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Earlier derived, [1] - [3], for the XY2 (C2v) and XY3 (C3v) molecules "expanded local mode model" is applied to the methane-type, XH4, molecules. Value of the ambiguity parameter, sin \_gamma, simple value of all transformation coefficients, l, are obtained for the CH4 molecule. It gives us possibility, on the one hand, 1). to derive simple relations between different spectroscopic parameters (harmonic frequencies, anharmonic parameters and vibrational tetrahedral coefficients, rotational-vibrational and rotational tetrahedral coefficients) of the CH4 molecule, and, on the other hand, 2). on the base of the general isotopic substitution theory (see, e:g:, [4]), to obtain very simple values of transformation l coefficients for di fferent deuterated species, CH3D, CH2D2, and CHD3, of the methane molecule. As the fi nal step, numerous isotopic relations between di fferent spectroscopic parameters of the mother molecule, CH4, and deuterated, CH3D, CH2D2, CHD3, species are derived. Comparison of the derived relations with the experimental values of spectroscopic parameters shows more than satisfactory correlation between the results. [1]. O. N. Ulenikov, R. N. Tolchenov, and Zhu Qing-Shi, Spectrochim. Acta A 52, 1829 - 1841 (1996). [2]. O. N. Ulenikov, S. N. Yurchenko, and R. N. Tolchenov, Spectrochim. Acta A 53, 329 - 334 (1997). [3]. O. N. Ulenikov, R. N. Tolchenov, and Zhu Qing-Shi, Spectrochim. Acta A 53, 845 - 853 (1997). [4]. A. D. Bykov, Yu. S. Makushkin, and O. N. Ulenikov, J. Molec. Spectrosc. 85, 462 - 479 (1981).

The main goal of the present study was to analyse rotational stuctures of two excited vibrational states, (120) and (021). Because both the band, v1+2v2 and 2v2+v3 one are extremally weak, a special efforts were faired to record very weak hot bands, v1+2v2−v2 and 2v2+v3−v2.Both of those bands are located in the region of considerably more stronger combinational bands, v1 + v2 and v2 + v3. On that reason, as the first step of analysis, we made assignments of transitions belonging to these v1 + v2 and v2 + v3 bands. As the result of analysis, we were able to assign three times more transitions to the bands v1 + v2 and v2 + v3 than it was known in the before literature. After "cleaning" the experimental spectrum from transitions belonging to the v1 + v2 and v2 + v3 strong bands, assignments of remaining weak transitions was made on the base of calculation scheme discussed in [1]. As the theoretical analysis of obtained "experimental" energies shown, some sets of ro-vibrational states of the (110) vibrational state are strongly pertubed by the (030) vibrational state. On that reason, in the fit of energy levels of the (110) and (011) vibrational states, the hamiltonian model that takes into account the presence of interactions with the (030) vibrational state, was used. At the same time, a ro-vibrational analysis of the (120) and (021) states shown that a fit can be made with a model of isolated vibrational state both for (120), and for (021). Obtained set of spectroscopic parameters reproduces the initial experimental energy values for all four vibrational states with an accuracy close to experimental uncertainties. [1] O. N. Ulenikov, E. S. Bekhtereva, O. V. Gromova, S. Alanko, V.-M. Horneman, and C. Leroy, Molec. Phys., 108(10), (2010).