Vibrational Relaxation in Carotenoids as an Explanation for Their

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B: Biophysics; Physical Chemistry of Biological Systems and Biomolecules

Vibrational Relaxation in Carotenoids as an Explanation for Their Rapid Optical Properties Jan Philipp Götze J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b09841 • Publication Date (Web): 19 Feb 2019 Downloaded from http://pubs.acs.org on February 19, 2019

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The Journal of Physical Chemistry

Vibrational Relaxation in Carotenoids as an Explanation for Their Rapid Optical Properties Jan P. Götze* Freie Universität Berlin, Institut für Chemie und Biochemie, Physikalische und Theoretische Chemie, Takustr. 3, 14195 Berlin e-mail: [email protected] Abstract We propose the ultrafast S2 (1Bu) to S1 (2Ag) “electronic internal conversion” observed in carotenoids to be a vibrational relaxation of the 1B u state. This suggestion arises from comparing excited state geometries computed with the CAM-B3LYP density functional to the ground states; it is found that each conjugated atom moves less than 5 pm for, e.g., violaxanthin. However, the changes of excitation energies are large, ranging from 0.4 to 1.2 eV. This is connected to the size of the conjugated system: While each atom only contributes 0.02 to 0.06 eV, the sum amounts to the observed shift. Additional analysis of computational data is provided, from new or already published calculations. As the mechanism may be valid for all linear polyenes, the model has implications that go beyond the presented case of carotenoids. Finally, four sets of experimental data on carotenoids published elsewhere are reinterpreted. The model predicts near-IR absorptions and transient femtosecond infrared spectra within 0.1 eV accuracy. Introduction In most photosynthetic organisms, antenna complexes provide the energy fueling the reaction centers.1 These complexes employ chlorophylls (Chls), performing core functions like energy absorption and transfer. Additional chromophores are often present; prominently, carotenoids (Crts) are found in many Chl-carrying proteins.2,3 Their role has been attributed to photoprotection and supporting the light absorption.4–6 The major difficulty regarding the role of Crts is the complexity of their spectroscopic features. Crts exhibit a rapid change in state energies upon excitation, with almost no further spectral evolution.7 It was thus proposed that Crts exhibit fast internal conversion (IC), making them attractive for deactivation of harmful Chl excitations, i.e., non-photochemical quenching.8 Measurements and simulations of several β-carotene-like Crts,7 like violaxanthin (here: Vx), zeaxanthin (Zx)9 and peridinin (Pn),10 have led to the IC proposal. Most Crts share a strong excitation from the ground state (1Ag) to a state with Bu symmetry (1Bu). A fast change to lower energies follows, which is interpreted as IC between the 1Bu and S1 (2Ag) states, fulfilling Kasha’s rule.11

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Figure 1: Features of the compounds presented in this study. A: Structures and abbreviations. B: Vertical electronic state scheme for xanthophylls/carotenoids with conjugated chain lengths comparable to β-carotene. Abs: Absorption, Fl: Fluorescence, IC: Internal conversion. Solid arrows: radiative, dashed arrows: non-radiative. Fluorescence reported to appear from 1Bu and weakly from 2Ag.43 A structural representation of the Crts investigated in this study is found in Figure 1A; a vertical Crt state order scheme is given in Figure 1B. The latter scheme is not trivial to obtain in simulations. The 2Ag state, when treated with single-reference methods such as configuration interaction singles (CIS12) or time-dependent density functional theory (TD-DFT13–15), is energetically not located between 1Ag and 1Bu, but higher energies. This is rationalized by a significant amount of double excitation character for 2A g.16–18 Using the Tamm-Dancoff approximation (TDA19,20), the problem can be partially overcome. Regardless, it is common to employ only relaxed ground state geometries and vertical excitations when modeling Crts. 21–24 Consequently, there are only few reports of relaxed excited state Crt geometries.16,25,26


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Figure 2: Changes between CAM-B3LYP/6-31G(d) geometries of various Crts. 1Ag (ground state, atom-specific colors) and 1Bu minimum (dark blue) of violaxanthin (Vx), zeaxanthin (Zx) in a continuum solvation model (acetone), peridinin (Pn) in cyclohexane and 8-apocarotenal (8apo) in chloroform. Numbers indicate the actual displacement of each conjugated carbon atom (in pm) after structural alignment. 1Bu geometry of Vx is shown, but the blue highlighting was omitted as the structures are so similar that the blue color would cover the whole molecule. Several research groups were able to obtain relaxed structures for the 1Bu state of Vx, Zx and Pn.17,25–29 Based on the related findings, this article will propose an alternative to the IC ACS Paragon Plus Environment


