  Linear scaling methods provide total energy, but no energy levels and
canonical wavefuctions. From the density matrix computed through the density
matrix purification methods, we propose an order-N (O(N)) method for
calculating both the energies and wavefuctions of band edge states, which are
important for optical properties and chemical reactions. In addition, we also
develop an O(N) algorithm to deal with doped semiconductors based on the O(N)
method for band edge states calculation. We illustrate the O(N) behavior of the
new method by applying it to boron nitride (BN) nanotubes and BN nanotubes with
an adsorbed hydrogen atom. The band gap of various BN nanotubes are
investigated systematicly and the acceptor levels of BN nanotubes with an
isolated adsorbed H atom are computed. Our methods are simple, robust, and
especially suited for the application in self-consistent field electronic
structure theory.
