Ion H$_2^+$ can dissociate in a strong magnetic field

In framework of a variational method the molecular ion H$_2^+$ in a magnetic field is studied. An optimal form of the vector potential corresponding to a given magnetic field (gauge fixing) is chosen variationally. It is shown that for any magnetic field strength as well as for any orientation of the molecular axis the system $(ppe)$ possesses a minimum in the potential energy. The stable configuration always corresponds to elongation along the magnetic line. However, for magnetic fields $B \gtrsim 5\cdot10^{11}\,$G and some orientations the ion H$_2^+$ becomes unstable decaying to H-atom${} + p$.