Symbolic representation of the molecular conformation of calixarenes

In calixarene chemistry there is a continuous search for new shaping units or substructures useful for molecular recognition or for the binding of ions. The problem of assigning their molecular conformations cannot be dealt with by the use of the dihedral angles as done until now, because this method contains intrinsic ambiguities. The new approach, proposed here, is based on the use of the set ofn pairs of torsion angles (conformational parameters) which involve the flexible part of the calixarene and it is free of ambiguities. Moreover, knowledge of the set of conformational parameters allows one to build straightforwardly three-dimensional molecular models. A symbolic representation of the molecular conformation of any calix[n]arene may be obtained by combining the Schöenflies symbol of the molecular symmetry together with the signs of the conformational parameters.     

Etude de la conformation des n-aryl azoles par la methode e.h.t. (extended hückel theory)

E.H.T. calculations of total energy as a function of dihedral angle are presented for 8 N-aryl azoles, six with dihedral angle α and two with dihedral angles α and β. The rotational barriers to the planar and to the orthogonal geometries are discussed. The dihedral angles α or β corresponding to the minimum of the calculated potential curve or surface are important; a uniform correction of these values is necessary to find the experimental values.     

From tropos to atropos: 5,5′-bridged 2,2′-bis(diphenylphosphino)biphenyls as chiral ligands for highly enantioselective palladium-catalyzed hydrogenation of α-phthalimide ketones

A class of atropisomeric diphosphine ligands with a wide range of dihedral angles has been developed. X-ray study of the Pd(II) complexes of these ligands showed that as the bridge length increased, the dihedral angles and the ligand bite angles increased as well, while an excessive increase in bridge length had a reverse effect. It was found that there was a correlation between the ligand dihedral angles and the enantioselectivity in Pd-catalyzed asymmetric hydrogenation of α-phthalimide ketones, and excellent enantioselectivities of up to 99% ee were afforded.     

抗癌药物冬凌草甲素的分子构型研究

本文用同核化学位移相关谱和二维J分解谱归属了冬凌草甲素的^1H谱, 测定了所有的质子标量偶合常数, 根据一系列的Karplus公式计算了二面角, 用自编WUPH计算程序, 计算出冬凌草甲素的分子构型。     

24 IPR isomers of fullerene C84: Cage deformation as geometrical characteristic of local strains

The structures of 24 IPR‐isomers of C₈₄ fullerene with distributed single, double and delocalized bonds are presented. Obtained results are fully supported by DFT quantum‐chemical calculations of electronic and geometrical structures of these isomers. Two reasons of instability of fullerene molecules are their radical origin and/or high local strain. Distortion of pentagons as well as hexagons with alternating single and double bonds is the most significant geometrical parameter reflecting local strain of a molecule. These distortions are measured as maximal dihedral angles of those cycles and reach 20 degrees in mostly deformed hexagons and pentagons. In contrast high values of dihedral angles in hexagons with delocalized π‐bonds are typical for stable isomers. Other geometric parameters such as valence angles, sums of valence angles and dihedral angles between approximate planes of fused rings have no marked influence on stability. The development of strain‐related criteria for fullerene stability will be helpful in the prediction which isomers might potentially be observable in experiment. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

17O NMR spectra of alpha-diesters

17O NMR spectra of title compounds were measured at natural abundance in acetonitrile solutions. Intercarbonyl dihedral angles have been estimated by molecular mechanics, which show invariance except in one case. Because of this invariance, contrary to other alpha-dicarbonyl compounds, a correlation between chemical shifts and dihedral intercarbonyl angles could not be developed. Spectroscopic and computational results allowed us to evaluate other conformational features.     

Cyclic peroxides: dihedral angle around the peroxide bond by microwave and photoelectron spectroscopic studies

Experimental COOC dihedral angles are used to support the relation proposed by Coughlin et al. for correlating the observed photoelectron splitting n(O)⁺- with the dihedral angle around the peroxide bond in cyclic peroxides.     

J-coupling constants for a trialanine peptide as a function of dihedral angles calculated by density functional theory over the full Ramachandran space

We present 13 (3)J, seven (2)J and four (1)J coupling constants (24 in all) calculated using B3LYP/D95** as a function of the φ and ψ Ramachandran dihedral angles of the acetyl(Ala)(3)NH(2) capped trialanine peptide over the entire Ramachandran space. With the exception of three of these J couplings, all show significant dependence upon both dihedral angles. For each J coupling considered, a two dimensional grid with respect to φ and ψ angles can be used to interpolate the values for any pair of φ and ψ values. Such simple interpolation is shown to be very accurate. Most of these calculated J couplings should prove useful for improving the accuracy of the determination of peptide and protein structures from NMR measurements in solution over that provided by the common procedure of treating the J couplings as functions of a single dihedral angle by means of Karplus-type fittings.     

