Analytical computer calculations for vibration-rotation spectroscopy of high-symmetry polyatomic molecules

Abstract A method has been developed for a computer system of analytical calculations, “REDUCE”, for the processing of complicated computations in perturbation theory, based on irreducible tensorial sets theory. The problem was to obtain exact analytical expressions for spectroscopic X Ω( k ,γ) νΓ, ν Γ constants of a high symmetry molecule up to high (third and fourth) orders of perturbation theory. The general scheme of the program package has been found to be useful for a wide range of similar problems. The obtained formulas for the X Ω( k ,γ) νΓ, ν Γ constants of the CH 4 molecule, being of special interest, are presented as results of the program package under discussion. The necessary theoretical background is supplied.