The solid-state electronic structure and the nature of the chemical bond of the ternary Zintl-phase Li8MgSi6. A tight-binding analysis

The electronic strcuture of the ternary Zintl-phase Li₈MgSi₆ has been investigated in the computational framework of a semi-empirical crystal orbital (CO) formalism based on the tight-binding approximation. Li₈MgSi₆ crystallizes in the space group P2₁/m-C_2h² with a = 12.701 Å, b = 4.347 Å, c = 10.507 Å and β = 107.58°. A self-consistent-field (SCF) Hartree-Fock (HF) INDO CO procedure has been employed for the numerical approach. In order to reduce the computational expenditure of the CO calculations we have adopted a one-dimensional (ID) model simulating the real solid. To allow for a clear theoretical analysis the ID system is divided into simpler subfragments (MgSi^2-, Li₃MgSi⁺, Li₅Si₅^?); the solid-state electronic structures of these moieties can be rationalized in a straightforward way. The band structure properties, density of states distributions, net charges and atomic orbital populations of Li₈MgSi₆ are interpreted. A forbidden band gap of 0.62 eV is calculated by the semi-empirical tight-binding scheme, a value that is in excellent agreement to the measured band gap of the semiconducting compound which amounts to = 0.7 eV. The nature of chemical bond in the Li₈MgSi₆ phase is analyzed by fragmenting the net diatomic interaction energies between SiSi, SiLi and MgSi pairs into covalent resonance elements as well as exchange and classical electrostatic (Coulomb) contributions. Partial coordination numbers (PCN) are defined for the various atomic species of the ternary phase that are labels of strongly stabilizing interactions (bonds) in the low-dimensional units. The calculated charge distributions show a striking 1:1 correspondence between the present CO results and the expectations derived on the basis of classical (Zintl-Klemm) electron-counting rules thus corroborating the utility of extended Zintl-Klemm conceptions in solids with atoms beyond the first two rows.