CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201402233

Carotenoids as a Shortcut for Chlorophyll Soret-to-Q Band Energy Flow Jan P. Gçtze,*[a] Dominik Krçner,[b] Shiladitya Banerjee,[b] Bora Karasulu,[a] and Walter Thiel[a] It is proposed that xanthophylls, and carotenoids in general, may assist in energy transfer from the chlorophyll Soret band to the Q band. Ground-state (1Ag) and excited-state (1Bu) optimizations of violaxanthin (Vx) and zeaxanthin (Zx) are performed in an environment mimicking the light-harvesting complex II (LHCII), including the closest chlorophyll b molecule (Chl). Time-dependent density functional theory (TD-DFT, CAMB3LYP functional) is used in combination with a semi-empirical description to obtain the excited-state geometries, supported

by additional DFT/multireference configuration interaction calculations, with and without point charges representing LHCII. In the ground state, Vx and Zx show similar properties. At the 1Bu minimum, the energy of the Zx 1Bu state is below the Chl Q band, in contrast to Vx. Both Vx and Zx may act as acceptors of Soret-state energy; transfer to the Q band seems to be favored for Vx. These findings suggest that carotenoids may generally mediate Soret-to-Q energy flow in LHCII.

1. Introduction Plants use sunlight to fuel their metabolism with the required energy. The reaction center of photosystem II (PSII) is supported by various associated antenna complexes, which provide much more energy than could be acquired by PSII alone.[1] The major light-harvesting complex IIb (LHCII) is a trimeric membrane protein that carries various chlorophyll and xanthophyll chromophores.[2] The former represent most of the light-absorbing molecules in a LHCII monomer, which contains eight and six molecules of chlorophyll a and b, respectively. The interconnection of chromophores and clusters within the LHCII complex has been thoroughly investigated to understand their energy-transfer capabilities.[1, 3] The basics of energy transfer and light harvesting are probably well understood, and there are many excellent reviews that provide collections of extensive experimental data as well as spectroscopic and mechanistic insight into these processes.[1, 3f, 4] Chlorophylls absorb in two ranges of the UV/Vis region.[5] The lower-energy Q band appears at about 1.9 eV (650 nm) and consists of two states Qy and Qx, with Qy providing significant oscillator strength.[6] The higher-energy Soret band appears at about 2.8 eV (440 nm) and contains various absorbing states depending on the type of chlorophyll.[7] For chlorophyll b, the Soret band absorbs more intensely than the Q band, whereas for chlorophyll a the Q band and Soret band [a] Dr. J. P. Gçtze, B. Karasulu, Prof. Dr. W. Thiel Max-Planck-Institut fr Kohlenforschung Kaiser-Wilhelm-Platz 1, 45470 Mlheim an der Ruhr (Germany) E-mail: [email protected] [b] Dr. D. Krçner, S. Banerjee Universitt Potsdam Institut fr Chemie, Theoretische Chemie Karl-Liebknecht-Str. 24-25, 14476 Potsdam (Germany) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402233.

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have maxima of similar height.[5] The Q band provides the energy to drive the reactions at the PSII by forming excitonic states delocalized over several chlorophyll molecules. The excitonic energy is then transmitted from LHCII to PSII;[8] chlorophyll a is the main exciton-forming chromophore, and chlorophyll b is a supporting element.[9] Diverse roles have been ascribed to the xanthophylls in LHCII.[3f, 4b] An LHCII monomer contains two lutein molecules, one violaxanthin (Vx) or zeaxanthin (Zx) molecule sharing the same binding site, and one neoxanthin molecule.[2] Owing to their different chemical compositions, it is intriguing to assume specific roles for each of the xanthophylls in LHCII. For example, violaxanthin was considered to be much less involved in the light-harvesting process than lutein.[7, 10] Xanthophylls were designated to be chlorophyll triplet quenchers,[11] oxygen scavengers,[12] and low-wavelength light harvesters;[7, 13] additionally, they were suspected to play a role in photoprotection mechanisms involving singlets.[14] From a chemical perspective, the xanthophylls are a subdivision of the carotenoid family. For example, zeaxanthin can be derived from the well-known b-carotene molecule just by replacing a hydrogen atom by a hydroxyl group in the two terminal rings. Other xanthophylls are more heavily chemically modified but still retain a chain of conjugated C=C double bonds. Thus, regardless of their exact chemical nature, all xanthophylls in LHCII are believed to absorb in approximately the same UV/Vis region. Their absorption is characterized by an onset around 2.5 eV (500 nm) with various maxima centered around 2.7 eV (ca. 450 nm) and a tail extending up to about 4 eV (ca. 300 nm).[3a, 15] This band is very broad and very intense. It arises from a single strongly dipole allowed transition, commonly denoted 1Ag !1Bu in an idealized C2h point group. There are at least two other states located in the UV/Vis region, 2Ag and 2Bu, which are energetically close to the 1Bu ChemPhysChem 2014, 15, 3392 – 3401

