  From the order-N electronic-structure formulation, a Hamiltonian is derived,
of which lowest eigen state is the generalized or composite-band Wannier state.
This Hamiltonian maps the locality of the Wannier state to that of a virtual
impurity state and to a perturbation from a bonding orbital. These theories are
demonstrated in the diamond-structure solids, where the Wannier states are
constructed by a practical order-N algorithm with the Hamiltonian. The results
give a prototypical picture of the Wannier states in covalent-bonded systems.
