Restricted density functional theory of linear time-dependent properties in open-shell molecules

A spin-restricted density functional formalism for linear time-dependent properties in open-shell molecules is presented. The formalism is a generalization of an approach for closed shell molecules that is based on an exponential parameterization of the density operator with the response functions defined through the Ehrenfest principle or alternatively through the quasienergy ansatz. It is proved that the formalism provides a numerically justified approach and a viable alternative to the unrestricted time-dependent DFT formalism for optical absorption spectra and static and dynamic polarizabilities of radicals.