Ab initio calculations of vibrational energies and wave-functions of triatomic molecules

A method is developed for the ab initio treatment of non-infinitesimal vibrations of triatomic molecules. The orientation of the moving system of axes fixed to the molecule is defined in a way that differs somewhat from that normally used. The transformation from internal coordinates into normal coordinates is accomplished by a combined diagonalization and numerical integration procedure; the vibrational functions themselves are expanded into products of one-dimensional harmonic oscillator functions. The method is applied to the calculation of vibrational levels of two states in HCN and deviation from the results obtained using the uncoupled harmonic approximation is discussed.