We use variational Monte Carlo techniques to calculate molecular energies at 26 internuclear distances as well as several energy derivatives at the equilibrium of the hydrogen molecular ion. With these values we compare three methods of computing four spectroscopic constants of this system and discuss their applicability to larger systems. Our best results for this molecule are obtained from a fit to the potential energy surface: omega(e) = 2323,98(8) cm(-1), omega(e)x(e) = 67.3(2) cm(-1), alpha(e) = 1.597(2) cm(-1) and B-c = 29.9626(2) cm(-1) (c) 2005 Elsevier B.V. All rights reserved.