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CHEMPHYSCHEM ARTICLES state. Both are optically dark, and thus it is difficult to experimentally determine their exact energy, especially if they are embedded in a complex environment with many other chromophores.[4a, 14a, 15, 16] Computationally, they pose a challenge as well, because of significant double-excitation character.[17] The xanthophyll energy levels depend on the length of the conjugated p system, but not in an entirely homogenous manner.[18] To assist in light harvesting, the presence of xanthophylls should lead to a higher population of the excitonic Q band. There is experimental evidence for energy transfer from the xanthophylls to chlorophyll.[3a, 13, 18, 19] However, it has been difficult to rationalize this process for carotenoids in general,[20] because the excitation energies for the Q band and the bright xanthophyll absorption are relatively far from each other (differences of 0.6–1 eV, see above). In the case of the bacterial light-harvesting complex LH2, the efficiency of energy transfer between 1Bu and the Q band is calculated to be low,[21] far less than experimental expectations.[16c] The mechanism of carotenoid-to-chlorophyll energy transfer is, however, experimentally well established, also for bacterial light harvesting.[22] It thus seems that the theoretical picture is lacking some crucial elements. Theoretical research on xanthophylls acting as elements in singlet photoprotective mechanisms initially focused on the violaxanthin/zeaxanthin pair, because these two xanthophylls exchange on light stress.[14a, 23] The corresponding “gear-shift” model assumes that the 2Ag state is either a Q-band energy donor or acceptor, depending on which xanthophyll is present. However, theoretical studies have struggled, until now, to show a distinct photophysical difference between Vx and Zx.[23c, d, 24] Recent experimental work indicated that nonphotochemical quenching is not at all xanthophyll dependent, but arises from chlorophylls alone;[25] this implies that xanthophylls may still play another role, beyond oxygen or triplet protection. A commonly used approach in computational studies on large systems is to derive excited-state properties of a system directly at the ground-state geometry. However, even if this may provide a good overview of the initial events, it is difficult to see all possibilities that open up for a system after photoabsorption. Excited-state geometry optimization is the next logical step, which, however, may become quite costly for large systems (e.g. when environmental effects are relevant and require the use of large models, as in proteins). Previously, we investigated the interactions of Vx and chlorophyll b (Chl in the following) in their natural LHCII environment on the basis of a static picture employing time-dependent density functional theory (TD-DFT).[24a] In another study, the properties of Vx and Zx were investigated in the gas phase and in solution by using a DFT multireference approach (DFT/MRCI[17c, 26]), which allowed determination of the energetic positions of the dark 2Ag and 2Bu states,[24b] similar to what had been done for b-carotene before.[17b, c, 27] The present study aims at a full analysis of all relevant states of Vx, Zx, and Chl and of their coupling at the ground-state geometry. We also investigate the events following the relaxation of the xanthophyll 1Bu state, the most strongly absorbing state  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org in these systems. We focus on the influence of the environment to elucidate the photophysical role of individual chromophores. It is known that especially the 1Ag !1Bu transition of the xanthophylls is sensitive to environmental polarization.[28] The article is organized as follows: First, we describe the computational methods and the molecular models used in the calculations. Therafter, we address the vertical transition energies and the relative orientations of the transition dipole moments, followed by a discussion of the potential roles of xanthophylls. We conclude with a brief summary.

Computational Methods Most quantum-chemical computations were done by using the Gaussian 09 package.[29] In the DFT/MRCI[17c, 26] calculations, the orbitals were generated with Turbomole.[30] We adopted the same computational approach as in a previous study.[24a] The target chromophores were optimized by using the CAM-B3LYP[31] density functional and a 6-31G(d) basis set,[32] and the environment was modeled with PM6.[33] DFT/MRCI calculations employed the SVP basis.[34] This choice of methods was based on our previous excellent experience with the CAM-B3LYP plus DFT/MRCI combination.[24b] The initial molecular model consisted of a xanthophyll/chlorophyll b pair and the immediate LHCII environment, a shell with a radius of approximately 4 . The model contains a total of 1463 atoms; see Section S1 of the Supporting Information for a detailed description. Initial coordinates were taken from the protein data base[2b] (PDB entry: 2BHW). The chromophores were optimized with the ONIOM[35] scheme, keeping the shell frozen and allowing only the target chromophores and all hydrogen atoms in the system to move. The shell was removed from the system after optimization, leaving 100 (Vx) or 98 (Zx) plus 136 Chl atoms. These isolated chromophores correspond to our “gas-phase” model, which also contains point charges (see below) of the Mg2 + -coordinating Tyr24 residue to avoid artifacts in the spectrum of Chl. Finally, in line with the excited-state optimizations (see below), we performed another optimization in which Chl was treated as a part of the environment (with only Vx or Zx in the CAM-B3LYP region and allowed to move). The geometry of the xanthophylls was found to be unaffected by this different treatment of Chl (< 0.001  difference in bond-length alternation (BLA), data not shown). To obtain a full treatment of the environment for the vertical excitation energies,[24a] the LHCII trimer was first inserted into a thylakoid membrane slab, and all atoms were replaced by point charges. The positions of all atoms that were allowed to move during the optimizations (see above) were updated to their optimum values before the spectral calculations. This setup is called the point charge field (PCF) model. More details can be found in the Supporting Information (Section S1) and elsewhere.[24a] A graphical representation of the individual molecular models used in this study is shown in Figure 1. The 1Bu excited-state geometries of Vx and Zx were optimized by using time-dependent[36] (TD-)CAM-B3LYP and the setup outlined above, starting from the ground-state minimum geometry. Chl was treated as part of the frozen shell, as a full xanthophyll/chlorophyll b TD-CAM-B3LYP optimization exceeded our computational resources. As part of the shell, the Chl non-hydrogen atoms were frozen during 1Bu optimization. ChemPhysChem 2014, 15, 3392 – 3401

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Figure 1. Optimized model systems (gas phase). For Zx + Chl (TD-DFT), Vx was replaced by Zx. For DFT/MRCI, the molecules were computed individually, and Chl was reduced to the displayed size (no phytyl chain). Tyr24 was present in the gas phase model to coordinate the Mg2 + ion. The full PCF model used identical atomic coordinates, but with a larger PCF (see Ref. [24a]).

