Tuning Two-Photon Absorption in Rhodopsin Chromophore via Backbone Modification: The Story Told by CC2 and TD-DFT

We investigate here a systematic way to tune two-photon transition strengths (δ^2PA) and two-photon absorption (2PA) cross sections (σ^2PA) of the rhodopsin's chromophore 11-<i>cis</i>-retinal protonated Schiff base (RPSB) via the modulation of the methyl groups pattern along its polyene chain. Our team employed the resolution of identity, coupled cluster approximate second order (RI-CC2) method with Dunning's aug-cc-pVDZ basis set, to determine the structural impact on δ^2PA, as well as its correlation to both transition dipole moments and permanent electric dipole moments. Seven structures were probed in vacuo, including five-double-bond-conjugated model of the native chromophore, shortened by the β-ionone ring (RPSB5), and its de/methylated analogues: 9-methyl, 13-methyl, planar and twisted models of 9,10-dimethyl and 9,10,13-trimethyl. Our results demonstrate that the magnitude of δ^2PA is dictated by both the position and number of methylated groups attached to its polyene chain as well as the degree of dihedral twist that is introduced due to the de/methylation. In fact, a strong correlation between δ^2PA enhancement and the presence of a C13-methyl group in the planar RPSB5 species is found. Trends in δ^2PA values follow the trends observed in their corresponding changes in the permanent dipole moment upon the S0-S1 excitation nearly exactly. The assessment of four DFT functionals, i.e., M11, MN15, CAM-B3LYP, and BHandHLYP, previously found most successful in predicting 2PA properties in biological chromophores, points to a long-range-corrected hybrid meta-GGA M11 as the top-performing functional, albeit still delivering underestimated δ^2PA and σ^2PA values by a factor of 3.3-5.3 with respect to the CC2 results. In the case of global-hybrid meta-NGA (MN15), as well as CAM-B3LYP and BHandHLYP functionals, this factor deteriorates significantly to 6.7-20.9 and is mostly related to significantly lower quality of the ground- and excited-state dipole moments.