Calculation of atomic excitation energies by time-dependent density functional theorywithin a modified linear response

Abstract

Time-dependent density functional theory (TDDFT) has become a standard tool forinvestigation of electronic excited states. However, for certain types of electronicexcitations, TDDFT is known to give systematically inaccurate results, which has beenattributed to the insufficiency of conventional exchange–correlation functionals, such as thelocal density approximation (LDA). To improve TDDFT performance withinLDA, a modified linear response (MLR) scheme was recently proposed, in whichthe responses from not only the ground state, but also the intermediate excitedstates are taken into account. This scheme was shown to greatly improve TDDFTperformance on the prediction of Rydberg and charge-transfer excitation energiesof molecules. Yet, for a validation of this TDDFT-MLR scheme for excitationenergies, there remain issues to be resolved regarding Rydberg transitions of singleatoms before going to larger systems. In the present work, we show an adaptedalgorithm to construct the intermediate excited states for rare-gas atoms. With thetechnique, Rydberg transition energies can be well decoded from LDA, as will also beshown in the application of the TDDFT-MLR scheme to other types of atoms.