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43 pages plus supplementary materialInternational audienceIn previous works, we  have introduced  analternative perturbation scheme to find approximate solutions of the spectralproblem for the rotation-vibration molecular Hamiltonian.An important feature of our approach is that the zero order Hamiltonian is the direct product of a purely vibrational Hamiltonianwith the identity on the rotational degrees of freedom.The convergence of our method for the methane vibrational ground statewas very satisfactory and our predictions were quantitative.In the present article, we provide further details on the implementationof the method in the degenerate and quasi-degenerate cases. The quasi degenerate version of the method is tested on excited polyads of methane,the results are assessed  with respect to a variational treatment.The optimal choice of the size of quasi-degenerate spaces is determined by a trade-offbetween speed of convergence of the perturbation series and the computational effortto obtain the effective super-Hamiltonian

Application of quasi-degenerate perturbation theory to the calculation of rotational energy levels of methane vibrational polyads