Local deformations of polymers with nonplanar rigid main‐chain internal coordinates

A procedure for local deformation of a polymer by concerted rotation of several main‐chain dihedral angles has been adapted recently to be an elementary move in Monte Carlo simulations. We expand the applicability of the move by generalizing the formalism to allow fixed dihedral angles that sequentially interrupt the rotatable bonds to be nonplanar. The method is applied to the simulation of a small protein in which the dihedral angles of the peptide bonds are allowed to deviate from their ideal values and to the simulation of an RNA hairpin loop in which the main chain (C3′ C4′) bonds that are constrained by the sugar rings are rigid but nonplanar. The move is found to increase the rate at which the systems explore their accessible configuration spaces. The relation of the results to previous studies and possible enhancements of the method are discussed. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1132–1144, 2000     

Realistic sampling of amino acid geometries for a multipolar polarizable force field

The Quantum Chemical Topological Force Field (QCTFF) uses the machine learning method kriging to map atomic multipole moments to the coordinates of all atoms in the molecular system. It is important that kriging operates on relevant and realistic training sets of molecular geometries. Therefore, we sampled single amino acid geometries directly from protein crystal structures stored in the Protein Databank (PDB). This sampling enhances the conformational realism (in terms of dihedral angles) of the training geometries. However, these geometries can be fraught with inaccurate bond lengths and valence angles due to artefacts of the refinement process of the X‐ray diffraction patterns, combined with experimentally invisible hydrogen atoms. This is why we developed a hybrid PDB/nonstationary normal modes (NM) sampling approach called PDB/NM. This method is superior over standard NM sampling, which captures only geometries optimized from the stationary points of single amino acids in the gas phase. Indeed, PDB/NM combines the sampling of relevant dihedral angles with chemically correct local geometries. Geometries sampled using PDB/NM were used to build kriging models for alanine and lysine, and their prediction accuracy was compared to models built from geometries sampled from three other sampling approaches. Bond length variation, as opposed to variation in dihedral angles, puts pressure on prediction accuracy, potentially lowering it. Hence, the larger coverage of dihedral angles of the PDB/NM method does not deteriorate the predictive accuracy of kriging models, compared to the NM sampling around local energetic minima used so far in the development of QCTFF. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Effect of torsional potential on the predicted phase behavior of n-alkanes

The effect of torsional potential on the predictions of simulation for vapor–liquid equilibria of n-alkanes is determined. Calculations are performed with histogram-reweighting Monte Carlo simulations in the grand canonical ensemble. Decreasing the magnitude of energy barriers to dihedral rotation or allowing free rotation is found to have no effect on the predicted vapor–liquid equilibria. Restriction of the dihedral angles to a Gaussian distribution around the minimum energy conformation causes an under-prediction of the liquid densities and critical temperatures by a maximum of 7% and 2%, respectively, with discrepancies increasing monotonically with the number of dihedral angles present in a molecule. No significant deviation in vapor pressure is observed for any compound, regardless of torsional potential used. An analysis of the conformational behavior reveals that restriction of the dihedral sampling has a measurable effect on excluded volume of the molecule, and this change of conformational behavior is responsible for the reduction in the predicted saturated liquid densities observed in this work. Similar calculations for force fields employing reduced dihedral potentials or freely jointed chains show little change in the predicted excluded volume compared to the reference force field.     

The conformations of bicyclo[3.1.0]hexane derivatives by 1H and 13C NMR

The ¹H and ¹³C spectra of bicyclo[3.1.0]hexanes and thujanes have been recorded and assigned. Application of the Karplus equation has yielded dihedral angles, and a computer calculation of the angle of ring buckle as a function of the main dihedral angles has been carried out. The calculated angles of ring buckle agree well with known values in the bicyclo[3.1.0]hexanes, but for 1-methylbicyclo[3.1.0]hexanes and thujanes the results are not self consistent. It is suggested that the bridgehead substituent causes the boat to twist, although the twist can be reduced by an axial methyl substituent on C-4.     

