Hybrid diagonal approximation in time-dependent auxiliary density functional theory: Rydberg excitation calculations

The accurate description of Rydberg excited states has historically been challenging for density functional theory due to the self-interaction error. With the rise of global and range-separated hybrid functionals this situation has been improved considerably, albeit with an increase in computational demand. In this work we present singlet-singlet Rydberg excitation energies calculated with the computational efficient hybrid diagonal approximation (HDA) implemented in the framework of time-dependent auxiliary density functional theory (TD-ADFT). This implementation allows the calculation of excitation energies with global and range-separated hybrid functionals albeit with a fraction of its usual computational cost. Validation calculations are performed on a test set of molecular Rydberg excitations, comparing the new HDA TD-ADFT implementation against high-level reference methods, such as CC3 and equation-of-motion coupled cluster calculations. This comparison shows that quantitative accurate singlet-singlet Rydberg excitations can be obtained with the HDA TD-ADFT CAM-B3LYP methodology.