Rotational temperature, atomic spectroscopy

Nelsen and coworkers determined a barrier to inversion through the planar form in 2 and 3 to be approximately 2 kcalmol-1 by variable temperature ESR spectroscopy [59]. Gerson and coworkers found, also by ESR spectroscopy, that the frequency of electron exchange between the two sites in 4, which is equivalent to rotation about the central bond, can vary between < 106 and > 109 s-1 depending the degree of steric hindrance to planarity [60]. Recent calculations also provide very small barriers to inversion through the planar form [56,57]. It is apparent, therefore, that for most synthetic purposes most alkene radical cations can be considered as essentially planar with effective delocalization over the two sp2-hybridized C atoms, and they will be considered as such in this chapter. 

The uncertainties Ay/yhave been calculated taking into account the errors on Io/Iat and L (thickness of the recombination boundary layer) but also on the flow parameters the diffusion coefficient Do,air determined using the Chapman-Enskog theory, the mean square atomic velocity V determined using the gas kinetic theory (rarefied gas). The accuracy on these two last values is due essentially to that of the gas temperature, measured by emission spectroscopy (N2 rotational temperature), this leads to a total accuracy of 35%. 

When rotation occurs about a bond there are two sources of strain energy. The first arises from the nonbonded interactions between the atoms attached to the two atoms of the bond (1,4-interactions) and these interactions are automatically included in most molecular mechanics models. The second source arises from reorganization of the electron density about the bonded atoms, which alters the degree of orbital overlap. The values for the force constants can be determined if a frequency for rotation about a bond in a model compound can be determined. For instance, the bond rotation frequencies of ethane and ethylamine have been determined by microwave spectroscopy. From the temperature dependence of the frequencies, the barriers to rotation have been determined as 12.1 and 8.28 kJ mol-1, respectively1243. The contribution to this barrier that arises from the nonbonded 1,4-interactions is then calculated using the potential functions to be employed in the force field. 

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