# Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?
## 2 Light Harvesting
### Numerical Modeling  
A different approach (not considering QM/MM method as discussed in the previous section) to study the EET in small PPCs has been recently proposed by [PERSON] and [PERSON] [83]. They opted for a view in which the PPC is considered as a series of interconnected nodes (i.e., the pigments) and edges (i.e., the electronic couplings between the pigments), forming together the PPC electronic subsystem. In this approach, the Hamiltonian is equivalent to the typical tight-binding model of n interacting molecules [84; 85; 41]. The proposed protocol comprises Hamiltonian and dynamics, in which the Haken-Strobl model was used to consider the environment as a pure dephasing effect in the pigment excitation energies. The Hamiltonian reported in Equation (1) is modified to include the exciton recombination effects \(\hat{H}_{\text{rec}}\) and energy trapping (electrons reach the \"sink\" pigment and then flows out towards the RC) \(\hat{H}_{\text{trap}}\):  
\[\hat{H}_{rec}=-i\hbar\Gamma\sum_{i=1}^{n}\lvert i\rangle\langle i\rvert\ \ ;\ \ \hat{H}_{trap}=-i\hbar\kappa\lvert k\rangle\langle k\rvert \tag{5}\]  
The recombination operator acts on all pigments while the trapping operator only acts at pigment \(k\) (PPC \"sink\" site). With this method it is possible to simulate the EET dynamics including both the electronic and the environmental parts, within the master equation approach described by the Haken-Strobl model [84; 85; 41]. It is important to note that explicit correlations between the electronic Hamiltonian and the environment are missing and that the protein is considered separately as Markovian fluctuations in the pigments' excitation energies, leading to dephasing effect at each pigment node. Despite the different approach followed, the presented model reproduces in a quantitative way experimental results for complex systems such as excitonic energies of FMO complex and LHC-II. As in the other methods described earlier in this review, the authors found that the key parameter for the efficiency of the EET is the protein-pigment interaction. The authors considered in their study FMO and LHC-II as model cases, and demonstrated that the description of these complexes as simple network of nodes and edges qualitatively reproduces the dynamical behavior of the whole proteins. Moreover, it is possible to identify different paths of the PPCs structure to the protein light-harvesting abilities and unravel the fundamental nodes needed to obtain an efficient ET, by systematic removing pigment. It is easy to foresee that this kind of analysis can be employed for the \"screening\" step in the design of novel networks of chromophores like the one used in artificial solar cells or photoinduced catalytic systems. Despite the qualitative nature of this  
Figure 7: BChl a site energies averaged over 100 structures with standard deviations shown as vertical error bars. (**a**) Gas-phase (without protein environment) site energies computed for structures directly extracted from MD snapshots (black) and after QM/MM geometry optimizations (orange). (**b**) Gas phase (orange), QM/MM (blue), QM/EFP-noPOL (green), and QM/EFP (red) site energies computed for structures after QM/MM geometry optimizations. Reprinted with permission from [74]. Copyright (2020) American Chemical Society. proposed approach, the computation is robust and allows the performance of fast quantum dynamic calculations on large systems. The next challenge would be to explicitly account for the pigment-environment coupling, in a computationally-simple manner. A different methodology for the simulation of energy- and charge-transfer processes is based on the iterative quasi-adiabatic propagator path integral (iQUAPI) approach [86]. This method relies on an improved numerical exact path integral quantum dynamics merging performance via mask-assisted coarse graining of Feynman-Vernon influence coefficients (MACGIC-iQUAPI).