Irreducible tensor operators and operations over them in the theory of molecular spectra

The explicit shape of symmetrized powers of three-dimensional representations of the groups Td and Oh is found in general form. Equations are obtained for calculating the vibrational commutators and matrix elements of irreducible tensor operators. Programs have been developed (in the C and FORTRAN languages) to remove the multiple-valued property of the vibrational-rotational Hamiltonian of spherical top molecules (CH₄, SiH₄, GeH₄, SF₆, and so on).Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 16–25, March, 1993.