Excited state properties of the astaxanthin radical cation: A quantum chemical study

Chemical Physics 373 (2010) 2–7

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Excited state properties of the astaxanthin radical cation: A quantum chemical study Andreas Dreuw *, Jan Hendrik Starcke, Josef Wachtveitl Institute of Physical and Theoretical Chemistry, Goethe-University Frankfurt, Max von Laue-Str. 7, 60438 Frankfurt am Main, Germany

a r t i c l e

i n f o

Article history: Received 6 October 2009 In final form 7 December 2009 Available online 11 December 2009 Keywords: Quantum chemical calculations Excited states Carbonyl carotenoids Time-dependent density functional theory Carotenoid radical cations

a b s t r a c t Using time-dependent density functional theory, the excited electronic states of the astaxanthin radical cation (AXT+) are investigated. While the optically allowed excited D1 and D3 states are typical pp* excited states, the D2 and D4 states are np* states. Special emphasis is put onto the influence of the carbonyl groups onto the excited states. For this objective, the excited states of four hypothetical carotenoids and zeaxanthin have been computed. Addition of a carbonyl group to a conjugated carbon double bond system does essentially not change the vertical excitation energies of the optically allowed pp* states due to two counter-acting effects: the excitation energy should increase due to the –M-effect of the carbonyl group and at the same time decrease owing to the elongation of the conjugated double bond system by the carbonyl group itself. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Astaxanthin (AXT) (3,30 -dihydroxy-diketo-b,b-carotene-4,40 dione) is a so-called C40 carotenoid and belongs to the group of xanthophylls (greek xanthos = yellow, phyllos = leaf). AXT is a natural pigment and, for instance, responsible for the red color of shellfish. Among the xanthophylls, AXT has a particular structure, since it possesses eleven conjugated carbon–carbon double bonds and in addition two conjugated carbonyl groups located within the terminal b-ionone rings (Fig. 1). Owing to its structure, AXT is a very strong anti-oxidant and, as a result, efficiently scavenges free radicals. Its anti-oxidant potential exceeds the one of b-carotene, for example [1,2]. It has thus been hypothesized that supplementation with astaxanthin might be a practical and beneficial strategy in management of human health due to its neuro-protective and immune-modulating potential [3]. Today, most astaxanthin is produced by total chemical synthesis and is sold at a price of about $2.500 kg1 [4]. Besides their capacity to scavenge radicals, xanthophylls in general are known to quench singlet as well as triplet states of electronically excited chlorophylls [5–7], and are thus key players in the photo-protection mechanisms of photosynthetic organisms [8]. In particular, violaxanthin and zeaxanthin are involved in non-photochemical quenching of green plants [9–11], and it is supposed that zeaxanthin may act as a terminal quencher of excess excitation energy possibly via radical cation formation [12]. Due to its increased conjugated double bond chain of AXT compared to zeaxanthin, one may speculate AXT to be also a more efficient * Corresponding author. Tel.: +49 (0)69 798 29441; fax: +49 (0)69 798 29709. E-mail address: [email protected] (A. Dreuw). 0301-0104/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2009.12.010

quencher of chlorophyll excitation energy. Indeed it is known that the AXT content increases in the green algae Haematococcus pluvialis upon high-light irradiation [13]. For a deeper understanding of the photo-protective potential of AXT, thorough investigation of the optical properties and excited electronic states of AXT is required. The absorption spectra of neutral closed-shell carotenoids are dominated by a strong absorption band in the visible range known to be due to the allowed S0 ? S2 transition [5,6]. The energetically lowest excited S1 state, on the other hand, is optically forbidden and thus not observable with standard spectroscopic techniques. However, this state dominates the excited state dynamics of carotenoids observed in time-resolved spectroscopy. From a theoretical point of view, the S1 state is symmetry forbidden, since it has the same spatial symmetry (Ag in C2h) as the electronic ground state. Moreover, the S1 state exhibits a high amount of double excitation character. In the molecular orbital picture it is best represented by a transition of two electrons from the highest occupied molecular orbital (HOMO) into the lowest unoccupied molecular orbital (LUMO) [6,14,15]. On the contrary, the S2 state is a clear single-electron transition from the HOMO to the LUMO with Bu symmetry. Although the optical properties of carotenoids are dominated by the P-electron conjugation along the carbon–carbon bond skeleton, they are of course further fine-tuned by individual structural factors, like the presence of functional groups r configurational and conformational twisting. Also the polarity and polarizability of the environment has an influence on the excited states and thus the absorption spectra [5,6]. Radical cations of carotenoids have recently been observed in light harvesting complexes of green plants and purple bacteria [12,16–21]. In principle, they can be generated artificially by

