A time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities

We present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, we implemented it in a real-space (basis-set free) code, and applied it to benchmark molecules, namely CO, H2O, and paranitroaniline (PNA). Our results are in agreement with experimental and previous theoretical studies, and fully validate our approach.