  A new method for calculating the total energy of Si systems is presented. The
method is based on the effective-medium theory concept of a reference system.
Instead of calculating the energy of an atom in the system of interest a
reference system is introduced where the local surroundings are similar. The
energy of the reference system can be calculated selfconsistently once and for
all while the energy difference to the reference system can be obtained
approximately. We propose to calculate it using the tight-binding LMTO scheme
with the Atomic-Sphere Approximation(ASA) for the potential, and by using the
ASA with charge-conserving spheres we are able to treat open system without
introducing empty spheres. All steps in the calculational method is {\em ab
initio} in the sense that all quantities entering are calculated from first
principles without any fitting to experiment. A complete and detailed
description of the method is given together with test calculations of the
energies of phonons, elastic constants, different structures, surfaces and
surface reconstructions. We compare the results to calculations using an
empirical tight-binding scheme.
