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.

• Received 21 September 2004

DOI:https://doi.org/10.1103/PhysRevB.71.235101