Application of Symbolic Computations in Calculation of Electronic–Vibrational Spectra of Molecules

An algorithm of calculation of multidimensional integrals of overlapping harmonic vibrational wave functions that employs symbolic computations has been developed. The algorithm is implemented in a Matlab 5.x system and allows one to perform calculations many orders of magnitude more rapidly than those described heretofore. The speed of computation by this algorithm depends weakly on the dimensionality of the overlap integral, and this makes it possible to use this integral to calculate the intensities of lines in the electronic–vibrational spectra of multiatomic molecules.