Symmetries and torsional splitting patterns in the overtone and combination vibrational states of molecules like ethane and methanol

The effects of head–tail coupling in the mechanism of formation of combinations and overtones of perpendicular vibrational modes, in molecules like ethane and methanol, is investigated. For uncoupled head and tail the perpendicular modes have higher degeneracies, and the species of the components of their combinations or overtones span the irreducible representations occurring in the direct products Gs×Gs in the G36(EM) group (ethane) and E×E in the G6(EM) group (methanol). Head–tail coupling operators can transform these uncoupled fundamental vibrational modes into coupled modes of lower symmetries, and then the symmetry species of combinations and overtones must be contained in the direct product of these lower symmetry sets. It is shown that the operators which generate coupled sets of fundamental vibrational states of given symmetries, also work to generate combinations and overtones with the symmetry species predicted from those of the combining fundamentals.These mechanisms are ruled by the torsional Coriolis operators, which can tune more or less to resonance basis levels linked by specific head–tail coupling operators.