Comparison of Linear Response Theory, Projected Initial MaximumOverlap Method, and Molecular Dynamics-Based Vibronic Spectra:The Case of Methylene Blue

The simulation of optical spectra is essential to molecular characterizationand, in many cases, critical for interpreting experimental spectra. The most commonmethod for simulating vibronic absorption spectra relies on the geometry optimization andcomputation of normal modes for ground and excited electronic states. In this report, weshow that the utilization of such a procedure within an adiabatic linear response (LR)theory framework may lead to state mixings and a breakdown of the Born-Oppenheimerapproximation, resulting in a poor description of absorption spectra. In contrast,computing excited states via a self-consistentfield method in conjunction with a maximumoverlap model produces states that are not subject to such mixings. We show that thislatter method produces vibronic spectra much more aligned with vertical gradient andmolecular dynamics (MD) trajectory-based approaches. For the methylene bluechromophore, we compare vibronic absorption spectra computed with the following: an adiabatic Hessian approach with LRtheory-optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlapmethod-optimized structures, and excitation energy time-correlation functions generated from an MD trajectory. Because of mixingbetween the bright S1and dark S2surfaces near the S1minimum, computing the adiabatic Hessian with LR theory and time-dependent density functional theory with the B3LYP density functional predicts a large vibronic shoulder for the absorptionspectrum that is not present for any of the other methods. Spectral densities are analyzed and we compare the behavior of the keynormal mode that in LR theory strongly couples to the optical excitation while showing S1/S2state mixings. Overall, our studyprovides a note of caution in computing vibronic spectra using the excited-state adiabatic Hessian of LR theory-optimized structuresand also showcases three alternatives that are less sensitive to adiabatic state mixing effects.