Tuning Two-Photon\nAbsorption in Rhodopsin Chromophore\nvia Backbone Modification: The Story Told by CC2 and TD-DFT

We investigate here a systematic way to tune two-photon\ntransition\nstrengths (δ<sup>2PA</sup>) and two-photon absorption (2PA)\ncross sections (σ<sup>2PA</sup>) of the rhodopsin’s chromophore\n11-<i>cis</i>-retinal protonated Schiff base (RPSB) via\nthe modulation of the methyl groups pattern along its polyene chain.\nOur team employed the resolution of identity, coupled cluster approximate\nsecond order (RI-CC2) method with Dunning’s aug-cc-pVDZ basis\nset, to determine the structural impact on δ<sup>2PA</sup>,\nas well as its correlation to both transition dipole moments and permanent\nelectric dipole moments. Seven structures were probed in vacuo, including\nfive-double-bond-conjugated model of the native chromophore, shortened\nby the β-ionone ring (RPSB5), and its de/methylated analogues:\n9-methyl, 13-methyl, planar and twisted models of 9,10-dimethyl and\n9,10,13-trimethyl. Our results demonstrate that the magnitude of δ<sup>2PA</sup> is dictated by both the position and number of methylated\ngroups attached to its polyene chain as well as the degree of dihedral\ntwist that is introduced due to the de/methylation. In fact, a strong\ncorrelation between δ<sup>2PA</sup> enhancement and the presence\nof a C13-methyl group in the planar RPSB5 species is found. Trends\nin δ<sup>2PA</sup> values follow the trends observed in their\ncorresponding changes in the permanent dipole moment upon the S0–S1\nexcitation nearly exactly. The assessment of four DFT functionals,\ni.e., M11, MN15, CAM-B3LYP, and BHandHLYP, previously found most successful\nin predicting 2PA properties in biological chromophores, points to\na long-range-corrected hybrid meta-GGA M11 as the top-performing functional,\nalbeit still delivering underestimated δ<sup>2PA</sup> and σ<sup>2PA</sup> values by a factor of 3.3–5.3 with respect to the\nCC2 results. In the case of global-hybrid meta-NGA (MN15), as well\nas CAM-B3LYP and BHandHLYP functionals, this factor deteriorates significantly\nto 6.7–20.9 and is mostly related to significantly lower quality\nof the ground- and excited-state dipole moments.