Optimal rates for electron transfer in Marcus theory

Contribution Factors of the First Kind Calculated for the Marcus Electron-Transfer Rate and Their Applications

In this study, we applied the concept of the "contribution factor of the first kind (CFFK)" to the original electron-transfer (ET) rate theory proposed by Marcus. Mathematical derivations provided simple and convenient formulas for estimating the relative contributions of ten physical and chemical parameters involved in the Marcus ET rate formula: (1) the maximum strength of the electronic coupling energy between two molecules, (2) the exponential decay rate of the electronic coupling energy versus the distance between both molecules, (3) the distance between both molecules, (4) the equilibrium distance between both molecules, (5) the Gibbs free energy, (6) reorganization free energy in the prefactor of the Marcus ET rate equation, (7) reorganization free energy in the denominator of the exponential term, (8) reorganization free energy in the argument of the exponential term, (9) Boltzmann constant times absolute temperature in the prefactor of the rate equation, and (10) Boltzmann constant times absolute temperature in the denominator of the exponential term. We applied our theories to (i) ET reactions at bacterial photosynthesis reaction centers, PSI and PSII, and soluble ferredoxins (Fd); (ii) intraprotein ET reactions for designed azurin mutants; and (iii) ET reactions in flavodoxin (Fld). The formulas and calculations suggest that the theory behind the CFFK is useful for quantitatively identifying major and minor physical and chemical factors and corresponding trade-offs, all of which affect the magnitude of the Marcus ET rate.

Stochastic resonance in a proton pumping Complex I of mitochondria membranes

We make use of the physical mechanism of proton pumping in the so-called Complex I within mitochondria membranes. Our model is based on sequential charge transfer assisted by conformational changes which facilitate the indirect electron-proton coupling. The equations of motion for the proton operators are derived and solved numerically in combination with the phenomenological Langevin equation describing the periodic conformational changes. We show that with an appropriate set of parameters, protons can be transferred against an applied voltage. In addition, we demonstrate that only the joint action of the periodic energy modulation and thermal noise leads to efficient uphill proton transfer, being a manifestation of stochastic resonance.

Biosolar cells: global artificial photosynthesis needs responsive matrices with quantum coherent kinetic control for high yield

This contribution discusses why we should consider developing artificial photosynthesis with the tandem approach followed by the Dutch BioSolar Cells consortium, a current operational paradigm for a global artificial photosynthesis project. We weigh the advantages and disadvantages of a tandem converter against other approaches, including biomass. Owing to the low density of solar energy per unit area, artificial photosynthetic systems must operate at high efficiency to minimize the land (or sea) area required. In particular, tandem converters are a much better option than biomass for densely populated countries and use two photons per electron extracted from water as the raw material into chemical conversion to hydrogen, or carbon-based fuel when CO₂ is also used. For the average total light sum of 40 mol m⁻² d⁻¹ for The Netherlands, the upper limits are many tons of hydrogen or carbon-based fuel per hectare per year. A principal challenge is to forge materials for quantitative conversion of photons to chemical products within the physical limitation of an internal potential of ca 2.9 V. When going from electric charge in the tandem to hydrogen and back to electricity, only the energy equivalent to 1.23 V can be stored in the fuel and regained. A critical step is then to learn from nature how to use the remaining difference of ca 1.7 V effectively by triple use of one overpotential for preventing recombination, kinetic stabilization of catalytic intermediates and finally generating targeted heat for the release of oxygen. Probably the only way to achieve this is by using bioinspired responsive matrices that have quantum–classical pathways for a coherent conversion of photons to fuels, similar to what has been achieved by natural selection in evolution. In appendix A for the expert, we derive a propagator that describes how catalytic reactions can proceed coherently by a convergence of time scales of quantum electron dynamics and classical nuclear dynamics. We propose that synergy gains by such processes form a basis for further progress towards high efficiency and yield for a global project on artificial photosynthesis. Finally, we look at artificial photosynthesis research in The Netherlands and use this as an example of how an interdisciplinary approach is beneficial to artificial photosynthesis research. We conclude with some of the potential societal consequences of a large-scale roll out of artificial photosynthesis.