Fig. 5: Absorption and 2D electronic spectra of SP.

a Experimentally estimated spectral density of the SP^{15, 61} is shown in black for an intra-pigment mode vibrational damping rate γ_k = (1 ps)⁻¹. Coarse-grained version for γ_k = (50 fs)⁻¹ is shown in red and the excitonic and vibronic splittings, Δ ≈ 1290 cm⁻¹ and \({{\Delta }}^{\prime} \approx 1800\,{{{{{{{{\rm{cm}}}}}}}}}^{-1}\), are highlighted. b Experimental absorption spectrum of the bacterial reaction center at 5 K, shown in green dots, and numerically exact absorption line shape, obtained by TEDOPA and HEOM, of the SP, shown in black. Approximate absorption spectrum of the SP computed by second-order cumulant expansion is shown in red where the energy-gap between absorption peaks at 803 and 897 nm is approximately Δ ≈ 1300 cm⁻¹. c Excitonic coherence dynamics for the experimentally estimated and coarse-grained environmental structures, shown in black and red, respectively, when only site 1 is initially excited. d Rephasing 2D spectra of the SP at waiting time T = 0. e, f 2D signals at a cross-peak R12, marked in (d), and corresponding Fourier transformation where ground and excited state signals are shown in red and blue, respectively. Note that excited state signals are dominated by vibronic coherence \(\left|{\psi }_{+}\right\rangle \left\langle {\psi }_{-}\right|\), leading to 2D oscillations with frequency \({{\Delta }}^{\prime} \approx 1800\,{{{{{{{{\rm{cm}}}}}}}}}^{-1}\). The transient of the other cross-peak R21 is provided in Supplementary Note 8 and all molecular parameters used in these simulations are given in Supplementary Note 5.