# Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?
## 3 Protein ET Mechanisms  
Electron transfer (ET) is one of the most fundamental process taking place in biological systems, in particular when dealing with photosynthesis and respiration [116; 117; 118]. The redox center of proteins plays here an important role and its coupling with the surrounding protein environment affect the ET abilities. The rate of ET process is described by the semiclassical Marcus theory for nonadiabatic electron transfer [106]:  
\[k=\ \frac{2\pi}{\hbar}V^{2}\frac{1}{\sqrt{4\pi\lambda kT}}\exp\left(\frac{-( \Delta G+\lambda)^{2}}{4\lambda kT}\right) \tag{8}\]  
where the key parameters controlling the ET rate are the electronic coupling \(V\), the reorganization energy \(\lambda\) and the driving force \(\Delta G\). The electronic coupling exponentially decays with the distance \(R\) as:  
\[V\ \sim\ V^{0}\exp\left[-\frac{\beta}{2}(R-R_{0})\right]. \tag{9}\]  
Figure 9: (**A**) Structural model of lutein 2 (orange) in LHCII monomer. (**B**) Structural model of rhodopin glucoside (orange) in LH2. The proximal (bacterio) chlorophyll, and amino acid residues that are within 3.5 Å of lutein are shown. These residues make up the QM layer in the QM/MM simulations. Reproduced from [114] with permission from National Academy of Sciences, 2017. The difference in the oxidation and reduction midpoint potentials determine the thermodynamic driving force [119]; \(\lambda\) is the energy difference between reactant and product states and the gap between these electronic states at the intersection point can determine the ET mechanism. In fact, if the gap is large, the crossover probability is one, leading to a tunneling ET mechanism, while when the gap is small the ET can occur via hopping mechanism. The electronic coupling \(V\) describes the degree of overlap of the reactant and product wavefunctions. As the coupling follows Equation (9), the distance between the donor and acceptor has a strong impact on the ET process, as well as the nature of the environment (quantified by the decay factor \(\beta\)). An alternative approach has been proposed by [PERSON] and [PERSON], adopting the [PERSON]'s semiclassical rate expression [120; 121]:  
\[\log k_{\text{ET}}=13-(1.2-0.8\rho)(R-R_{0}) \tag{10}\]  
which is a tunneling expression which leads to good accuracy when adjusted to an optimal driving force value \(\Delta\)G\(=-\lambda\). \(\rho\) is the packing density of the medium which equals the fraction of the volume in between the chromophores within the van der Waals radius of intervening atoms, and \(R_{0}\) is the vdW contact distance. From this expression is possible to obtain the decay factor \(\beta\) as:  
\[\beta=ln10(1.2-0.8\rho) \tag{11}\]  
This packing density model is able to describe the physics of the tunneling pathway model, which complements the [PERSON] theory [122]. To understand the ET mechanism, knowledge of the electrochemical properties of the investigated systems are essential. Moreover, the nature of the protein is a determinant aspect in defining the ET process. As the protein is an heterogeneous matrix, local changes in proximity of the redox center might have strong impact on the ET ability of the system [123]. Commonly, two approaches are used to determine the effect of the protein on ET; (i) pathway (through bond tunneling), in which the decay constant \(\beta\) is determined for each through-bond and through-space segments and \(V\) is proportional to the product of all the \(\beta\) values; (ii) direct approach, in which \(\beta\) is related to the donor-acceptor distance and electrons \"hops\" through space [120; 121]. Evolution perfected this process as proteins have tuned their environment to maximize the ET efficiency. Yet, a critical parameters remain the ET distance; there is a limit to the distance over which ET can occur at a rate sufficient to support biological activity.