# Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?
## 2 Light Harvesting
### Post HF Methods  
As shown in the previous sections, the majority of computational methods used to describe the PPCs electron transfer and absorption mechanisms are based on QM/MM approaches, which in turn heavily rely on TD-DFT. Yet, post Hartree-Fock methods start now to be considered in such studies, especially thanks to strong improvement in hardware efficiency. We recall here the two main problems related to the use of TD-DFT: Inability to  
Figure 8: Long time electronic energy transfer (EET) dynamics in the 24-state model of the FMO trimer complex (\(T=300\) K) for initial excitation of BCh1 1 (**a**), BCh1 6 (**b**), and BCh1 8 (**c**), respectively. The population of all 24 states is shown for initial excitation of BCh1 of FMO monomer 2 (**d**), \(k_{\text{eff}}=8,=10^{-7}\). Reproduced from [86] with permission from AIP, 2017.  
properly describe charge transfer (CT) states and the impossibility of having multiconfigurational character. The CT problem can be strongly reduced by introducing long-range corrected functionals, while the latter requires the use of multi-reference methods, such as MRCI-DFT [88]. MRCI-DFT has been successfully applied to describe the peridinin carotenoid present in LH, for which even the slightest fluctuation in the bond length amplitude results in significant modification of the character of the excited states [89]. Despite the common use of accurate non-DFT QM methods for benchmark purposes [90], application to PPCs started to appear only in the last few years. A complete active space method combined with perturbation theory (CASPT2) has been recently used to study bacteriochlorophylls of LH2, to determine the geometrical variations affecting the absorption spectrum, and in particular the causes of the observed blue-shift [91]. The authors considered the highest-quality multistate multiconfiguration restricted active space with second-order perturbation theory correction (MS-RASPT2) method to compute excitation energies, combined with TD-DFT. With the combination of these two approaches, the authors were able to obtain high accuracy and speed in computation. They found that the changes in geometry of selected torsional angles are responsible for the blue-shift observed, due to the modification of the chlorophyll curvature. This is a consequence of the presence of different protein residues in proximity of the pigment, which push and pull it, regulating the excitation energy. Another approach is to combine the approximate second-order coupled cluster (CC2) with reduced virtual space (RVS) [92; 93] and the algebraic diagrammatic construction through second-order (ADC(2)) [94; 95], which has been applied to study chlorophyll pigments of PSI [96]. In this study, the authors computed the lowest excited states of chlorophyll dimers, showing that the excitonic and electrostatic coupling are responsible for the red-shift observed in the absorption spectra. More interesting, the comparison with TD-DFT demonstrate how the later has difficulties to provide the correct shift in excitation energies, especially for excitonically coupled pigments. A final approach consists in the use of the Bethe-Salpeter equation coupled with the GW approximation (BSE/GW), which has been successfully used to compute the EET of pigments found in the PE545 complex [97]. The suggested methodology has the advantage of being applicable with high precision for both molecular and periodic systems, opening to the possibility of studying systems with various sizes. Focusing on model dimers, the authors found that their approach reproduces almost exactly the experimental excitation energies, despite the approximations used (dimer pairs and no environment considered). The advantage of this method over TD-DFT is that BSE can accurately describe the CT excitations as the long-range Coulomb interaction is fully considered [98; 99; 100].