Time saving techniques for electronic structure calculations of infinite and semi-infinite crystals, interfaces, and slabs of arbitrary thickness

Hard confined functions (HCF) are proposed as a basis set for electronic structure calculations. The basis functions have enough number of continuous derivatives to perform space integrations numerically with desired accuracy. Replacing unconfined basis functions in ADF-BAND package by HCF with cut-off radiuses of the order of the nearest neighbor distance leads to the reduction of the time of computations without losing the accuracy. For the crystals with surfaces, special techniques based on representation of the wave function as a linear combination of a finite number of HCF and Bloch waves, were elaborated. Exact finite sets of equations for coefficients of HCF and Bloch waves have been developed. The order of the sets depends only on the thickness of a perturbed region, but not on the size of the whole system. For integration of the density of states over perpendicular to the surface wave vector component and energy, the residue theorem and a shift of the energy path into the complex plane are used.