Electronic dephasing of polyatomic molecules interacting with mixed quantum-classical media

Empirical asymmetric phonon sideband due to phonons in the protein matrix present in photosynthetic complexes: Time-domain response theory

The phonon spectral density plays a key role in probing the dynamical and spectral behavior of molecular aggregates. One may utilize the intimate connection between the one-phonon profile and the phonon spectral density to extract a plausible form of the spectral density of media with rich structure using advanced optical spectroscopy. The excitonic transition is normally accompanied by a broad, asymmetric phonon-side band due to the coupling to the phonons in the surrounding protein matrix present in photosynthetic complexes. The asymmetry in the one-phonon profile of a homogeneous absorption spectrum and other experiments performed on photosynthetic bacterial reaction centers (BRCs) led the Small group to employ a half-Gaussian distribution function on the red side and half-Lorentzian distribution function on the blue side of the absorption lineshape to account for the one-phonon profile asymmetrical shape and relaxation effects contributing to spectroscopy and dynamics of BRCs at hand. Different research groups successfully employed the theory of Small to simulate their photosynthetic spectral data so they could calculate the homogeneous absorption and hole-burned spectra of photosynthetic complexes. Although this report does not directly use the formulae of homogeneous absorption, hole-burning, and fluorescence line-narrowed spectra of BRCs, and photosynthetic complexes, developed by Hayes-Small, it builds on their idea of the phonon sideband asymmetric shape in deriving an accurate and computationally efficient linear electronic transition dipole moment time correlation function. Besides the compelling tractability and efficiency of this correlation function, it accounts for excitonic coupling and eliminates all the inconsistencies arising in the Hayes-Small theory.

Mixed Quantum-Classical Liouville Equation Treatment of Electronic Spectroscopy of Condensed Systems: Harmonic and Anharmonic Electron-Phonon Coupling

This Review integrates the use of electronic optical response function theory and the mixed quantum-classical (MQC) Liouville equation (MQCLE), thereby leading to electronic spectroscopy in MQC media. It further sheds light on the applicability, utility, and efficiency of the mixed quantum-classical dynamics (MQCD) formalism, which starts off with the MQCLE, in probing spectroscopy and dynamics of condensed systems, whereby quantum mechanics and classical mechanics are combined systematically. The author has been exploring and implementing MQCD to investigate electron-phonon coupling effects on electronic dephasing in harmonic and anharmonic systems by calculating linear and nonlinear optical transition analytically and numerically dipole moment time correlation functions in an MQC environment, thereby presenting an in depth spectral profile analysis and their shape and symmetry. The distinctive capability of the MQC time correlation functions is that ergodicity and stationarity properties are inherently satisfied as part of the mixed quantum-classical dynamics (MQCD) framework, unlike classical correlation functions. While some research groups have applied MQCLE to calculate vibrational spectra to study hydrogen-bonded complexes in a MQC environment and other groups calculated Optical response function to probe electron transfer dynamics using the basis mapping technique, the approach, purpose, rigor, applications, and path to the end results reported herein are different. Finally, the same framework is employed to study dissipative systems in the MQC limit, whereby the zero-phonon line adopts the correct width and eliminates its asymmetry. While the full quantum mechanical model, like the multimode Brownian oscillator (MBO) model, yields the correct width and inaccurate shape in the low-temperature limit, the MQCD formalism seems to produce an accurate zero-phonon profile. Nonlinear optical signals are also reviewed in MQC media to show the applicability and utility of this approach. The vibronic optical response functions developed here will account for geometry change, frequency change, and anharmonicity upon electronic excitation to accurately probe electronic dephasing, electron-phonon coupling, shape, and symmetry of profiles and present differences and similarities to the MBO model on pure electronic dephasing. Frequency change and anharmonicity are vitally crucial for accurately assessing electron-phonon coupling upon electronic excitation. This is an additional unique result obtained by the author to further demonstrate the applicability and utility of this approach over other approximation schemes in probing electronic dephasing including that of the MBO model.

Low-temperature vibronic spectroscopy of condensed chromophore exhibiting inhomogeneous distribution of vibrational frequencies in a mixed quantum-classical environment

This work has been motivated by the recent paper by the author [M. Toutounji, Phys. Chem. Chem. Phys., 2021, 23, 21981] whereby a mixed quantum-classical Liouville equation was used to probe the spectroscopy and dynamics of a spin-boson system. A mixed quantum-classical Liouville equation treats the system of interest quantum mechanically, the bath classically, and the coupling term mixed quantum-classical mechanically. This paper offers a two-fold advantage: correcting the treatment of the electronic transition decay (width in frequency domain) and assessing the local heterogeneous vibrational structure. The homogeneous linear absorption spectrum of a chromophore embedded in a mixed quantum-classical environment at low temperature is composed of a sharp peak called a zero-phonon line (ZPL) and a broad phonon sideband (PSB), whereby the ZPL and the PSB are assimilated by a Lorentzian function and Voigt profiles, respectively. The PSB, in this case, is characterized by a local heterogeneous structure due to a dispersive medium of vibrations, modeled by vibrational Gaussian distributions to represent the arising inhomogeneous broadening and Lorentzians to model the homogeneous vibrations. This description seems to model proteins and amorphous solids exhibiting a local heterogeneous structure as both electronic and vibrational inhomogeneous broadening seems to be large in these media. This work provides a derivation of linear absorption lineshape and vibronic transition dipole moment time correlation functions, both of which account for pure electronic dephasing (ZPL width) the Voigt profile description of the phonon profiles (PSB) in dispersive media.