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Dihedral angle

About: Dihedral angle is a research topic. Over the lifetime, 15718 publications have been published within this topic receiving 174904 citations.


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TL;DR: Haddon and Scott as mentioned in this paper showed that the skeletal dihedral angle may be a poor index of ir-orbital alignment, and that rehybridization from sp2 may have a significant effect on ir-orbital alignment.
Abstract: The field of bridged annulene chemistry began twenty years ago with the synthesis of 1,6methano[10]annulene, and since that time a great many variations on this theme have been reported. By their very nature it is usually impossible for these systems to attain complete coplanarity, and irorbital misalignment often occurs in the periphery. In many cases these deformations have been confirmed by structural, spectroscopic and theoretical investigation, and it has often been noted that these compounds tolerate remarkably high ir-orbital misalignment (as measured by the peripheral dihedral (torsional) angles), without quenching of the cyclic delocalization and aromatic character. It is the purpose of this communication to point out that in nonplanar conjugated molecules: (i) the skeletal dihedral angle may be a poor index of ir-orbital alignment; (ii) rehybridization (from sp2) may have a significant effect on ir-orbital alignment; (iii) the ir-orbital alignment obtained in molecules such as the bridged annulenes is far better than hitherto realized. This process is accomplished by development of a general analytical method for the location of the ir-orbital axis vector (POAV) in nonplanar conjugated molecules. The field of bridged annulene chemistry began twenty years ago with the synthesis of 1,6-methanoL 10]annulene,' and since that time a great many variations on this theme have been reported.2 By their very nature it is usually impossible for these systems to attain complete coplanarity, and ir-orbital misalignment often occurs in the periphery. In many cases these deformations have been confirmed by structural, spectroscopic and theoretical investigation,328 and it has often been noted that these compounds tolerate remarkably high ir-orbital misalignment (as measured by the peripheral (skeletal) dihedral angles), without quenching of the cyclic delocalization and aromatic character.29 It is the purpose of this study to point out that in nonplanar conjugated molecules: (i) the skeletal dihedral angle may be a poor index of ir-orbital alignment; (ii) rehybridization (from sp2) may have a significant effect on ir-orbital alignment; (iii) the ir-orbital alignment obtained in molecules such as the bridged annulenes is far better than hitherto realized. This process is accomplished by development of a general analytical method for the location of the ir-orbital axis vector (POAV) in nonplanar conjugated molecules. We begin by noting that in order for the dihedral (torsional) angle to provide a unique and accurate picture of ir-orbital alignment, each of the bonded pair of atoms must (separately) lie in the same plane as its nearest neighbors. Thus Cl, C2, C3 and R2 (Figure 1) are required to be coplanar, as are C2, C3, C4 and R3 if the dihedral angle (usually taken as Cl, C2, C3, C4) is to provide a meaningful index of ir-orbital alignment. Clearly as the restriction on coplanarity is removed, the dihedral angle is no longer unique, and in general there exist four possible choices (Cl, C2, C3, C4; Cl, C2, C3, R3; R2, C2, C3, C4; R2, C2, C3, R3). The point really at issue of course, is the state of hybridization of C2 and C3, and a more fruitful approach is to pursue the ir-orbital axis vector (POAV) directly, which is the real quantity of interest in the present context. 137 138 ft C. HADDON and L. T. SCOTT X2 — + JPx) Figure 2. Hybrid orbitals Xi, • X for hybridization intermediate between sp2 and sp3. Xi is colinear with the ic-orbital axis vector and is constructed so as to make an equal inclination to the edges of the trihedral angle formed by Xi X3 and X4 and is defined to lie along the Z-axis. 0 is the angle of inclination made by X2, X3 and X4 to the X, Y plane. X3 — — jPx — .jPy) X4 = —=(s — + /fpy) and Xi — Fs + /Pz) X2 — }(s — *Pz + jfpx) 1 1 X3 — Pz — .JfPx — JPy) X4 --(s *PzJfPx +py) (pure sp2)

247 citations

Journal ArticleDOI
TL;DR: The determination of the three‐dimensional solution structure of α1‐purothionin is that of the capital letter L, similar to that of crambin, with the longer arm comprising two approximately parallel α‐helices and the shorter arm a strand and a mini anti‐parallel β sheet.
Abstract: The determination of the three-dimensional solution structure of α1-purothionin using a combination of metric matrix distance geometry and restrained molecular dynamics calculations based on n.m.r. data is presented. The experimental data comprise complete sequence-specific proton resonance assignments, a set of 310 approximate interproton distance restraints derived from nuclear Overhauser effects, 27 O backbone torsion angle restraints derived from vicinal coupling constants, 4 distance restraints from hydrogen bonds and 12 distance restraints from disulphide bridges. The average atomic rms difference between the final nine converged structures and the mean structure obtained by averaging their coordinates is 1.5 ± 0.1 a for the backbone atoms and 2.0 ± 0.1 a for all atoms. The overall shape of α1-purothionin is that of the capital letter L, similar to that of crambin, with the longer arm comprising two approximately parallel α-helices and the shorter arm a strand and a mini anti-parallel β sheet.

