Electronic Spectra of Structurally Deformed Lutein - ACS Publications

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Electronic Spectra of Structurally Deformed Lutein Mindaugas Macernis,*,†,‡ Juozas Sulskus,† Christopher D. P. Duffy,§ Alexander V. Ruban,§ and Leonas Valkunas†,‡ †

Theoretical Physics Department, Faculty of Physics, Vilnius University, Saulėtekio al. 9, LT-10222 Vilnius, Lithuania Center for Physical Sciences and Technology, Savanorių 231, LT-02300 Vilnius, Lithuania § School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road, London E1 4TN, U.K. ‡

ABSTRACT: Quantum chemical calculations have been employed for the investigation of the lowest excited electronic states of lutein, with particular reference to its function within light harvesting antenna complexes of higher plants. Through comparative analysis obtained by using different methods based on gas-phase calculations of the spectra, it was determined that variations in the lengths of the long C−C valence bonds and the dihedral angles of the polyene chain are the dominant factors in determining the spectral properties of Lut 1 and Lut 2 corresponding to the deformed lutein molecules taken from crystallographic data of the major pigment−protein complex of photosystem II. By MNDO-CAS-CI method, it was determined that the two singlet Bu states of lutein (nominally 1Bu−* and 1Bu+) arise as a result of mixing of the canonical 1Bu− and 1Bu+ states of the all-trans polyene due to the presence of the ending rings in lutein. The 1Bu−* state of lutein is optically allowed, while the 1Bu− of a pure all-trans polyene chain is optically forbidden. As demonstrated, the Bu states are much more sensitive to minor distortions of the conjugated chain due to mixing of the canonical states, resulting in states of poorly defined particle−hole symmetry. Conversely, the Ag states are relatively robust with respect to geometric distortion, and their respective inversion and particle−hole symmetries remain relatively well-defined. mechanism still remains a matter of debate.8 Of the many proposed NPQ mechanisms, several involve xanthophylls. One proposed mechanism is based on the assumption that a radical or a charge-transfer state of a Chl−Car pair may be responsible for NPQ.9−11 In particular, Lutein 1 in LHCII has been identified as a strong candidate for the site of NPQ12 assuming that NPQ occurs via the incoherent transfer of energy from the chlorophyll terminal emitter to the S1 state of Lutein 1. More recently,13 a complex charge transfer state involving Lutein 1 and two Chls as an intermediate state in quenching by Lutein 1 has been identified. The crystallographic data for the LHCII complex implies that this lutein molecule (Lut1) exists in a distorted configuration, and it is hypothesized that this distortion is a significant feature of the NPQ mechanism.12−15 Resonance Raman spectra also support the conclusion about the structural changes of xantophylls in LHCII complexes at various light conditions. For instance, a correlation between quenching and deformation of neoxantin and lutein as well as their binding domains is identified for plants.16 The notion of lutein (or another Car) as a quencher is attractive due, in part, to the fact that it possesses a very short (∼10 ps) excited state lifetime. This lifetime is likely to be the result of a readily accessible conical intersection between the potential energy surfaces of the S1 state and the ground state, which one could hypothesize will be strongly effected by distortions. As a result,

1. INTRODUCTION Chlorophylls (Chls) and carotenoids (Cars) are the principle pigment molecules responsible for performing the initial stages of photosynthesis. Assembled within the proteins of lightharvesting antennae, they are involved in the accumulation of light energy via excitation energy transfer to specific pigment− protein complexes, the reaction centers, where charge transfer across the photosynthetic membrane is initiated.1 In addition to the principle excitation pathway fulfilled mainly by singlet electronic excited states of Chl molecules, a triplet state population is also probable as a result of intersystem crossing. In the triplet state, Chl molecules contain sufficient energy to convert ground state triplet molecular oxygen to an excited singlet state, known to be destructive to the surrounding medium. Formation of singlet oxygen is inhibited by Car molecules as they accept Chl triplets through triplet energy transfer, and the resulting Car triplet excitation is energetically too low to excite singlet oxygen.2−4 However, at high light, the amount of absorbed excitation energy exceeds the maximum turnover rate of the reaction center (RC), potentially leading to an increase in the yield of singlet oxygen and other hazardous reactive oxygen species (ROS). To cope with this, plants have evolved a defensive mechanism by which absorbed excitation excess is harmlessly dissipated as heat. This process is commonly referred to as nonphotochemical quenching (NPQ).4−7 The NPQ mechanism ensures that photosynthesis remains efficient under very different light conditions up to very high intensities. Though the significance of NPQ in green plants is well identified, the exact nature of the underlying © 2012 American Chemical Society

