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The high resolution Fourier transform spectra of AsH3 in the region of 9720-9900 cm-1, which had been recorded at a resolution of 0.015 cm-1, were assigned to the (500; A1) and (500; E) local mode overtones and rotationally analyzed. The effective spectroscopic parameters were obtained by nonlinear least-squares fitting the vibration-rotational Hamiltonian with the rotational energy levels up to J=6 (98 levels in all) included. The evolution of the rotational energy patterns from v=1 to v=6 shows that the tendency of normal mode to local mode vibration evolution has been stopped by perturbations in relatively high energy region.

Anharmonic Klambda mu nu parameters of the CH4 molecule potential function are derived from the experimental rotational, tetrahedral splitting and resonance parameters of CH4 and CH2D2. As an illustration of the correctness of the potential parameters obtained, the original spectroscopic constants of CH4 and CH2D2 are theoretically reproduced. Calculations of the spectroscopic constants of CH3D and CHD3 molecules are also given for illustrations.

Irreducible tensorial sets of the point-symmetry groups are used to determine the general formulae for calculating the matrix elements of the reduced dipole moment operator of a polyatomic molecule. These general expressions allow different types of intramolecular interactions and accidental resonances to be considered. Transitions from one type of molecule to another are accounted for by substitution of isoscalar factors and 9 Gamma symbols of the point-symmetry group in the formulae. As an illustration the general expressions obtained are used to analyse the dependences of matrix elements of the reduced dipole moment on the rotational quantum numbers for some vibrational absorption bands of molecules with D3h, C3v and Td symmetries. For allowed transitions contributions to the reduced dipole moment operator which are linear and quadratic in Jalpha are taken into account. for forbidden transitions the main contributions are taken into account. It is shown that the general formulae obtained describe the generalised Herman-Wallis effect (1955) for polyatomic molecules.

The symmetrised form of the operator Van Vleck perturbation theory is considered (the irreducible tensorial set theory is used as the mathematical basis of this consideration). General formulae which define spectroscopic rotational, centrifugal and resonance constants of molecules as functions of reduced matrix elements of vibrational operators are obtained. Algorithms for the ES-1055 computer have been derived on the basis of the formulae obtained, and a system of analytical calculations using the language 'REDUCE' has been created. The dyad and pentad of the CH4-type molecule are considered for illustration. Formulae are obtained which connect spectroscopic and intramolecular constants not only for isolated but also for interacting vibrational states.

The isoscalar factors which determine both the qualitative and, to a great extend, the quantitative picture of spectra of the Td symmetry quantum mechanical systems have been obtained as analytical functions of the rotational quantum number J.