242 citations

Journal ArticleDOI
TL;DR: The effects of hapten binding on the molecular structure can be analyzed by the difference Fourier technique with more reliability and the calculated phases based on the refined structure are much improved compared to isomorphous phases.
Abstract: The structure of the variable portions of a K-type Bence-Jones protein REI forming a dimer has been determined by X-ray diffraction to a resolution of 2.0 A. The structure has been refined using a constrained crystallographic refinement procedure. The final R value is 0.24 for 15000 significantly measured reflections; the estimated standard deviation of atomic positions is 0.09 A. A more objective assessment of the error in the atomic positions is possible by comparing the two independently refined monomers. The mean deviation of main-chain atoms of the two chains in internal segments in 0.22 A, of main-chain dihedral angles 6.3 degrees for these segments. The unrefined molecular structure of the VREI dimer has been published (Epp, O., Colman, P., Fehlhammer, H., Bode, W., Schiffer, M., Huber, R., and Palm, W. (1974), Eur. J. Biochem. 45, 513). Now a detailed analysis is presented in terms of hydrogen bonds and conformational angles. Secondary structural elements (antiparallel beta structure, reverse turns) are defined. A more precise atomic arrangement of the amino acid residues forming the contact region and the hapten binding site is given as well as the localization of solvent molecules. Two cis-prolines (Pro-8 and Pro-95) were detected. The intrachain disulfide bridge (Cys-23-Cys-88) occurs statistically in two alternative conformations. The structure suggests reasons for strong conservation of several amino acid residues. The knowledge of the refined molecular structure enables crystal structure analyses of related molecules to be made by Patterson search techniques. The calculated phases based on the refined structure are much improved compared to isomorphous phases. Therefore the effects of hapten binding on the molecular structure can be analyzed by the difference Fourier technique with more reliability. Hapten binding studies have been started.

240 citations

Journal ArticleDOI
TL;DR: The interactions revealed in crystal structures and EPR spectra provide an important link between the dynamics of the R1 side chain, reflected in the EPR spectrum, and local protein structure.
Abstract: High resolution (1.43-1.8 A) crystal structures and the corresponding electron paramagnetic resonance (EPR) spectra were determined for T4 lysozyme derivatives with a disulfide-linked nitroxide side chain [-CH(2)-S-S-CH(2)-(3-[2,2,5,5-tetramethyl pyrroline-1-oxyl]) identical with R1] substituted at solvent-exposed helix surface sites (Lys65, Arg80, Arg119) or a tertiary contact site (Val75). In each case, electron density is clearly resolved for the disulfide group, revealing distinct rotamers of the side chain, defined by the dihedral angles X(1) and X(2). The electron density associated with the nitroxide ring in the different mutants is inversely correlated with its mobility determined from the EPR spectrum. Residue 80R1 assumes a single g(+)()g(+)() conformation (Chi(1) = 286, X(2) = 294). Residue 119R1 has two EPR spectral components, apparently corresponding to two rotamers, one similar to that for 80R1 and the other in a tg(-)() conformation (Chi(1) = 175, X(2) = 54). The latter state is apparently stabilized by interaction of the disulfide with a Gln at i + 4, a situation also observed at 65R1. R1 residues at helix surface site 65 and tertiary contact site 75 make intra- as well as intermolecular contacts in the crystal and serve to identify the kind of molecular interactions possible for the R1 side chain. A single conformation of the entire 75R1 side chain is stabilized by a variety of interactions with the nitroxide ring, including hydrophobic contacts and two unconventional C-H.O hydrogen bonds, one in which the nitroxide acts as a donor (with tyrosine) and the other in which it acts as an acceptor (with phenylalanine). The interactions revealed in these structures provide an important link between the dynamics of the R1 side chain, reflected in the EPR spectrum, and local protein structure. A library of such interactions will provide a basis for the quantitative interpretation of EPR spectra in terms of protein structure and dynamics.

238 citations

Journal ArticleDOI
TL;DR: A complete, isostructural series of complexes with La-Lu (except Pm) with the ligand TREN-1,2-HOIQO has been synthesized and structurally characterized by means of single-crystal X-ray analysis, providing a significant advance for the prediction and rationalization of the geometric features of the corresponding lanthanide complexes.
Abstract: A complete, isostructural series of complexes with La−Lu (except Pm) with the ligand TREN-1,2-HOIQO has been synthesized and structurally characterized by means of single-crystal X-ray analysis. All complexes are 1D-polymeric species in the solid state, with the lanthanide being in an eight-coordinate, distorted trigonal-dodecahedral environment with a donor set of eight unique oxygen atoms. This series constitutes the first complete set of isostructural complexes from La−Lu (without Pm) with a ligand of denticity greater than two. The geometric arrangement of the chelating moieties slightly deviates across the lanthanide series, as analyzed by a shape parameter metric based on the comparison of the dihedral angles along all edges of the coordination polyhedron. The apparent lanthanide contraction in the individual Ln−O bond lengths deviates considerably from the expected quadratic decrease that was found previously in a number of complexes with ligands of low denticity. The sum of all bond lengths around...

231 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023203
2022473
2021160
2020195
2019193
2018216