# Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?
## 3 Protein ET Mechanisms
Treating the environment with an implicit solvent approximation eliminated the need of conformational sampling search, strongly reducing the computational cost [142; 143]. Yet, these homogeneous models cannot be used to describe explicit contribution and coupling between the redox center and the environment, where polarization can play a crucial role [144]. Explicit residues surrounding the redox center and water molecules must be present, even in a minimal environment description. Once more, QM/MM is the method of choice also for ET studies. Figure 10: Active site structure of azurin as drawn from the 4 AZU pdb file. Reprinted with permission from [140]. Copyright (2017) Wiley-VCH. In a recent study [145], QM/MM minimum free energy path (QM/MM-MFEP) method has been suggested to obtain accurate reduction potentials of azurin. In this approach the active site's geometry is minimized on the potential mean force (PMF) surface of QM coordinates [146; 147] and is additionally combined with the fractional number of electron (FNE) method for the study of redox reactions [148; 149]. The mutual dependence of the QM and MM subsystems is iteratively solved in a self-consistent manner by performing the QM geometry optimization and the MM conformational sampling. After this first step, an interpolation of the reduced/oxidized QM states is performed and the FNE is used to efficiently connect the two redox states (the full procedure is reported in [145]). In this way the direct MD sampling is replaced by an iterative active site optimization, leading to a very good balance between accuracy and computational efficiency. The authors obtained that the QM/MM-MFEP+FNE method is very accurate and efficient to describe the electronic structures of ET redox centers, when the anisotropic environment is explicitly considered and as input it needs only the protein structure. Moreover, the MD sampling performed is not dependent on the specific protein/solvent configuration, making this method general, transferable and able to handle systems with more than 1000 heavy atoms. In addition, the study shows that the presence of mutations (i.e., structural effect in axial ligand and outer sphere) are mostly electrostatic and additive, suggesting the possible use of this method to design novel redox centers for artificial photosynthesis. The central question in determining the ET ability of proteins from a computational point of view and also for the design of novel, highly efficient redox machines, is how much the environment affects the ET. If the protein provides a tunneling continuum shielding water from the active centers, the only variable to consider is the redox potential of cofactors (i.e., iron-sulfur clusters as present for PSI). As a consequence, the activation barrier is determined by the driving force and the reorganization energy for which a commonly assumed value range is \(\lambda\simeq\) 0.7-0.8 eV [121]. In addition, detailed studies have shown that the exponential decay \(\beta\) value depends on the secondary structure of the protein, and can vary in the \(\beta\simeq\)1-1.4 A\({}^{-1}\) range [150; 151]. Only the free energy or reaction (i.e., the driving force) is thus needed to calculate the ET rate. The small energy range of possible values for both \(\lambda\) and \(\beta\) put strong restrictions in the design of ET chains, resulting in efficient ET transfer for edge-to-edge distances not exceeding 14 A [121; 152]. In addition, studies on electron tunneling of different PPCs revealed that the presence of structural water occupying the protein pocket along the ET pathway strongly enhances the protein's ET ability [153]. These results dismiss the previously exposed idea that the environment  
Figure 11: Flow diagram used to decide which computational method to use to compute the predicted reduction potential of an azurin mutant (CE = continuum electrostatics). Reprinted with permission from [140]. Copyright (2017) Wiley-VCH.