Importance of nonadiabatic effects in modeling absorption spectra of indole and cyanoindole derivatives in solution

Nonadiabatic effects arising from conical intersections between excited states play a crucial role in the optical properties of a wide range of chromophores and must be accounted for in first-principles modeling of spectral lineshapes. In this work, we investigate the importance of nonadiabatic effects in the absorption spectra of indole and cyanoindole derivatives by contrasting three modeling approaches. In the Gaussian-Condon and Gaussian-non-Condon theory formalisms, the linear response function is computed from excitation energy fluctuations of independent adiabatic excited states sampled along molecular dynamics trajectories, with the latter approach additionally including transition dipole moment fluctuations to account for Herzberg-Teller-type effects. In contrast, the tensor-network-based thermalized time-evolving density-matrix with orthogonal polynomials (T-TEDOPA) approach allows for numerically exact quantum dynamics simulations of explicitly coupled diabatic excited states. We find that only the explicit coupling of the two lowest-lying excited states, La and Lb, within the T-TEDOPA approach yields accurate absorption spectra for all systems, while an adiabatic treatment underestimates spectral contributions from excitations into states with highly mixed electronic character. We further elucidate the role of polar solvent stabilization of the charge-transfer character La state by comparing indole in vacuum and in water, showing that solvent effects significantly shape the ultrafast population transfer between excited states and contribute to differences in the experimental absorption lineshapes. Finally, we discuss the influence of cyano substituent position on the optical properties of cyanoindole derivatives through changes in the energy ordering of La and Lb, their relative transition dipole moments, and the stabilization of the charge-transfer state in a polar solvent.