POLARITY‑EXTENDED 8‑Neff RULE FOR Cu-CHALCOPYRITE MATERIALS

Semiconductors play a pivotal role in technological innovation, including the development of systems essential for achieving climate neutrality. Over the last decades, research has increasingly focused on chalcopyrite-based materials, particularly for their promising thermoelectric [1] and photovoltaic applications [2]. Despite extensive efforts devoted to understanding and improving their physical properties, comparatively few studies have investigated the nature of chemical bonding in these compounds [3,4]. This work focuses on the CuECh2 (E = Al, Ga, In, Tl; Ch = S, Se, Te) compounds, all crystallizing with the tI12-CuFeS2 (space group I4̅2d; No. 122) structure, related by symmetry reduction to the diamond aristotype. As a consequence, all atomic species exhibit tetrahedral-like environments, both homoleptic (Cu@Ch4, E@Ch4) and heteroleptic (Se@Cu2E2). Due to these structural features, the bonding is typically described as polar‑covalent, with atomic charges still treated in terms of oxidation states (Cu+)(E3+)(Ch2–). Here, we provide a consistent and quantitative bonding picture by means of quantum‑chemical techniques in position space based on the Bader’s Quantum Theory for Atoms In Molecules (QTAIM) and the Electron Localizability Indicator (ELI-D). The ELI‑D distribution shows four maxima along the Ch–E and Ch–Cu contacts, interpreted as polar‑covalent interactions based on the ELI-D/QTAIM basin intersections, with the Ch–E bonds being more covalent. Based on these results, the overall bonding scenario is described by applying the polarity-extended 8-N rule in position space, previously employed for semiconducting main-group compounds of the cubic MgAgAs and TiNiSi types [5,6]. Each heteropolar Ch–E and Ch–Cu interaction is decomposed into two-electron covalent bonds (Ncb) and (hidden) lone-pair (Nlp), which quantify the covalent and polar contributions, respectively. These sum up to 4, thus fulfilling the octet rule. The nature of the chalcogenide species has the main influence on the number of covalent bonds per Ch atom, Ncb(Ch), amounting to approximately 1.10, 1.25, and 1.50 for sulfides, selenides, and tellurides, respectively. The studied compounds exhibit a substantial deviation from the limiting scenarios of purely ionic or purely covalent interactions, corresponding to Ncb(Ch) values of 0 and 4, respectively. These results enable further investigations into the effects of point defects and extrinsic alkali-ion doping on chemical bonding, essential for the rational design of photovoltaic materials, particularly based on CuGaSe2 and CuInSe2. This work was carried out under the project of national relevance (PRIN 2022) LEGACY (healing wide-gap chalcopyrite, grant No. 20223ZP4WP). [1] H. Xie, S. Hao, S. Cai, T.P. Bailey, C. Uher, C. Wolverton, V.P. Dravid, M.G. Kanatzidis, Energy Environ. Sci. 13 (2020) 3693-3705. [2] D. Colombara, K. Conley, M. Malitckaya, H.-P. Komsa, M.J. Puska, J. Mater. Chem. A 8 (2020) 6471-6479. [3] J.E. Jaffe, A. Zunger, Phys. Rev. B 28 (1983) 5822. [4] T. Maeda, T. Wada, Jpn. J. Appl. Phys. 49 (2010) 04DP07. [5] D. Bende, F.R. Wanger, Yu. Grin, Inorg. Chem. 54(8) (2015) 3970-3978. [6] R. Freccero, Yu. Grin, F.R. Wagner, Dalton Trans. 52 (2023) 8222-8236.