An unrestricted Hartree-Fock evaluation of the diagonal. Born-Oppenheimer correction is reported. The correction is calculated for He-2(+) and F + H-2 --> FH + H. For He-2(+) it is found that on addition of the correction the mean deviation of the best theoretical transition energies is increased (when compared with experiment) by the same order of magnitude (0.04 cm(-1)) as the value of the previous mean deviation. The correction increases the barrier height for the F + H-2 reaction by 0.04 kcal mol(-1).