The Herzberg I band system of the oxygen molecule is electric-dipole forbidden and its absorption strength has been explained by intensity borrowing models which include the spin-orbit (SO) and L-uncoupling (RO) interactions as perturbations. We employed three different levels of theoretical models to evaluate these two interactions, and obtained the rotational and vibronic absorption strengths using the ab initio method. The first model calculates the transition moments induced by the SO interaction variationally with the SO configuration interaction method (SOCI), and uses the first-order perturbation theory for the RO interaction, and is called SOCI. The second is based on the first-order perturbation theory for both the SO and RO interactions, and is called Pert (Full). The last is a limited version of Pert(Full), in that the first-order perturbation wavefunction for the initial and final state is represented by only one dominant basis, namely the 13Πg and B3Σu- state, respectively, as originally used by England et al. [Can. J. Phys. 74 (1996) 185], and is called Pert(England). The vibronic oscillator strengths calculated by these three models were in good agreement with the experimental values. As for the integrated rotational linestrengths, the SOCI and Pert(Full) models reproduced the experimental results very well, however the Pert(England) model did not give satisfactory results. Since the Pert(England) model takes only the 1 3Πg and B3Σu- states into consideration, it cannot contain the complicated configuration interactions with highly excited states induced by the SO and RO interaction, which plays an important role for calculating the delicate integrated rotational linestrength. This result suggests that the configuration interaction with highly excited states due to some perturbations cannot be neglected in the case of very weak absorption band systems.
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