Dynamical Hyperpolarizabilities from Real-Time Density Functional Theory

The explicitly time dependent wave function obtained in the framework of Real-Space, Time-Dependent Density Functional Theory captures the essential physics and allows a non-perturbative calculations of important observables. We generalize finite-difference method typically used to calculate static hyperpolarizabilities to the dynamical case \footnote{V. A. Goncharov and K. Varga, \emph{J. Chem. Phys.}, 2012, 137, 094111} and compute nonlinear optical response functions to the third order inclusively. The method is simple and free of errors associated with basis function based methods. Comparison with experimental results for a range of molecules including $C_{60}$ is presented.