On the 'expanded local mode' approach applied to the methane molecule: Isotopic substitutions CH₃D ←cH₄ and CHD₃ ←cH₄

Operator perturbation theory and the symmetry properties of the axially symmetric XYZ₃ (C_3v) type molecules are used for the determination of the spectroscopic parameters in the form of functions of structural parameters and parameters of the intramolecular potential function. Several relations between sets of spectroscopic parameters of these molecules are obtained. The 'expanded local mode' model and the general isotopic substitution theory are used to estimate the relations between spectroscopic parameters of CH₃D and CHD₃, on one hand, and with the T_d symmetric isotopic species, CH₄, on the other hand. Test calculations with the isotopic relations show that even without including prior information about the CH₃D and CHD₃ species, numerical results of calculations are in a good agreement both with experimental data and with results of ab initio calculations.