Internal rotation: Single diagonalization approach versus standard approaches, application to the methyl peroxy radical (A)over-tilde ← (X)over-tilde transition

A new approach avoiding double (two-step) diagonalization is proposed to deal with internal rotation. The development of this method was stimulated by the jet-cooled high resolution spectrum of the vibrationless (A) over tilde <- (X) over tilde transition of the deuterated species of the methyl peroxy radical. This spectrum, originally analyzed with a rigid rotor Hamiltonian including spin-rotation but neglecting internal rotation, has been revisited in the previous paper (P. Dupre, J. Chem. Phys. 134, 244308 (2011)) and a determinable yaw of the molecular principal axes of inertia about the c-axis (axis-switching) during the electronic transition was established. The spectral resolution of the jet-cooled data of the vibrationless transition (similar to 7355 - 7390 cm(-1)) does not allow the observation of splitting due to internal rotation of the methyl top, but when these data are combined with the low resolution room temperature data (similar to 7200 - 8000 cm(-1)) accurate fits or simulations of the two sets of data are possible. A recent study of the room temperature data has been reported in this journal (G. M. P. Just et al., J. Chem. Phys. 127, 044310 (2007)) showing evidence of the internal rotation coupling by analyzing the intensity of the torsional mode energy progression. That investigation combined ab initio quantum chemistry calculations and the rho-axis-method (RAM) to model the internal rotation. Here, a comparison of full spectral intensity analyses based on both the usual RAM and on the new approach requiring a single-diagonalization principal-axis-method is presented. The comparison favors the single-diagonalization approach. Axis-switching and spin-rotation coupling are incorporated in the analysis, in which the use of the principal axes of inertia is maintained. Symmetries, energy levels, and advantages are carefully discussed for all methods. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3599954]