Pseudorotation, vibration-rotation

Further experimental confirmation of the preferred geometry of oxepane (1) has been obtained from its IR and Raman spectra. These vibrational and rotational spectra have been rationalized in terms of the lowest energy twist-chair conformations pseudorotating via a chair form (771A2866,2876). 

From (8.23) and (8.24) one can see two special cases when the potential becomes separable. In the first case c12 = 0, we have two independent anharmonic modes, each having two equilibrium positions. In the second case, the angular part of the potential (8.23) Vr is zero, and the motion breaks up into radial vibration in the double well V0(q) and a free rotation, i.e. propagation of the waves of transverse displacements along the ring. The latter case is called free pseudorotation. Since the displacements of atomic groups in the wave are purely transverse, they do not contribute to the total angular momentum. 

The eigenvalues of pseudorotation for various vibrational states n = 0,1,. . . , Emn = Bnm2, are characterized by rotational constants ... 

The term pseudorotation was first appUed to cyclopentane like inversion, it has an atomic analogue in 5-coordinate compounds (e.g. PF5). ) The name means false rotation , and it is therefore appropriate for any conformational process which results in a conformation superposable on the original, and which differs from the original in being apparenUy rotated about one or more axes. Pseudorotation, in analogy with real molecular and internal rotations, can be free, as in cyclopentane, or more or less hindered, eis in cycloheptane and higher cycloalkanes. In moderately to severely hindered pseudorotation, it is appropriate to consider distinct stable conformations which are pseudorotation partners, and these cases are often amenable to study by dynamic nmr methods. When the barrier to pseudorotation is very low, or in the limit when pseudorotation is free, it is not really justified to talk about separate stable conformations (e.g. the C2 and Cg forms of cyclopentane), because strictly there is only one conformation, and the pseudorotation is simply a molecular vibration. 

The dipolar structure (rdipolar interactions without correction for vibrations, but in which slower motions, if present (e.g., the rotation of methyl groups and the interconversion of conformers such as ring inversion or pseudorotation), have been accounted for. 

The various physical techniques that we might use to study molecular species depend on a variety of proeesses. The conclusions we could draw about structures are related to the timescales associated with these proeesses, and it is important for us to understand these if we are to avoid making erroneous deductions. In relation to any one type of experiment, there are in fact four different times for us to consider the time during which a quantum of radiation or a particle can interact with a molecule the lifetime of any excited state of the molecule the minimum lifetime that the species being studied must have to allow it to be seen as a distinct species and the total duration of an experiment in which the species is observed, which may be as much as several hours or as little as 10 s. Before we consider these further, we must look at the timescales of typical molecular processes so that we can relate them to timescales associated with structural techniques. Typical vibrational frequencies are of the order of lO to 10 Hz, while rotational frequencies are around 10 ° to 10 Hz. The inversion of ammonia has a rate of about 10 Hz at room temperature, while the corresponding rate for phosphine is 10 Hz. The inversion rate for methane is 10 Hz, so any one molecule inverts, on average, once every 100 million years But remember that there are 6 x 10 molecules in a mole of gas, so in fact the inversion is by no means a rare occurrence. Pseudorotation in PF5, which switches axial and equatorial fluorine atoms, has a rate of about 10 Hz at room temperature, while the rate for PCI5 is 10 Hz. 

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