# Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?
## 2 Light Harvesting
### Triplet-Triplet Energy Transfer  
Apart from ET present in natural photosynthetic apparatus, through singlet states, the triplet-triplet energy transfer (TTET) also plays an important role [101]. As discussed in the previous section, water plays a crucial role in mediating ET, yet only few investigations has been reported on its effect on TTET [102; 103; 104]. The same parameters governing the ETare also involved in the TTET process, based on the Dexter exchange mechanism [105] in which the rate constant, in the weak coupling limit is defined as [106]:  
\[k_{\rm TTET}=\frac{2\pi}{\hbar}\big{|}V_{ij}\big{|}^{2}\delta\big{(}E_{i}-E_{j} \big{)} \tag{6}\]  
where \(\delta\) is a function accounting for energy conservation during the transition and \(V_{ij}\) is the electronic coupling between the triplet states of the donor and acceptor, which is defined as:  
\[V_{ij}=\frac{H_{\rm DA}-1/2(E_{\rm D}+E_{\rm A})S_{\rm DA}}{1-S_{\rm DA}^{2}} \tag{7}\]  
where \(E_{\rm A}\) and \(E_{\rm D}\) are the diabatic energy of the acceptor and donor, \(S\) is the overlap and \(H\) the Hamiltonian between D and A. We would like to remind here that the spin is conserved between the initial and final state of the transition (\({}^{3}\)DA\(\rightarrow\)D\({}^{3}\)A) and the forbidden nature of the spin makes the Coulombic term of the coupling null. As TTET involved the simultaneous exchange of two electrons of different spin between the lowest unoccupied molecular orbitals (LUMO) and the highest occupied molecular orbitals (HOMO), its rate depends on the two overlap integral product, explaining why the exponential decay of TTET with the distance is twice that of ET [107]. Since this process is important at shorter distances with respect to ET, the presence of a bridge molecule (i.e., structural water, amino acid residue) can extend the overlap between the donor and acceptor wavefunction, thus enhancing the energy transfer, as described in the superexchange model [108; 109]. This model allows the virtual population of triplet state localized on the bridge [110]. In this view, the donor-bridge, bridge-acceptor distance, their relative orientation and distribution, and the nodal pattern of the orbital involved in the ET affect the strength of the coupling. This mechanism is of outmost importance, as it is crucial for the photoproduction from singlet oxygen formation. Interestingly, different LH systems present different TTET timescales, from nanosecond in purple bacteria LHC [111] to sub-nanosecond timescale for LHC of oxygenic organisms [112], and the mechanism underneath this difference is still not fully understood. It has been suggested that the ultrafast TTET occurring between the chlorophyll and carotenoid molecules leads to a localization of the triplet state over the carotenoid, affecting the electronic transition of the chlorophyll [113] and subsequent perturbations in the absorption spectra. It is thus of interest to determine the role of the electronic structure underlying the electronic coupling observed in the TTET. Computation can assess structural features underlying the TTET process, and in addition provide evidence of spin localization, which his of importance to enhance the stability of the system. QM/MM method have been applied to study both the LHC-II and LH2 structures (Figure 9) by considering the ONIOM formalism, describing the Chl/carotenoid pair at the DFT level and the environment with the MM AMBER force field [114]. In this study the authors observed that the interchromophore interactions for closely interacting subunit pairs are responsible for the triplet state geometry perturbation, which is at the origin of the Raman shift experimentally observed [114]. In details, QM/MM calculations indicate that after the TTET, when the chromophore pair is in the Chl(S\({}_{0}\))Car(T\({}_{1}\)) electronic state, the geometry of the carotenoid changes enough to give rise to the resonance Raman signal.