  A new 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 {\it
correction} due to the rest of the atoms. The one-center (two-center) term is
evaluated directly, while the {\it correction} is calculated using a variation
of the Sankey-Niklewski \cite{Sankey89} approach generalized for arbitrary
atomic-like basis sets. The proposed scheme for exchange-correlation part
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) or simple (Al) metals, a
semiconductor (Si) and the transition metal oxide Ti$O_2$ with the new method
to demonstrate its flexibility and good accuracy.
