A simple variational-numerical approach to the ro-vibrational spectrum of diatomic molecules. An application to CH+

We describe a simple way of obtaining numerically the manifold of energies for ro-vibrational transitions for a centrifugally distorted oscillator, starting from the potential energy of the non-rotating oscillator calculated by an accurate ab initio method. It is shown that the energies so obtained compare well with those obtained variationally. The species of astrophysical interest methylidyne ion, CH(+), has been selected as an example that allow us to show the computational efficiency of the method with respect to the variational one. It is applied for the determination of ro-vibrational levels up J=6, and the spectroscopic parameters corresponding to the ground electronic state X(1)Sigma(+). From the potential energy surface computed at the MRCI/cc-pV5Z level, the fundamental frequency, B(0) and D(0) are determined to be 2724.8, 13.85688 and -1.53322x10(-3)cm(-1), respectively. We provide also an estimation of anharmonic constants.