Semi-classical methods for vibrational energy levels of triatomic molecules

The method recently proposed by Chapman, Garrett and Miller for semi-classical eigenvalues of non-separable systems has been applied to the triatomics SO2 and H2O. The Hamiltonian is expressed in normal coordinates, using potentials V=V(Δr1, Δr2, Δθ). The energy levels are compared with corresponding quantum mechanical energy levels. For SO2, the fundamental frequencies differ by at most 0.1 cm–1, and for H2O they differ by at most 1.6 cm–1.