Assessment of Excited-State Methods for One- and Two-Photon Absorption in the Retinal Protonated Schiff Base

The retinal protonated Schiff base (rPSB) is the chromophore of rhodopsins, a family of light-sensitive proteins employed in optogenetics and biomedical research. Accurate computational prediction of its optical properties is essential for the in silico design of rhodopsin variants. While multiconfigurational methods are required to describe the photochemical isomerization of rPSB, the vertical absorption properties can be reliably assessed with more cost-effective electronic-structure approaches. In this work, we benchmark vertical excitation energies (ΔE_abs), oscillator strengths, and two-photon absorption (TPA) transition strengths (δ_TPA) for the S₀-S₁ transition of rPSB across a representative sample of its configurational space. Results obtained with ISR-ADC(2), LR/QR-CC2, and range-separated TDDFT functionals are compared against EOM-EE-CCSD, with both the aug-cc-pVDZ and 6-31+G* basis sets. ISR-ADC(2) shows a strong correlation with EOM-EE-CCSD for all properties. LR/QR-CC2 exhibits lower and less consistent agreement, particularly for δ_TPA^S₀-S₁. The considered TDDFT methods reproduce excitation energies and oscillator strengths with excellent accuracy, although standard CAM-B3LYP slightly underperforms relative to other functionals. For TPA strengths, functionals with appropriate long-range exchange corrections display good correlation with EOM-EE-CCSD but systematically underestimates absolute values by approximately a factor of 4. It is indicated how to tune the exchange parameters of DFT functionals in order to adhere more to EOM-EE-CCSD or LR/QR-CC2 results.