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pathway. Specifically, it was found that relaxed 1Bu geometries are very close to the ground state structure, i.e., the Franck-Condon (FC) point.25 Still, the structures show drastically different excitation energies (|ΔΔE(1Ag →1Bu)| >= 0.4 eV, up to 1.2 eV). TD-DFT and a DFTbased multireference configuration interaction approach (DFT/MRCI 17,30) support this picture; the results agree with the Pn photophysics proposed by Wagner et al., 27 who used CIS and equation of motion coupled cluster singles doubles (EOM-CCSD31). As we find Vx and Zx to be similar,28 the strong change in 1Bu energy upon relaxation might be a common feature for βcarotene-like Crts. A vibrational relaxation pathway Despite the displacements during excited state relaxation being minute (Figure 2), they still affect the Crt energies. We propose that the apparent ultrafast IC process in Crts is truly a vibrational relaxation of the 1Bu state, which might be fast due to almost negligible displacements. After presenting the employed methods, we will discuss the conformations of 1Ag and 1Bu. Then, four experiments from various sources will be reinterpreted using our model. Note that we do not deny the possibility of 2Ag being the “state of interest”. Without a reliable computational approach towards 2Ag gradients and Hessians, this is not possible. We instead aim to show that the 1Bu state suffices for the interpretation of Crt spectra. Methods Our approach resembles earlier calculations; all DFT/MRCI16,30 data is from earlier work, with kind permission from Prof. Walter Thiel. A review of the method reliability can be found in the SI. For new calculations, the CAM-B3LYP32 functional and a 6-31G(d)33 basis set were employed using the Gaussian16 program package. 34 The PCM35 solvation was used, in contrast to CPCM36 from earlier work, with equilibrium solvation.37 Images were created using VMD.38 Regarding the possibility of using TDA: TDA-TD-DFT with CAM-B3LYP did not show any improvements compared to regular TD-CAM-B3LYP; in line with the results reported elsewhere.19 2Ag remains inaccessible within the CAM-B3LYP framework. Recently, procedures have been devised to directly obtain UV/vis excitation energies from longrange corrected TD-DFT, as the vertical energies from those approaches are typically blue shifted with regards to the experimental maxima.39,40 It should be noted that we do not employ these corrections as we mostly aim for a qualitative comparison. For quantitative results, we also prefer the vibrational broadening of our spectra, which has been shown to produce excellent results (see SI). Results Model outline (I) 1Bu and 1Ag geometry The conformational changes upon relaxing the 1Bu state for various Crts is provided in Figure 2. The Vx/Zx structures are from previous work.25 The changes in geometry between 1Ag and 1Bu are mostly in the range of 1-15 pm for the ring-terminated Crts. These differences are slightly larger for Zx, due to the conjugated system extending into the terminal rings. It is known ACS Paragon Plus Environment

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that excitation of compounds like Zx and β-carotene leads to ring rotation.25,29,41 8apo exhibits the largest displacements, which we attribute to the lack of one terminal ring. At last for Zx, the ring rotations do not affect the vertical absorption energies (ΔE); those are controlled by bond length alternation (BLA).16,17,26,28 It was shown that the effect of the terminal rings does not exceed 0.05 eV.25 The cases in acetone or cyclohexane are likely more prone to geometry changes than protein-embedded Crts (see SI). A protein reduces conformational flexibility, slightly diminishing the differences between 1Ag and 1Bu. Therefore, we expect the changes in ΔE to be similar throughout all presented compounds. (II) Vertical energies before/after 1Bu relaxation Table 1: Vertical 1Ag →1Bu excitation energies (ΔE, in eV) of different Crts at their respective state minimum geometries; their differences and average contribution per conjugated atom to the difference. DFT/MRCI (Pn: gas phase) data from elsewhere;25 for Zx, the energetically most stable rotamer was chosen. Pn with CAM-B3LYP/6-31G(d) in cyclohexane; Vx or Zx in acetone (all cases). DFT/MRCI data on 8apo not available, see SI. CAM-B3LYP

