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 X1Σ+. From the potential energy surface computed at the MRCI/cc-pV5Z level, the fundamental frequency, B0 and D0 are determined to be 2724.8, 13.85688 and -1.53322 × 10-3 cm-1, respectively. We provide also an estimation of anharmonic constants. © 2006 Elsevier B.V. All rights reserved.This work has been funded by CONICYT-FONDECYT, Chile, Grant No. 1040923 and Ministerio de Educación y Ciencia of Spain, grant AYA2002-02117 and AYA2005-00702. Support from the Millennium Nucleus for Applied Quantum Mechanics, contract No. P02-004-F and from the grant 2004Cl0001 (CSIC-Universidad de Chile) are also gratefully acknowledged.Peer Reviewe