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Topologically trivial insulators come in two kinds: atomic, where the Wanniercharge centers (WCCs) are localized on the atoms, and obstructed atomic, wherethe WCCs are located away from the atoms. The latter, which can exhibitinteresting surface states and possibly have much larger band gaps than thetopological insulators, have so far not been classified in three-dimensional(3D) crystalline materials. In this paper, we developed the 3D real spaceinvariants (RSIs) for the 1651 Shubnikov space groups with the spin-orbitcoupling and provide the full classification of 3D obstructed atomic insulators(OAIs) by the RSIs. We then apply the theory to the entire database ofmaterials on the Topological Quantum Chemistry website and Topological MagneticMaterials website, obtaining all the OAIs so far existing in nature. We findthat, out of the 34013 paramagnetic and 296 magnetic topologically trivialinsulators, there are 3383 paramagnetic and 30 magnetic OAIs. All of thempresent a filling anomaly under certain open-boundary conditions and exhibitobstructed surface states (OSSs). We further refine the atomic insulatorconcept to obtain the orbital-selected OAIs (OOAIs), where the WCC of thesystem is located at a Wyckoff position occupied by an atom but forms asymmetric representation that does not belong to the outer-shell electrons ofthe given atom. In such a way, we obtain a further 121 OOAIs. Furthermore, weanalyze the catalytic properties of one of the OAIs in a "proof of principle"experiment. By using the single crystal of 2H-MoS2 as a hydrogen evolutioncatalyst, we directly prove that the catalytic activities arise from thesurfaces with OSSs. Additional potential applications of the 3D RSIs and OAIsin, for example, electrochemistry, asymmetric catalysis, superconductivity, andJosephson diode will be discussed.

Three-Dimensional Real Space Invariants, Obstructed Atomic Insulators and A New Principle for Active Catalytic Sites