Accurate prediction of excitation energies to high-lying Rydberg electronic states: Rydberg states of acetylene as a case study

Ab initio outer-valence Green functions (OVGF), equation-of-motion coupled cluster (EOM-CCSD), and Hartree-Fock (HF) calculations with specially constructed basis sets have been carried out to predict excitation energies to Rydberg electronic states of acetylene with principal quantum numbers n up to 11. A comparison of calculated energies with experiment shows that the OVGF method gives accurate results for a broad energy range of 8-11.5 eV. The deviations from experimental data are as low as 0.03-0.04 eV for n=5-8 and are slightly larger for the higher states, similar to0.05 eV for n=9-11. The OVGF calculations are thus demonstrated to be able to reproduce excitation energies for high-lying Rydberg states with a good precision, higher than that provided by the EOM-CCSD method, if one uses experimental or high-level calculated values of the ionization potential. With an increase of the principal quantum number for the Rydberg state, the OVGF corrections to the HF-calculated energies decrease and one can use the HF approach to compute orbital energy levels and excitation energies for higher Rydberg states. The energy levels for high-lying Rydberg states are shown to be insensitive to the molecular geometry, so that the energy gaps between vertical absorption and vertical emission for these states should be similar and can be estimated by the relaxation energy of the neutral system starting from geometry of the positive ion. (C) 2003 American Institute of Physics.