# Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?
## 2 Light Harvesting
To take into account the effect of the surrounding of the chromophore, and overcome the aforementioned limitations, additional terms in the electronic Hamiltonian must be added, to account for factors such as vibrations and polarization response of the protein environment. The total Hamiltonian for the QM part in Equations (1) and (3) thus must be rewritten to include the exciton (\(H_{\text{e}}\)), the environment (or bath, \(H_{\text{b}}\)) and the interaction between the two parts (\(H_{\text{be}}\)):  
\[H_{\text{QM}}=\ H_{\text{e}}+H_{\text{b}}+H_{\text{be}}. \tag{4}\]  
In this expression, all the degree of freedoms coupled to the exciton states, such as nuclear degrees of freedom of the protein residues and pigment molecules, are considered, as well as the electronic degrees of freedom not directly involved in the electronic excitations of chromophores. All these terms are needed for a quantitative characterization of the excitons, to obtain a reliable assessment of the migration mechanism of the excitons from one chromophore to another in the LHCs, and paving the way to a general design principle for each LHC. The bath-electron Hamiltonian (\(H_{\text{be}}\)) is often considered as a set of harmonic oscillators, in which only diagonal terms are considered, while off-diagonal terms are assumed to be negligible. For a detailed review on the theoretical derivation of these terms, together with a detailed description of the spectroscopic observables which can be derived, we refer here to [16]. Depending on the strength of both the electronic coupling and the coupling to the environment, the EET rate can be described either by the Forster regime in which the square of the electronic coupling is assumed to be much weaker than the reorganization energy, or by the Redfield regime where the excitonic coupling are much larger than the coupling to the environment. In the last case the process is dominated by relaxation and not EET. We would like to stress here that these regimes are extreme cases, and natural and artificial PPCs are often found in between them, reaching maximum efficiency [41, 42]. A detailed description of both regimes lies outside the scope of this review, but we indicate here a few literature references in which both methods are discussed in details [12, 16, 43, 44]. What we would like to stress in here is the different type of systems for which either one or the other description is applicable. In fact, while the Forster theory can be applied for chromophores which are distant from each other (more than 1.4 nm) for which the coupling is weak, leading to a localization of the excitons, the Redfield theory should be used when at least a partial delocalization of photosynthetic excitons is present, and chromophores are strongly coupled, for which the transfer between weakly coupled aggregates with strong intra-aggregate excitonic couplings is present. However, many complexes are in the intermediate coupling regime that can be described by numerically exact approaches for which appropriate methods as generalized Forster theory exists [12]. In this intermediate regime, the accurate computation of quantum dissipative dynamics are obtained with nonperturbative numerical methods [45, 46]. These methods are of particular interest when the excitation localized when the nuclei relax (described as dynamic localization). The hierarchically coupled equations of motion (HEOM) [45] and other nonperturbative approaches on the other hand treat in principle all couplings exactly. However, many quantum chemical studies on multichromophoric complexes only deal with the electronic part, computing site energies and exciton couplings, due to the complexity of the suggested methods and the high computational time required. In this section, different approaches describing the EET processes are presented, focusing on QM/MM, network modeling and post HF methods nowadays available. The section ends with a short view on the TTET and the challenges present when dealing with spin forbidden transitions.