[en] Total potential energy surfaces (PES) are scanned in order to study the isomerization of the A₂H₃^- (A = Al, Ga) anions. Al₂H₃^- PES is characterized by six minima and seven transition structures which are connectable with themselves. Indeed of these 12 same extrema, the Ga₂H₃^- PES has three other minima and four TSs. These structures exhibit an activated H₂ molecule in one or both Ga atoms coordination sphere where the Ga atom seems imply its metallic character via its occupied d-orbital. We have also localized two unusual structures: a minimum having M₂(μ-H)(μ-H₂)-like structure and a transition with M₂(μ-H₃)-like arrangement where the H₃ entity is coordinated to both Ga atoms. The connectivity of all these extrema brings to the fore an eventual fluxional behaviour of these compounds