The effective Hamiltonian for the coupling between inversion-torsion states in methylamine

The Hougen’s formalism of group-theoretical effective Hamiltonian has been extended to include the resonances between the wagging, ν₉, and third or fourth excited torsional, 3ν₁₅ and 4ν₁₅, states in methylamine. The presented Hamiltonian treats explicitly these couplings. For each of these bands the rovibrational sublevels belong to all symmetry species of the G₁₂ group of methylamine. On the other hand the vibrational states for ν₉ and 4ν₁₅ are symmetric with respect to reflection in the symmetry plane of the NH₂ group, and antisymmetric for 3ν₁₅. We have shown that the coupling terms between the ν₉ and 3ν₁₅ states are limited to Coriolis-like coupling, and no Fermi-type interactions are allowed. For the coupling between the ν₉ and 4ν₁₅ states all kind of interaction terms are possible.