Mixed crystals Bloch functions

How does this come about There are two ways to talk about it. Locally, the donor function of one monomer (z2) can interact with the acceptor function (z) of its neighbor. This is shown in 30. The overlap is good, but the energy match is poor.11 So the interaction is small, but it s there. Alternatively, one could think about interaction of the Bloch functions, or symmetry-adapted z and z2 crystal orbitals. At k = 0 and it la, they don t mix. But at every interior point in the Brillouin zone, the... 

This result also demonstrates clearly that the Wannier functions are not eigenfunctions of the Hamiltonian of a periodic crystal. Therefore in many applications, when one applies the Wannier functions to describe local perturbations, it is more advantageous to start from a mixed representation in which some matrix elements are expressed with the help of Wannier functions and others with the aid of Bloch functions. 

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