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

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 states. In this report, we show that utilization of such a procedure within an adiabatic linear response 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 eld 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 excitation procedures, such as those computed from a vertical gradient or molecular dynamics trajectory-based approach. For the methylene blue chromophore, we compare vibronic absorption spectra computed with: an adiabatic Hessian approach with linear response 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 a molecular dynamics trajectory. Due to mixing between the bright S1 and dark S2 surfaces near the S1 minimum, computing the adiabatic Hessian with linear response theory 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 linear response theory strongly couples to the optical excitation while showing S1/ S2 state mixings. Overall, our study provides a note of caution in computing vibronic spectra using the excited state adiabatic Hessian of linear response theory optimized structures and also showcases three alternatives that are not as subject to adiabatic state mixing effects.