Partition function and the level density of the hindered rotor

MATHEMATICA 3.0 is used for calculating the eigenvalues, partitions function and level density of the hindered rotor by solving the appropriate Mathieu equation. An independent approach is the steepest-descent approximation for the level density. The necessary precise partition function is provided by the Wigner-Kirkwood approximation to order h̵4. The two methods agree, thus solving the problem of level density in reaction kinetics.