On the simple determination of the self-consistent atomic charges and Madelung potentials in ionic crystals

Abstract

A simple method for the self-consistent calculation of the atomic charges and Madelung potentials in ionic crystals is suggested. The method is based on electronegativity equalization and permits the obtaining of good charge distributions. Test calculations are carried out for a number of structures like cubic perovskites, high-T c copper oxides and mixed valence crystals. © 1997 Published by Elsevier Science B.V.Electrostatic or Madelung potentials are important characteristics of ionic and near ionic crystals, determining their electronic structure and physical properties. Numerous calculations of the electronic structure of crystals and molecular fragments of crystals have shown that the Madelung potentials must be included in the calculation schemes to obtain the correct energy level ordering, adequate values of the atomic charges and energy gaps [1][2][3][4]. Evaluation of the Madelung potentials implies knowledge of the atomic charges which in their turn can be obtained as the result of complicated quantum chemistry calculations. In this connection the elaboration of simple quantitative methods seems worthwhile. In this Letter a procedure for the self-consistent calculation of atomic charges and Madelung potentials in ionic crystals based on the electronegativity equalization method (EEM) [5] is suggested. It permits the obtaining of good charge distributions and is further simplified for ionic crystals of cubic symmetry.The electronic energy of an ionic crystal is supposed to be a function of atomic charges qk only and is presented in the form N

Physical meaning of conditionally convergent series: the calculation of the Madelung constant

“…The calculation of the Madelung constant is one of the topics commonly studied in introductory courses of Solid State Physics mainly because of its interest in the computation of the cohesive energy of ionic crystals [1,2]. Apart from elementary applications such as the prediction of crystal structures of alkali halides [1], the Madelung constant has also importance in other fields of material science such as the determination of optical phonon modes in ionic uniaxial crystals [3], exciton energies in alkali halides [4], evaluation of ionization energies of rare-earth ions doped into ionic crystals [5] or even study of properties of copper oxides of high critical temperature [6].…”