1. Fig. S1: Theoretical thermodynamic cost as a function of wavelength. Based on the detailed balance limit as given in Shokley and Quiesser 1961. The thermodynamic cost is in units of electron-volt.

2. Fig.S2: Wavelength of maximal efficiency of the reaction center as a function of the effective value of the over-potential cost. The analysis described in the text was repeated for given values of the overpotential cost. The steps in the curve comes from the troughs in the solar spectrum.

3. Fig.S3: Optimal RCE for wavelength dependent overpotential cost. Wavelength of maximal efficiency of the reaction center as a function of the slope of the overpotential cost. The wavelength dependency is approximated by a linear function around 680nm. A value of 1.05eV is assumed at 680nm and a linear dependence with the given slope for other reaction center wavelengths. The optimal value was calculated numerically as in the text. The steps in the curve comes from the troughs in the solar spectrum.

4. Fig.S4: Energy flux of sunlight today and with the cooler sun that existed 3 billion years ago. The curve for sea level with the cooler sun is calculated on the basis of the present-day atmosphere. Energy Flux [J/m 2 /sec/nm]

5. Efficiency [%] Fig.S5: Efficiency of photosystem accounting for charge separation cost and assuming a colder sun. Assuming that 1.05eV is a constant cost necessary for running the energy transformation and that the sun’s output is 30% lower than it is today. Maximum efficiency is achieved at 716nm.

6. Fig.S6: Geometrical interpretation of optimality condition. The condition for maximal harvesting of the sun’s spectrum can be understood geometrically. The x axis represents the energy of the band gap in the reaction center and the y axis is the cumulative photon flux with energy larger than the given energy. The area of a rectangle within the curve is proportional to the overall energy harvested. An optimal wavelength for the reaction center is an energy value where the corresponding rectangle will have the largest area (red rectangle). Inclusion of the overpotential cost is equivalent to a shifting of the reference point for the area (black dotted vertical line). In this case the optimal energy value has the corresponding green rectangle. [PSOptimalityGeo2.m]

7. Fig.S7a: Transmittance as a function of wavelength for pure water. [change cutoff to 2500, PSOptimalityWaterEffectBatch1] Transmittance

8. Fig.S7b: Effect of water absorption on solar spectrum. [change cutoff to 2500, PSOptimalityWaterEffectBatch1] Energy Flux [J/m 2 /sec/nm]

9. Fig.S7c: Effect of water column on harvesting efficiency. [PSOptimalityWaterEffectBatch2]

10. Fig.S8: SQ or detailed balance limit on efficiency

11. Fig.S9: The Z scheme. The energy of two photons, one absorbed in PSI and one in PSI is utilized to drive an electron through a cascade of electron carriers with the end result of chemical energy storage in the form of redox poteintial in NADPH and a proton gradient across the thylakoid membrane [Figure from Lodish et al.]

12. Fig.S10: The different architectures of reaction centers found in photosynthetic organisms. [Figure from Blankenship, R.E. Photosynth. Res. (1992), 33, 91]