Internal vibrational and rotational partition functions are calculated for nine molecules that are abundant in the terrestrial atmosphere and some are also observed in planetary and exoplanet atmospheres. These molecules are often observed in non-local thermodynamic equilibrium (NLTE) conditions. Calculations are made for all isotopologues of these molecules for which data are available, generally for the temperature range T = 1–5000 K. The methods of calculation of the vibrational and rotational partition functions, Qv and Qr, respectively, the convergence, and the uncertainties for each isotopologue are discussed. Finally, a FORTRAN program, NLTE_TIPS_2021.FOR, to recall the NLTE partition sums is discussed.