The Zx/Chl pair was constructed by deleting the epoxide oxygen atoms at the Vx ground-state minimum structure (currently there is no experimental LHCII structure with Zx available). In the Zx models, Chl was kept in the Vx/Chl optimized ground-state geometry (analogous to the 1Bu optimization). Apart from saving computational effort, this approach also allows for a direct comparison of all systems, because any changes can only arise from the differences in the Vx or Zx part. Owing to computational limitations, we had to use different molecular models in the TD-DFT and DFT/MRCI calculations. TD-DFT is

able to handle both molecules of a given pair (Vx/Chl or Zx/Chl) at the same time, unlike DFT/MRCI, with which we can treat only one chromophore at a time (in the Chl case even with the phytyl chain replaced by a methyl group). We can thus obtain the properties of intermolecular charge-transfer (CT) states only from TD-DFT, whereas DFT/MRCI provides us with the location of the dark 2Ag and 2Bu states of Vx or Zx, which are of double-excitation character and thus inaccessible through TDDFT.[17a, c] We thus need to join the two types of calculations to obtain a complete picture.

2. Results 2.1. Geometries: 1Ag and 1Bu Minima In this section, we evaluate the geometrical properties of the xanthophyll models depicted in Figure 1. We found neither large differences (except for the epoxide oxygen atom) between the optimized ground-state geometries of Vx and Zx, nor drastic changes on electronic excitation to the 1Bu state for either of them. In our previous calculations on free Vx or

Figure 2. BLA in Vx and Zx for the (TD-)CAM-B3LYP/6-31G(d) structures. BLA is defined[17c] as (riri + 1)(1)i, where r is the length of bond i. BLA of b-carotene from crystal structure.[37]

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Zx,[24b] the most stable Zx conTable 1. TD-DFT vertical excitation energies [eV] and oscillator strengths from the ground to the given target formation was found to be close state at the CAM-B3LYP/6-31G(d) minimum geometry of the 1Ag or 1Bu state. Change from the gas phase to the most stable Vx conformagiven in parentheses. Bold values are not available from DFT/MRCI (see Table 2). tion. The latter is similar to the Vx/Zx 1Ag geometry in PCF (change from gas phase) Vx conformation present in the Vx + Chl Zx + Chl crystal structure. Hence, Vx, and Target state DE f DE f likely Zx as well, are not strongly Qy 2.25 (0.03) 0.08 (0.03) 2.25 (0.03) 0.08 (0.03) distorted from their gas-phase 2.53 (0.06) 0.00 (+ 0.00) 2.53 (0.06) 0.00 (+ 0.00) Qx minima when embedded in 2.84 (0.08) 3.31 (0.13) 2.80 (0.11) 3.35 (0.16) 1Bu 2.87 (0.19) 0.00 (0.01) 2.86 (0.21) 0.00 (0.01) CT1: XAT + /Chl LHCII. Comparing the 1Ag and Soret1 3.14 (0.14) 0.88 (0.18) 3.15 (0.13) 0.87 (0.18) 1Bu geometries, there is only 3.17 (0.35) 0.02 (0.01) 3.17 (0.36) 0.02 (0.01) CT2: XAT + /Chl a single obvious difference visiSoret2 3.23 (0.19) 0.87 (+ 0.06) 3.24 (0.19) 0.83 (+ 0.03) ble in Figure 1, namely, an apVx/Zx 1Bu geometry in PCF (change from gas phase) proximately 608 rotation of the Vx + Chl Zx + Chl central methyl group on one Target state DE f DE f side of the xanthophyll chain. 2.15 (0.05) 3.45 (+ 0.13) 2.07 (0.08) 3.62 (+ 0.02) 1Bu Otherwise, the 1Ag and 1Bu opti2.25 (0.03) 0.21 (0.22) 2.25 (0.03) 0.17 (0.08) Qy mized structures show no quali2.36 (0.25) 0.00 (+ 0.00) 2.33 (0.27) 0.00 (0.01) CT1: XAT + /Chl 2.53 (0.06) 0.00 (0.01) 2.53 (0.04) 0.00 (0.01) Qx tative differences that could be 2.65 (0.41) 0.00 (+ 0.00) 2.65 (0.39) 0.00 (+ 0.00) CT2: XAT + /Chl spotted from visual inspection. Soret1 3.14 (0.13) 0.81 (0.08) 3.14 (0.15) 0.70 (+ 0.05)[a] For a more quantitative evaluaSoret2 3.23 (0.19) 0.74 (+ 0.00) 3.26 (0.17) 0.62 (0.12)[a] tion, we thus rely on a BLA anal[a] Loses some oscillator strength to an energetically close CT state (not shown). ysis (see Figure 2), as done previously for gas-phase structures.[17c, 24b] Table 2. DFT/MRCI vertical excitation energies [eV] and oscillator strengths from the ground to the given Figure 2 allows us to identify target state at the CAM-B3LYP/6-31 G(d) minimum geometry of the 1Ag or 1Bu state. SE is the amount of a slight anisotropy in terms of single-electron excitation character in the given transition. Change from the gas phase given in parentheses. BLA, especially for Zx. We find Bold values are not available from TD-DFT (see Table 1). that Vx and Zx are very similar Vx/Zx 1Ag geometry in PCF (change from gas phase) towards the Chl side, whereas Zx Vx or Chl[a] they differ towards the protein Target state DE SE f DE SE f side. The effect is more pro2.01 (+ 0.01) 0.84 (0.01) 0.11 (0.05) – – – Qy nounced for Zx than for Vx in 2.04 (0.01) 0.78 (+ 0.00) 0.00 (+ 0.00) – – – Qx the 1Bu state. The differences 2.39 (+ 0.04) 0.63 (+ 0.33) 1.37 (+ 1.36) 2.35 (+ 0.07) 0.72 (+ 0.41) 1.85 (+ 1.84) 2Ag between Vx and Zx in the termi2.66 (0.04) 0.64 (0.24) 2.31 (1.45) 2.65 (+ 0.02) 0.59 (0.29) 1.85 (2.11) 1Bu Soret1 2.69 (0.07) 0.77 (+ 0.00) 0.54 (+ 0.17) – nal regions have been described 2.78 0.72 0.50 – Soret2[b] before,[24b] and they exist be3.08 (+ 0.08) 0.46 (+ 0.35) 0.05 (+ 0.00) 3.05 (+ 0.15) 0.49 (+ 0.14) 0.08 (+ 0.06) 2Bu cause the system of conjugated Vx/Zx 1Bu geometry in PCF (change from gas phase) double bonds does not extend Vx Zx into the terminal rings of Vx. Target state DE SE f DE SE f Due to the different anisotropy 1.54 (+ 0.07) 0.26 (+ 0.01) 0.00 (+ 0.00) 1.50 (+ 0.09) 0.28 (+ 0.05) 0.01 (+ 0.01) 2Ag of Vx and Zx in the protein envi2.12 (0.19) 0.82 (0.01) 3.33 (0.17) 1.98 (0.22) 0.82 (+ 0.03) 3.37 (+ 0.06) 1Bu ronment, which becomes more 2Bu 2.25 (+ 0.09) 0.35 (+ 0.02) 0.17 (0.08) 2.18 (+ 0.12) 0.35 (+ 0.00) 0.11 (0.28) pronounced in the 1Bu geome[a] Chl values obtained in a PCF containing Vx. [b] State not present in gas-phase calculation; see the Supporttry, we may expect some differing Information, Section S2. ences in state energies or intermolecular energy transfer (see below).