A. Dreuw et al. / Chemical Physics 373 (2010) 2–7

Fig. 1. Molecular structure of astaxanthin.

chemical oxidation or via photo-ionization [22,23]. The optical properties of the open-shell carotenoid radical cations are significantly different than the ones of the neutral parent carotenoids. The absorption spectra are generally strongly red-shifted by about 200–300 nm and the energetically lowest D1 state possesses substantial oscillator strength such that a peak is observed in the near IR-region of the optical spectrum. Elaborate femtosecond pump– probe experiments on the radical cations of lutein and b-carotene in combination with quantum chemical calculations have demonstrated the existence of an additional excited electronic state between the well-known D1 and D3 states (the latter previously known as D2) [22]. For the explanation of excited state dynamics of carotenoid radical cations one thus has to take three electronic states into account. Since AXT is known to be an even stronger anti-oxidant than lutein or b-carotene, i.e. it is a better electron donor, it should also be able to act as quencher of chlorophyll fluorescence by electron transfer. In this paper, we study the optical properties of the carotenoid radical cation of AXT using quantum chemical methods based on density functional theory. Besides the investigation of the vertical excited states of the AXT+, we put special emphasis on the distribution of the positive charge in the different excited states and on the influence of the conjugated carbonyl groups on the excitation energies of the optically allowed D1 and D3 states. For the latter objective, hypothetical carotenoids have been studied, in which the conjugated carbonyl groups of AXT+ are successively replaced by methylene groups or two hydrogen atoms eventually leading to zeaxanthin (ZEA).

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electronic ground state. Using DFT the spin contamination vanishes and one obtains values of 0.81 for the expectation value of Sˆ2 for AXT+, which is very close to the correct one of 0.75. The excited doublet states exhibit a somewhat larger spin contamination at the theoretical level of TDDFT with values of at most 0.96. While for small molecules this can indeed corrupt the quality of the results, for large molecules it is mitigated, since significantly more orbitals contribute to the expectation value of Sˆ2. Thus, at the same value of hSˆ2i, the spatial symmetry breaking of the a- and b-orbitals is much more pronounced in smaller molecules than in larger ones. 3. Results and discussion 3.1. Ground state properties of the astaxanthin radical cation As first step of our quantum chemical investigation, the ground state equilibrium structures of the neutral parent astaxanthin (AXT) (Fig. 1) and its radical cation (AXT+) have been optimized at the theoretical level of DFT/B3LYP/6-31G* without imposing molecular symmetry onto the nuclear framework. The optimized structure of the radical cation is displayed in Fig. 2. The equilibrium structure of neutral AXT is very similar, and both are overall practically indistinguishable by eye. However, analyses of the detailed geometrical parameters reveal some important effects of the ionization onto the bond lengths alternation of the conjugated double bond chain (Fig. 3). All other geometrical parameters are essen-

2. Computational approach The computational investigation of the radical cations of AXT and its hypothetical derivatives comprises optimization of their ground state equilibrium geometries using conventional density functional theory (DFT) [24] as well as calculation of the vertical excited states employing time-dependent DFT (TDDFT) [25,26] with the standard B3LYP [27] exchange–correlation functional and the 6-31G* basis set as implemented in the Q-Chem 3.0 package of quantum chemistry programs [28]. For the analysis of the charge distribution of the excited states, we have used Mulliken charge analyses to study where the charge of the radical cation is located in the electronic ground state and how the charge is moved upon vertical excitation into the three lowest excited states D1–D3. While for neutral carotenoids it has been shown that the inclusion of doubly excited states is crucial for a proper description of the lowest excited S1 state [15,29], high-level computations with the extended algebraic diagrammatic construction scheme of second order (ADC(2)-x) [30,31] on radical cations of linear polyenes with up to eight conjugated double bonds have shown that doubly excited configurations do not play important roles for the lowest excited states of carotenoid radical cations [32]. Thus, TDDFT calculations are much better suited for the description of radical cations of carotenoids than for neutral. However, carotenoid radical cations possess an odd number of electrons and are therefore generally subject to an unrestricted treatment. At the Hartree–Fock level, one observes a large amount of spin contamination in the

Fig. 2. Optimized equilibrium ground state structure of the AXT radical cation (top: side view; bottom: top view).

