Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue

Abstract

Modeling linear absorption spectra of solvated chromophores is highly challenging as contributions are present both from coupling of the electronic states to nuclear vibrations and from solute–solvent interactions. In systems where excited states intersect in the Condon region, significant non-adiabatic contributions to absorption line shapes can also be observed. Here, we introduce a robust approach to model linear absorption spectra accounting for both environmental and non-adiabatic effects from first principles. This model parameterizes a linear vibronic coupling (LVC) Hamiltonian directly from energy gap fluctuations calculated along molecular dynamics (MD) trajectories of the chromophore in solution, accounting for both anharmonicity in the potential and direct solute–solvent interactions. The resulting system dynamics described by the LVC Hamiltonian are solved exactly using the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA). The approach is applied to the linear absorption spectrum of methylene blue in water. We show that the strong shoulder in the experimental spectrum is caused by vibrationally driven population transfer between the bright S1 and the dark S2 states. The treatment of the solvent environment is one of many factors that strongly influence the population transfer and line shape; accurate modeling can only be achieved through the use of explicit quantum mechanical solvation. The efficiency of T-TEDOPA, combined with LVC Hamiltonian parameterizations from MD, leads to an attractive method for describing a large variety of systems in complex environments from first principles.

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

“…Upon analyzing the S 1 and S 2 LR-TDDFT states along the AIMD trajectory, we find substantial excited state reordering and mixing for the LR-TD-B3LYP states, confirming the need for a nonadiabatic treatment of the spectra as we applied in previous work . The LR-TD-CAM-B3LYP states do not mix during the trajectory.…”

“…A recent study by de Queiroz et al of the S 0 → S 1 Franck–Condon vibronic spectrum in vacuo, obtained at the LR-TDDFT B3LYP/def2-SV­(P) level of theory, predicts a very large vibronic shoulder . However, very recent work by some of the authors of this paper suggests that the LR-TD-B3LYP S 0 → S 1 vibronic shoulder may be due to S 1 /S 2 state mixing and a potential breakdown of the Born–Oppenheimer approximation . Such state mixing and a breakdown of the Born–Oppenheimer approximation requires inclusion of nonadiabatic effects to account for coupling between states and population transfer between the S 1 and S 2 state; the standard approaches for modeling vibronic spectra mentioned above therefore likely cannot be accurately applied to methylene blue.…”

“…Although nonadiabatic methods that account for population transfer between the S 1 and S 2 surfaces should be used to accurately model the spectrum of methylene blue, we here compare the spectra computed with only consideration of a vertical transition from the ground state to the S 1 excited state. These methods ignore nonadiabatic effects, but this comparison highlights differences between methods and offers a new diagnostic for when nonadiabatic effects should be considered.…”

“…This cumulant expansion method expands the dipole response function for a two-level system, allowing the use of MD-based energy gap correlation functions instead of nuclear wave functions in the response function. In the previous study of methylene blue in solution by some of the authors, we made use of these MD-derived correlation functions and spectral densities to parametrize a linear vibronic coupling Hamiltonian for three states while directly capturing solvent coupling to chromophore motion . The linear vibronic coupling Hamiltonian often employs the highly accurate but very expensive multiconfigurational time-dependent Hartree approach, but in our recent study of methylene blue we used a matrix product states/tensor network ansatz with the spectral densities employing the second-order cumulant expansion to describe the system–bath coupling between electronic states.…”

The Influence of Electronic Polarization on Nonlinear Optical Spectroscopy

“…Additionally, the methods employed here are only able to capture short time scale relaxation processes that do not involve additional excited states. Incorporating additional states in modeling the optical spectroscopy would require going beyond a two-state model, necessitating more advanced quantum dynamics methods. − …”