Three states global fittings with improved long range: singlet and triplet states of H.

Full dimensional analytical fits of the coupled potential energy surfaces for the three lower singlet and triplet adiabatic states of H are developed, providing analytic derivatives and non-adiabatic coupling matrix elements. The fits are highly accurate and include an improved description of the long range interactions, including new terms for the description of the long range in the diatomic fits and the atom-diatom dissociation channels. The fits are based on the DIM formalism including three body terms in Hamiltonian matrix elements, each of them obeying S ₂ permutational symmetry, where the positive charge is placed in either of the three hydrogen atoms, but the full system obeys S ₃ permutational symmetry, invariant under all permutations of the nuclei. The ab initio points used in the fitting are obtained from a complete basis set extrapolation, made for all electronic states. Total root mean square errors of the fits are 27 and 12 cm ^-1 , for the singlet and triplet states, respectively. The errors in the channels are lower than 2 cm ^-1 and 6 cm ^-1 for the H + H and H ⁺ + H ₂ channels respectively. The new fits have been used to calculate the rovibrational bound states of the lowest singlet and lowest triplet states showing very good agreement with previous calculations in the literature.