Charge transfer from the carotenoid can quench chlorophyll excitation in antenna complexes of plants

The photosynthetic apparatus of higher plants can dissipate excess excitation energy during high light exposure, by deactivating excited chlorophylls through a mechanism called nonphotochemical quenching (NPQ). However, the precise molecular details of quenching and the mechanism regulating the quenching level are still not completely understood. Focusing on the major light-harvesting complex LHCII of Photosystem II, we show that a charge transfer state involving Lutein can efficiently quench chlorophyll excitation, and reduce the excitation lifetime of LHCII to the levels measured in the deeply quenched LHCII aggregates. Through a combination of molecular dynamics simulations, multiscale quantum chemical calculations, and kinetic modeling, we demonstrate that the quenching level can be finely tuned by the protein, by regulating the energy of the charge transfer state. Our results suggest that a limited conformational rearrangement of the protein scaffold could act as a molecular switch to activate or deactivate the quenching mechanism.

the crystal conformation. This is probably due to the interaction between the monomers in the trimeric structure (See Figure 1b of the main text) where the N-termini interact with the helix C of the other monomers. We also analyze the torsional angle between helices A and D as suggested by Daskalakis et al. 9 S3 by computing the φ Ramachandran angle of Gly204. The results, reported in Figure 3, show that helix D does not change conformation with respect to the crystal structure. This is consistent with our LHCII model remaining close to the "quenched" conformation.

Benchmark of charge transfer states
The difficulties of TD-DFT, with or without the application of the Tamm-Dancoff approximation, in describing on an equal footing both CT and local excited states are well known. [10][11][12] In order for TD(A)-DFT to reproduce the correct 1 R asymptotic behaviour of a long-range CT, it is necessary to introduce exact exchange in the DFT functional. Long-range corrected functionals can recover such a correct asymptotic behaviour, even exactly when the contribution of exact exchange becomes 100% at long interelectronic distance. [13][14][15][16] Whilst such long-range corrected functionals do provide accurate CT transition energies, they tend to overestimate the transition energy of local excited states. 17 In order to appraise the quality of our level of theory, we benchmarked the excitation energies of Lut-Chl dimers using second-order wavefunction approaches. More in details, we performed secondorder coupled-cluster (CC2) and Algebraic Diagrammatic Construction [ADC (2)] calculations on four Lut-Chl dimer structures extracted from the 240 structures used in DFT calculations. These ADC(2) and CC2 calculations have been performed with the Turbomole program, 18 applying the RI approximation and selecting def2-SV(P) basis set. Such choice is dictated by the size of the investigated dimers (171 atoms). The comparisons are reported in Table 1 considering different key excited states. Globally, one notices that the ADC(2) transition energies are slightly smaller than their CC2 counterparts, especially for the low-lying LE transitions, which is a typical outcome for transitions close or below than 2 eV. 19 We therefore consider the CC2 values as reference here. For the CT state, we find that the TDA/ωB97X-D values agree quite well with the CC2 results, with a mean/maximum deviation of 0.096/0.14 eV, which is significantly better than the expected accuracy of TD-DFT (ca. 0.25 eV). In contrast, the ωB97X functional overestimates the CT energies by ∼0.5 eV, a quire large value, which is probably the consequence of the larger attenuation parameter in ωB97X than ωB97X-D; the former functional presenting a steeper onset of exact exchange. 16,20 Supplementary

Analysis of charge-transfer energies
CT energies in vacuo.
In order to disentangle the effects of internal geometry of the dimer from the effects of the environment on the CT transitions energies, we use calculations in vacuo for dimers a612 /Lut1 and a603 /Lut2 of monomer 2 along 80 frames of the trajectory. These calculations allow to test which geometrical features contribute the most to the variability of the CT energy. A multivariate linear regression is performed in order to assess the influence of various structural parameters on the CT energy. The choice of geometrical parameters is based on physical reasoning. The energy of a D → A CT transition depends on the HOMO/LUMO difference as well as on the distance between the donor and acceptor: for large R, clearly f (R) → 1/R; however, for close separations, the exact functional dependence is more complicated than a simple inverse function with the center/center distance. The E A LUMO and E D HOMO energies, as a first approximation, mainly depend on internal DOFs of each chromophore. Therefore, we need to include both intra-chromophore and inter-chromophore coordinates in order S5 to explain geometrically the variability of CT energies.
We define two internal coordinates for each chromophore (Lut and Chla), based on the bond length alternation (BLA) between single and double bonds along the conjugation paths highlighted in Figure 3a of the main text. The BLA is defined as where n single/double are the number of single and double bonds, and l i/j are the lengths of single and double bonds, respectively.
In order to capture the intermolecular dependence of the CT energy, we define the density overlap 21 between the atoms in Lut and Chla highlighted in Figure 3b of the main text. This overlap is the integral of a product of spherical densities centered on the atoms of the two molecules: where r i and r j are the positions of atoms i and j, and σ i and σ j are the respective van der Waals radii. Finally, we take the position (x, y, z) of the lutein center on a reference frame defined by the chlorin plane of the Chla. 1 The internal BLA coordinates considered alone explain more than 50% of the variability of the CT energy in vacuo and already give a good correlation with the QM calculations (See Figure 4). Inclusion of the intermolecular coordinates allows to explain more than 70% of the total variance of the CT energy (Figure 4, blue points). As this model includes the main intermolecular degrees of freedom, the unexplained variability originates from other intramolecular coordinates of Lut and Chla. The above analysis shows that the CT energy is mainly modulated by the internal coordinates Lut and Chla, respectively through the HOMO and LUMO. From the regression parameters ( Table 4) we estimate that an increase of 1×10 −2Å3 in the overlap would result in a decrease of ∼400 cm −1 in the CT energy.
Effect of the environment on the CT energy.
In Figure 5 we report the distributions of the environment shift on the CT energy (MMPol minus vacuum), for sites L1 and L2. If both distributions are broad, spanning a few thousands of cm −1 , there is a significant difference (320 ± 120 cm −1 ) between L2 and L1.
Supplementary Figure 5: Histogram of the environment-induced shift of the CT energy for sites L1 and L2.

Inter-chlorophyll charge transfer states
Supplementary Table 2: Average values and 95% confidence intervals of energies (E) and couplings (V) in the Chl-Chl dimers. Coupling averages are given as root-mean-square (RMS) instead of arithmetic mean. Reorganization energies (λ) and driving forces (∆G) are also given, as estimated from the variance of the CT and LE energies. All values in cm −1 . CT always indicates the lowest CT state of the dimer.

Dependence of LHCII lifetime on the CT energetics
We show in Figure 6 how the lifetime of LHCII depends on the driving force of charge separation in site L1. The shaded region represents the variation of the LHCII lifetime obtained by doubling or halving the charge-recombination rate to the GS. For the value computed in the present work (∼ -80 cm −1 ) we obtain a lifetime at the lower bound of the lifetimes for crystal LHCII (0.3-0.7 ns), whereas for ∆G 700 cm −1 we obtain values compatible with LHCII in the photosynthetic membrane. 22 Note that this analysis assumes a fixed value for the CT coupling and for all parameters of the L2 site.
Supplementary Figure 6: Dependence of the LHCII lifetime on the free energy of charge separation in the L1 site (red line). The parameters of the kinetic model are the same as in Figure 2b of the main text, except for the forward and reverse charge-separation rates for the a612 -Lut1 dimer, which are both determined by ∆G on the x-axis. The shaded region corresponds to varying the rate for charge-recombination to the ground state from 20 ps (upper bound) to 5 ps (lower bound).

Supplementary Tables
Supplementary