On the Subsystem Formulation of Linear-Response Time-Dependent DFT
A new and thorough derivation of linear-response subsystem time-dependent density functional theory (TD-DFT) is presented and analyzed in detail. Two equivalent derivations are presented and naturally yield self-consistent subsystem TD-DFT equations. One reduces to the subsystem TD-DFT formalism of Neugebauer [J. Chem. Phys. 126, 134116 (2007)10.1063/1.2713754]. The other yields Dyson type equations involving three types of subsystem response functions: coupled, uncoupled, and Kohn-Sham. The Dyson type equations for subsystem TD-DFT are derived here for the first time. The response function formalism reveals previously hidden qualities and complications of subsystem TD-DFT compared with the regular TD-DFT of the supersystem. For example, analysis of the pole structure of the subsystem response functions shows that each function contains information about the electronic spectrum of the entire supersystem. In addition, comparison of the subsystem and supersystem response functions shows that, while the correlated response is subsystem additive, the Kohn-Sham response is not. Comparison with the non-subjective partition DFT theory shows that this non-additivity is largely an artifact introduced by the subjective nature of the density partitioning in subsystem DFT.