In nature, the photosynthetic apparatus is connected to a steady-state network of catalytic conversion reactions in the organism that is continuously dissipating energy and generating entropy. From a biological perspective, photosynthesis is an expensive process in terms of resources required, and organisms generally produce only the photosynthetic capacity that they need to serve their requirements within the limits of the environmental and developmental constraints. At low light intensities, however, the productive storage of energy is an efficient chemical thermodynamics process, which is optimized against depletion by wasteful back reactions that feed into the decay of the absorber with rate
g = 1/τ from the excited chlorophyll state into the ground state at the start of the conversion chain [
3]. Natural photosynthesis requires coupling of primary conversion into biochemical networks and catalytic cycles that are subject to regulation for protection against excess light, leading to limited photosynthetic capacity. In contrast, for artificial photosynthesis it is necessary to consider the minimal design requirements for the most efficient solar-to-fuel conversion process, operating close to the theoretical limits on solar energy conversion.
To understand how thermodynamic constraints can guide the design of artificial systems for photochemical storage, it is best to start from minimal models that consider the thermodynamic constraints on the photovoltaic or photochemical solar energy conversion by exploring the analogy with efficient conversion in the solar or photovoltaic cell [
3–
5]. In productive photochemical conversion, the storage or downstream utilization is described as a single step conversion of solar energy into Gibbs free energy. Like the silicon solar cell, the photosynthetic solar cell is in its simplest form a molecular absorber that is excited and produces energy conversion by charge separation with rate
I into an electron and hole in dynamic equilibrium with the absorber (Fig. ). The excitation of a molecular Chl absorber in exchange with the field of solar irradiation leads to a difference in chemical potential
with
p and
p0 being the populations of the excited and ground state of the absorber, respectively [
4]. In the dark, the excited and ground state are in equilibrium and Δ
μabs = 0, leading to
p/p0 = exp(−
hv0/
kBT), the Boltzmann distribution. For Chl
a in green plants,
hν0 = 1.8 eV. Detailed balance has been used to calculate the upper limit at the absorber stage, which leads to the maximum efficiency
η = 1 − 4
T/3
TS = 93%, for reversible operation, due to entropic losses originating from the different temperatures of the incoming radiation at
TS ~ 5800 K and of the heat reservoir at
T ~ 300 K [
3,
5,
6].
A photovoltaic (PV) solar cell produces electricity, while a photosynthetic reaction center produces a photochemical steady state with a voltage over the membrane and charge separation in dynamic equilibrium with the absorber. Recently, the solar energy conversion has been considered in a general setting, including both the photochemical and photovoltaic mechanisms [
4]. The equation
represents the difference in chemical potential or free energy produced by light-induced charge separation and contains an electronic term
eΔ
ψ. In addition, a photochemical term

measures the concentration
p′
q′ of the charge separated state, i.e., the probabilities of electron and hole occupation of the acceptor and donor states, in the light relative to the concentration
p0′
q0′ in the dark. This term is proportional to the temperature. Equation (
2) illustrates how the electrochemical potential Δ
μe−h can comprise a light-induced electrostatic potential or charge separation
eΔ
ψ, a photochemical

, or both, as in photosynthesis [
4].
The net production rate of the charge separation and energy storage in a photosynthetic process can then be described by the solar cell equation
with
If and
Ib being the forward and backward reaction rates, respectively [
6,
7]. The difference
I represents the energy extraction. For PV, this is electrical energy, and for artificial photosynthesis,
I is the net flow of energy into proton-coupled electron transfer and temporary storage, followed by the multi-electron chemical reaction that oxidizes water or produces fuel.
The second principle of thermodynamics, stating that entropy cannot be destroyed, limits the efficiency of solar energy conversion to 0.93 for reversible operation [
6]. Extraction of energy implies a non-reversible process with a theoretical limit less than 93% for the reversible process [
3]. Processing the incident solar energy current is thus not possible without lowering the efficiency, and Eq. (
2) can be generalized according to
with a quantum yield
Here the first factor is due to the kinetics of the steady state, while δ measures the thermodynamic activity of the trap [
3]. Hence, in order to favor the forward reaction over the backward process, the energy of the combined products is lower than for the excited state by at least
kBTln(δ). The maximum power is generated for δ ~
kBT/μ
max, a compromise between a high conversion efficiency and a high storage efficiency.
Since multi-electron catalysis for water oxidation or hydrogen production requires storage for downstream accumulation of electronic charges at longer time scales than the initial light absorption process, a catalytic site in an artificial photosynthesis device will be in Boltzmann equilibrium with the initial excited state throughout the entire process, both during the accumulation of charge and during the actual catalytic reaction. This makes that the processes of storage and catalysis have to go hand in hand. Catalytic processes operate on the millisecond time scale, and the accumulation of several electrons or holes on this time scale is rate limiting. Thus, Δ
μst inside the catalyst should be sufficiently low to trap electrons or holes for allowing multi-electron catalysis to proceed against back reactions. For efficient solar-to-fuel conversion, the overall rate of energy extraction has to be close to the net rate of excitation of the molecular absorber at the start of the conversion chain. When the absorber operates at an energy
hν0 with an excited state lifetime
τ, the theoretical limit to the electrochemical potential Δ
μst that can be established inside the catalyst in a reversible process in a multi-electron catalytic chain will depend on the required storage time
t for accumulation prior to the actual catalytic process, according to [
2,
8]
and will decrease in order to establish a net energy flow
I through the catalyst for the chemical reaction, in line with Eqs. (
3)–(
5).