Influence of Electronic Polarization on the Spectral Density

Abstract

Accurate spectral densities are necessary for computing realistic exciton dynamics and nonlinear optical spectra of chromophores in condensedphase environments, including multichromophore 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) electronic polarization of the environment is key to obtaining accurate spectral densities and line shapes 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 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.

Nonlinear Spectroscopy in the Condensed Phase: The Role of Duschinsky Rotations and Third Order Cumulant Contributions

“…48,60,[95][96][97][98] Snapshots are extracted every 2 fs, and TDDFT vertical excitation energies are computed using the Tamm-Dancoff approximation, where all solvent molecules within 6Å of the chromophore are treated fully quantum mechanically to capture polarization effects from first principles. 28,31,34,35,38,39,41,42,46 All other surrounding water molecules are included in the excited state calculation as classical point charges. Although this QM treatment of the solvent when computing the vertical excitation energies leads to a small Hamiltonian mismatch between dynamics and excited state calculations, we have found in previous studies that this polarization can rather dramatically affect the spectral densities and we choose here to include the environment at the QM level.…”

“…Truncation at second order maps the system dynamics onto a fictitious bath of linearly coupled harmonic oscillators, for which linear and nonlinear spectroscopy signals can be computed analytically. 47 The electronic-vibrational coupling in the system is then fully defined by the autocorrelation function of energy gap fluctuations, which can be efficiently obtained in complex condensed phase systems by computing vertical excitation energies along molecular dynamics (MD) trajectories [23][24][25][26][27]46,[48][49][50] and using quantum correction factors (QCF) 49,[51][52][53] to account for nuclear quantum effects.…”

Nonlinear Spectroscopy in the Condensed Phase: The Role of Duschinsky Rotations and Third Order Cumulant Contributions

“…[51][52][53] Classical correlation functions are generally much easier to compute than their quantum counterparts and can, for example, be constructed by calculating vertical excitation energies along an MD trajectory. [23][24][25][26][27]46,[48][49][50] Although the choice of QCF is not unique, 49,52 a commonly used approximation for the energy-gap autocorrelation function C {2} δU (t) is the harmonic QCF, where…”

Nonlinear spectroscopy in the condensed phase: The role of Duschinsky rotations and third order cumulant contributions

“…[43][44][45] We have recently shown that the electronic-vibrational coupling strength of fast chromophore degrees of freedom to an electronic excitation can also be heavily influenced by the quantum mechanical treatment of the environment. 46 An appealing way to account for the effect of the complex environment and the coupling of nuclear motion to the optical excitation in linear and nonlinear spectroscopy is the cumulant approach, 47 where the response function of the system is expressed in terms of a cumulant expansion of the energy gap operator between the electronic ground and excited state. If the energy gap fluctuations obey Gaussian statistics, as they do for harmonic ground and excited state potential energy surfaces (PESs) of the same curvature, then the cumulant expansion is exact at second order.…”

“…Truncation at second order maps the system dynamics onto a fictitious bath of linearly coupled harmonic oscillators, for which linear and nonlinear spectroscopy signals can be computed analytically. 47 The electronic-vibrational coupling in the system is then fully defined by the autocorrelation function of energy gap fluctuations, which can be efficiently obtained in complex condensed phase systems by computing vertical excitation energies along molecular dynamics (MD) trajectories [23][24][25][26][27]46,[48][49][50] and using quantum correction factors (QCF) 49,[51][52][53] to account for nuclear quantum effects.…”