The Influence of Polarization on the Spectral Density
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Accurate spectral densities are necessary for computing realistic exciton dynamics and nonlinear optical spectra of chromophores in condensed phase environments, including multi-chromophore pigment-protein systems. However, due to the significant computational cost of computing spectral densities from first principles, requiring many thousands of excited state calculations, most simulations of realistic systems rely on treating the environment as fixed point charges. Here, using a number of representative systems ranging from solvated chromophores to the photoactive yellow protein (PYP), we demonstrate that the quantum mechanical (QM) polarization of the environment is key to obtaining accurate spectral densities and lineshapes within the cumulant framework. We show that the QM environment can enhance or depress the coupling of fast chromophore degrees of freedom to the energy gap, altering the electronic-vibrational coupling and the resulting vibronic progressions in the absorption spectrum. In analyzing the physical origin of peaks in the spectral density, we identify vibrational modes that couple the electron and the hole as being particularly sensitive to the QM screening of the environment. For PYP, we reveal the need for a careful determination of the appropriate QM region to obtain reliable spectral densities. Our results indicate that the QM polarization of the environment can be crucial not just for excitation energies, but also for electronic-vibrational coupling in complex systems, with implications for the correct modeling of linear and nonlinear optical spectroscopy in the condensed phase, as well as energy transfer in pigment-protein complexes.