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

The simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited electronic states. In this report, we show 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-Oppenheimer approximation, resulting in a poor description of absorption spectra. In contrast, computing excited states via a self-consistent field method in conjunction with a maximum overlap model produces states that are not subject to such mixings. We show that this latter method produces vibronic spectra much more aligned with vertical gradient and molecular dynamics (MD) trajectory-based approaches. For the methylene blue chromophore, we compare vibronic absorption spectra computed with the following: an adiabatic Hessian approach with LR theory-optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlap method-optimized structures, and excitation energy time-correlation functions generated from an MD trajectory. Because of mixing between the bright S and dark S surfaces near the S minimum, 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 absorption spectrum that is not present for any of the other methods. Spectral densities are analyzed and we compare the behavior of the key normal mode that in LR theory strongly couples to the optical excitation while showing S/S state mixings. Overall, our study provides a note of caution in computing vibronic spectra using the excited-state adiabatic Hessian of LR theory-optimized structures and also showcases three alternatives that are less sensitive to adiabatic state mixing effects.