Pseudo-rotation

Pseudo-rotation.— The concept of pseudo-rotation was introduced by Kilpatrick, Pitzer, and Spitzer to account for the thermodynamic and spectroscopic properties of cyclopentane. Although the basis of the 

The two degrees of freedom associated with the ring puckering are, therefore, an ordinary vibration and a type of one-dimensional rotation in which the phase of the puckering moves around the ring the latter is not, however, a true rotation since there in no angular momentum about the axis of rotation, and so is described as a pseudo-rotation . This separation of the wave equation is not exact, but it has been stated that exact separation is possible and, on the assumptions of harmonic oscillations and small amplitudes of vibrations, leads to the same results as those given. 

The contributions of pseudo-rotation to C jLk is then 0.5 and to S Lk is [i + i ln(87i /r 7yA (T ) ] where a is the symmetry number and has the value 10 for cyclopentane. (The value 5 is in error a further factor of two for the identity of the two sides of the molecule is required. ) In the original calculations, the puckering vibration was assigned to a Raman line at 288 cm (with an anharmonicity coefficient of 0.03) and a value for q of 23.6pm (corresponding to /, = 10.468 x 10 gem ) was chosen to give agreement with the measured entropy and heat capacity. 

Later workers contended that pseudo-rotation was an unnecessary concept and made vibrational assignments for cyclopentane in which the ring-puckering motion was treated as two genuine degrees of freedom.  

Such assignments are in error, however, even though one of them is based on a normal-co-ordinate calculation, and are quite unable, with or without a contribution of pseudo-rotation, to reproduce the measured heat capacity. The most accurate values of the measured thermodynamic properties require, for agreement within 0.1%, that /, = 10.59 x 10 gem a small contribution of anharmonicity was treated by equations (15). A subsequent molecular vibrational analysis led to some revision of the vibrational assignment, but excellent agreement with the measured heat capacity values is still obtained from it-provided the contribution of pseudo-rotation is included. The details of the selection rules for cyclopentane have been discussed.  

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Even more complex experiments have been performed on matrix isolated Fe(C0)4, generated by UV photolysis of Fe(C0)5. Isotopic labelling coupled with CW-CO laser pumping (65) of the CO stretching vibrations ( 1900 cnrl) showed that the rearrangement mode of Fe(C0)4 follows an inverse Berry pseudo-rotation as shown in Figure 8. 

Fig. 7. Structures of five-coordinate Cu2+ from first principles molecular dynamics. A Berry twist mechanism for the interconversion of the two structures is shown (from left to right) the reorientation of the main axis of a square pyramidal configuration by pseudo-rotations via a trigonal bipyramidal configuration. The grey atoms in the plane of the trigonal bipyramid are all candidates for becoming apical atoms in a square pyramid.

Bernoulli principle, 11 656-657 Berry pseudo-rotation, 16 62 Bertrandite, 3 638, 640-641 Bertrand lens, 16 470-471 Beryl, 3 638, 640 color, 7 329... 

Fig. 7.11 Reaction profiles for L-catalyzed isomerization of cis-to-trans ML2X2. In (A) an ionic intermediate is favored by a polar solvent. In (B) ion-pair formation arises with a less polar solvent. In (C) a non-polar solvent promotes a 5-coordinated intermediate. In (C), pseudo-rotation occurs. Based on D. G. Cooper and J. Powell, J. Amer. Chem. Soc. 95, 1102 (1973) see also Ref. 90. Reproduced with permission from D. G. Cooper and J. Powell, J. Amer. Chem. Soc. 95, 1102 (1973). (1973) American Chemical Society.

The foregoing considerations show that, in order to reproduce the stereochemical trends, it is not necessary to introduce either d orbitals for the silicon atom or pseudo-rotations for the transition state. Conversely, the stereochemistry of substitution reactions on silicon compounds cannot be taken as a proof of d orbitals intervention in silicon chemistry. 

The potential energy surface displayed in Figures 5a and 5b shows that there is no potential energy barrier between the square pyramid at A = >B = 101.3° and the two trigonal bipyramids situated at the two minima. Movement along the reaction coordinate connecting the two trigonal bipyramids is usually described as the Berry pseudo-rotation.13... 

Allyl complexes (with tungsten carbonyls and isocyanides, 5, 688-689 rc-Allyl complexes with Cr, 5, 305 with Cr(II), 5, 300 with Cr(III), 5, 300 and cyclodextrins, 12, 789 in enyne carbometallation, 10, 328 with rhodium, 7, 220-221 (j-Allyl complexes, with iron, 6, 98 5-Allyldiisopinocampheylboranes, in asymmetric allylboration, 9, 198... 

CS tensors for complex spectra, 1, 463 dicyclopentadienylberyllium compounds, 2, 74 tj4-diene and rf-allyl pseudo-rotations, 1, 416 half-integer quadrupolar nuclei, central transition, 1, 457 half-integer spin quadrupolar nuclei central transition,... 

Table 2. Comparison of JT stabilization energies E3T and barriers for pseudo-rotation E11 for...

In fullerene anions C%q, the n electrons outside closed shells occupy /lu triplet electronic states. Jahn-Teller (JT) coupling between these states and 5-fold h-type vibrations has important consequences for many properties of the fullerene anions. It is therefore important to understand the JT effect experienced by these ions from a theoretical point of view. We will study the cases of n = 2 and 4, where the lowest adiabatic potential energy surface is found to consist of a two-dimensional trough in linear coupling. The motion of the system therefore consists of vibrations in three directions across the trough and pseudo-rotations in two directions around the trough. Analytical expressions for states of the system that reflect this motion are obtained and the resultant energies determined. 

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