Using a single trial function, we perform an accurate calculation of t
he ground state 1 sigma(g) of the hydrogenic molecular ion H-2(+) in a
constant uniform magnetic field ranging from 0 to 10(13) G. We show t
hat this trial function also makes it possible to study the negative p
arity ground state 1 sigma(u). We show that, over the whole range of m
agnetic fields studied the calculated binding energies are in most cas
es larger than binding energies obtained previously by other authors u
sing different methods. [S1050-2947(97)08311-X].