Rotational thermodynamic parameters for asymmetric-top molecules: classical vs. quantum approaches and new analytical partition function

Abstract

We investigated classical and quantum rotational partition functions, rotational energies and rotational entropies for asymmetric-top molecules in a canonical system within a wide range of temperatures under the rigid rotor approximation. We then derived the temperature, , below which classical approach is not valid, and the complex quantum approach is strongly recommended. This temperature certainly increases with the inertia moment of the molecule and follows a power function when rotational partition functions are considered. As for linear-, spherical- and symmetric-top molecules, quantum approach is not needed at all for energetic rotational parameters, whatever the temperature for asymmetric-top molecules. Therefore, there is no real frontier between the classical and quantum approaches when energetic rotational parameters are concerned, though the frontier is naturally a bounded decreasing sequence converging to zero when rotational partition functions are rather concerned. Particularly, classical approach fails describing rotational partition functions for light molecules or molecules at low temperatures. Moreover, all the closed-form expressions proposed in the whole literature fail drastically approaching quantum and exact results for light molecules or molecules at low temperatures. In regard to the importance of partition functions in the evaluation of rate constants for chemical reactions and accurate intensities lines in spectroscopy, we proposed new accurate and simple analytic expression of the rotational partition functions of asymmetric-top molecules, valid at all temperatures.