THEORETICAL INCREMENTS AND INDEXES FOR REACTIVITY, ACIDITY, AND BASICITY WITHIN SOLID-STATE MATERIALS

With the aim of aiding the design of solid-state chemical syntheses, we construct some quantum mechanical indicators of reactivity, acidity, and basicity in crystal chemistry. These definitions are based on three-dimensional electronic structure calculations. After referring back to the concept of density-functional theory of Kohn and Sham and, in particular, the definition of absolute hardness due to Parr and Pearson, we first give a short overview of what is known in the field of molecular quantum chemistry. We then proceed to derive local reactivity, electrophilicity (acidity), and nucleophilicity (basicity) increments and indices both for atoms and bonds in any possible crystal structure. Our definitions are formulated in terms of a one-electron picture, and the first concrete calculations are performed within the framework of the semiempirical extended Huckel tight-binding method. However, the definitions are not restricted to the latter method and are quite easily generalized for ab initio numerical techniques to solve the complex eigenvalue problem in k-space. As an illustrative application, we investigate the acid-base solid-state reaction from K2Ti4O9 to K2Ti8O17. A comparison of our approach, which is suited (but not restricted) to the solid state, with another scheme from molecular orbital calculations is attempted. In detail, we (i) determine the compound's resistance to electronic attack for different electron counts, (ii) analyze all atoms with respect to their electronic reactivity, acidity, and basicity, and (iii) clearly identify the chemically most basic oxygen atom by its outstanding atomic nucleophilicity (basicity) index. In fact, the changing connectivity of this single O atom governs the structural change from K2Ti4O9 to K2Ti8O17. We perform a numerical investigation of Rouxel's hypothesis that the basicity of this particular O atom could be decreased by replacing one Ti atom by a Nb atom, and finally we elucidate the resulting changes in the electronic structure in detail.