Received: May 5, 2012 Revised: August 6, 2012 Published: September 13, 2012 9843

dx.doi.org/10.1021/jp304363q | J. Phys. Chem. A 2012, 116, 9843−9853

The Journal of Physical Chemistry A

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provided by low temperature measurements.29,30 The model explains many experimental observations but is not without problems. The predicted conformational change during the 11Bu+−S* relaxation does not explain the enhanced S* population for Cars bound within the PSII antennae proteins.32−35 One would expect such an isomerization to result in a measurable conformational change of the pigment protein complex, such as the opsin conformational change induced by the photoisomerization of retinal in the eye. However, no such observation has been reported. The carotenoid excited state scheme corresponding to two photon experiments is also consistent with proposal that the S* state is associated with a twisted conformation of carotenoids.36−38 However, recent experiments combined with the modeling of saturation curves support the notion that the S* state is actually a hot (vibrationally excited) ground state populated through some nonlinear process.39,40 This hypothesis is also consistent with the results of the two-photon experiments.41 The question of whether the S* state is a hot S0 state or an altogether separate excited electronic state remains open. It was hypothesized that the charge transfer state mentioned previously could either be a twisted intramolecular charge transfer (TICT) state or a nontwisted intramolecular charge transfer (ICT) state,42 whose energies are known to be highly susceptible to the solvent environment as demonstrated by experiments on aminocoumarins43 and related compounds.44,45 In nonpolar solvents, the charge transfer state could be higher in energy than the 21Ag− state, yet sufficiently close that it may be thermally populated after light absorption and fast relaxation from 11Bu+. The proposed model assumes that the S1 state (21Ag−) surface is comprised of two strongly coupled states, 21Ag− and a CT state, which depend on the polar or nonpolar nature of the solvent. The model suggests that 21Ag− and CT energy difference is similar to the thermal energy.42 However, it is still not clear what the molecular nature of the CT state is. Several additional ideas suggest that it is either an entirely separate electronic state from 21Ag−,46−50 quantum mechanically mixed with 21Ag−51,52 or it is 21Ag− with a large intrinsic dipole moment.53 The creation of the lowest-lying CT state requires extensive mixing of the lowest-lying 11Bu+-like ionic and 21Ag−-like covalent states to form a new state with extensive bond order reversal and charge transfer character.54 The CT state is therefore proposed to be an ionic-like CT state with extensive (covalent-like) bond order reversal.54 A detailed knowledge of the electronic spectra of Cars is required for an understanding of their light-harvesting functions and, in particular, for identification of their possible role in NPQ. This can only be achieved by means of extensive quantum mechanical calculations, which take the potential configuration changes of Cars into account and also by considering likely impact of the protein environment on their electronic spectra. Quantum chemical methods were applied to studies of the excited electronic states of planar polyene chains.25,55,56 Time-dependent density functional theory55,57,58 within the Tam−Dancoff approximation (TD-DFT/TDA)59,60 using the Becke−Lee−Yang−Parr (BLYP) exchange-correlation functional59,61 was initially considered a promising approach for such calculations.61 Methods such as CIS or TD-DFT predict two excited states that have approximately the same energy as the physical 2Ag− and 1Bu+ states. However, inspection reveals that these states have incorrect symmetries and characters when compared to the physical states. This is due to the fact that single excitation methods such as these

