The ionic model: Extension to spatial charge distributions,derivation of an interaction potential for silica polymorphs

An interatomic interaction potential for silica polymorphs is derived based on the SCD model (cfr. Tijskens et al. 1994). This interaction potential incorporates all classical electrostatic interactions arising from the spherical part of the spatial extent of the atoms including many body interactions. The potential is derived from Hartree-Fock energies and electron densities for a set 72 [SiO₄]^4-- and [Si₂O₇]^6--clusters with variable configuration. The long range impact of the surroundings on these clusters in the infinite system has been successfully mimicked by embedding the clusters in a finite three-dimensional array of point charges. This three-dimensional array of point charges is optimized as to reproduce the average site potential and its gradient occurring in II–IV-coordinated silica polymorphs at the central atoms of the clusters. The resulting interaction potential consists of two functions of the configurational coordinates, ?, describing spherical “atomic” electron densities, σ_a(x, ?) for A=Si, O. All classical electrostatic interactions are derived from these densities. A Born-Mayer type correction term ΔE _qm(?) models the quantum mechanical interactions and the electrostatic interactions arising from the non-spherosymmetrical component of the electron density. The new interaction potential model shows a slightly improved reproduction of the potential surface with respect to the classical Born-Mayer ionic model and demonstrates the importance of many body interactions as charge transfer and expansion/contraction of the atomic electron densities in these systems. Also the dependence of the quantum mechanical correction term ΔE _qm(?) on the Si-O-Si-bond angle proves covalent effects to be larger than suggested by the classical Born-Mayer ionic model thereby clarifying the controversy in literature on the importance of covalent effects in silica polymorphs and polymerised silicates in general.