The vibration-rotation problem in triatomic molecules allowing for two large-amplitude stretching vibrations
An expression for the Hamiltonian of a vibration-rotating triatomic molecule is derived, using two curvilinear stretching coordinates ϱ1 and ϱ3 and one rectilinear bending coordinate S 2, in such a way that the Hamiltonian obtained is applicable to any bent triatomic molecule and allows for large displacements along the stretching coordinates. From this, a zeroth-order Hamiltonian H s0 ( ϱ1, ϱ3) is obtained, describing the energy levels associated with the two stretching vibrations ν1 and ν3. The vibrational energy levels ( v1, v3even) of an XY 2 molecule having unequal bond lengths at equilibrium are then calculated. The kinetic energy T 0 ( ϱ1, ϱ3) of the Hamiltonian effectively takes into account the two large-amplitude motions in ν1 and ν3 together with their interaction. A model calculation is described for a bent XY 2 molecule (SO 2 in its 1A' ( 1B 2) excited state) in which the ν3 oscillation occurs in a double-minimum potential. Coupling by kinetic energy terms in the Hamiltonian turns out to be very small in this example.