  We describe a method to calculate the electronic properties of an insulator
under an applied electric field. It is based on the minimization of an electric
enthalpy functional with respect to the orbitals, which behave as Wannier
functions under crystal translations, but are not necessarily orthogonal. This
paper extends the approach of Nunes and Vanderbilt (NV) [Phys. Rev. Lett. 73,
712 (1994)], who demonstrated that a Wannier function representation can be
used to study insulating crystals in the presence of a finite electric field.
According to a study by Fern\'{a}ndez et al. [Phys. Rev. B. 58, R7480 (1998)],
first-principles implementations of the NV approach suffer from the impact of
the localization constraint on the orthogonal wave functions, what affects the
accuracy of the physical results. We show that because non-orthogonal
generalized Wannier functions can be more localized than their orthogonal
counterparts, the error due to localization constraints is reduced, thus
improving the accuracy of the calculated physical quantities.
