The calculation of molecular energy level sums and densities is necessary for the treatment
of many physical and chemical problems including reaction rates. An extension of Beyer and
Swinehart's algorithm for directly computing harmonic oscillator eigenstate sums and
densities is described. With this new algorithm it is possible to compute exact or near‐exact
energy level sums and densities for degrees of freedom such as free and hindered rotors
and anharmonic oscillators so long as the energy levels for each degree of freedom can be …