2.2. Electronically Excited States at the 1Ag Minimum 2.2.1. TD-DFT and DFT/MRCI: Complementary Findings We report the TD-DFT and DFT/MRCI vertical excitation energies and oscillator strengths in Tables 1 and 2, respectively. We use them to assess the quality of the TD-DFT and DFT/MRCI approaches, as well as to characterize the photophysics during and immediately after the excitation process.  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

For both methods, we find the two states of the Q band, Qy and Qx, and also two states forming the Soret band of Chl, named Soret1 and Soret2. These four states are the lowest local p!p* Chl states, in agreement with the work by Duffy et al.[7] (TD-DFT). We did not find any unexpected dark states that would go beyond the Gouterman model;[38] such states were reported in some previous TD-DFT or DFT/MRCI studies on chlorophyll a.[39] This difference may be due to the fact that the coordination sphere of the magnesium ion is different in ChemPhysChem 2014, 15, 3392 – 3401

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CHEMPHYSCHEM ARTICLES our case, but one would also not expect chlorophyll b to show states identical to chlorophyll a. The bright xanthophyll 1Bu state was also found in both approaches, whereas the dark 2Ag and 2Bu states were obtained only from DFT/MRCI. The TD-DFT model predicts CT states, two of which are in the spectral region of interest. These states are termed CT1 and CT2; both correspond to intermolecular electron transfer to Chl. It is reasonable to assume that CT1 corresponds to a CT state discussed before elsewhere.[20] However, it is difficult to draw a closer analogy, because the state energies and employed methods are drastically different (e.g. CT1 energy at 1Ag geometry for Vx/Chl in our study: 3.06 eV; in Ref. [20]: ca. 2.1 eV). To underline the strengths and weaknesses of TD-DFT and DFT/MRCI, the results obtained exclusively from either approach are marked in bold in Tables 1 and 2. In our previous work, the TD-DFT excitation energies at the 1Ag minimum geometry of Vx were presented by using an average of the results for the three LHCII Vx binding sites.[24a] Here, we only computed the energies for a single binding site (PDB structure 2BHW,[2b] chain A). We chose one specific binding site because the differences to the averaged excitation energies for all sites are smaller than 0.05 eV for any state (see Ref. [24a]). Our previous work also showed that modeling the chromophores individually changes excitation energies only by about 0.05 eV compared to a model including both chromophores.[24a] We now address the differences between the TD-DFT and DFT/MRCI results. For the purpose of this study, the main advantage of DFT/MRCI over TD-DFT is the ability to treat multielectron excitation character, and thus properly describe 2Ag and 2Bu.[17a, c] Generally speaking, contributions from multi-electron excitations should stabilize all excited states, even those dominated by single excitations (albeit to a smaller extent). By comparing the values for identical states in Tables 1 and 2, it can be seen that the excitation energies from TD-CAM-B3LYP are indeed always larger than those from DFT/MRCI. The differences range from 0.15 eV for 1Bu of Zx/Chl to 0.55 eV for the Soret2 band of Vx/Chl in the PCF. The latter shift may suggest that multi-electron excitation character is important also for the Soret states and that a linear response description is thus not sufficient; however, closer analysis of the individual states (see the Supporting Information, Section S2) confirms that the Soret states remain dominated by singly excited configurations. Based on benchmarking[40] and our previous work,[24b] we consider DFT/MRCI to be generally more reliable than TD-DFT, which is also supported by comparisons to experimental data (see below). Nevertheless, we will continue to present and analyze the results from both approaches. 