Fig. 3. Bond lengths alternation pattern of the conjugated double bond chains in neutral AXT (solid line) and its radical cation AXT+ (dashed line). The equilibrium structures have been optimized using DFT/B3LYP/6-31G*. The inset gives the numbering scheme of the involved bonds.

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tially not affected and exhibit typical values for carotenoids. While in neutral AXT, single and double bond character can clearly be assigned to the bonds according to their lengths, this is not possible in AXT+, since the bond lengths alternation decreases upon ionization, i.e. upon removal of an electron from the HOMO. This effect is particularly pronounced in the central part of the conjugated double bond chain. It is also important to note that the structure of the AXT radical cation is not fully symmetric, which manifests itself in the bond lengths of the carbonyl groups (Fig. 3) and in the distribution of the positive charge in the cation (see below). The observed bond length equilibration in the radical cation is due to two major effects. The removal of an electron from the pHOMO leads to a decrease of the binding interactions within the double bonds and to an increase within the single bonds. A similar but far less pronounced effect has been observed when the equilibrium structure of the S1 state of neutral carotenoids has previously been optimized [14]. It is surprising that the bond length equilibration is less in the S1 state of neutral AXT than in the ground state of AXT+, since besides the removal of an electron from the HOMO the LUMO becomes also occupied in S1 of neutral AXT allegedly further supporting equilibration. Thus, the removal of an electron from the HOMO in AXT+ cannot be the only explanation for the bond length equilibration. Before answering the question of the additional factor resulting in equilibration, let us first inspect where the positive charge is localized in AXT+. For this objective, we have computed the Mulliken atomic charges of neutral AXT and of its radical cation at their respective equilibrium geometries. Then the individual atomic charges of AXT were subtracted from those of AXT+, and the resulting difference is plotted in Fig. 4. As can be readily recognized, the positive charge is essentially delocalized over the entire conjugated double bond chain. In a valence bond or Lewis-structure view, this delocalization can be rationalized by a superposition of two resonance structures, in which the radical cation is located on either one or the other side of AXT+. Since the double bond character is formally shifted by one bond in the resonance structures, the bond lengths alternation decreases in the cation. A famous example for bond length equilibration due to charge delocalization are cyanines [NH2–(CH2)n–NH2]+ [33], where also two equivalent valence bond structures exist with the charge on one of both nitrogens. In summary, due to the charge delocalization and the existence of two equivalent resonance structures, the bond length equilibration of the conjugated double bonds in the electronic ground state of AXT+ is strongly enhanced and even more pronounced than in the S1 state of neutral AXT, at the DFT level of theory.

3.2. Excited state properties of the astaxanthin radical cation For the theoretical investigation of the optical properties of the AXT+, the vertical excited states have been computed using TDDFT with the B3LYP exchange–correlation functional and the 6-31G* basis set at the equilibrium geometry of the radical cation. In a previous investigation of the radical cations of b-carotene and lutein, this approach achieved good agreement with the experimental data [22]. In addition, an investigation of the excited states of polyene radical cations using high-level ab initio excited state methods has demonstrated that, in contrast to neutral polyenes, doubly excited states are only of minor importance in the description of the lowest excited electronic states of the radical cations [32]. Therefore, TDDFT/B3LYP can be expected to give reliable results for the lowest excited states of AXT+. As reference for the TDDFT calculations serves an unrestricted Kohn–Sham determinant, which exhibits essentially no spin contamination with an S2 expectation value of 0.80 close to the expected one of 0.75. This can also be seen at the molecular orbital level. Despite the fact that within the unrestricted Kohn–Sham formalism each electron has its own orbital and a- and b-orbitals are thus not necessarily identical, for AXT+ their spatial appearance is practically identical. Therefore, only the a-orbitals are depicted in Fig. 5, and we use the following nomenclature: spatial orbitals that are doubly occupied are referred to as HOMOs, doubly unoccupied orbitals as LUMOs and the singly occupied molecular orbital will be named SOMO. In Table 1, the computational results for the four lowest excited states of AXT+ are compiled, which according to their hS2i expectation value can be clearly assigned to doublet states. At the TDDFT/ B3LYP level of theory, the lowest excited D1 states has an excitation energy of only 0.93 eV corresponding to an excitation wavelength of about 1333 nm and a small oscillator strength. This is in agree-

Charge difference Cation-Neutral 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 -0.005

1

5

10

15

20

25

-0.01 -0.015

Fig. 4. Distribution of the positive charge in AXT+ along the conjugated double bond chain calculated as the difference of the Mulliken atomic charge distributions of AXT and AXT+ at the level of DFT/B3LYP/6-31G*. The atoms are consecutively numbered from one carbonyl oxygen to the other along the double bond chain in analogy to the bond numbering scheme in Fig. 3.

