Large-amplitude motions, particularly internal rotations, significantly affect thermochemical properties and reaction rates. The conventional method for computing partition functions, developed by Pitzer more than 50 years ago, is based on the assumption of large-amplitude motion being completely separable from other vibrational degrees of freedom. However, no convenient method is available to assess the accuracy of Pitzer's approximation. A precise variational method, suitable for computing the coupling between large- and small-amplitude motions in small molecules, has previously been developed by Tew, Carter, Handy, and co-workers and applied to a few cases. Here, a method is presented for computing the effects of this coupling that is more suitable for routine computations of partition functions of large polyatomics. The couplings of all the vibrational modes to a large-amplitude torsion are analysed in the molecule ortho-chlorotoluene. An approach to defining the internal rotational angle along the torsional coordinate for symmetric rotors is also discussed. Finally, the error introduced by the conventional separability assumption is computed to identify which cases require a higher level treatment.