Nonlinear Spectroscopy in Chlorophyll Dimers Embedded in an Asymmetric Phonon Bath

The electronic transition dipole moment 4-point time correlation function for a dimeric photosynthetic complex, from which nonlinear optical time-domain signals may be obtained. This 4-point time correlation function draws on an experimentally fit spectral density of the surrounding phonons of the photosynthetic protein. The spectral density of the photosynthetic phonons renders a phonon-sideband characterized by its asymmetry, caused by the unequal contribution from the photosynthetic phonons (bath) to the low- and high-energy sides of the optical signals. This spectral density manifests its asymmetry explicitly in the 1-phonon profile, due to the intimate spectral connection between them, which will in turn reflect in the entire phononic part of the absorption spectrum. The asymmetry plays an important role in characterizing the exciton–phonon coupling strength and the phonon relaxation mechanism, thereby providing flexibility in modeling the degree of symmetry needed for the bath and imparting the capability of fine-tuning the nature of electron–phonon coupling caused by pigment–protein interaction. To this end, the obtained nonlinear optical electronic transition dipole moment time correlation functions (Liouville space pathways) whereby both excitonic and exciton–phonon couplings are accounted for are deemed convenient, more tractable, and computationally expedient, a unique advantageous feature in the case of a multimode system, which is often the case in photosynthetic complexes. Linear spectra and photon echo signals to probe pigment–protein complexes, in which pure electronic dephasing, vibrational relaxation effects, 1-phonon profile asymmetry, exciton–exciton coupling, and exciton–phonon coupling in bacterial reaction centers and photosynthetic complexes are provided.