Ah, thanks, that's a helpful way to think about it.
But then wouldn't I have to perform some sort of correction for the difference between the rotational partition function for linear and nonlinear molecules, I assume, related to 2kT(pi) and a term related to the reduction of the inertial terms?
freeh gives the two different formulae for the rotational partition function, but it's not clear to me whether the difference is something I have to work out how to include myself or something that is produced 'automatically' by the way Turbomole obtains the result.