In our previous work [P. Itskowitz and M. L. Berkowitz, J. Phys. Chem. A 101, 5687 (1997)], we showed how in the framework of the density functional theory the energy of a molecule can be expressed as a functional of the perturbations on atomic densities. In the present work we discuss the forms of the atomic hardness kernels that enter the energy expression and apply our approach to the problem of finding the response of molecules to an applied electric field. We obtain a system of linear equations for the density perturbations on each atom in a molecule due to the applied electric field. The calculated values of polarization tensor components of several planar molecules are reported.