Site-exciton models

The following figures and data are our benchmarking results (for detailed discussion please see ref¹).

Figure 11. Results of population dynamics of the 7-state FMO model at 77 K. 50 nuclear (bath) modes in the discretization scheme are employed for each state in the simulations. In each panel, the red, blue, green, orange, purple, brown and cyan solid lines represent the population of states 1−7, respectively. Panel (a): NaF-cc. Panel (b): NaF-cx. Panel (c): NaF-TW. Panel (d): NaF-TW2. Panel (e): NaF-HW. Panel (f) NaF-HW2. Panel (g): SH-1. Panel (h): SH-2. Note that SH-3 is not applicable for this 7-state model. The numerically exact results produced by TD-DMRG²for the same effective Hamiltonian in the discretization scheme are demonstrated by dashed lines with corresponding colors in each panel. data

Figure 12. $\rho_{12}$ $\rho_{13},$ $\rho_{15}$ $\rho_{34}$ , respectively. Panel (a): NaF-cc. Panel (b): NaF-cx. Panel (c): NaF-TW. Panel (d): NaF-TW2. Panel (e): NaF-HW. Panel (f) NaF-HW2. Panel (g): SH-1. Panel (h): SH-2. Note that SH-3 is not applicable for this 7-state model. The numerically exact results produced by TD-DMRG² for the same effective Hamiltonian in the discretization scheme are demonstrated by dashed lines with corresponding colors in each panel. data

FigureS1

Figure S1. Panels (a) and (b) are similar to panel (d) of Figure 11 and Figure 12, respectively, but the solid lines represent the results of NaF-TW with nuclear force represented in the diabatic representation, while the hollow circles with corresponding colors denote the results of NaF-TW with nuclear force represented in the adiabatic representation. data

FigureS5

Figure S5. Results of population dynamics of the 7-state FMO model at zero temperature. 100 nuclear (bath) modes in the discretization scheme are employed for each state in the simulations. In each panel, the red, blue, green, orange, purple, brown and cyan solid lines represent the population of states 1−7, respectively. Panel (a): NaF-cc. Panel (b): NaF-cx. Panel (c): NaF-TW. Panel (d): NaF-TW2. Panel (e): NaF-HW. Panel (f) NaF-HW2. Panel (g): SH-1. Panel (h): SH-2. Note that SH-3 is not applicable for this 7-state model. The numerically exact results produced by TD-DMRG²for the same effective Hamiltonian in the discretization scheme are demonstrated by dashed lines with corresponding colors in each panel. data

FigureS6

Figure S6. $\rho_{12}$ $\rho_{13},$ $\rho_{15}$ $\rho_{34}$ , respectively. Panel (a): NaF-cc. Panel (b): NaF-cx. Panel (c): NaF-TW. Panel (d): NaF-TW2. Panel (e): NaF-HW. Panel (f) NaF-HW2. Panel (g): SH-1. Panel (h): SH-2. Note that SH-3 is not applicable for this 7-state model. The numerically exact results produced by TD-DMRG² for the same effective Hamiltonian in the discretization scheme are demonstrated by dashed lines with corresponding colors in each panel. data

Figure 13. Population dynamics of the SF model. 200 nuclear modes are employed for each state in the simulations. In each panel, the black, red and cyan solid lines represent the population of the S1, TT and CT state, respectively. Panel (a): NaF-cc. Panel (b): NaF-cx. Panel (c): NaF-TW. Panel (d): NaF-TW2. Panel (e): NaF-HW. Panel (f) NaF-HW2. Panel (g): SH-1. Panel (h): SH-2. Note that SH-3 is not applicable for this 3-state model. The numerically exact results produced by HEOM³ are demonstrated by dashed lines with corresponding colors in each panel. data

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