Sixty-nine points of the Born-Oppenheimer (BO) potential energy surface (PES) for the ground state of H: have been computed using explicitly correlated Gaussian wave functions with optimized nonlinear parameters. The calculated points have an absolute error of about 0.02 cm(-1) (0.1 microhartree), i.e., they are by at least one order of:magnitude more accurate than ever reported. Similarly accurate adiabatic and relativistic corrections have also been evaluated by means of the Born-Handy formula and by direct perturbation theory (DPT), respectively.