Abstract
We present a real-space method for computing the linear and nonlinear polarizabilities in the time-dependent density-functional theory. In our method, the three-dimensional Cartesian coordinate is discretized on a uniform grid and the wave functions are represented on the grid points. The dynamic polarizabilities may be calculated perturbatively by expanding the dipole moment in a power series of the external field strength or directly by integrating the real-time equations of motion under the time-varying external field. We describe the equations and computational techniques for the both methods. Besides calculating second-order and third-order hyperpolarizabilities, the method can be applied to photon-absorption cross sections, and we show examples of this application as well. We also present here for the first time calculations of the nonlinear polarizabilities using the real-time method.