Fig. 5. Frontier orbitals of the AXT radical cation as obtained by DFT/B3LYP/6-31G*.

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Table 1 Excitation energies (xex) and oscillator strengths (in parantheses), excitation wavelengths (kex), expectation value of S2 operator, configuration of the wavefunction, and nature of the four lowest doublet excited states of the radical cation of astaxanthin at the theoretical level of TDDFT/B3LYP/6-31G*.

D1 D2 D3 D4 a

xex (eV) (Osc.)

kex (nm)

hS2ia

Main configurations

0.93 1.42 1.54 1.66

1333 873 810 746

0.81 0.90 0.96 0.91

0.65 0.96 0.70 0.89

(0.03) (0.00) (3.52) (0.17)

(SOMO ? LUMO)a + 0.75 (HOMO ? LUMO)b (HOMO  1 ? SOMO)b (SOMO ? LUMO)a  0.63 (HOMO ? LUMO)b (HOMO  2 ? SOMO)b

Nature

pp* np* pp* np*

Taken from TDA/B3LYP/6-31G*.

ment with experimental findings, since a weak absorption band of AXT+ could be identified around 1300 nm in the near-IR region of the absorption spectrum in chloroform [34]. In the molecular orbital picture, the D1 state is best represented by a linear combination of two almost equally weighted Slater determinants: one in which an a-electron is excited from the SOMO to the LUMO and one in which a b-electron is excited from the HOMO to the SOMO (Table 1, Fig. 5). The involved p-orbitals identify the D1 state thus as a typical pp* electronic transition. Since AXT+ is positively charged, one may ask whether the electronic excitation has also an influence on the charge distribution. To answer this question, we have computed atomic Mulliken charges for the D1 state and subtracted the corresponding atomic charges of the electronic ground state. The obtained difference is plotted in the upper panel of Fig. 6. As can be seen, the positive charge moves slightly by one atom, but remains delocalized over the complete conjugated p-system. The second excited doublet state D2 has a vertical excitation energy of 1.42 eV (873 nm) and exhibits practically no oscillator strength. In contrast to the D1 state, D2 is best represented by an electronic transition of a b-electron from HOMO-1 into the SOMO (Table 1). According to the character of the orbitals (Fig. 5), this state can clearly be assigned to be an np* state. This manifests itself also in the computed atomic charge differences between the D2 state and the electronic ground state (Fig. 6, middle). It is readily apparent that positive charge moves from the conjugated p-system to the carbonyl oxygen upon excitation, or from the perspective of the electrons, that an electron is transferred from the carbonyl group into the p-system. The most strongly allowed electronic transition of AXT+ is D0 ? D3 as revealed by its huge oscillator strength of the D3 state of 3.52 at theoretical level of TDDFT/B3LYP/6-31G*. The computed excitation energy is 1.54 eV corresponding to an excitation wavelength of 810 nm (Table 1). Experimentally this main absorption band has been found at 870 nm in acetone [34]. The wavefunction of the D3 state is best characterized by the same determinants like the D1 state, i.e. one in which an a-electron is excited from the SOMO to the LUMO and one in which a b-electron is excited from the HOMO to the SOMO (Fig. 5), but in a different linear combination (Table 1). In analogy to D1, also D3 corresponds to a pp* excitation. Also the change in charge distribution in AXT+ upon excitation into D3 is very similar to the change upon excitation into D1, as can be seen in Fig. 6, the positive charge remains essentially delocalized over the whole p-system. The fourth energetically lowest excited doublet state of AXT+ is like D2 an np* excited state, and is best represented by an excitation of a b-electron out of the HOMO-2 into the SOMO (Fig. 5). At the level of TDDFT/B3LYP/6-31G*, the D4 state possesses a vertical excitation energy of 1.66 eV and an oscillator strength of 0.17. The relatively large oscillator strength of D4 compared to D2 is due to the energetically close-lying D3 state, which results in weak electronic configuration mixing and some intensity borrowing. Obviously, a small asymmetric distortion of the equilibrium geometry of AXT+ makes one np* state (D2) energetically more favorable than the other (D4), which at a fully symmetric geometry would be energetically degenerate.

