Method of solving the inverse spectral problem

We describe a method of solving the inverse spectral problem which is applicable to free molecules as well as to molecules in a medium. We give a criterion for the uniqueness of the definition of the force matrix. This criterion links the necessary number of normal proper vibrations of a molecule with a number of necessary form parameters. We calculate the force matrix of tetrahedral molecules CH₄, CD₄, and CT₄. When we use zero-point values for frequencies of normal vibrations the relative discrepancy in the corresponding force-matrix elements does not exceed 0.3%.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 52–57, April, 1987.