The ground state potential energy surfaces (PESs) of MH(2)(n+) (M = Li, Be, Na, Mg, K, Ca; n = 1, 2) have been investigated using relativistically corrected, coupled-cluster (CC) and multi-reference configuration interaction (MRCI) methods. The PESs for MH(2)(+) (M = Li, Na, K) and MH(2)(n+) (M = Be, Mg, Ca; n = 1, 2) exhibit global minima corresponding to C(2v) symmetry equilibrium structures, with local minima for D(∞h) and C(∞v) symmetry states. Conversely, the ground state PESs of LiH(2)(2+), NaH(2)(2+) and KH(2)(2+) are repulsive. In all cases, the D(∞h) states resulting from the insertion of M(n+) into the H(2) moiety were significantly higher in energy than the co-linear C(2v) states. It is generally assumed a priori that these species are the result of the interaction between the metal ion charge state and the quadrupole moment of the H(2) moiety. However, analysis of the functional ΔΘ(αα)(R(M(n+)-H(2))) = Θ(αα)(MH(2)(n+)) - Θ(αα)(M(n+)) (which is effectively the difference between traceless quadrupole moments (Θ(αα)) of MH(2)(n+) and the isolated M(n+) ion computed using MRCI) as a function of M(n+)-H(2) distance demonstrates that a local maximum in ΔΘ(αα) along the molecular C(2) axis is necessary for the formation of a thermodynamically stable complex. It is concluded that the topology of ΔΘ(αα) provides a convenient indicator of the stability of such molecular ion-quadrupole complexes.