Electronic Dephasing in Mixed Quantum–classical Molecular Systems Using the Spin-Boson Model

Pure electronic dephasing is investigated using the spin-boson Hamiltonian in mixed quantum–classical environment. The spin-boson model used here is a composite system made up of a quantum subsystem, an electronic 2-level subsystem linearly coupled to harmonic vibrations, interacting with a classical bath. Experimental results for a multitude of molecular systems indicate that the zero-phonon line (ZPL) profile is determined by electronic dephasing, which is not accounted for in the multimode Brownian oscillator (MBO) model due to the unphysical contribution from the MBO bath modes to the ZPL profile. Mixed quantum–classical dynamics formalism of non-equilibrium systems is employed to assess the contribution of the bath modes to pure electronic dephasing by probing the ZPL profile when coupled to a classical bath in the mixed quantum–classical condensed systems. Pure electronic dephasing is discussed in the context of mixed quantum–classical dynamics formalism which starts with mixed quantum–classical Liouville equation in a mixed quantum–classical environment. It is noteworthy, however, that the fundamental difference between the fully quantum MBO model and the mixed quantum–classical Brownian oscillator, is that the zero-phonon line calculated by the former shows unphysical asymmetry on the low-energy side as it has not been observed in real systems, whereas the ZPL reported herein eliminates this asymmetry. A systematic approach using matrix mechanics is developed to treat this phenomenon. To this end, a closed-form expression of linear and nonlinear optical electronic transition dipole moment time correlation functions in a dissipative media are derived. Linear absorption spectra and 4-wave mixing signals at various temperatures showing a sound thermal broadening, temporal decay, and accurate pure dephasing further ratify the applicability and correctness of the mixed quantum–classical dynamics approach to spectroscopy and dynamics are computed.