Test of Laplace Transform Technique for Energy-Level Density Calculations

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Abstract
The series obtained by Haarhoff and Thiele for the density of vibrational states by the Laplace transform expansion technique has been generalized to obtain the density of vibration—rotation states. The resulting series expression is compared at several energies with the exact count and with a compact formula due to Haarhoff. Two cases are considered: a ``large'' molecule with many vibrations and rotations and a ``small'' molecule with few vibrations and rotations. The series expression gives a much better approximation than Haarhoff's formula for the ``large'' molecule, but there is little to choose between the two in the case of the ``small'' molecule.