First principles tight-binding method for investigating electronic properties of surfaces, interfaces, and bulk solids

A brief discussion of first principles extended tight binding (ETB) (also known as linear combination of atomic orbitals, LCAO) method for studying electronic structure of solids is presented. As the name suggests, the method is nonempirical and employs a linear combination of Bloch-adapted Gaussian orbitals as its basis set. Hamiltonian and overlap matrix elements required for calculating electronic structure in solids can be obtained analytically using Gaussian functions. Various matrix elements are computed to convergence (which may involve interactions up to 10–12 neighbors), eigenvalues and eigenvectors are obtained by solving ∥H−ES∥−0. Since the tight binding wave functions are constructed from s, p, d, ... type of orbitals, the ETB method offers conceptual simplicity in understanding the nature of chemical bonds at a surface. Furthermore, the identification of surface states can be readily accomplished in terms of atomic localization, a quantity which is straightforward to calculate within the framework of this method. The method is illustrated by (i) absorbate band formation in CO monolayers and (ii) chemisorption studies of Cl on Si(111) surface. Future likely developments of the ETB method are briefly commented upon.