  Using a single trial function we perform an accurate calculation of the
ground state $1\sigma_g$ of the hydrogenic molecular ion $H^+_2$ in a constant
uniform magnetic field ranging $0-10^{13}$ G. We show that this trial function
also makes it possible to study the negative parity ground state $1\sigma_u$.
We obtain that over the whole range of magnetic fields studied, the calculated
binding energies are in most cases larger than binding energies obtained
previously by other authors using different methods.
