. The Laplace transformation approach-saddle point approximation method of very high accuracy and application to the calculation of density of vibrational states of molecules in unimolecular reaction kinetics.

Abstract

In the paper the calculation of density of molecular vibrational states has been performed by Laplace transformation approach, i.e reduced to the evaluation of inverse Laplace transform of partition function by the aid of saddle point approximation method: The exponential of intergrand in inverse Laplace integral is presented in Taylor series, in which at the saddle point the first derivative vanishes. then. the density of vibrational states - the inverse Laplace transform is integrated through the steepest descent which is in imaginary direction having the saddle point as abscissa on the real axis. Finally, this process of treament give the expression of density of vibrational states containing terms of from first up to fifth orders of accuracy, which have beeneasily calculated on computer