2.2.2. Environmental Effects The influence of the environment on the vertical spectra is different for the two computational methods. In TD-DFT, we find the spectrum in the PCF to be generally redshifted compared to the gas phase (Table 1), with an increase in the electronic energy of the system that is slightly larger in the ground state than in the excited states (data not shown). The relatively large  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org change in CT state energies (up to 0.41 eV in the PCF) could be anticipated, since CT states are much more sensitive to the environmental charge distribution than local excitations. However, the high sensitivity of the Soret states to the PCF, with shifts of up to 0.19 eV in the case of Soret2 (as large as the shift of the lowest CT state) was unexpected. An orbital analysis (see the Supporting Information, Section S2) helped to identify the likely origin of the strong shift: the orbitals involved in the dominant excitations of Soret2 in the PCF are partly located on Vx or Zx, which imparts some partial CT character on Soret2. This is not the case in the gas phase, and the rather pronounced sensitivity of Soret2 to the environment can thus be attributed to the partial CT character in the PCF. DFT/MRCI tells a slightly different story: It predicts the states within the Q or Soret bands of Chl to be almost degenerate (< 0.1 eV difference), in contrast to TD-DFT (gap of 0.28 eV). In addition, the effect of the PCF on the vertical energies of Chl is small (shifts < 0.1 eV) with a trend towards smaller excitation energies. Furthermore, the energies of Vx and Zx are affected slightly more than the Chl energies, but still with shifts not greater than 0.15 eV (2Bu of Zx). Both DFT/MRCI and TD-DFT give small shifts for the local excitations. In DFT/MRCI, the Soret band seems specifically sensitive to the environment, since some Soret states only appear in our calculations in the PCF environment (see the Supporting Information, Section S2); in such cases, we do not have a gas-phase state that is comparable to the PCF Soret2 state in the DFT/MRCI calculations. In terms of oscillator strength, DFT/MRCI and TD-DFT agree roughly for Vx, Zx, and the Chl Q bands. However, for the Chl Soret bands, the oscillator strengths from DFT/MRCI are lower than those from TD-DFT. Another difference is that TD-DFT oscillator strengths are nearly unaffected by the PCF (with a slight drop for Soret1), whereas the DFT/MRCI oscillator strength of the Soret1 state rises in the presence of the point charges (from 0.37 to 0.54). The latter is likely due to a slight loss in CT character of the Soret1 state on PCF activation (see the Supporting Information, Section S2). Which of the two approaches gives results that are closer to the experimental picture? Because the energies of individual LHCII chromophores are hard to determine in the presence of multiple chromophores of the same type, we matched our gas-phase results to single-chromophore spectra in a solvent. Comparing the gas-phase Chl energies to experimental spectra in acetone,[5] DFT/MRCI reproduces the excitation band maxima very well (within < 0.1 eV). Even though vertical excitations do not strictly match experimental peaks, they should be energetically close.[24b] We can thus conclude that DFT/MRCI likely provides us with a trustworthy picture for Chl. In the case of Vx and Zx, we made a more elaborate comparison to experiment (see the Supporting Information, Section S3). Briefly, we find that both CAM-B3LYP and DFT/MRCI provide a qualitatively good description of the Vx/Zx 1Ag !1Bu absorption, with the TD-DFT results being slightly blueshifted compared to experiment. This is in line with what we had found before for the case of the isolated Vx and Zx molecules in the gas phase or in acetone, for which the results of the CAM-B3LYP plus

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CHEMPHYSCHEM ARTICLES DFT/MRCI approach are typically within 0.1 eV of the experimental values.[24] A noteworthy effect observed at the DFT/MRCI level of theory is the strong mixing of the xanthophyll 2Ag and 1Bu states in the PCF (e.g. indicated by the sharing of oscillator strength), which makes the 2Ag state actually appear “bright” through increased single-excitation character. The energy difference between the two states is similar in the gas phase (0.35 eV) and in the PCF (0.27–0.3 eV), but the oscillator strength is shared only in the PCF, both for Vx and Zx. The two lowest singlet excited states of Zx are indeed quite mixed in the PCF (for detailed data see the Supporting Information, Section S4). Unfortunately, it is difficult to assess this further by comparison to experimental data, because this would require measurements on single chromophores within a chromophore cluster (not yet available). It is, however, experimentally known that the fluorescence of xanthophylls is negligible, which implies fast internal conversion down to the ground state.[41] The current DFT/MRCI results support the notion that the LHCII environment induces some mixing between excited states, at least for the 1Bu/2Ag pair at the ground-state geometry.

