Angle of internal rotation

Variation of the potential energy U(a) for torsional vibration a is the angle of internal rotation in a molecule like ethane. The energy levels above the potential maxima have been omitted. For -0°, 120°, and - 120°, we have the staggered form. 

This approach has been frequently used in the treatment of molecules with internal rotation. In these molecules, the top and frame parts of the non-rigid reference configuration follow essentially the internal rotation internal rotation is not considered as a vibrational motion but rather as a part of the rotational motion described by a new dynamical variable — the angle of internal rotation. 

The equilibrium angle of internal rotation of one of the amino groups in the hydrazine molecule with respect to the other is almost exactly 90° (Fig. 20). This means that inversion of an amino group leads almost exactly to a symmetrically equivalent equilibrium configuration. In methylamine, on the contrary, an internal rotation is required, after the inversion of the amino group takes place, to reach an equilibrium configuration [see paper for a nice physical discussion of this problem and for further references]. 

Molecules like N2H4 and N2F4 take the trans (C2 ), gauche (C2), or cis (C21 ) structure depending on the angle of internal rotation. Evidently, the presence of lone-pair electrons on the X atom is responsible for the deviation of the X-XY2 plane from the planarity. Most of these compounds exist as the trans or gauche isomer or as a mixture of both. The trans isomer shows 6, whereas the gauche isomer shows 12 fundamentals in the infrared. 

Z8CH 111.3 C88C dihedral angle of internal rotation 85 ... 

This volume contains data on the geometric parameters (intemuclear distances, bond angles, dihedral angles of internal rotation etc.) of free polyatomic molecules including free radicals and molecular ions. (For the diatomic stmctures measured by high-resolution spectroscopy, see [1], and for molecular stmctures in crystals, see [2].)... 

Fig. 8-4. Potential energy, V, versus angle of internal rotation, .

Just as the equilibrium conformational properties of macromolecules, the theory of which has been developed in well-known classical works by Kuhn, Flory, Volken-stein and others " the kinetic properties of polymer chains can be determined by two main mechanisms of intramolecular mobility. First, it is the discrete rotational isomeric (rotameric) mechanism of mobility caused by the jump of small-chain segments (kinetic units) from certain energically stable allowed conformers into others ° 1S4-16S) gg ond it is the continuous mechanism of motion determined by the accumulation of vibrational displacements of units owing to the twisting or bending vibrations (and librations) or valence angles and angles of internal rotation 45 i - ... 

The change of frequency caused by the conformational change is mainly due to the kinetic energy terms, since the potential energy is not much influenced by the change in the angle of internal rotation. 

Fig. 5. Backbone vibrations of molecules with four heavy atoms. The line with a circle denotes the CH wagging vibration coupled with the CH2 wagging and the backbone vibrations. Cis, gauche, skew and trans denote the rotational isomers with the angle of internal rotation for the main chain atoms near 0°, + 60°, + 120°, and 180°, respectively...

Generally, no torsion fine stracture appears in the rotational spectrum because the moments of inertia of a symmetric top do not depend directly on the angle of internal rotation, but the internal rotation affects the moments of inertia through interactions with the other vibrational modes, which in turn interact with the overall rotational motion. The effective rotational constant for the torsional state v is given by [54Kiv, 84Gor] ... 

The metrical aspects of the sulphone molecules are dealt with in the present discussion. They are only one, though a very important one, of the characteristics of the molecular structure. The metrical aspects of the molecule, i.e. its geometry, are determined by the relative spacial positions of the atoms constituting the molecule. This is the same as to characterize the molecule with all the internuclear distances, or more descriptively, with the bond lengths, bond angles, and the angles of internal rotation. 

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