Using variational Monte Carlo and a simple explicitly correlated wave function we have computed the Born-Oppenheimer energy of the H-2 ground state (X (1)Sigma(g)(+)) at 24 internuclear distances. We have also calculated the diagonal correction to the Born-Oppenheimer approximation and the lowest-order relativistic corrections at each distance using variational Monte Carlo techniques. The nonadiabatic values are evaluated from numerical derivatives of the wave function with respect to the nuclear coordinates. With this potential energy surface we have computed several of the lowest vibrational-rotational energies for this system. Our results are in good agreement with the best values found in the literature. (C) 2004 American Institute of Physics.