2.3. Electronically Excited States at the 1Bu Minimum 2.3.1. The Effect of the Environment on Xanthophyll State Crossing In the 1Bu geometry optimizations of our model systems, all non-hydrogen atoms of Chl were kept frozen (see above). It is thus not surprising that TD-DFT predicts the changes in the Chl excited-state energies to be less than 0.05 eV on going from the 1Ag to the 1Bu minimum structure (except for a drop by about 0.5 eV for the CT states, see Table 1). At the TD-DFT level of theory, the 1Bu state is lowest in energy, that is, below the Chl Q states, and there are only minor differences between its gas-phase and PCF energies (at most 0.08 eV, for both Vx and Zx). At the DFT/MRCI level of theory, all xanthophyll states show a significant drop in energy, and introducing the environment leads to an effect that we had already observed before in computations with implicit solvent (albeit in the opposite direction):[24b] On going from the 1Ag to the 1Bu minimum, 2Bu drops below 1Bu in the gas phase, but accounting for the environment prevents this state crossing. Considering the computational error bars, it is hard to tell whether the environment actually prevents or provokes a state crossing. However, the results do indicate that state crossings generally depend on environmental conditions. This is in line with what we had found before for free Vx and Zx in the gas phase and acetone.[24b] 2.3.2. Differences between Vx and Zx We now investigate whether Vx and Zx exhibit any special photophysical features. At the 1Ag ground-state geometry, there were no obvious differences between the two xanthophylls (e.g. with regard to state order, state character, etc.). This is not surprising in view of their geometric similarity (general orientation: Figure 1, BLA: Figure 2).  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org At the 1Bu excited-state minimum, however, the Zx 1Bu state relaxes below the Chl Q states, whereas the Vx 1Bu state stays energetically above according to DFT/MRCI calculations on frozen Chl and PCF. As already explained, this effect is created to some degree by the presence of the PCF: in the gas phase, the 1Bu state of Vx and Zx remains above the Q band, and 2Bu below. To our knowledge, this is the first instance of a small, yet potentially important, photophysical difference between Vx and Zx in computational modeling. In summary: 1) The PCF apparently causes a systematic spectral redshift at the TD-DFT level of theory (especially for the CT states) that is not found at the DFT/MRCI level of theory. 2) In the presence of the PCF, the 2Ag and 1Bu states of Vx/Zx seem to mix more strongly, since they readily share oscillator strength. This mixing is seen at the 1Ag minimum, but not at the 1Bu minimum. 3) An environment-dependent change in 1Bu/2Bu state order is observed when the PCF is switched on and off, in agreement with our previous report.[24b] 4) The energies of the Vx and Zx 1Bu minimum structures are above and below the Chl Q band, respectively, when taking account of the protein environment through the PCF. 2.4.

Transition Dipole Orientation

We showed above that the relative positions of the state energies change on going from the 1Ag to the 1Bu minimum; the resulting state order is different for Vx and Zx. We now address the question whether there is an effect on intermolecular energy transfer as well. For this, we look at the relative orientation of the transition dipoles ~ m. We only discuss the DFT/MRCI results, because they allow for a more complete picture covering the bright and dark states of Vx/Zx. At the DFT/MRCI level of theory, we compute each chromophore individually, and hence the sign of the scalar product of two ~ m is arbitrary. Thus, we focus on the collinearity [Eq. (1)]: c ¼ jqð~ m0n ;~ m0m Þ  ðp=2Þj=ðp=2Þ

ð1Þ

where qð~ m0n ;~ m0m Þ represents the angle between the transition dipole moments ~ m for the transition from the ground state to state n or m. c can take on values between 0 and 1, with 0 repm0m Þ value of p/2 and 1 a qð~ m0n ;~ m0m Þ value of resenting a qð~ m0n ;~ 0 or p. In a simple point-dipole picture, collinearity of the transition dipole moments is a basic prerequisite for two transitions to exhibit state coupling, and a lack of collinearity (angle of p/2 between the two transition dipoles) prevents interaction between the states.[42] Other factors, such as the lengths of the transition dipoles and the distance between the chromophores, are also important for the coupling strength; however, the latter does not change on PCF activation and the former stays roughly the same, except for a few cases of strongly changing oscillator strengths that were discussed above. Table 3 lists the c values obtained from DFT/MRCI for the PCF models at the ground-state minimum and their changes relative to the gas phase. The use of efficient wave-function-based methods might allow for excited-state calculations on the complete system in the future and thus solve the sign probChemPhysChem 2014, 15, 3392 – 3401

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Table 3. DFT/MRCI collinearities of the transition dipole moments ~ m for the given pair of states [Eq. (1)] at the 1Ag or 1Bu minimum geometries.

States

1Ag, PCF (change from gas phase) Vx or Chl Zx or Chl[a]

1Bu, PCF (change from gas phase) Vx or Chl[a] Zx or Chl[a]

2Ag/Qy 2Ag/Qx 1Bu/Qy 1Bu/Qx 2Bu/Qy 2Bu/Qx 2Ag/Soret1 2Ag/Soret2[b] 1Bu/Soret1 1Bu/Soret2[b] 2Bu/Soret1 2Bu/Soret2[b]

0.28 0.40 0.26 0.39 0.21 0.33 0.31 0.52 0.30 0.50 0.33 0.44

0.19 0.22 0.27 0.40 0.26 0.39 0.30 0.34 0.32 0.52 0.31 0.50

(+ 0.09) (+ 0.13) (+ 0.04) (+ 0.14) (0.03) (+ 0.12) (0.13) (0.12) (0.04)

0.28 (+ 0.09) 0.40 (+ 0.13) 0.26 (+ 0.04) 0.39 (+ 0.14) 0.21 (0.03) 0.33 (+ 0.12) 0.31 (0.14) 0.52 0.30 (0.13) 0.50 0.33 (0.01) 0.44

(+ 0.04) (0.09) (+ 0.05) (+ 0.14) (+ 0.04) (+ 0.12) (0.17) (0.11) (0.13)

0.24 0.33 0.27 0.40 0.26 0.38 0.42 0.50 0.33 0.52 0.32 0.50

(+ 0.10) (0.01) (+ 0.05) (+ 0.13) (+ 0.04) (+ 0.10) (0.09) (0.12) (0.14)

[a] Only a single Chl DFT/MRCI calculation was performed in the presence of the Vx field at the 1Ag geometry. [b] Soret2 state not present in gasphase calculation (see the Supporting Information, Section S2).

lem.[43] Also, one could go beyond the simple picture of transition dipoles and employ the transition density cube method.[21] For the study at hand, we consider the point-dipole model to be an effective and sufficient tool.[42]

Figure 3. Graphical representation of the change in collinearity of transition dipole moments at the 1Ag minimum structure on introduction of the PCF (see Table 3). CT energies from TD-DFT; other data from DFT/MRCI. Vx and Zx have identical coupling schemes and similar energies; Zx energies shown. Dashed states only shown for reference, as discussed in the text and the Supporting Information (Section S2) for Soret2.