DFT/MRCI

1Ag

1Bu

ΔΔE per conj. atom

1Ag

1Bu

ΔΔE per conj. atom

Vx

2.82

1.73

-1.09 -0.054

2.68

2.29

-0.39 -0.020

Zx

2.77

1.53

-1.24 -0.056

2.56

2.15

-0.41 -0.019

Pn

2.72

2.03

-0.68 -0.040 to -0.034 2.77

2.31

-0.46 -0.027 to 0.021

For the cases shown in Figure 2, the absorption energies at different geometries are listed in Table 1 (with the exception of 8apo due to the lack of DFT/MRCI; see SI). Both DFT and DFT/MRCI predict a strong drop in excitation energy for all presented cases when forming the 1Bu minimum, about 0.7 to 1.2 or 0.4 eV, respectively. The structurally more complex Pn exhibits about half the ΔΔE of Vx or Zx. Looking at the minute displacements of few pm per conjugated carbon atom, ΔΔE is surprisingly large. ΔΔE is mostly controlled by two factors: First, as 1Bu is optimized, 1Ag goes up in energy. This is a consequence of the FC point being the 1Ag minimum, and it is the reason for the differences in ΔΔE between DFT and DFT/MRCI (DFT/MRCI 1Ag is almost unaffected by 1Bu relaxation; data not shown). The second factor is the size of Crt conjugated system. This has broader implications, as minute changes in the BLA lead to a strong total ΔΔE. We can break down ΔΔE in DFT (or DFT/MRCI) into the average contribution for each conjugated atom. For Vx, 20 conjugated carbon atoms are present, resulting in an average contribution of only -0.054 (-0.020) eV. For Zx with 22 conjugated carbons, the contribution is 0.056 (-0.019) eV. Pn is different as it involves an sp-hybrid carbon, as well as a lactone ring. Pn conjugation therefore may range from 17 up to 20 atoms, leading to an average contribution between -0.040 (-0.027) to -0.034 (-0.021) eV. The supporting information contains this analysis for 8apo, but only on the level of DFT. It was found that the average contribution in 8apo is -0.031 (gas phase) and about -0.050 (solvent) eV per conjugated atom. Apparently, the effect of a solvent environment on ΔΔE is strong and needs to be properly represented, that might explain the differences between DFT and DFT/MRCI. Combining Figure 2 and Table 1, doubts arise regarding the 1Bu → 2Ag IC mechanism. The energy differences from the conformational relaxation alone may already explain the changes ACS Paragon Plus Environment


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in measured spectra. Relaxation can be expected to occur fast as the distances are small. The BLA can thus be expected to adapt within the time frame of C-C stretch oscillations. (III) Time estimate After 1Bu normal mode analysis (see SI), the mode to likely control the BLA in Vx (Zx) is at 1630 (1567) cm-1. The oscillations take 20.5 (21.3) fs; the corresponding BLA may thus be reached within far less than 1 ps. For a purely IC-based mechanism, the atoms would thus have to be basically frozen in position during the 1Bu life time. (IV) 2Ag energy at 1Bu minimum Figure 2 and Table 1 only provide data regarding the relative positions of 1B u and 1Ag. Regarding the dark 2Ag state, DFT/MRCI calculations have shown that the 1Bu-2Ag energy gap becomes larger when relaxing 1Bu (see also Figure 3).26 For Vx in acetone it has been reported that the vertical energy difference between 1Bu and 2Ag is 0.35 eV at the FC point, but 0.80 eV at the 1Bu minimum geometry.25 IC between 2Ag and 1Bu thus appears to become less likely when 1Bu relaxes: the energy surfaces are divergent. Note that in Pn, the two states are indeed crossing/mixing. Looking at the work by Wagner et al.,42 this is likely the major feature distinguishing Pn from other β-carotene-like Crts.28 Without a computational method to efficiently scan the 2Ag surface, conclusions regarding a 1Bu/2Ag crossing remain speculative.

Figure 3: DFT/MRCI energy levels at the 1Ag and 1Bu DFT minima. Energies relative to 1Ag at its minimum geometry. The exact methodology can be found elsewhere. 29 Left: Vx in in a light harvesting complex II environment. To preserve binding pocket polarization for the DFT/MRCI approach, a continuum model mimicking acetone was applied during the generation of the orbitals. Percentages indicate the sum of multi-electron excitation character in the respective state, compared to the DFT single reference ground state configuration. Right: Pn in the gas phase. For each state, oscillator strengths are given above (for the 1Ag case, as this does not require special implementation, the oscillator strengths for an acetone environment are provided in parentheses). ACS Paragon Plus Environment

