  Two-dimensional (2D) materials can have an excellent capability to handle
high rates of charge in ion batteries since metal ions need not diffuse in a 3D
lattice structure. However graphene, which is the most important 2D material,
is known to have no Li capacity. Herein, adsorption of Li, as well as Na, K,
and Ca on Ti$_3$C$_2$, one representative MXene, is predicted by
first-principles density functional calculations. In our study, we observed
that these alkali ions exhibit different adsorption energy depending on the
coverage. The adsorption energies of Na, K and Ca decrease as coverage
increases, while Li shows little sensitivity to variance in coverage. This
observed relationship between adsorption energies and coverage of alkali ions
on Ti$_3$C$_2$ can be explained by their effective ionic radii. A larger
effective ionic radius increases interaction between alkali atoms, thus lower
capacity and coverage are obtained. Our calculated capacity values for Li, Na,
K and Ca on Ti$_3$C$_2$ are 639.5, 319.8, 191.8 and 159.9 mAh g$^{-1}$,
respectively. Compared to materials currently used in Li ion battery anodes,
MXene shows great promise in increasing overall battery performance.
