The application of numerical inversion of the laplace transform to calculate the density of molecular states

To estimate the rate constants of monomolecular reactions using quasi-equilibrium statistical theory, information on the density of discrete states of molecules is required. In the present work, a new approach to calculating the density of discrete states of stable molecules and transition complexes is proposed, which is based on the numerical inversion of the Laplace transform. To test the method, the calculations of model systems including H₂O, NH₃, CD4 and с-C₃H₆ molecules were carried out. It is shown that at energies less than 200 kcal/mol, the relative error in calculating the density of discrete states does not exceed 0.5%. The results obtained by this method can be used, for instance, to estimate the rate constants of reactions involving organic radicals formed in the troposphere and tropopause.