Cars are intrinsically dissipative and therefore do not exhibit fluorescence. Interestingly, according to recent model simulations, the excitation quenching mechanism at the heart of NPQ should be very fast, possessing a characteristic time of a few picoseconds or even less.17 To determine the possible role of Cars and to disclose the details of the mechanism of quenching, the dependence of the Cars energy spectra on the protein surroundings should be analyzed.18 In addition to the mechanisms determining the possible switching ability of excitation quenching in the light-harvesting complexes of plants at different external conditions already mentioned above, other mechanisms are also suggested and discussed in the literature. For instance, the modulation possibility of interactions between Cars and Chls,19 or the energy position of the Car molecule interacting with Chls20 might be attributed to the quenching ability of chlorophyll dimers as due to changes in their mutual interaction driven by an anisotropic polar environment.21 It is noteworthy that Car molecules are considered to be involved in the excitation quenching ability depending on the light conditions in almost all of the models that are suggested so far. Therefore, in the work presented in this article, we analyze the effects of the small geometric distortions imposed by the protein surrounding on the structure of the Cars, with particular emphasis on lutein. Cars are pigments in which the linear polyene chain is primarily responsible for the electronic transitions that are relevant to the absorption of visible light.22 The lowest singlet excited state of the linear polyene chain, labeled simply as S1 or labeled according to its symmetries as 21Ag−, is of the same symmetry as the ground state, labeled S0 or 11Ag−, and therefore, according to the selection rules for electric dipole transitions, the S0 → S1 transition is optically forbidden.23 The transition to the third singlet excited state (traditionally labeled S2), which is of the 11Bu+ symmetry, is optically accessible. Between 21Ag− and 11Bu+ states, there is an additional, optically forbidden singlet excited state, which is labeled 11Bu− in accordance with its symmetry. The strong electron correlations in the conjugated chains of linear polyenes and Cars play a decisive role in determining the positions of the excited states and the oscillator strengths of the corresponding optical transitions.22−27 Because of this, the electronic spectra of Cars are expected to be sensitive to any type of deformation caused by their protein surrounding. Experimentally, it has been demonstrated that some additional excited states are inherent to the Car molecule.27−29 The presence of an additional dark singlet excited state, the S* state, has been demonstrated through pump−probe spectroscopy.22 However, its possible role in excitation relaxation processes is a controversial issue in modern Car photophysics. The origin of the S* excited state defined by pump−probe spectroscopy is not well understood. From a series of studies,29,30 it was proposed that S* is in fact the 21Ag− state of a twisted Car conformation. The model suggests that, upon excitation into the 11Bu+ state, there is a certain probability of the Car backbone adopting a twisted conformation. In the ensemble, this results in a splitting of the originally uniform 11Bu+ population into two subpopulations. The first subpopulation retains the all-trans symmetry and corresponds to the standard 21Ag− state. The second one is twisted, leading to the S* state. The two sub populations both decay separately to a common ground state with the original all-trans conformation. The S* model as a twisted 21Ag− state also explains triplet formation.30,31 Strong support for the S* model hypothesis was 9844



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Figure 1. Quantum mechanically optimized Lut QM and crystalographic Lut 1 and Lut 2 structures in the ground electronic state (a) and bond numbering between the carbon atoms in the polyene chain (b).

cannot account for the double excitation characters of the 21Ag− and 11Bu− states.62,63 It should be noted that the first singlet excited state predicted by these methods is largely a single HOMO → LUMO excitation in nature, meaning it has the same symmetry and character as the physical 11Bu+ state. Indeed, if a long distance corrected functional (such as CAMB3LYP) is used, then TD-DFT can be used to effectively model the S0 → S2 transition in carotenoids. However, both the 21Ag and 11Bu states are absent due to the explicit neglect of doubly excited determinants in such methods. Thus, the TD-DFT/ TDA method is not suitable for the investigation of electronic excitations of polyene chains and similar structures where double and higher order excitations must be accounted for. However, other methods such as semiempirical CAS-CI and ab initio CASSCF methods, while generating excited states with the correct doubly (2 1 A g −) or singly (1 1B u +) excited configurations character and with the correct optical properties, tend to overestimate the excitation energies. Recently, the excited states of Cars were calculated using configuration interaction (CI), time-dependent density functional theory within the Tam−Dancoff approximation (TDDFT/TDA) within the framework of the BLYP exchangecorrelation functional, SAC−CI with the 6-31G(d) basis set, CI using the MNDO Hamiltonian and ab initio SACSCF with the cc-(p)VDZ basis set.27,55,64−66 Here, we present results based on quantum mechanical calculations, which enable us to disclose the potential effects resulting from distortions to their structure. The electronic spectra of a specific xantophyll molecule−lutein and its sensitivity to polyene chain deformations, which emerge from interactions with a protein environment, are analyzed. We regarded deformations of the polyene chain, which were either small or large with respect to thermal energies (∼0.02 eV).

