**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Dihedral angle

Summary

A dihedral angle is the angle between two intersecting planes or half-planes. In chemistry, it is the clockwise angle between half-planes through two sets of three atoms, having two atoms in common. In solid geometry, it is defined as the union of a line and two half-planes that have this line as a common edge. In higher dimensions, a dihedral angle represents the angle between two hyperplanes.
The planes of a flying machine are said to be at positive dihedral angle when both starboard and port main planes (commonly called "wings") are upwardly inclined to the lateral axis; when downwardly inclined they are said to be at a negative dihedral angle.
Mathematical background
When the two intersecting planes are described in terms of Cartesian coordinates by the two equations
: a_1 x + b_1 y + c_1 z + d_1 = 0

:a_2 x + b_2 y + c_2 z + d_2 = 0 the dihedral angle, \varphi between them is given by: :\cos \varphi = \frac{\left\vert a

:a_2 x + b_2 y + c_2 z + d_2 = 0 the dihedral angle, \varphi between them is given by: :\cos \varphi = \frac{\left\vert a

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people (1)

Related units (1)

Related publications (21)

Loading

Loading

Loading

Related courses (11)

BIO-212: Biological chemistry I

Biochemistry is a key discipline for the Life Sciences. Biological Chemistry I and II are two tightly interconnected courses that aim to describe and understand in molecular terms the processes that make life possible.

CH-351: Molecular dynamics and Monte-Carlo simulations

Introduction to molecular dynamics and Monte-Carlo simulation methods.

PHYS-100: Advanced physics I (mechanics)

La Physique Générale I (avancée) couvre la mécanique du point et du solide indéformable. Apprendre la mécanique, c'est apprendre à mettre sous forme mathématique un phénomène physique, en modélisant la situation et appliquant les lois de la physique.

Priscilla Caliandro, Arata Nakajo, Lucie Navratilova, Giorgio Rinaldi, Jan Van Herle

This study examines the effect of Ni migration near the interface with the electrolyte after fuel cell (SOFC) and electrolysis mode (SOEC) operation on nickel-yttria stabilized zirconia (Ni-YSZ) electrodes. The experimental dataset consists in a series of short-stacks tested under different polarization conditions and durations. Selected zones have been imaged by 3-D FIB-SEM serial sectioning. After reconstruction and segmentation, the spatial variations of metric and topological properties have been quantified along the direction perpendicular to the interface with the YSZ electrolyte, including TPB density, volume fraction, dihedral angles and interfacial curvature. Their spatial distribution and time evolution have been analysed to advance the understanding of the driving forces that cause Ni depletion near the YSZ electrolyte.

2019The direct construction of stereogenic axes by enantioselective C-H arylation has been regarded as a very challenging transformation. Very few examples have been reported, despite the indisputable straight-forwardness of the methodology. This is due to the antagonistic relationship between the steric requirement of the substrates for atropostability and their chemical reactivity. This thesis focuses on our efforts to develop an efficient catalytic system to achieve the atropo-enantioselective C-H arylation of heteroarenes.
Following an investigation of various MOP-type and bisphosphine monoxide ligands, it was identified that H8-BINAPO enables a highly atropo-enantioselective C-H functionalization of 1,2,3-triazoles and pyrazoles, heteroarenes of great relevance in medicinal chemistry and agrochemistry. Careful optimization of reaction parameters (notably temperature and time) ensured that the erosion of enantioselectivity is minimized. A double C-H functionalization was also demonstrated in order to provide a compound with two stereogenic axes. The C-H arylation of other heteroarenes, namely imidazo[1,2-a]pyrimidines and thiazoles, was also explored.
Mechanistic investigation by KIE studies led to conclusions that the rate-determining C-H activation step operates mainly through the concerted metalation-deprotonation mechanism. Experimental data combined with DFT calculations suggested a relation between the dihedral angle of the ligands and the origin of the enantioselectivity of the process. The successful development of this atropo-enantioselective transformation allows for the construction of complex three-dimensional scaffolds from much simpler starting materials.

Related lectures (25)

Gervais Chapuis, Philip Pattison

N-Salicylideneaniline (SA), C13H11NO, belongs to the large family of aromatic Schiff bases. It is of particular importance owing to its reversible photoreactivity. SA forms two photochromic polymorphs, both with two non-coplanar benzene rings. In addition, we have recently discovered a planar polymorph, named the β-polymorph, which will be discussed in a subsequent paper. We report here the structure of the α(2)-polymorph in the orthorhombic crystal system. This compound exhibits a strong intramolecular O-H&BULL;&BULL;&BULL; N hydrogen bond and the dihedral angle between the two rings varies with temperature.

2005Related concepts (31)

In chemistry, conformational isomerism is a form of stereoisomerism in which the isomers can be interconverted just by rotations about formally single bonds (refer to figure on single bond rotation)

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a d

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Angles formed by two rays are also known a