Theory of polarization of crystalline solids

We consider the change in polarization \ensuremath{\Delta}P which occurs upon making an adiabatic change in the Kohn-Sham Hamiltonian of the solid. A simple expression for \ensuremath{\Delta}P is derived in terms of the valence-band wave functions of the initial and final Hamiltonians. We show that physically \ensuremath{\Delta}P can be interpreted as a displacement of the center of charge of the Wannier functions. The formulation is successfully applied to compute the piezoelectric tensor of GaAs in a first-principles pseudopotential calculation.