At the 1Ag minimum (see Table 3 and Figure 3), there is not shift mechanism.[14a] The excitation of higher states, namely, much difference between Vx and Zx and we therefore discuss 1Bu and the Soret band, is more involved. Assuming moderate them together. The close correspondence between Vx and Zx coupling, one might be inclined to expect population transfer is consistent with our expectation from their geometrical simibetween the Soret states and 1Bu, but also 2Bu and possibly larity. The collinearity between Chl and xanthophyll states is CT2 as well. Hence, the path of energy transfer does not seem slightly increased on introduction of the PCF, with one excepto be unique. Test calculations with geometry optimization of tion (the lowering between Soret1 and the xanthophyll states). a Soret state do not provide any change in state order and are In general, all Chl states are coupled to the xanthophyll states with c ranging from 0.21 to 0.52. The strongest coupling is found for Soret2 (c > 0.43 for all xanthophyll states), followed by Qx (all c > 0.32) and Soret1 (all c > 0.30). Since the differences between the interstate couplings are quite small on introduction of the PCF, the PCF seems to play the role of an equalizer that slightly increases collinearity in most cases at the cost of a decrease for a single state (Soret1). Let us consider an excitation event within the framework of our model. A Q-band excitation is trivial; the energy cannot decrease any further, except by decay to the ground state. Our present results thus do not allow for the transfer of excess Figure 4. Graphical representation of the change in collinearity of transition dipole moments at the 1Bu minimum Q-band energy via the 2Ag structure on introduction of the PCF (see Table 3). CT energies from TD-DFT; other data from DFT/MRCI. Dashed state, as proposed for the gearstates only shown for reference, as discussed in the text and the Supporting Information (Section S2) for Soret2.  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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CHEMPHYSCHEM ARTICLES therefore not discussed (data not shown). However, as outlined above, 1Bu optimization has a drastic effect on the order of states, and therefore we now analyze the situation at the 1Bu minimum in more detail. At the optimized 1Bu excited-state geometry (see Table 3 and Figure 4), the collinearities found at the 1Ag minimum are mostly conserved. This is surprising, because the geometry of the xanthophyll strongly affects the state energies and the state order. Also, the effect of the environment at the 1Ag and 1Bu minima is very similar, with a single exception: the transition dipoles of 2Ag and Qx are more collinear at the 1Ag than at the 1Bu minimum (0.40 versus 0.22 for Vx or 0.33 for Zx). This change arises from the environment: the PCF enhances the collinearity at 1Ag (+ 0.13) and reduces it at 1Bu (0.09 for Vx, 0.01 for Zx). However, at the 1Bu minimum, 2Ag cannot act as a donor/acceptor state for the Q band, since the system is in the 1Bu state. Therefore, the increased 2Ag/Qx coupling in the PCF can be regarded as irrelevant for population transfer. For a populated 1Bu state, the coupling picture roughly remains the same at both minimum structures with regard to the influence of the PCF and the equivalence of Vx and Zx (except for the 2Ag/Q coupling). In this section we rely on DFT/MRCI results for the transition dipoles, and hence we miss the CT states in our analysis (not computed at the DFT/MRCI level of theory). We emphasize, however, that the employed point-dipole scheme of Equation (1) strictly only holds for excitations located at different chromophores. Since the investigated CT states involve both chromophores simultaneously, they cannot be treated by the point-dipole approximation. An assessment of the effects of CT states on intermolecular energy transfer would thus require a more elaborate approach, for example, by using excitedstate scans of models including both chromophores to find state crossing points.

www.chemphyschem.org states. If we add up the oscillator strengths of Soret1 and Soret2 (about 0.5 each), we obtain a ratio f(Soret)/f(1Bu) of about 1:3.5; thus, one should expect that about one in five absorption events actually excites the high-energy Chl bands. This, of course, is for the case of a single Chl/Vx pair; in the full system, there are a multitude of chlorophylls present in LHCII that may absorb as well. If Soret absorption occurs, the 1Bu state seems energetically well positioned to accept Soret Chl population and then evolve as outlined below. We note that a Soret1 test minimization gave an energy drop from the Franck–Condon point to the Soret1 minimum of less than 0.1 eV (data not shown). Consequently, the 1Bu state should remain in reach even after Soret relaxation. Direct energy transfer from the Soret to the Q band is likely to be more difficult because the energy gap is larger than 0.5 eV (experimental value in solution).[46] A radiationless coupling mechanism involving a strong geometric distortion to overcome a gap of 0.5 eV may be problematic in the framework of a restricted protein environment.[49]

3. Discussion Our computational model predicts the Vx or Zx 1Bu excitation energy to be in the range of the Soret band at the groundstate geometry, and in the range of the Q band at the relaxed 1Bu geometry. This may well be expected to be a general feature of carotenoids. Given the evidence for an overall medium coupling between the states of Chl and Vx or Zx, it appears that Soret-state energy may be transferred to 1Bu and then converted into Q-band energy. We address this in more detail below, after discussing other possible pathways. Transfer of excess Q-band energy via 2Ag appears unlikely,[14a] because the 2Ag state is computed to be energetically above the Q band at the 1Ag geometry for both compounds. Taking into account the methodological error (about 0.2 eV[40] compared to high level theoretical methods), the energy gap (about 0.35 eV) between 2Ag and the Chl Q states is large enough to cast doubt on a direct (uphill) Q!2Ag energy transfer for the investigated chromophores. In our model, the Q bands are the lowest excited states at the 1Ag geometry, and there are no xanthophyll-based acceptor states, including CT states.[20] Other potentially absorbing states are the Soret  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Figure 5. Proposed Soret!1Bu !Q transfer scheme; potentially less efficient for Zx (minimum below Q).

