  We present a systematic study clarifying an electronic correlation trend of
electrides from first principles. By using the maximally localized Wannier
function and the constrained random phase approximation, we calculated the
electronic correlation strength $(U-U_{nn})/|t|$ of 19 inorganic electrides,
where $U$, $U_{nn}$, and $t$ are the effective onsite Coulomb repulsion,
nearest-neighbor Coulomb repulsion, and the nearest-neighbor transfer
integrals, respectively. The electronic correlation was found to be highly
correlated with the dimensionality of the Wannier-function network of anionic
electrons in electrides; the correlation strength varies in the order 0D $>>$
1D $>$ 2D $\sim$ 3D, showing good correspondence with experimental trends, and
exceeds 10 (a measure for the emergence of exotic properties) in all the 0D
systems and some of the 1D materials. We also found that the electronic
correlation depends on the cation species surrounding the anionic electrons; in
the 1D electrides, the electronic correlation becomes stronger for cationic
walls consisting of $\mathrm{Ca^{2+}}$, $\mathrm{Sr^{2+}}$, and
$\mathrm{Ba^{2+}}$ in this order, and the correlation strength exceeds 10 for
$\mathrm{Ba_5As_3}$. The theoretical results indicate that 0- and 1-dimensional
electrides will be new research targets for studies on strongly correlated
electron systems.
