Internal rotation, centrifugal distortion, reduction and molecular reference frames

This paper supplements two papers by the same author [J. Chem. Phys. 134, 244308 and 224309, (2011)] devoted to the analysis of the experimental spectra of methyl radicals CH3O2 and CD3O2. It is devoted to the analysis of the lowest order terms of the rotational and of the centrifugal distortion Hamiltonian of molecules exhibiting an internal rotation (three-fold potential) or requiring a rotation of the reference frame with the perspective of determining the line intensity. It deals with different Hamiltonian expansions by keeping the uniqueness of the molecular parameters referenced in the principal-inertia-axis system (PAS) reference frame. The reduction of the effective second-order internal rotation Hamiltonian is discussed in the PAS and rho-axis-system (RAS) frames for application to standard (double-diagonalization) and new ‘non-approximate’ (single-diagonalization) approaches, i.e. PAM, RAM, SDPAM or SDRAM, which have been implemented to analyse the methyl peroxy radical spectra.