Quantum mechanics

Theoretical physics

Valence (chemistry)

Chemical physics

Materials science

Electronic structure

Position and momentum space

Physics

Nanotechnology

Mathematics

Computational chemistry

Combinatorics

Chemistry

Topology (electrical circuits)

Science Bulletin

The complete band representations (BRs) have been constructed in the work of topological quantum chemistry. Each BR is expressed by either a localized orbital at a Wyckoff site in real space, or by a set of irreducible representations in momentum space. In this work, we define unconventional materials with a common feature of the mismatch between average electronic centers and atomic positions. They can be effectively diagnosed as whose occupied bands can be expressed as a sum of elementary BRs (eBRs), but not a sum of atomic-orbital-induced BRs (aBRs). The existence of an essential BR at an empty site is described by nonzero real-space invariants (RSIs). The "valence" states can be derived by the aBR decomposition, and unconventional materials are supposed to have an uncompensated total "valence" state. The high-throughput screening for unconventional materials has been performed through the first-principles calculations. We have discovered 423 unconventional compounds, including thermoelectronic materials, higher-order topological insulators, electrides, hydrogen storage materials, hydrogen evolution reaction electrocatalysts, electrodes, and superconductors. The diversity of these interesting properties and applications would be widely studied in the future.

Unconventional materials: the mismatch between electronic charge centers and atomic positions