Born-Oppenheimer potential and adiabatic corrections for the H (H) over bar(1) Sigma(g)(+), state of the hydrogen molecule are given for internuclear distances up to 80 a.u. Term values in the outer well are computed for J less than or equal to 5. A comparison with experiment shows that the theoretical total energies are too low by about 1 cm(-1). The source of this discrepancy is briefly discussed.