Consider LaCrSb₃, whose structure is shown below (left). To a reasonable approximation, this structure can be described as independent CrSb₂²⁻ layers and Sb⁻ layers separated by La³⁺ ions [3]. If we neglect subtle distortions, the Sb⁻ layer can be approximated as a 2D square lattice of Sb⁻ ions. There is one atom per unit cell, and the Sb–Sb separation is 3.1 Å. The calculated band structure for the idealized Sb⁻ layer is shown below, on the right.

(a) Show the orbital overlap for the Sb 5s and 5p orbitals at Γ, X, and M. Characterize the nearest-neighbor interactions for each band as (σ or π) bonding, antibonding, or nonbonding at each of these k points.

(b) Determine the orbital character of each band, numbered 1–4 in the diagram.

(c) LaCrSb₃ is a metallic conductor. From the band structure above, would you expect the Sb⁻ layers to contribute to the conductivity?

CrSb2- layer Sb-layer La+ energy (eV) 12 6 0 49 -12 -18 -24 r 3 2 X EF M