2. GROUND STATE CALCULATIONS OF LUTEIN STRUCTURES Possible conformations of Cars can be extracted from known crystallographic data corresponding to specific pigment− proteins67 or identified by using vibrational spectroscopy.68 Conformational structures of Cars should vary depending on external conditions. For instance, the crystallographic data show two types of Lutein (Figure 1a), Lut 1 and Lut 2, in the major light−harvesting complex of Photosystem II (LHCII). For both structures, the polyene chain deviates significantly from planarity, while a quantum mechanical geometry optimization (Lut QM structure in our notation) gives a structure that is practically planar (Figure 1a, inset). The ε-ring shown on the right side in Figure 1a is almost perpendicular to the polyene chain and the β-ring shown on the left side is slightly out of the plane of the polyene chain.68,69 For comparative purposes, the geometries of the Lut 1 and Lut 2 molecules were determined via quantum chemical computations, neglecting any external influences, using standard ground-state DFT70 with the three-parameter Becke3− Lee−Yang−Parr (B3LYP)71 exchange-correlation functional and the 6-311++G(2d,p) basis set. The Gaussian03 quantum chemistry package72 was used in this case. The Lut 1 and Lut 2 structures obtained from the crystallographic data are lacking hydrogen atoms. The hydrogen atoms were added using the Gaussian package prior to the quantum mechanical computations. At the next step, the positions of hydrogen atoms were optimized for Lut 1 and Lut 2, while the geometry of the frame of heavy atoms (C and O in this case) was fixed. However, the geometries are not entirely physically realistic, certainly not to a level where they can be immediately used for the quantum mechanical type of modeling. This is due to the finite resolution 9845



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of the crystal structure (2.72 Å for the structure used in these calculations), which is mostly based on force field modeling, but the distortion of the dihedral angles are quite accurate in the crystal structure due to their large-scale motions.67 As a result, the smallest bond-lengths present within these structures are likely to be unphysical, as will be demonstrated later in this article. Nevertheless, the deformation of the Lut1 and Lut2 structures demonstrates the tendency of a protein environment to induce conformational distortions. Such a level of deformation is likely to result in changes to the lutein electronic spectrum, and we will apply them to the fully optimized lutein structure. Lutein geometry was fully optimized (Lut QM) using the b3lyp/6-311++G(2d,p) method. All our analyzed Lutein structures have all-trans-polyene chain, but they have different β-ring positions. According to atom C1 position (Figure 1b) from the β-ring, we labeled stable all-trans-Lutein structures in the ground electronic state as follows: all-trans-Lutein cis β 1 (Lut QM cis 1), all-trans-Lutein cis β 2 (Lut cis 2), and all-transLutein trans β (Lut trans). In all described cases, the atom C1 partially extends the polyene chain. These three stable structures are resolved in accordance with recent demonstration.69 In all of these Lut QM structures, the all-trans-polyene chain remains essentially planar. The energy of the Lut QM trans configuration is higher in comparison to the two cis conformers (Lut QM cis 1 and Lut QM cis 2). Results achieved using the B3LYP/6-311++G(2d,p) method and basis set show that the energy difference between the two cis conformers is 0.049 eV, while the trans isomer is positioned 0.282 eV higher than the lowest cis isomer. The results achieved for the cis conformers of Lut QM are quite similar to those defined previously (0.052 and 0.178 eV)69 despite the fact that the 631G(d) basis set used in the latter case is less sophisticated. The computations based on a broader basis set (6-31+ +G(2d,p)) led us to conclude that the trans configuration is even less energetically accessible. Using the same method and the basis set (B3LYP/6-311+ +G(2d,p)), it was determined that the ground state (S0 labeled as 11Ag− type) of the Lut 1 structure is energetically higher by 0.93 eV than the ground state of the Lut QM cis 1, the cis conformer with the lowest energy (Figure 2 inset). Evidently, the deformation energy of Lut 1 is very large when compared with typical thermal energies. The same applies to the Lut 2 structure, which is energetically higher by 1.16 eV. The cis conformer of Lut QM (Lut QM cis 1) with the lowest energy will be considered as the reference configuration for further calculations of excitation energies.

Figure 2. Electronic excitation energies of different lutein structures obtained by MNDO-CAS-CI method. Polyene N = 10: pure all-trans polyene chain with 10 CC double bonds. Lut QM cis 1, Lut QM cis 2, Lut QM trans: different lutein structures with quantum mechanically optimized ground state geometries corresponding to structures with differend β-ring positions with respect to the plane of the polyene chain. Lut 1 and Lut 2: crystallographic lutein structures with optimized positions of hydrogen atoms. The relative ground state energies (inset) are calculated at the B3LYP/6-311++G(2d,p) level.

