The complete band representations (BRs) have been constructed in the work of topological quantum chemistry. Each BR is expressed by either a certain orbital at a set of Wyckoff sites in realspace, or by a set of irreducible representations in momentum space. In this work, we define unconventional materials as the topologically trivial compounds whose occupied bands can be expressedas a sum of elementary BRs, but not a sum of atomic-orbital-induced BRs (aBRs). Namely, these materials possess the unconventional feature of the mismatch between average electronic centers and atomic positions. The existence of an essential BR at an empty site is described by nonzero real-space invariants. The valence states can be derived by the aBR decomposition, and unconventional materials are supposed to have an uncompensatedtotal valence state. The high-throughput screening for unconventional materials has been performed through the first-principles calculations. We have discovered 392 unconventional compounds with detailed information in the table of the results, including thermoelectronic materials, higher-order topological insulators, electrides, hydrogenstorage materials, hydrogen evolution reaction electrocatalysts, electrodes, and superconductors. The diversity of their interesting properties and applications would be widely studied in the future.
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