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

Abstract

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 1 and dark S 2 surfaces near the S 1 minimum, computing the adiabatic Hessian with LR theory and timedependent 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 1 /S 2 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.

Calculations of Excited Electronic States by Converging on Saddle Points Using Generalized Mode Following

“…The most common approach in mean-field calculations of the electronic structure is the SCF method, which is based on Hamiltonian matrix diagonalization. The term “ΔSCF” is often used in the literature for calculations where the excitation energy is computed as the difference between the energy of the ground state and an energy value obtained by converging an SCF calculation on an excited state. ,,− , Such calculations typically use the same iterative eigensolvers that have been developed for ground state calculations, such as the direct inversion in the iterative subspace (DIIS), , but in addition employ the maximum overlap method ,, (MOM) to reduce the likelihood of converging on the ground state or a lower-energy excited state, which is often referred to as “variational collapse” (we will refer to this approach of using an SCF procedure with MOM as SCF-MOM). Although methods based on SCF can converge on saddle points, they are better suited for the energy minimization in ground state calculations.…”