response of the density where Here and in the following it is assumed that primed variables are integrated. Within the linear-response domain, the variation of the Hartree (H) and the exchange-correlation (xc) potential to linear order may be expanded with respect to the density variation and Finally, inserting this relation in the response equation for the KS system and comparing the resultant equation with the response equation for the physical system yields the Dyson equation of TDDFT: From this last equation it is possible to derive the excitation energies of the system, as these are simply the poles of the response function. Other linear-response approaches include the Casida formalism (an expansion in electron-hole pairs) and the Sternheimer equation (density-functional perturbation theory). Key papers Books on TDDFT TDDFT codes ELK Firefly GAMESS-US Gaussian Amsterdam Density Functional deMon2k CP2K Dalton NWChem Octopus pw-teleman library PARSEC Qbox/Qb@ll Q-Chem Spartan TeraChem TURBOMOLE YAMBO code ORCA Jaguar GPAW ONETEP VASP Quantum ESPRESSO References External links tddft.org Brief introduction of TD-DFT Density functional theory Computational chemistry Computational physics Quantum chemistry Theoretical chemistry