  Topological materials are recently regarded as the idea catalysts due to the
protected surface metallic states and high carrier mobility, however the
fundamental mechanism and the underlying relationship between the catalytic
performance and topological states are in debate. Here, by means of symmetry
analysis and first-principles calculations, we discover that the electride
material of C12A7 hosts the multiple-fold fermions due to the
interstitial-electrons, with the sixfold- and fourfold- degenerate points
locating at high symmetric points near the Fermi energy, which are identified
as the underlying reason of the enhanced catalytic ability in C12A7-based
catalysts. The multiple-fold fermions exhibit much longer Fermi arcs on the
(001) surface than traditional Weyl/Dirac fermions, the surface is thus highly
chemical active and possesses a low Gibbs free energy for the hydrogen
evolution reaction. The underlying relationship between catalytic performance
and the topological surface state is explicitly verified by artificially hole
doping, external strain and similar electride without the Fermi arcs, where the
Gibbs free energies are significantly increased when the Fermi arcs is shifted
to higher energy level. This work offers a guiding principle for understanding
catalytic nature of electrides and the topological quantum catalysts.
