We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard LennardJones oscillator, and to the ab-initio potential of the H2 molecule. ...

We introduce a point of view for treating the dynamical tunneling splitting of symmetric local mode vibrational states in ABA molecules (A = H typically) which is the one we have employed in treating the vibrational spectroscopy of CH overtones in molecules such as (CXs),YCCH. Namely, the vibrational coupling corresponding to the dynamical tunneling in semiclassical mechanics via many intermedi...