The rovibrational partition functions of diatomic molecules are calculated using a classical framework plus quantum, semiclassical, and semiempirical corrections, The most popular methods to calculate such corrections are briefly reviewed and applied to the benchmark H-2 molecule. A novel hybrid scheme is proposed and applied to H-2, HCl, and ArO. Each method is analyzed with a view to find an economical way to calculate such corrections for polyatomic systems.