On the Meaning of De-Excitations in Time-Dependent Density Functional Theory Computations

De-excitations play a prominent role within the mathematical formalism of time-dependent density functional theory (TDDFT) and other excited-state response methods. However, their physical meaning remains largely unexplored and poorly understood. It is the purpose of this work to shed new light on this issue. The main thesis developed here is that de-excitations are not a peculiarity of TDDFT but that they are a more fundamental property of the underlying wave functions reflecting how electrons are excited between partially occupied orbitals. The paraquinodimethane (pQDM) molecule is chosen as a convenient model system whose open-shell character can be modulated via twisting of its methylene groups. Using the one-electron transition density matrix as a rigorous basis for our analysis, we highlight qualitative and quantitative parallels in the way that de-excitations are reflected in multireference wave function and TDDFT computations. As a physically observable consequence, we highlight a lowering of the transition dipole moment that derives from destructive interference between the excitation and de-excitation contributions. In summary, we hope that this work will shed new light on formal and practical aspects regarding the application of TDDFT to excited-state computations, especially of diradicaloid systems.