Charge difference Cation D1-D0 0.06 0.04 0.02 0 -0.02 -0.04 -0.06

Charge difference Cation D2-D0

0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 Charge difference Cation D3-D0 0.06 0.04 0.02 0 -0.02 -0.04 -0.06

Fig. 6. Difference between the Mulliken atomic charges of the first three excited states and the electronic ground state of AXT+ along the conjugated double bond chain. The numbering scheme is the same as in Fig. 4.

Overall, our findings are in agreement with previous works on the radical cations of lutein and b-carotene, in which the same state ordering has been identified [22]. In fact, our results nicely corroborate femtosecond pump–probe experiments on AXT+ [34], since for an explanation of the observed excited state dynamics, three excited electronic states are needed. Upon excitation into the D3 state, excited AXT+ molecules decay rapidly within about 100 fs into the D2 state, from where they further decay into the D1 state within less than a picosecond. The population of the D1 state has been identified to return back to the electronic ground

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state via two different decay channels with lifetimes of about 5 and 43 ps. The latter decay channels are yet unknown and will be subject to further investigations. 3.3. Influence of the carbonyl groups on the excited states One of the structurally most interesting aspects of AXT are the two conjugated carbonyl groups at the ends of the conjugated C@C double bond chain located within the b-ionone rings (Fig. 1). Carbonyl groups can have a large influence onto the properties of carotenoids. Thus is it just natural to ask how the carbonyl group affects the properties of AXT+, in particular the excitation energies of the observable pp* excited states D1 and D3. For this objective, we have computed the vertical excited states of a set of derivatives of AXT+ at the same theoretical level as above, i.e. TDDFT/B3LYP/6-31G*. We have constructed the following derivatives: by successive replacement of the C@O carbonyl groups against C@CH2 methylene groups (Fig. 7), we have obtained two hypothetical carotenoids 1 and 2 (Table 2). Furthermore, we have removed the carbonyl groups successively, i.e. we replaced the C@O group with a CH2 group. The removal of one carbonyl group gives the hypothetical carotenoid 3 (Table 2), while removal of both carbonyl groups results in the carotenoid zeaxanthin (ZEA). A fourth hypothetical carotenoid 4 is possible, if one C@O group is replaced by methylene and one is removed (Table 2). The results of our TDDFT/B3LYP/6-31G* calculations of the vertical excited states of the D1 and D3 states of the carotenoid radical cations are compiled in Table 3. Comparison of the vertical excitation energies of AXT+, 1+ and 2+ allows for an estimate of the electronic effect of the carbonyl group without influence of the length of the conjugated p-system and keeping its 13 conjugated double bonds. In this series, the excitation energies of the D1 state decrease from 0.93 to 0.88 and 0.84 eV and the ones of the D3 state

HO

HO

HO

O

C H

H

Fig. 7. The original carbonyl groups (left) in the b-ionone rings of AXT+ have been successively replaced by methylene groups (right) or by hydrogen atoms (middle).

Table 2 Substitution pattern of the b-ionone rings in AXT, the hypothetical carotenoids generated by replacement of the carbonyl groups by either methylene groups or hydrogen atoms, and zeaxanthin. Carotenoid

b-Ionone (left)

b-Ionone (right)

AXT 1 2 3 4 Zea

C@O C@O C@CH2 C@O C@CH2 CH2

C@O C@CH2 C@CH2 CH2 CH2 CH2

Table 3 Vertical excitation energies of the two energetically lowest allowed pp* states, D1 and D3, of AXT+, the radical cations of the hypothetical carotenoids 1–4 (see Table 2) and, Zea+ at the theoretical level of TDDFT/B3LYP/6-31G*.

