Non-linear response in time-dependent density functional theory

In the study of electronic excitations, in most cases, the response up to first order in the external perturbation is considered. When intense fields are treated, however, non-linear effects become more relevant and a proper theoretical description of the phenomena is required. This involves additional complexity with respect to the linear case both at the formulation and computational cost levels.

In this talk we will discuss the application of time-dependent density functional for the modeling of properties beyond the linear response regime, focusing on its application to realistic systems. Two distinct and complementary formulations will be addressed, real-time propagation and the Sternheimer equation. We will review what are the properties that can be obtained and what is the precision we can expect from present adiabatic exchange and correlation functionals.