The interdependence of the description of the internal geometry and the corresponding kinetic energy operator (T) over cap is investigated in detail for a general n-atomic molecule. For both space-fixed and body-fixed reference frames compact expressions of (T) over cap are derived which are applicable to any set of n-1 translationally and rotationally invariant internal vectors in a spherical polar parametrization. Simple analytical forms are given for reduced masses and kinetic coupling constants, which are the only vector specific parameters in the final rovibrational kinetic energy expression. The kinetic energy assumes the most separable form for an entirely orthogonal set of internal vectors. A highly efficient computer program for the calculation of rovibrational spectra of tetratomic molecules has been developed on the basis of this formulation. Calculations on the HF dimer and the metastable molecule HOCO illustrate the accuracy and flexibility of this approach.