Improved TDDFT Excitation Energies with an Accurate Kohn–Sham Potential: Reassessment of the Double-Excitation Character of the Low Lying 2 ¹ <i>A</i> _<i>g</i> Excited State of s-Trans-1,3-Butadiene

Extensive benchmarks and reviews of time-dependent density functional theory (TDDFT) have been published, covering at least 50 functionals. Here, we do not use one of the (meta)GGA or hybrid functionals but highlight the particular TDDFT method that does not use the Kohn-Sham (KS) potential of some exchange-correlation functional, but uses the exact Kohn-Sham potential or a close approximation to it in the SCF calculations. Such KS-potential-based TDDFT results have been proven to yield excellent results. For routine application, it is required that a computationally simple approximation (as a density functional) to the exact KS potential is available. In this paper, we benchmark TDDFT calculations with a recently developed model KS potential and compare them to advanced quantum chemical methods and experimental data. The target systems here are medium-sized molecules. These TDDFT calculations based on good KS potentials prove to be competitive in accuracy with sophisticated <i>ab initio</i> methods. An advantage is the possibility to use large basis sets (also for large molecules), enabling a description of valence excitations and Rydberg (or mixed valence-Rydberg) excitations on the same footing. This is necessary for high accuracy; a sophisticated but expensive method that cannot handle large basis sets cannot achieve high accuracy. An advantage of the use of a (close to) exact Kohn-Sham potential is the realistic nature (shape and energy) of both the occupied and the virtual KS orbitals, affording an interpretation of excitations in terms of one or a few single orbital-to-orbital transitions. This obviates the need for extensive optimization of the virtual orbitals for the purpose of interpreting excitations. To highlight the importance of the realistic nature of the KS virtuals, including the Rydberg orbitals, we discuss and reassess the nature of the 2¹ <i>A</i>_<i>g</i> state of s-trans-1,3-butadiene, which has been widely considered as a prototype excitation with large double excitation character. Charge-transfer and true double excitations cannot be handled by the simple ALDA kernel used here.