  Topologically trivial insulators come in two kinds: atomic, where the Wannier
charge centers (WCCs) are localized on the atoms, and obstructed atomic, where
the WCCs are located away from the atoms. The latter, which can exhibit
interesting surface states and possibly have much larger band gaps than the
topological insulators, have so far not been classified in three-dimensional
(3D) crystalline materials. In this paper, we developed the 3D real space
invariants (RSIs) for the 1651 Shubnikov space groups with the spin-orbit
coupling and provide the full classification of 3D obstructed atomic insulators
(OAIs) by the RSIs. We then apply the theory to the entire database of
materials on the Topological Quantum Chemistry website and Topological Magnetic
Materials website, obtaining all the OAIs so far existing in nature. We find
that, out of the 34013 paramagnetic and 296 magnetic topologically trivial
insulators, there are 3383 paramagnetic and 30 magnetic OAIs. All of them
present a filling anomaly under certain open-boundary conditions and exhibit
obstructed surface states (OSSs). We further refine the atomic insulator
concept to obtain the orbital-selected OAIs (OOAIs), where the WCC of the
system is located at a Wyckoff position occupied by an atom but forms a
symmetric representation that does not belong to the outer-shell electrons of
the given atom. In such a way, we obtain a further 121 OOAIs. Furthermore, we
analyze 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 evolution
catalyst, we directly prove that the catalytic activities arise from the
surfaces with OSSs. Additional potential applications of the 3D RSIs and OAIs
in, for example, electrochemistry, asymmetric catalysis, superconductivity, and
Josephson diode will be discussed.
