Three-Center Bonds in an Al–Pd–Co Quasicrystalline Approximant: Wannier Function-Based Chemical Bonding Analysis

The relationship between the valence electronic state and crystal structure of aluminum–transition-metal quasicrystals and their approximants remains to be elucidated. The origin of the semiconducting band structure on the Katz–Gratias–Boudard-type 1/1 approximants has yet to be clarified. We calculated the electronic structure of an Al–Pd–Co 1/1 quasicrystalline approximant (Al92Pd8Co28 per unit cell) using density functional theory and analyzed the approximant's valence orbital character by constructing maximally localized Wannier functions. Among the 304 Wannier functions constructed from the valence bands, 288 were localized around transition metal atoms and 12 were localized between two Co atoms. The other four functions were localized around the center of three-membered rings of Co atoms, which indicates the presence of three-center bonds in this approximant. This situation is an exception to the Yannello–Fredrickson and Kitahara's electron rules, which explain the valence electronic states of aluminum–transition metal approximants and their related intermetallic compound semiconductors considering only two-center bonds. In this study, these rules are expanded to consider three-center bonds, making it possible to explain the semiconducting origin. This work indicates that the electron rule considering three-center bonds can be applied to quasicrystals and other approximants that have triangle networks.