Effect of the local exchange-correlation correction to electron density on the properties of inorganic solids

In the density-functional theory one attempts to get the best possible functional for energy. Then the functional is used in the calculation of the properties of solids. In the present paper a very simple form for the functional is preserved but the density is corrected. The correction has negative sign and its main sense is to take into account the lowering of electron density due to the collective effect of the exchange and the correlation holes. The correction is postulated in the form of the Laplace operator acting on the exchange-correlation potential of the Wigner–Seitz–Slater type. The presence of the correction in the models based on the Thomas–Fermi–Dirac or Thomas–Fermi–Dirac–Gombás energy functionals makes it possible to get cohesion for monatomic solids of all elements in the periodic system; in the absence of the correction, the positive cohesive energy could not be obtained for any element in both models mentioned above. The volume dependence of the Grüneisen parameter for a number of metals has been calculated and a new derivation of the Dugdale–MacDonald formula is presented. It has been shown that the pressure of the electron gas on the ion boundary in an ionic crystal is adequate for an explanation of the repulsive forces between ions in the crystal. Values of the exponents of these forces, which usually are determined experimentally from the compressibility data, have been calculated theoretically. The ratios of the ab initio values of the ionic radii which are obtained from (a) the distances between the ionic nuclei and the boundaries of the ions, (b) the positions of the minima of electron density for ionic pairs, resemble respectively, the ratios of the semiempirical Pauling’s radii and the ratios of the similar radii obtained by Fumi and Tosi. On the basis of set (a) of the theoretical radii the structural properties of a number of binary compounds containing one metal ion and a number of ternary compounds containing several metal ions (perovskites, ilmenites, and spinels) have been examined. The predicted crystal structures are, in general, close to those observed in reality.