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Model applications (I) Transient near-IR spectra of violaxanthin and zeaxanthin Transient near-IR spectra represent the transition from and to electronically excited states. For Vx, DFT/MRCI spectra for Vx/Zx 1Ag and 1Bu geometries were computed in a protein environment,26 therefore a comparison to published transient near-infrared spectra43 is possible. Figure 3 shows the corresponding energies and labels. The multi-electron excitation character is very similar (65%/65%/70%); additional analysis is thus required. Proper labeling is required to make predictions on which transitions are experimentally observable. We tentatively assign the labels in Figure 3, right side, based on the 1Ag → X oscillator strengths found in Table S 3 (see SI for corresponding discussion). Our 1Bu → X absorptions at the 1Bu minimum reproduce the transient near-IR absorption spectra. The computed ΔE values of the 1Bu → X transitions are 1048 (2Bu) and 6533 cm-1 (3Ag), of which only the latter should be allowed. Taking the transient absorption spectra from Polivka et al. (methanol or protein),43 experimental peaks are located at 6950 cm-1 in methanol and 6500 cm-1 for protein. For Zx, the analogous discussion as above can be derived from the energy values reported elsewhere.26 The corresponding computational Zx signal is located at 6372 cm-1, compared to an experimental 6200 cm-1 in protein. Hence, the new model works well for Vx (Zx) transient near-IR spectra, reinterpreting the experimental 6500 (6200) cm-1 signals to be a 1Bu → 3Ag transition computed at 6533 (6372) cm-1. However, a similar agreement for a 2Ag → X transition computed at a 2Ag minimum cannot be ruled out. For example, a 2Ag → 2Bu transition at the 1Bu minimum would produce a Vx signal at 5800 cm-1, which is also within an acceptable range compared to the experiment. We will thus now discuss the more complex case of Pn. (II) Transient near-IR spectra of peridinin For Pn in n-hexane, the excited state absorption should arise from the corresponding non-polar excited state minimum. DFT/MRCI (gas phase, including unpublished data28) predicts the 1Bu → X excitations, in cm-1, to be located at 3145 (Ag), 7178 (Bu), 7743 (Ag), 9275 (Ag), 10727 (Bu), 11777 (Ag) and 11856 (Bu) with state labels assigned based on their 1Ag → X oscillator strengths. Note that the state at 3145 cm-1 was given Bu symmetry in the original paper, this is hereby corrected (Figure 3, left). Measured 1Bu → X absorption peaks should thus be close to 3145, 7743, 9275 and 11777 cm -1. The experiment, starting at 5500 cm-1, shows a large peak until 8000 cm-1, a small peak at 9600 cm-1 and a larger peak at 11450 cm-1.44 Thus, taking 1Bu as the starting point of the spectrum generation reproduces the measured excited state absorption within 0.05 eV (about 400 cm-1) accuracy. A discussion of a recent related experiment by Redeckas et al.45 can be found in the SI.



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Figure 4: DFT-calculated TIR spectra of Pn (FWHM: 15 cm-1); linear combinations of 1Ag and 1Bu spectra, weights indicated in legend, minus the 1Ag spectrum. Calculated spectra shifted by -25 cm-1 to account for errors of harmonic approximation. Experimental spectra (excitation at 400 nm) given for comparison, adapted with permission from Di Donato and coworkers, The Journal of Chemical Physics (2015), Vol. 142, article 212409. (III) Transient infrared spectra of peridinin Di Donato and coworkers have shown the transient infrared (TIR) spectra (200 fs to 300 ps delay) of Pn in cyclohexane and chloroform.46 In our model, the spectroscopically relevant movement of the nuclei may occur in the sub-200 fs region, inaccessible to the measurements. Still, the computational Crt model should be able to predict the IR spectra. As it may also explain ACS Paragon Plus Environment

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Figure 5: DFT-calculated TIR spectra of 8-apocarotenal (FWHM: 15 cm-1). Spectra are linear combinations of 1Ag and 1Bu spectra (weights indicated in legend) minus the 1Ag spectrum. All spectra shifted by -25 cm-1 to account for errors of harmonic approximation. Experimental spectra (excitation at 400 nm) given for comparison, adapted with permission from Di Donato and coworkers, The Journal of Physical Chemistry B (2014), Vol. 118, pages 9613-9630. the temporal evolution of the IR signals, a qualitative analysis of the spectral evolution can be found in the SI. Taking our Crt model for Pn (Figure 3, right), two initially excited populations exist.27,28 Those states are very close in energy and oscillator strength, which is different from other β-caroteneACS Paragon Plus Environment


