Band Structure Calculations of Two-Dimensional (2 D) Models of the Phases LiBC and CaAl2Si2

Abstract

The electronic structures of the phases LiBC and CaAl2Si2 have been investigated by two dimensional crystal orbital calculations. The corresponding solid-state ensembles have been separated into anionic (e.g. [BC]-, [AlSi]- , [Al2Si2]2-) and cationic substructures. The employed fragmentation is topologically related to the electron counting schemes used in the classical Zintl approach. The band structures of the anionic fragments have been determined by a semiempirical Hartree-Fock crystal orbital (CO ) Hamiltonian on the basis of the tight-binding approximation. The adopted self-consistent-field variant is an intermediate neglect of differential overlap (INDO ) scheme. The influence of the cationic substructure has been simulated by an electrostatic point-charge model. The computational formalism allows for a suitable explanation of the conformations of the anionic subunits of the studied solids. In the CaAl2Si2 model the site symmetry in the anionic substructure has been studied in larger detail. The Al atoms show a tetrahedral coordination while an inverted tetrahedron (i.e. umbrella-like structure) is realized at the more electronegative Si centers. This local geometry is stabilized by the Coulomb interaction between the anionic [Al2Si2]2- layer and the cationic substructure. The energetic sources leading to the different conformations in LiBC and CaAl2Si2 are also quantified. The observed geometric preferences are rationalized by means of an energy fragmentation into covalent resonance (kinetic energy of the electrons) and classical Coulomb elements. This energy decomposition in the planar and chair-like conformations of LiBC and CaAl2Si2 shows that the kinetic energy favours the former, the electrostatic part the latter conformation. The dimerization of two anionic substructures (CaAl2Si2 structure) is also studied by the tight-binding formalism . The observed geometric differences between intra- and interlayer bonds are satisfactorily reproduced by the semiempirical CO model.