  Density functional theory $(DFT)$ studies show that doping of $3d TM$ atoms
into $Mg_4^{0,+} (TMMg_3^{0,+})$ can alter the endothermic nature of molecular
hydrogen adsorption on bare $Mg_4^{0,+}$. $H_2$ adsorption on $TMMg_3^{0,+}$
clusters depends on the $TM(3d)$ orbital contribution to the frontier molecular
orbitals of the clusters. In $H_2TMMg_3^{0,+}$ complexes, $H_2$ is adsorbed
through donation and back donation of electronic charges with $TMMg_3^{0,+}$
clusters. $H_2$ binding energy is the maximum for $NiMg_3$ (-0.76 eV) and
$FeMg_3^+$ (-0.48 eV) among the neutral and cationic $TMMg_3$ clusters,
respectively. The geometry of $H_2$ adsorption complex entirely depends on the
geometry of the host cluster. The lowest energy symmetrical structures of both
$NiMg_3$ and $FeMg_3^+$ clusters are less efficient than some slightly higher
energy low symmetrical geometrical isomers for adsorption of multiple hydrogen
molecules (13.28 $H_2$ $wt\%$ for $NiMg_3$ and 7.89 $H_2$ $wt\%$ for
$FeMg_3^+$). Greater exposer of $TM^{0,+}$ along with its lower Mg coordination
number make host clusters more suitable for hydrogen storage.