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like Crts. A special feature of Pn appears to be that the polarity of the environment determines the relative absorption intensities. This solvent sensitivity is experimentally well established.10 It was shown computationally that more polar environments affect the absorption strength of the lower-energy 1Ag → 2Ag transition.16,28 The Pn 2Ag state is a state with partial charge transfer character, resulting in its solvent sensitivity. A direct comparison of calculated Pn spectra at the 1A g and 1Bu minima in gas phase, cyclohexane and chloroform can be found in Figure 4. The resulting spectra qualitatively represent the experimental peaks, with wavenumbers shifted upwards. E.g., in the case of chloroform, a small feature at 1533 cm-1 and a large feature at 1630 cm-1 is expected from experiment; they are found at 1560 cm -1 and 1790 cm-1. A system including two explicit chloroform molecules forming hydrogen bonds to the lactone ring section slightly improved the spectrum, indicating that a full explicit solvation might result in proper peak for the region >1650 cm-1. Still, the Pn case suffers from the major drawback that the nature of the final relaxed state is defined by the solvent polarity. It is therefore difficult to argue that the spectra in Figure 4 represent the conformations and electronic states of interest, although all required features are present. We will thus continue with a simpler carotenoid in the next section. (IV) Transient infrared spectra of 8apo The 8apo TIR spectra can be found in Figure 5. The spectra match the experiment well for cyclohexane/gas phase (non-polar).47 For chloroform, we find a moderate agreement only for explicit solvent; and only for up to 1600 cm-1. The signals between 1600 and 1800 cm -1 in the experiment likely arise from various solvent orientations. Regardless of the chloroform results, the match between theory and experiment in the non-polar case is remarkable. The experimental spectrum in cyclohexane shows a band at 1750 cm-1 which is delayed by 13 ps compared to the rest of the spectrum. Just as for Pn, we suggest that this is due to solvent reorganization, as the delayed band is a signal from the polar, solvent-exposed terminal ketone group. Discussion A model for the initial photoabsorption of Crts has been presented. A crucial novelty is the prediction of very small changes in geometry upon formation of the brightly absorbing 1Bu state, which are still impactful for the energies. We reproduce the experimental excitation and fluorescence spectra with 0.05 to 0.1 eV accuracy. The model agrees with several sets of transient infrared and near-IR spectra. As the model strictly does not require any 1Bu → 2Ag IC process, it also does not violate pseudoparity selection rules.48,49 Even though for Crts like Zx relaxation is more involved due to ring rotations, we expect spectroscopically relevant changes to take place within a few C-C stretch mode oscillations (less than 1 ps). On average, each conjugated atom is found to contribute 0.050 (TD-DFT) or 0.02 (DFT/MRCI) eV to ΔΔE. The model was put to the test by application to several published experiments. TIR spectra for Pn and 8apo are well represented. Transient absorption spectra are reinterpreted as a 1Bu → 3Ag process. The computed excitation energies compare well to experiment (Vx: 6500 cm-1 exp. vs. 6533 cm-1 comp.; Zx: 6200 cm-1 vs. 6372 cm-1). The model is also able to reproduce Pn excited state absorption to 0.05 eV accuracy. Broader implications ACS Paragon Plus Environment

