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.