Simulating Absorption Spectra of Multiexcitonic Systems via Quasiclassical Mapping Hamiltonian Methods

In this paper, we compare the ability of different quasiclassical mapping Hamiltonian methods to accurately simulate the absorption spectra of multiexcitonic molecular systems. Two distinctly different approaches for simulating the absorption spectra are considered: (1) a perturbative approach, which relies on the first-order perturbation theory with respect to the field-matter interaction; (2) a nonperturbative approach, which mimics the experimental measurement of the absorption spectra from the free-induction decay that follows a short laser pulse. The methods compared are several variations of the linearized semiclassical (LSC) method, the symmetrical quasiclassical (SQC) method, and the mean-field (Ehrenfest) method. The comparison is performed in the context of a biexcitonic model and a seven-excitonic model of the Fenna-Matthews-Olson (FMO) complex. The accuracy of the various methods is tested by comparing their predictions to the quantum-mechanically exact results obtained via the hierarchy of the equations of motion (HEOM) method, as well as to the results based on the Redfield quantum master equation. The results show that the LSC-based quasiclassical mapping Hamiltonian methods can yield the accurate and robust absorption spectra in the high-temperature and/or slow-bath limit, where the nuclear degrees of freedom can be treated as classical.