The vibrationrotation problem in triatomic molecules allowing for two largeamplitude stretching vibrations
Abstract
An expression for the Hamiltonian of a vibrationrotating triatomic molecule is derived, using two curvilinear stretching coordinates ϱ_{1} and ϱ_{3} 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 zerothorder Hamiltonian H _{s}^{0} ( ϱ_{1}, ϱ_{3}) is obtained, describing the energy levels associated with the two stretching vibrations ν_{1} and ν_{3}. The vibrational energy levels ( v_{1}, v_{3}^{even}) of an XY _{2} molecule having unequal bond lengths at equilibrium are then calculated. The kinetic energy T _{0} ( ϱ_{1}, ϱ_{3}) of the Hamiltonian effectively takes into account the two largeamplitude motions in ν_{1} and ν_{3} together with their interaction. A model calculation is described for a bent XY _{2} molecule (SO _{2} in its ^{1}A' ( ^{1}B _{2}) excited state) in which the ν_{3} oscillation occurs in a doubleminimum potential. Coupling by kinetic energy terms in the Hamiltonian turns out to be very small in this example.
 Publication:

Journal of Molecular Spectroscopy
 Pub Date:
 June 1976
 DOI:
 10.1016/00222852(76)903271
 Bibcode:
 1976JMoSp..61..360B