The general one-dimensional potential energy function, including centrifugal distortion, for a diatomic molecule is morphed with a series of Morse-like functions for each of the rotational quantum numbers . For each of the morphed potential, explicit formulae for the matrix elements of the complete energy matrix, on the basis of the solutions of the one-dimensional harmonic oscillator, are given and these may be used in connection with the variational procedure to solve the corresponding vibrational Schrodinger equation. From the set of vibrational levels the ro-vibrational transitions can be deduced.