D1 D3

AXT+

1+

2+

3+

4+

Zea+

0.93 1.55

0.88 1.47

0.84 1.39

0.92 1.53

0.86 1.43

0.90 1.51

from 1.55 to 1.47 and 1.39 eV, respectively. Apparently, the –M-effect of the carbonyl group leads to an increase of the excitation energy compared to a fully conjugated C@C double bond system of the same length. Analysis of the excited states of the carotenoid radical cations 2+, 4+, Zea+, on the other hand, reveals the influence of the number of conjugated C@C double bonds, since the number decreases successively from 13 (2+), to 12 (4+) and 11 (Zea+). Not surprisingly, the vertical excitation energies of the D1 state increase with decreasing conjugated chain length from 0.84 to 0.86 and 0.90 eV from 2+ to Zea+, respectively. The same is true for the D3 state, where the excitation energies increase from 1.39 to 1.43 and 1.51 eV. Most interesting, however, is the series of carotenoids AXT+, 3+ and Zea+, since here the carbonyl groups are successively removed, i.e. the excitation energy increase due to the –M-effect of the carbonyl group as well as the decrease owing to the extended conjugation length are removed at the same time. As one can see in Table 3, the vertical excitation energies of D1 and D3 change only slightly from 0.93 and 1.55 eV for AXT+ to 0.92 and 1.53 eV for 3+ and 0.90 and 1.51 eV for Zea+, respectively. Thus indeed, the two counter-acting effects of a carbonyl group onto the excited states of a polyene chain do indeed practically cancel each other.

4. Summary and conclusions In this work, standard quantum chemical methods based on density functional theory have been used to study the electronic ground state of the astaxanthin radical cation (AXT+) and the four energetically lowest excited states D1–D4. The ground state equilibrium structure exhibits a pronounced equilibration of the central carbon bond lengths of the conjugated double bond chain. The origin of the equilibration has been rationalized in a valencebond picture in analogy to the famous cyanines: two resonance structures exist, in which the radical cation is located on either one or the other side of AXT+. Since the double bond character is formally shifted by one bond in the resonance structures, the bond lengths alternation decreases in the cation. Calculations of the vertical excited states of AXT+ employing time-dependent density functional theory revealed a similar picture as has been found previously for the radical cations of lutein and b-carotene: a strongly allowed pp* excited state as D3 and one with smaller oscillator strength as D1. In between an optically dark np* state is identified as D2. The computed excitation wavelengths of the D1 and D3 states of 1333 and 810 nm are in nice agreement with experimental values of 1300 and 870 nm in chloroform, respectively. The state ordering is also in agreement with pump–probe experiments on AXT+, in which it is demonstrated that the initial excited state population of D3 decays rapidly into D2 and finally via D1 back to the ground state [34]. Mulliken atomic charge analysis has been used to investigate how the positive charge is moved upon excitation into the vertical excited states. While in the D1 and D3 states the positive charge remains delocalized within the p-system, it is largely transferred to the carbonyl group in the D2 state. Together with an analysis of the involved molecular orbitals, a consistent picture of the electronic properties of the excited states of AXT+ is obtained. Special attention has been paid to the influence of the carbonyl groups onto the excitation energies of the optically allowed pp* excited states D1 and D3. To gain detailed insight into the effects, a set of hypothetical carotenoids has been generated by replacing the carbonyl groups successively with methylene groups thus removing the electronic effects without shortening the polyene chain. In a second set, first one and then both carbonyl groups have been removed from AXT+, the latter leading to the zeaxanthin radical cation. Finally one carbonyl group has been removed and the

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remaining one replaced with a methylene group. For all these carotenoids, the vertical excited states have been computed at time-dependent density functional theory level. Comparison of the excitation energies of the allowed pp* excited states of the different sets of hypothetical carotenoid radical cations with AXT+ and Zea+ revealed that carbonyl groups have two counter-acting effects onto the excitation energy. On one hand their –M-effect leads to an increase of the excitation energy, but on the other hand the extension of the conjugated p-system through the carbonyl group itself lowers the excitation energy. In summary, both effects largely cancel each other such that addition of a carbonyl group to a polyene has practically no effect onto the excitation energies of the pp* states of the polyene. All calculations have been performed without taking solvent effects into account. Nevertheless, the results agree very favorably with recent experimental findings. Certainly, this good agreement is partially due to fortuitous cancellation of errors and solvent effects, but still the qualitative picture is valid and can, in particular, nicely explain time-resolved pump–probe experiments. In the future, solvent effects onto the optical properties of carotenoid radical cations need to be addressed in detail from a theoretical as well as experimental point of view. For only little is known about the influence of polarity and polarizability of the solvent, hydrogen bonding or formation of solute–solvent complexes onto the excited states of carotenoid radical cations. This is a particularly important issue when one wants to understand their role in a more complex environment like in pigment proteins. Acknowledgements This work has been supported by the CEF ‘‘Macromolecular Complexes” of the University of Frankfurt. A.D. is supported by the Deutsche Forschungsgemeinschaft as a Heisenberg professor. Computation time has been generously provided by the Center of Scientific computing of the University of Frankfurt. References [1] S.M. Lawlor, N.M. Obrien, Nutr. Res. 15 (1995) 1695.

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