Energy transfer from Vx/Zx to Chl, however, seems feasible, with a slight preference for Vx!Chl transfer, because the Zx 1Bu state apparently relaxes to an energy below the Chl Q band. Many experiments in the past have produced a picture much in favor of an efficient carotenoid!chlorophyll energy transfer,[13, 44] although there are also some experiments with contrasting results.[10] We note in this context that the cited experimental work involved chlorophyll a, whereas we investigated coupling to chlorophyll b. A graphical representation of the proposed Soret!1Bu !Q pathway is given in Figure 5. For the xanthophylls, energy transfer seems more likely for Vx than for Zx, because the 1Bu state hovers energetically slightly above the Chl Q band after relaxation, which mostly involves (presumably fast) changes in the BLA. We found that ChemPhysChem 2014, 15, 3392 – 3401

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CHEMPHYSCHEM ARTICLES the minimum-energy path of Zx/1Bu ends up below the Qband energy. It may be still in range for hot 1Bu vibrational substates to reach the Q band, but owing to the well-known fast internal conversion in carotenoids, quick relaxation to the ground state could be the dominant mechanism.[41, 45] As the relevant computed energy differences are in the range of the methodological uncertainties, comparison to experimental data is imperative. It is known that the Qy absorption band of LHCII displays a shoulder at 650 nm,[46] which corresponds to chlorophyll b absorption at 1.9 eV. Assuming this to be close to the Qy 0–0 transition energy, our computed value should be slightly higher, owing to missing zero-point energy (ZPE) and relaxation effects. As such, our DFT/MRCI value of 2.01 eV seems realistic. What remains are potential errors in the Vx/Zx 1Bu energies, yet these are probably small, because we have shown before that the DFT/MRCI plus TD-CAM-B3LYP approach is a good combination for describing Vx/Zx excited-state geometries (see also the Supporting Information, Section S3).[24b] From the calculated energies at the 1Bu minimum, we would expect 1Bu fluorescence to occur around 1.98 eV (Zx) and 2.12 eV (Vx), potentially at slightly lower energies, owing to ZPE effects and transitions to higher vibrational levels of the ground state. This puts the signal of the 1Bu state in the range around 600 nm, a region indeed attributed to the fluorescence from the 1Bu state.[45] There is some experimental evidence for a state crossing in solution (the so-called S* state would correspond to 2Bu here), which leads to a ladder of states all the way down to the ground state through internal conversion.[16c, 17b, c] In the DFT/MRCI calculations, introduction of the PCF around Vx (Zx) changes the 1Bu energy by 0.19 (0.22 eV), increases the 2Bu energy by 0.09 (0.12 eV), and thus prevents state crossing in the LHCII environment. The present LHCII/PCF results are qualitatively similar to our previous gasphase results for free Vx and Zx (no state crossing).[24b] However, given the small computed energy differences and their error bars, we can only safely state that the two Bu states become close in energy on 1Bu relaxation, regardless of the environment, but we cannot be definite about the occurrence or absence of state crossing. Overall our present model is consistent with recent measurements and theoretical findings from previous DFT/MRCI calculations on carotenoids.[16c, 17b, c] In any event, it is intriguing that the presence of the environment (through its impact on the chromophores) exerts some degree of control on the 1Bu/2Bu crossing, and thus possibly on the 1Bu lifetime. Concerning the proposed[47] potential excitonic coupling between Vx/Zx and Chl, an incomplete TD-DFT geometry optimization of the 1Bu state of the Vx/Chl pair (both chromophores free to move, see the Supporting Information, Section S5) indicates that the orbital mixing between Qy and 1Bu increases during the optimization, which terminated on approaching state degeneracy. This may be taken as support for the possibility of 1Bu/Qy state coupling and for the notion that the xanthophyll molecules may play a role in donating population to the Q band.[13, 15] With this in mind, it appears that xanthophylls, and possibly carotenoids in general, can play two roles with regard to sin 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

www.chemphyschem.org glet energy pathways. First, they may reduce Chl Soret excitation by competing for photons in the same energy range. Second, if Soret excitation occurs, they may serve as an acceptor of Soret energy. There would seem to be at least two benefits of such a Soret!1Bu pathway. On one hand, 1Bu could possibly transfer energy to the Q-band states by the mechanisms outlined above. On the other hand, Chl is de-excited out of the Soret band and ready to receive a new photon. Thus, carotenoids might effectively act as a Soret!Q shortcut.

4. Conclusions By using TD-DFT and DFT/MRCI, we investigated whether xanthophylls, and carotenoids in general, may assist in energy transfer from the chlorophyll Soret band to the Q band. All relevant UV/Vis states of Vx, Zx, and Chl and their couplings were analyzed at selected ground- and excited-state geometries; the events following the relaxation of the xanthophyll 1Bu state, the most strongly absorbing state in these systems, were studied. In the ground state, Vx and Zx show similar properties. At the 1Bu minimum, the energy of the Zx 1Bu state is below the Chl Q band, in contrast to Vx. Both Vx and Zx may act as acceptors of Soret-state energy; transfer to the Q band seems to be favored for Vx. These findings suggest that carotenoids may generally mediate Soret-to-Q energy flow in LHCII.

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Received: April 11, 2014 Published online on September 1, 2014

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