Theory of the band-gap anomaly in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>AB</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>chalcopyrite semiconductors

Using self-consistent band-structure methods, we analyze the remarkable anomalies (&gt;50%) in the energy-band gaps of the ternary $\mathrm{I}B\ensuremath{-}\mathrm{I}\mathrm{I}\mathrm{I}A\ensuremath{-}\mathrm{V}\mathrm{I}{A}_{2}$ chalcopyrite semiconductors (e.g., CuGa${\mathrm{S}}_{2}$) relative to their binary zinc-blende analogs $\mathrm{II}B\ensuremath{-}\mathrm{V}\mathrm{I}A$ (e.g., ZnS), in terms of a chemical factor $\ensuremath{\Delta}{E}_{g}^{\mathrm{chem}}$ and a structural factor $\ensuremath{\Delta}{E}_{g}^{S}$. We show that $\ensuremath{\Delta}{E}_{g}^{\mathrm{chem}}$ is controlled by a $p\ensuremath{-}d$ hybridization effect $\ensuremath{\Delta}{E}_{g}^{d}$ and by a cation electronegativity effect $D{E}_{g}^{\mathrm{CE}}$, whereas the structural contribution to the anomaly is controlled by the existence of bond alternation (${R}_{\mathrm{AC}}\ensuremath{\ne}{R}_{\mathrm{BC}}$) in the ternary system, manifested by nonideal anion displacements $u\ensuremath{-}\frac{1}{4}\ensuremath{\ne}0$. All contributions are calculated self-consistently from band-structure theory, and are in good agreement with experiment. We further show how the nonideal anion displacement and the cubic lattice constants of all ternary chalcopyrites can be obtained from elemental coordinates (atomic radii) without using ternary-compound experimental data. This establishes a relationship between the electronic anomalies and the atomic sizes in these systems.