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The model is based on the notion that a larger conjugated system results in smaller structural changes upon UV/vis excitation. Consequently, the large change in energy is highly unintuitive, but it can be understood as the sum of many small changes of BLA. The larger the conjugated system becomes, the closer should be FC point and excited state minimum. Interestingly, the harmonic approximation becomes thus more valid the larger the system gets. Vibrationally broadened spectra in harmonic approximation are hence more justified than for smaller compounds. This may explain the corresponding recent successes concerning Crts.25,29,47 Energy transfer to Chl The Crt-Chl-coupling in biological systems is affected by our proposed model. Most importantly, interaction between 2Ag and the Chl Q band becomes nearly impossible from an energetical perspective. A relaxed 2Ag state should be located near the far-red end of the Chl fluorescence, making Förster transfer to Chl inefficient. Taking Figure 3 as example, 2Ag is at ~1.5 eV, about 800 nm (cf. the experiment by Frank and coworkers50). Switching to the 2Ag surface and subsequent relaxation could increase the excitation energy, but 1Ag would have to go down in energy. However, 1Ag has almost no potential to do so, as the minimum is energetically not far below. For DFT, it only is 0.3-0.4 eV above its minimum value. This sheds doubt on 2Ag relevance in terms of Chl coupling. Indeed, a recent femtosecond experiment on a lycopene/bacteriochlorophyll system reported no transfer to 2A g throughout the course of the measurements.4 Conclusions In our model, a relaxed 1Bu takes the former roles of 2Ag. With relaxation of the 1Bu state as explanation for the observed carotenoid spectroscopy, the only remaining “unusual” feature of Crts would be a violation of Kasha’s rule, which can be attributed to pseudoparity selection rules preventing a 1Bu → 2Ag IC. Supporting Information The online supporting information contains (I) an example of the geometry changes of Zx upon excitation in a protein environment, (II) information on the ΔΔE values for 8apo, (III) normal mode analysis for Vx and Zx, (IV) an analysis on the reliability of CAM-B3LYP in the context of Crts, (V) oscillator strengths of Vx at the 1Bu minimum. Further, we discuss an additional experiment as well as a more in-depth analysis of the temporal evolution during the transient IR spectra. Acknowledgements We thank the Deutsche Forschungsgemeinschaft (DFG) for funding (project 393271229), Dr. habil. Heiko Lokstein for advice and discussions, Prof. Walter Thiel for permission to use previously unpublished data. Credit also goes to Dr. Mariangela Di Donato, who shared spectra and valuable information, and Prof. Bettina Keller for providing resources and reading the manuscript.



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Quenching in Green Plants: Energies of the Lowest Excited Singlet States of Violaxanthin and Zeaxanthin. Biochemistry 2000, 39, 2831–2837.



TOC Graphic


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Features of the compounds presented in this study. A: Structures and abbreviations. B: Vertical electronic state scheme for xanthophylls/carotenoids with conjugated chain lengths comparable to β-carotene. Abs: Absorption, Fl: Fluorescence, IC: Internal conversion. Solid arrows: radiative, dashed arrows: non-radiative. Fluorescence reported to appear from 1Bu and weakly from 2Ag. 357x204mm (72 x 72 DPI)



Changes between CAM-B3LYP/6-31G(d) geometries of various Crts. 1Ag (ground state, atom-specific colors) and 1Bu minimum (dark blue) of violaxanthin (Vx), zeaxanthin (Zx) in a continuum solvation model (acetone), peridinin (Pn) in cyclohexane and 8-apocarotenal (8apo) in chloroform. Numbers indicate the actual displacement of each conjugated carbon atom (in pm) after structural alignment. 1Bu geometry of Vx is shown, but the blue highlighting was omitted as the structures are so similar that the blue color would cover the whole molecule. 364x402mm (72 x 72 DPI)


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DFT/MRCI energy levels at the 1Ag and 1Bu DFT minima. Energies relative to 1Ag at its minimum geometry. The exact methodology can be found elsewhere.29 Left: Vx in in a light harvesting complex II environment. To preserve binding pocket polarization for the DFT/MRCI approach, a continuum model mimicking acetone was applied during the generation of the orbitals. Percentages indicate the sum of multi-electron excitation character in the respective state, compared to the DFT single reference ground state configuration. Right: Pn in the gas phase. For each state, oscillator strengths are given above (for the 1Ag case, as this does not require special implementation, the oscillator strengths for an acetone environment are provided in parentheses). 311x197mm (72 x 72 DPI)



DFT-calculated TIR spectra of Pn (FWHM: 15 cm-1); linear combinations of 1Ag and 1Bu spectra, weights indicated in legend, minus the 1Ag spectrum. Calculated spectra shifted by -25 cm-1 to account for errors of harmonic approximation. Experimental spectra (excitation at 400 nm) given for comparison, adapted with permission from Di Donato and coworkers, The Journal of Chemical Physics (2015), Vol. 142, article 212409. 364x348mm (72 x 72 DPI)


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DFT-calculated TIR spectra of 8-apocarotenal (FWHM: 15 cm-1). Spectra are linear combinations of 1Ag and 1Bu spectra (weights indicated in legend) minus the 1Ag spectrum. All spectra shifted by -25 cm-1 to account for errors of harmonic approximation. Experimental spectra (excitation at 400 nm) given for comparison, adapted with permission from Di Donato and coworkers, The Journal of Physical Chemistry B (2014), Vol. 118, pages 9613-9630. 350x388mm (72 x 72 DPI)


Vibrational Relaxation in Carotenoids as an Explanation for Their

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