  We propose a fully ab initio theory to compute the electron density response
under the perturbation in the local field. This method is based on our recently
developed local dielectric response theory [Phys. Rev. B 92, 241107(R), 2015],
which provides a rigorous theoretical framework to treat local electronic
excitations in extended systems beyond the commonly employed dipole
approximation. We have applied this method to study the electronic part of the
molecular polarizability of water in ice Ih and liquid water. Our results
reveal that the crystal field of the hydrogen-bond network has strong
anisotropic effects, which significantly enhance the out-of-plane component and
suppress the in-plane component perpendicular to the bisector direction. The
contribution from the charge transfer is equally important, which increases the
isotropic molecular polarizability by 5-6%. Our study provides new insights
into the dielectric properties of water, which form the basis to understand the
electronic excitations in water and to develop accurate polarizable force
fields of water.
