Real-space, real-time calculation of dynamic hyperpolarizabilities.

The finite-difference method to calculate hyperpolarizabilities is generalized for dynamical case. The calculation of the dynamical hyperpolarizabilities from non-perturbative, explicitly time-dependent single particle states obtained in the framework of the time-dependent density functional theory, is implemented in real space and real time. The optical response functions up to the third order are extracted in frequency domain. The present approach is free of deficiencies associated with atom centered basis sets and allows treatment of large molecules. The calculated results are in good agreement with experiments and with other theoretical calculations for various test cases.