On the 'expanded local mode' approach applied to the methane molecule: Isotopic substitution CH ₂D ₂ ←CH ₄

On the basis of a compilation of the expanded local mode model and the general isotopic substitution theory, sets of simple analytical relations between different spectroscopic parameters (harmonic frequencies, ω _λ, anharmonic coefficients, x _λμ, ro-vibrational coefficients, α _λ ^βdifferent kinds of Fermi- and Coriolis-type interaction parameters) of the CH ₂D ₂ molecule are derived. All of them are expressed as simple functions of a few initial spectroscopic parameters of the mother, CH ₄, molecule. Test calculations with the derived isotopic relations show that, in spite of a total absence of initial information about the CH ₂D ₂ species, the numerical results of the calculations have a very good correlation both with experimental data, and results of ab initio calculations.