We develop a theoretical electronic structure based approach suitable for the study of complex silicas, and apply it to three different silica polymorphs. The method is first principles but simplified to cope with large systems. Charge transfer between ions is included in a self-consistent fashion. The method is found to be adequate to describe the relative energies and the electronic structure of silica and is used to construct a simplified model energy for the structural transition of high cristobalite. In addition we have studied the moderately complex silica, melanophlogite. Melanophlogite, although a clathrate structure belonging to the group of silica polymorphs known as clathrasils, is found to be only 10 kJ/mol above α-quartz, in accord with the recent thermochemical study of the stability of zeolites.

An approximate method to calculate exchange-correlation contributions in the framework of first-principles tight-binding molecular dynamics methods has been developed. In the proposed scheme on-site (off-site) exchange-correlation matrix elements are expressed as a one-center (two-center) term plus a correction due to other neighboring atoms. The one-center (two-center) term is evaluated directly, while the correction is calculated using a generalization of the [Sankey-Niklewski Phys. Rev. B 40, 3979 (1989)] approach valid for arbitrary atomiclike basis sets. The proposed scheme for exchange-correlation terms, called the multi-center weighted exchange-correlation density approximation (McWEDA), permits the accurate and computationally efficient calculation of corresponding tight-binding matrices and atomic forces for complex systems. We calculate bulk properties of selected transition (W,Pd), noble (Au), and simple (Al) metals, a semiconductor (Si), and the transition metal oxide $\mathrm{Ti}{\mathrm{O}}_2$ with the method to demonstrate its flexibility and accuracy.

Improvements to the Sankey-Niklewaki method [O. F. Sankey and D. J. Niklewski, Phys. Rev. B 40, 3979 (1989)] for computing total energies and forces, within an ab initio tight-binding formalism, are presented here. In particular, the improved method (called FIREBALL) uses the separable pseudopotential (Hamann or Troullier) and goes beyond the minimal ${\mathrm{sp}}^2$ basis set of the Sankey-Niklewski method, allowing for double numerical basis sets with the addition of polarization orbitals and d orbitals to the basis set. A major improvement includes the use of more complex exchange-correlation functionals, such as Becke exchange with the Lee-Yang-Parr correlation. Results for Cu and GaN band structures using d orbitals within the improved method are reported; the results for GaN are greatly improved compared to the minimal basis results. Finally, to demonstrate the flexibility of the method, results for the ${\mathrm{H}}_2\mathrm{O}$ dimer system and the energetics of a gas-phase octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine molecule are reported.