Density-functional theory of linear and nonlinear time-dependent molecular properties

The density-functional theory for linear and nonlinear response functions using an explicit exponential parametrization of the density operator is presented. The response functions are derived using two alternative variation principles, giving different but numerically equivalent formulas. The calculations of dynamical hyperpolarizabilities for hybrid functionals including exchange-correlation functionals at the general gradient-approximation level and fractional exact Hartree-Fock exchange are presented.