We consider the change in polarization {Δ}P which occurs upon making an adiabatic change in the Kohn-Sham Hamiltonian of the solid. A simple expression for {Δ}P is derived in terms of the valence-band wave functions of the initial and final Hamiltonians. We show that physically {Δ}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.
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King-Smith et al. (1993) studied this question.
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