Numerical Laplace transform density of states calculation for medium and large molecules

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Abstract
A novel implementation of the Laplace transform method for the calculation of the density of states of molecules, for which the partition function can be explicitly given is described. It consists of doing the inverse Laplace transform numerically after multiplying the integrand by a smoothing factor. This evaluation is more accurate than the method of steepest descent, and the computation can still be done on a PC in a few minutes. By first order expansion of the partition function in the anharmonic parameters we have been able to calculate the density of states for a model molecule composed by anharmonically coupled anharmonic oscillators, which cannot be treated by the well known Beyer–Swinehart algorithm.