  We present a method for the calculation of electronic structure of systems
that contain tens of thousands of atoms. The method is based on the division of
the system into mutually overlapping fragments and the representation of the
single-particle Hamiltonian in the basis of eigenstates of these fragments. In
practice, for the range of system size that we studied (up to tens of thousands
of atoms), {the dominant part of the calculation scales} linearly with the size
of the system when all the states within a fixed energy interval are required.
The method is highly suitable for making good use of parallel computing
architectures. We illustrate the method by applying it to diagonalize the
single-particle Hamiltonian obtained using the density functional theory based
charge patching method in the case of amorphous alkane and polythiophene
polymers.
