crystal, molecules are connected by weak C—H...O interactions, forming a three-dimensional network.

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44

Nesterov, Volodymyr V., Andrea Suina, Mikhail Yu Antipin, Tatiana V. Timofeeva, Stephen Barlow, and Seth R. Marder. "N,N-Dimethyl-N′-[(1E,2E)-3-(4-nitrophenyl)prop-2-enylidene]benzene-1,4-diamine and N,N-dimethyl-4-[(1E,3E)-4-(4-nitrophenyl)buta-1,3-dienyl]-1-naphthylamine." Acta Crystallographica Section C Crystal Structure Communications 59, no. 11 (2003): o625—o628. http://dx.doi.org/10.1107/s0108270103020985.

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Syntheses and X-ray structural investigations have been carried out for the two title compounds, viz. C17H17N3O2, (I), and C22H20N2O2, (II). The molecular skeleton of (I) is slightly non-planar; the dihedral angles between the conjugated linkage and the p-(dimethylamino)phenyl ring, and between the linkage and the p-nitrophenyl ring are 13.0 (2) and 13.8 (2)°, respectively. The dihedral angle between the slightly pyramidal dimethylamine substituent and the aromatic ring is 23.3 (1)°. The molecular skeleton of (II) is not planar; the dihedral angles between the conjugated linkage and the naphth

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45

Zhang, Shu-Ping, Zhao-Di Liu, and Si-Chang Shao. "4-(4-Chlorophenyl)-5-(4-methylphenyl)-3-(2-pyridyl)-4H-1,2,4-triazole." Acta Crystallographica Section E Structure Reports Online 62, no. 4 (2006): o1279—o1280. http://dx.doi.org/10.1107/s1600536806007690.

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In the title compound, C20H15ClN4, the two benzene rings form dihedral angles of 30.95 (9) and 70.69 (6)° with the triazole ring, and the dihedral angle between the triazole and the pyridine rings is 43.38 (8)°. Intermolecular C—H...N hydrogen bonds are observed in the crystal structure.

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46

Zhang, Shu-Ping, Zhao-Di Liu, Shui-Deng Chen, Song Yang, and Si-Chang Shao. "4-(4-Methoxyphenyl)-5-(4-methylphenyl)-3-(2-pyridyl)-4H-1,2,4-triazole." Acta Crystallographica Section E Structure Reports Online 62, no. 4 (2006): o1516—o1517. http://dx.doi.org/10.1107/s1600536806009718.

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In the title compound, C21H18N4O, the p-methoxyphenyl and p-tolyl rings form dihedral angles of 61.33 (7) and 31.16 (7)°, respectively, with the triazole ring, and the dihedral angle between the triazole and pyridine rings is 46.25 (7)°. Intermolecular C—H...N hydrogen bonds link inversion-related molecules into chains.

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47

Rao, H. Surya Prakash, Ramalingam Gunasundari, and Jayaraman Muthukumaran. "Crystal structure analysis of ethyl 3-(4-chlorophenyl)-1,6-dimethyl-4-methylsulfanyl-1H-pyrazolo[3,4-b]pyridine-5-carboxylate." Acta Crystallographica Section E Crystallographic Communications 76, no. 3 (2020): 443–45. http://dx.doi.org/10.1107/s2056989020002479.

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In the title compound, C18H18ClN3O2S, the dihedral angle between the fused pyrazole and pyridine rings is 3.81 (9)°. The benzene ring forms dihedral angles of 35.08 (10) and 36.26 (9)° with the pyrazole and pyridine rings, respectively. In the crystal, weak C—H...O hydrogen bonds connect molecules along [100].

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48

Mohamed, Shaaban K., Joel T. Mague, Mehmet Akkurt, Mustafa R. Albayati, and Alaa F. Mohamed. "Crystal structure of 1-(2,4-dinitrophenyl)-3,5-diphenyl-1H-pyrazole." Acta Crystallographica Section E Crystallographic Communications 71, no. 12 (2015): o931—o932. http://dx.doi.org/10.1107/s2056989015021350.

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In the title molecule, C21H14N4O4, the phenyl rings make dihedral angles of 39.61 (8) and 9.4 (1)°, respectively, with the central pyrazole ring. The dihedral angle between the pyrazole and dinitrophenyl rings is 46.95 (5)°. In the crystal, molecules pack in helical stacks parallel to theaaxis aided by weak C—H...O interactions.

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49

Butler, James P., and James A. Reeds. "Stereology of Dihedral Angles I: First Two Moments." SIAM Journal on Applied Mathematics 47, no. 3 (1987): 670–77. http://dx.doi.org/10.1137/0147045.

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50

Roeder, R. K. W. "Compact hyperbolic tetrahedra with non-obtuse dihedral angles." Publicacions Matemàtiques 50 (January 1, 2006): 211–27. http://dx.doi.org/10.5565/publmat_50106_12.

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