The EF and GK[formula omitted] states of hydrogen : Adiabatic calculation of vibronic states in H 2, HD, and D 2

Abstract

The Born-Oppenheimer energies of the first two excited 1 Σ g + states of hydrogen, EF and GK, are computed with higher accuracy (70-term wavefunctions) and over larger R ranges (1 a.u. < R ≤ 15 a.u.) than previously available. Less accurate results over the same large R range are also presented for the third excited 1 Σ g + state, H, whose potential curve is found to exhibit a broad and flat outer minimum, H , near R = 11 a.u., similar to the one in the third 1 Σ u + state, B . The diagonal corrections for nuclear motion in the GK state and the energies and B values of the vibrational states in the EF and GK potentials are computed in the adiabatic approximation up to the dissociation limit. The GK potential curve has two minima, each of which accommodates one single vibrational level, while all other levels lie above the potential barrier. These ab initio results, in which the effects of nuclear-momentum coupling between different electronic states are neglected, agree surprisingly well with experimental data although the electronic GK wavefunction goes through two marked changes of character within the R range of the lowest vibrational levels, viz., in the regions of the potential barrier and of the outer minimum. All of the experimentally established and irregular singlet- g levels of H 2, which had been given electronic labels Q, 3 K, 3 D, L, M, U, and N by Richardson and by Dieke, can now be attributed to the two electronic Born-Oppenheimer states EF and GK, both of whose vibration-rotation structures are characterized by double-minimum potential curves. The experimental energy levels reveal perturbations whose quantitative explanation requires nonadiabatic computations of rovibronic states; results of such a treatment will be presented separately. In this first paper we include a preliminary survey of the experimental evidence regarding the magnitudes of these vibronic interactions within the 1 Σ g + states and of the coupling between electronic motion and nuclear rotation, i.e., 1 Σ g +- 1 Π g- 1 Δ g interactions ( l-uncoupling).