  Projection of Bloch states obtained from quantum-mechanical calculations onto
atomic orbitals is the fastest scheme to construct ab-initio tight-binding
Hamiltonian matrices. However, the presence of spurious states and unphysical
hybridizations of the tight-binding eigenstates has hindered the applicability
of this construction. Here we demonstrate that those spurious effects are due
to the inclusion of Bloch states with low projectability. The mechanism for the
formation of those effects is derived analytically. We present an improved
scheme for the removal of the spurious states which results in an efficient
scheme for the construction of highly accurate ab-initio tight-binding
Hamiltonians.
