Linear Relationship between Weighted-Average Madelung Constants and Density Functional Theory Energies for MgO Nanotubes

Abstract

For systems containing large numbers of ions, calculations using Density Functional Theory (DFT) are often impractical because of the amount of time needed to perform the computations. In this paper, we show that weighted-average Madelung constants of MgO nanotubes correlate in an essentially perfectly linear way with cohesive energies determined by DFT. We discuss this correlation in terms of the relationship between lattice energies and cohesive energies. Through this linear correlation, Madelung constants are used to predict cohesive energies and average ion charges of nanostructures containing up to 3940 ions. Cohesive energies of MgO nanotubes are shown to converge to a value lower than those of bulk MgO. Using the slopes of the DFT versus Madelung constant plots, the average charges on the ions in the nanotubes are determined. For nanotubes containing the same number of ions, the relative stability of longer tubes versus disc-like structures is discussed.