In this contribution we first report new ab initio self-consistent field configuration interaction calculations of the first excited adiabatic potential of (1)Σ(+) symmetry, the 2(1)Σ(+) or B(1)Σ(+) state, which presents two minima and can thus be seen as made up of the Rydberg E(1)Σ(+) and the valence V(1)Σ(+) states. Based on the computed 2(1)Σ(+) potential, we devised a theoretical procedure to compute the vibronic structure in order to try to explain the energy levels observed in the region above 76 254.4 cm(-1) which display an irregular vibrational structure, indicative of spectral perturbations. We try to find out which representation of the electronic states, the diabatic or the adiabatic one, is best suited to replicate the lowest observed vibronic levels of the E and V states. To this end, we deduce, from the 2(1)Σ(+) potential and its complementary adiabatic potential, two diabatic potentials. We then carry out a coupled equation treatment based on these diabatic potentials. The results of this treatment indicate that, in the present case, the adiabatic representation is better than the diabatic one to describe the observed vibronic levels. This is due, as expected, to the existence of a strong electrostatic interaction between the two diabatic potentials.