Algebraic force-field Hamiltonian expansion for a strongly anharmonic potential: application to the C̃ state of SO2

A new, algebraically expanded Hamiltonian is proposed to describe vibrations of strongly anharmonic polyatomic molecules. This Hamiltonian is used to study the vibrational-level energies of the C̃ state of SO2. A comparison with the conventional force-field method is made. Results of fitting the experimental vibrational-level energies show that (i) the algebraic Hamiltonian expansion reproduces the experimental level energies with a nearly equal root-mean-square deviation of the force-field expansion but with fewer parameters and that (ii) convergence for the suggested algebraic Hamiltonian expansion is much faster than that of the force-field expansion.