The Electronic Structure of Crystalline Li21Si5. A Cluster Approach to a γ-Brass Structure

Abstract

The electronic structure of crystalline Li₂₁Si₅ is investigated by semiempirical MO (molecular orbital) calculations of the INDO (intermediate neglect of differential overlap) type in the framework of a finite cluster approach. The complex solid-state ensemble with 416 atoms per unit cell is divided into 16 cluster units M₂₆ that form the three-dimensional structure. These M₂₆ clusters have two different chemical compositions and act as formal donor and acceptor fragments, namely D = (Li₂₀Si₆) and A = (Li₂₂Si₄), having the formal net charges q(D ) = - 4 and q(A) = + 4. The electronic structures of these finite building units are rationalized by the semiempirical MO model. The one-electron energies of (Li₂₀Si₆)^4- and (Li₂₂Si₄)⁴⁺ are derived on the basis of fragment interactions between the site sets (tetrahedral, octahedral, cube-octahedral) that build up the different M₂₆ units. The canonical MO’s are transformed by means of the Edmiston-Ruedenberg localization procedure in order to come to a clear representation of the chemical bond in the two clusters. In (Li₂₀Si₆)^4- a coincidence of the classical valence rules and the existence of nonclassical many-center bonds is found. (Li₂₂Si₄)⁴⁺ on the other side violates the counting schemes because of an excess of 2 electrons (electron octets at Si). The model calculations show however that the octet rule is strictly fulfilled in the Si subspace. The Li centers allow for the formation of an additional bonding cage orbital due to in-phase interactions between the Li 2s AO’s. This MO is occupied by the two excess electrons which are left after filling the valence orbitals associated to Si. The formation of such a one-electron level is not considered in classical models. The Li-Si interaction in Li₂₁Si₅ is of covalent nature and is comparable to the metal-nonmetal bonds in other lithium silicides. The Li-Li contacts are nonbonding in the framework of the Hartree-Fock approximation. The observed solid-state structure of the binary phase can be explained by intercluster interactions between the different donor and acceptor fragments.