Diederwinkel

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The dihedral - or torsion in describing geometry the angle between two plane defined by three points planar surfaces. This is especially true within the chiral structure of a chemical compound for the angle between two flat surfaces spanned by atoms. The dihedral angle α is defined on the line of intersection by a pair of two atoms on this line of intersection and the positions of two further atoms to one another. In the example of the organic compound ethane, this corresponds to the angle that the two planes intersecting at the line and spanned through and spanned by each other, as shown in the following figure ( and are the two connected carbon atoms, and two of the bound hydrogen atoms):

Graphic representation of the dihedral angle in ethane ; The situation is analogous with hydrogen peroxide , for example , here the bond axis O – O, R and R 'would again each be a hydrogen atom, the dihedral angle

If the two carbon atoms are connected by a single bond (σ bond) and are not locked in a cyclic molecule, the dihedral angle can continuously assume all values ​​from 0 ° to 180 °. Due to the repulsive interactions of the substituents and , an angle of ( trans , see below) is usually the most favorable.

The fact that many sugars unexpectedly adopt a conformation in which some substituents prefer a dihedral angle of is attributed to the anomeric effect .

The enthalpy of the molecule, which varies with the rotation around the bond, can be calculated approximately using a special function:

with E : torsional energy; A , B , C : scaling factors; α : dihedral angle

The potential curve resulting from this function (approximated with values ​​for and as for n-butane) is shown below for illustration.

Energy differences in butane depending on the dihedral angle

In the case of ethane, A and B become zero, whereby the equation changes into the Pitzer potential. The barriers to rotation are usually a few kJ / mol. This means that a small part (<20%) of the molecules always have a dihedral angle of . It must also be taken into account that the gauche forms have an entropy advantage of 1.7 kJ / mol, since they occur in two rotational isomers (+/- synclinal). The conformers that arise for certain values ​​of the dihedral angle have their own designations:

angle shape Explicit description Short name
α = 0 ° ecliptic, hidden syn-periplanar cis / syn
α = 60 ° staggered (+) - synclinal gauche
α = 120 ° ecliptic, hidden (+) - anticlinal -
α = 180 ° staggered antiperiplanar trans / anti
α = 240 ° ecliptic, hidden (-) - anticlinal -
α = 300 ° staggered (-) - synclinal gauche
α = 360 ° ecliptic, hidden syn-periplanar cis / syn

The forms with and are enantiomers . If the barrier to rotation is too high, the two resulting shapes will not be able to rotate into one another. They can then possibly be isolated individually. In the case of special binaphthyl derivatives , this is used to obtain extremely selective reagents.

If there is a double bond between the carbon atoms, the rotation is severely restricted, since this would require a bond break. Only two angles are possible: ( trans / anti ) and ( cis ). If the substituents are very voluminous, in the latter case there may be deviations from the 0 ° angle.

Various methods are available to determine the dihedral angle of real connections. This includes the measurement of the dipole moment , the recording of electron diffraction spectra , the measurement of coupling constants by means of NMR or the calculation of the optimal molecular geometry by means of special computer programs.

Torsion angles in proteins

The torsion angles ω, φ and ψ of the backbone of proteins

The torsion angle of the backbone of proteins will be

  • ω (between C α - C '- N - C α )
  • φ (between C '- N - C α - C')
  • ψ (between N - C α - C '- N) and

called. Thereby controls the φ angle the distance between two carbonyl - carbon atoms , ψ the distance between two amide -Stickstoffe ω and the distance between two α-carbons.

The planarity of the peptide bond usually forces the ω angle to 180 ° (the common trans configuration ) or 0 ° (the rare cis configuration). The distance between the α-carbon atoms in the trans and cis configurations is about 3.8 and 2.8 Å, respectively . The cis configuration can mainly be observed in the X- Pro peptide bond (X is any amino acid), which is why proline is a structure breaker alongside achiral glycine . The dihedral angles φ and ψ of a protein are shown in the Ramachandran plot and should be over 80% in the core areas and at most occasionally in the forbidden areas of the map. With the particularly favorable α-helices z. For example, the φ angle is approximately −60 °, the ψ angle approximately −30 °, with both angles allowing a tolerance of approximately ± 30 °.

The torsion angles of the side chains are denoted by χ 1 to χ 5 , depending on the distance to the backbone. χ 1 is the torsion angle between the atoms N - C α - C β - C γ , χ 2 between C α - C β - C γ - C δ etc.

The side chain torsion angles seem to pile up around 180 °, 60 ° and −60 °. These conformations are called anti (or trans ), (+) - gauche and (-) - gauche (or (+) - or (-) - synclinal). Which torsion angle is present in a side chain is determined by the number of adjacent side chains and the backbone; the (+) - gauche conformation seldom follows a further (+) - gauche conformation (as is the case with (-) - gauche), because this increases the probability of an atomic collision. The dihedral angles of the amino acid side chains (χ 1 and χ 2 ) can be shown in a Janin plot .

See also

Individual evidence

  1. ^ AF Holleman , E. Wiberg , N. Wiberg : Textbook of Inorganic Chemistry . 102nd edition. Walter de Gruyter, Berlin 2007, ISBN 978-3-11-017770-1 .