Four Important Factors in the ab initio Determination of Accurate Inter-Ionic Potentials

Abstract

The accurate ab initio determination of inter-ionic potentials requires the consideration of four important factors. These are relativistic effects for ions of high atomic number, the environmentally induced modifications of ion wavefunctions, the damping of reliably calculated inter-ionic dispersive attractions and the avoidance of density functional descriptions of the uncorrelated potentials.

The relativistic modifications of the behaviour of valence electrons in elements heavier than those of the third series of transition elements are too large to be treated by first order perturbation theory. The relativistic integrals programme (RIP), which works directly with the Dirac equation and four component wavefunctions for the individual electrons, is used to compute fully relativistic inter-ionic potentials.

The mechanisms through which ion wavefunctions are modified by their environment in the crystal are discussed. A simple yet physically realistic model for computing such wavefunctions is presented. The contractions of anion wave functions caused by their environment in the crystal are shown to be sufficiently significant that the use of free ion wavefunctions is inadequate for accurate work. The crystalline environment leaves unaffected the wavefunctions and polarizabilities of cations having s ² or p ⁶ outermost electronic configurations.

The inter-ionic dispersive (van der Waals) attractions are shown to contribute significantly to the crystal cohesion. The overlap of the ion wavefunctions damps these attractions sufficiently that predictions derived neglecting this damping are unreliable. A trustworthy method for deriving values of dipole–dipole dispersion coefficients for ions in crystals is presented.

Density functional predictions of inter-ionic potentials are tested against the RIP programme which yields results that are exact once the ion wavefunctions have been specified. Density functional theory must be judged to fail for many cation—cation and anion—anion interactions because its predictions bear little relation to those derived from RIP calculations. Although density functional theory gives a fair account of the cohesion of many crystals, the use of RIP rather than density functional potentials significantly improves the predictions. Density functional theory fails for AgF.

Key Words:

• Ab initio
• inter-ionic potentials
• relativistic effects
• relativistic integrals programme
• dispersion energy
• density functional theory