Free rotor correlation function

Correlation functions for free rotation include, for a plane rotor... 

Consider now the case of a gas of linear molecules that is sufficiently dilute that intermolecular interactions can be ignored. The free rotor correlation functions for a rigid linear molecule are quite different from those for spherical tops. This is now demonstrated. As in Section 7.3, letu be a unit vector pointing along the axis of the rotor. Then for a free rotor... 

It is possible to evaluate C (n, t) in terms of the free-rotor correlation function C <0)(t). First we note that... 

Thus if we know the free rotor functions C f t) which is always possible we can evaluate through their Laplace transforms the orientational correlation times r. ... 

A completely adiabatic correlation between nQ> and ljQ> states would assume that n equals j a result which unlike the partial 0-correlation is not borne out by coupled channel calculations. Physically this adiabatic correlation is untenable because the spatial character of free-rotor and bending wave-functions is quite different and so non-adiabatic coupling is certain to be large. Thus the change between the free-rotor and bending wavefunctions is better described by a sudden correlation. 

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