Development of Axially Chiral Cyclo‐Biaryldiol Ligands with Adjustable Dihedral Angles

A new type of axially chiral cyclo‐[1,1′‐biphenyl]‐2,2′‐diol (CYCNOL) ligands with adjustable dihedral angles have been developed by varying the bridge chain length. Eight‐, nine‐ and ten‐membered cyclo‐ligands were prepared and evaluated by using two representative examples: enantioselective additions of diethylzinc to aldehydes and organometallic reagents to enones. The results revealed that the fine regulation of dihedral angles through variation of the bridge chain length was effective in the asymmetric synthesis.     

Induction correction model for rotation of two or three dihedral angles

In a previous work we have introduced an intramolecular induction correction model. In this work we have used the model to calculate the total dipol moment of six molecules as a function of two or three dihedral angles that are simultaneously varied in the molecules. It is found that the induction model behaves very well for the systems studied when compared with a regular force field model where fixed charges and dipoles are rotated along with the atoms of the molecules. This suggests that the proposed induction correction model can be used to model systems containing several dihedral angles around which rotations are performed.     

Conformational analysis of nucleic acid molecules with flexible furanose rings in dihedral angle space

The computational algorithm that works in the coordinate space of dihedral angles (i.e., bond lengths and bond angles are kept fixed and only rotatable dihedral angles are treated as independent variables) is extended to deal with the pseudorotational m otion of furanose rings by introducing a variable of pseudorotation. Then, this algorithm is applied to a distance geometry calculation that generates three-dimensional (3D) structures that are consistent with given constraints of interatomic distances. This method efficiently generates 3D structures of an RNA hairpin loop which satisfy a set of experimental NMR data. © 1996 by John Wiley & Sons, Inc.     

Dihedral‐Angle‐Controlled Crossover from Static Hole Delocalization to Dynamic Hopping in Biaryl Cation Radicals

In cases of coherent charge‐transfer mechanism in biaryl compounds the rates follow a squared cosine trend with varying dihedral angle. Herein we demonstrate using a series of biaryl cation radicals with varying dihedral angles that the hole stabilization shows two different regimes where the mechanism of the hole stabilization switches over from (static) delocalization over both aryl rings to (dynamic) hopping. The experimental data and DFT calculations of biaryls with different dihedral angles unequivocally support that a crossover from delocalization to hopping occurs at a unique dihedral angle where the electronic coupling (H _ab) is one half of reorganization (λ ), that is, H _ab=λ /2. The implication of this finding in non‐coherent charge‐transfer rates is being investigated.     

Conformational memories with variable bond angles

Conformational Memories (CM) is a simulated annealing/Monte Carlo method that explores peptide and protein dihedral conformational space completely and efficiently, independent of the original conformation. Here we extend the CM method to include the variation of a randomly chosen bond angle, in addition to the standard variation of two or three randomly chosen dihedral angles, in each Monte Carlo trial of the CM exploratory and biased phases. We test the hypothesis that the inclusion of variable bond angles in CM leads to an improved sampling of conformational space. We compare the results with variable bond angles to CM with no bond angle variation for the following systems: (1) the pentapeptide Met-enkephalin, which is a standard test case for conformational search methods; (2) the proline ring pucker in a 17mer model peptide, (Ala)(8)Pro(Ala)(8); and (3) the conformations of the Ser 7.39 chi(1) in transmembrane helix 7 (TMH7) of the cannabinoid CB1 receptor, a 25-residue system. In each case, analysis of the CM results shows that the inclusion of variable bond angles results in sampling of regions of conformational space that are inaccessible to CM calculations with only variable dihedral angles, and/or a shift in conformational populations from those calculated when variable bond angles are not included. The incorporation of variable bond angles leads to an improved sampling of conformational space without loss of efficiency. Our examples show that this improved sampling leads to better exploration of biologically relevant conformations that have been experimentally validated.     

Stereochemistry of cyclopentane derivatives from (2,3)J(CH) dependence on dihedral angle (theta H--C--C--X)

The (2,3)J(CH) dependence on dihedral angle (theta H--C--C--X) for cyclopentane derivatives was investigated. We observed that the combined use of experimentally obtained (2,3)J(CH) values and the theoretically determined dihedral angles between the corresponding nuclei can be used to infer the relative stereochemistry of the ring substituents in cyclopentane derivatives. There is a good correlation between the magnitude of (3)J(CH) and the dihedral angle between the hydrogen and the coupled carbon (R2 = 0.88).