Non-condon effects on the doubly resonant sum frequency generation of rhodamine 6G

We report first-principles simulations of the doubly resonance sum-frequency generation (DR-SFG) spectrum for rhodamine 6G (R6G). The simulations are done using a time-dependent formalism that includes both Franck-Condon (FC) and Herzberg-Teller (HT) terms in combination with time-dependent density functional theory (TDDFT) calculations. The simulated spectrum matches experiments, allowing a detailed assignment of the DR-SFG spectrum. Our work also shows that non-Condon effects are important and the DR-SFG spectrum of R6G is highly dependent on both FC and HT modes. This is surprising as R6G is known to be a strong FC resonant Raman scatterer. The simulations predict an orientation where the xanthene plane of R6G is perpendicular to the surface with binding through one of the ethyl amine groups. Our results show the importance of first-principles simulations for providing a detailed assignment of DR-SFG experiments, especially for large molecules where such an assignment is complicated due close-lying vibrational modes.