We apply the Liouville space hierarchical equations of motion method to calculate the linear and two-dimensional (2D) electronic spectra of the Fenna-Matthews-Olson (FMO) protein complex from Chlorobium tepidum, using a widely used model Hamiltonian. The absorption and linear dichroism spectra of the FMO complex, as well as the main features of the 2D spectra are well reproduced. However, comparison with the recent experimental 2D spectra reveals several limitations of the current model: (1) The homogeneous and inhomogeneous broadening seems to be overestimated for the first exciton peak, but may be underestimated for several other exciton peaks. (2) The calculated oscillations of the diagonal and off-diagonal peaks in the 2D spectra are much weaker than the experimental observations, which indicates that an improved model is needed for the excitonic dynamics of the FMO complex.

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Inspired by the recent observation of correlated excitation energy fluctuations of neighboring chromophores (Lee et al. Science 2007, 316, 1462), quantum chemistry calculations and molecular dynamics simulations were employed to calculate the electronic-vibrational coupling in the excited states of the photosynthetic reaction center of purple bacteria Rhodobacter (Rb.) sphaeroides. The ground states and lowest excited (Q(y)) states of isolated bacteriochlorophyll a (BChl a) and bacteriopheophytin (BPhe) molecules were first optimized using density functional theory (DFT) and time-dependent density functional theory (TDDFT). Normal mode analyses were then performed to calculate the Huang-Rhys factors of the intramolecular vibrational modes. To account for intermolecular electronic-vibrational coupling, molecular dynamics simulations were first performed. The ZINDO/S method and partial charge coupling method were then used to calculate the excitation energy fluctuations caused by the protein environment and obtain the spectral density. No obvious correlations in transition energy fluctuations between BChl a and BPhe pigments were observed in the time scale of our MD simulation. Finally, by comparing the calculated absorption spectra with experimental ones, magnitudes of inhomogeneous broadening due to the static disorder were estimated. The large amplitude of the static disorder indicates that a large portion of the spectral density and their correlations may still be hidden in the inhomogeneous broadening due to the finite MD simulation time.