Successfully computing the rovibrational spectrum of a polyatomic molecule requires the consideration of several factors. Among them is the representation of the kinetic energy operator (KEO), the choice of body-fixed (BF) frame, and the use of the molecular symmetry group. The work detailed in this thesis develops all three and forms a part of the ExoMol project which is concerned with the calculation of molecular line lists of astronomical significance. For the first factor, we enhanced one of the main programs of the ExoMol project, TROVE, by enabling the use of externally programmed and analytic KEOs in variational calculations. We utilised this approach in the marvelised line list calculation of H2CS which covers the 0 cm−1 to 8000 cm−1 range for states up to J = 120. We also collated all experimentally available transitions and, with the marvel program, converted them to highly accurate experimental energy levels. The energies of the calculated line list were then replaced by marvel energies when available. The states of all such line lists in TROVE have an assigned symmetry label according to their appropriate molecular symmetry group. A robust symmetrisation procedure is one of the main features in TROVE. We further exploited group theory by constructing and implementing an artificial symmetry group for use in TROVE’s 3N − 6 approach for the variational calculations of linear molecules. This allowed much of the pre-existing infrastructure to be used with minimal changes. An analytic KEO complicates matters by necessitating a BF frame alternative to the usual Eckart frame. We elucidate the choice of BF frames which permit rotational symmetrisation and suggest example alternative frames. Finally, one of the suggested frames is used for the analytic KEO of C2H6. The preliminary work on this molecule is described, with a focus of our implementation of its molecular symmetry group in TROVE.