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 opticalresponse functiontheory and the mixed quantum-classical (MQC) Liouville equation (MQCLE),thereby leading to electronic spectroscopy in MQC media. It furthersheds light on the applicability, utility, and efficiency of the mixedquantum-classical dynamics (MQCD) formalism, which starts off withthe 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 investigateelectron-phonon coupling effects on electronic dephasing inharmonic and anharmonic systems by calculating linear and nonlinearoptical transition analytically and numerically dipolemoment time correlation functions in an MQC environment, thereby presentingan in depth spectral profile analysis and their shape and symmetry.The distinctive capability of the MQC time correlation functions isthat ergodicity and stationarity properties are inherently satisfiedas part of the mixed quantum-classical dynamics (MQCD) framework,unlike classical correlation functions. While some research groupshave applied MQCLE to calculate vibrational spectra to study hydrogen-bondedcomplexes in a MQC environment and other groups calculated Opticalresponse function to probe electron transfer dynamics using the basismapping technique, the approach, purpose, rigor, applications, and path to the end results reported herein are different. Finally, thesame framework is employed to study dissipative systems in the MQClimit, whereby the zero-phonon line adopts the correct width and eliminatesits asymmetry. While the full quantum mechanical model, like the multimodeBrownian oscillator (MBO) model, yields the correct width and inaccurateshape in the low-temperature limit, the MQCD formalism seems to producean accurate zero-phonon profile. Nonlinear optical signals are alsoreviewed in MQC media to show the applicability and utility of thisapproach. The vibronic optical response functions developed here willaccount for geometry change, frequency change, and anharmonicity uponelectronic excitation to accurately probe electronic dephasing, electron-phononcoupling, shape, and symmetry of profiles and present differencesand similarities to the MBO model on pure electronic dephasing. Frequencychange and anharmonicity are vitally crucial for accurately assessing electron-phonon coupling upon electronic excitation. Thisis an additional unique result obtained by the author to further demonstratethe applicability and utility of this approach over other approximationschemes in probing electronic dephasing including that of the MBOmodel.

Automated summary

This review combines electronic optical response function theory with the mixed quantum-classical (MQC) Liouville equation (MQCLE) to investigate electronic spectroscopy in MQC media. The study demonstrates the utility and efficiency of the mixed quantum-classical dynamics (MQCD) formalism in probing condensed systems, where quantum mechanics and classical mechanics are combined. The author applies the MQCD framework to analyze electronic dephasing, electron-phonon coupling, and the shape and symmetry of spectral profiles, providing novel insights and accurate results. Rating: 9/10