  We present the results of theoretical investigation on the electronic
structure, bonding nature and ground state properties of Th$_2$Al and
Th$_2$AlH$_4$ using generalized-gradient-corrected first-principles
full-potential density-functional calculations. Th$_2$AlH$_4$ has been reported
to violate the "2 \AA rule" of H-H separation in hydrides. From our total
energy as well as force-minimization calculations, we found a shortest H-H
separation of 1.95 {\AA} in accordance with recent high resolution powder
neutron diffraction experiments. When the Th$_2$Al matrix is hydrogenated, the
volume expansion is highly anisotropic, which is quite opposite to other
hydrides having the same crystal structure. The bonding nature of these
materials are analyzed from the density of states, crystal-orbital Hamiltonian
population and valence-charge-density analyses. Our calculation predicts
different nature of bonding for the H atoms along $a$ and $c$. The strongest
bonding in Th$_2$AlH$_4$ is between Th and H along $c$ which form dumb-bell
shaped H-Th-H subunits. Due to this strong covalent interaction there is very
small amount of electrons present between H atoms along $c$ which makes
repulsive interaction between the H atoms smaller and this is the precise
reason why the 2 {\AA} rule is violated. The large difference in the
interatomic distances between the interstitial region where one can accommodate
H in the $ac$ and $ab$ planes along with the strong covalent interaction
between Th and H are the main reasons for highly anisotropic volume expansion
on hydrogenation of Th$_2$Al.
