  The past years have witnessed impressive advances in electronic structure
calculation, especially in the complexity and size of the systems studied, as
well as in computation time. Linear scaling methods based on empirical
tight-binding Hamiltonians which can describe chemical bonding, and have a
computational time proportional to the number of atoms N in the system, are of
particular interest for simulations in material science. By contrast
conventional diagonalization schemes scale as $N^{3}$. In combination with
judiciously fitted parameters and an implementation suited for MD, it is
possible to apply such \emph{O(N)} methods to structural, electronic and
dynamical properties of large systems which include up to 1000 atoms on a
workstation.
  Following a brief review of a tight-binding based linear-scaling method based
on a local orbital formulation and of parametrizations appropriate for
covalently bonded systems, we present recent test calculations on
\emph{Si(111)-5 $\times$}5 and \emph{Si(001)-c(4$\times$}2) reconstructed
surfaces in this framework, and compare our results with previous tight-binding
and \emph{ab-initio} calculations.