Fortunately, there are several promising methods that can be used to obtain reasonable results. The computationally expensive CASSCF method with the cc-(p)VDZ basis set, as implemented in the ORCA package73 was used for the calculation of the excited states of Lut QM cis 1. The active space of 6 occupied and 6 unoccupied orbitals was used. The CASSCF method produces both 21Ag and 11Bu+ type state wave functions with the correct characters and energetic ordering (Figure 3). However, the CASSCF method overestimates excitation energies by a factor of 2 (Figure 3). The SAC−CI72 method by default (using SD-R) does not find the 21Ag−electronic state because the initial states are formed of single excitations only. In order to start from states with double excitations, additional subroutines, which require

3. EXCITED STATE CALCULATION METHODOLOGY 3.1. Excited State Calculations of Structures Containing the Polyene Chain. The lutein structure consists of a polyene chain terminated by an ε-ring at one end and a β-ring at the other (Figure 1), meaning that the excited state calculations are of the same level of complexity as for a pure polyene chain. The rings further complicate matters. The ideal polyene chain structure belongs to the C2h point group, and therefore, group theory can be used to simplify our calculations. Becuase of the presence of the end rings, lutein does not have well-defined symmetry (it belongs to the trivial C1 point group), and the group theory cannot be employed. The major problem is that electron correlations are strong for the lowlying electronic states, and therefore, doubly excited configurations have considerable weights in their wave functions.

Figure 3. Electronic excitation energies of the Lut QM cis 1 structure calculated by different methods with quantum mechanically optimized geometry in the ground electronic state at the B3LYP/6-311+ +G(2d,p) level and corresponding experimental values for excitation energies.18 9846



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large computational resources, must be added. The default SAC−CI calculations are very expensive from a computational point of view, while the excitation energy of the 11Bu+ state is predicted quite well in comparison with the experimental data. The excitation energies of linear polyenes and various lutein structures were computed using MNDO-CAS-CI as implemented by the MOPAC semiempirical package.74 The results for excitation energies of the Lut QM structure are quite close to the corresponding experimental values (Figure 3) with respect to results achieved by other methods. However, the energies are still overestimated relative to the experimental data, and as we will show later in the article, for polyene chains, the 21Ag−, 11Bu−, 11Bu+ and 31A g− excited states are found in the correct energetic order and, more importantly, possess the correct single/double excitation character. Particularly, we know from previous TD-DFT work75 that the 11Bu+ state is predominantly a single HOMO−LUMO excitation. Conversely, the well-established failure of single excitation methods to correctly predict the polyene 21Ag− state implies its multielectron structure. In order to choose suitable active space, semiempirical calculations of pure polyene chains were fulfilled, and results were compared with known experimental and theoretical results as described in the next section. 3.2. Semiempirical Excited State Calculations of Polyenes. The calculated results for polyene chains were analyzed by comparing data achieved by the semiempirical MNDO-CAS-CI method as implemented in the MOPAC package74 with that produced by other methods, such as CASCI-MRMP,24 ADC(2)-x,25 CIS(D),25 and modified AM1-CASCI,76 and obtained through experiment.77 The number of active electrons and the active orbital space of the MNDO-CAS-CI wave function were chosen on the grounds of comparison of the calculated electronic excitation energies and wave functions with those obtained by the CASCI-MRMP method.24 The symmetry notations used are from the C2h symmetry point group. Alternant symmetry signs (plus and minus) come from pairing properties (also know as particle−hole symmetry) and were classified by analyzing the main configurations of the wave functions. The symmetry properties were first utilized by Pariser78 who distinguished the states as plus or minus. The highest occupied orbitals of polyenes are of π-type. We number the occupied orbitals HOMO, HOMO − 1, ..., as 1, 2, ..., and the unoccupied orbitals LUMO, LUMO + 1, ..., as 1′, 2′, ..., is in accord with conventional notation.19 There can be 2 electrons in one orbital with α and β spin functions. The excitation energy from orbital i to orbital j′ equal that obtained by excitation from j to i′ due to the pairing property. Excited configurations of type i → i′ behave like plus states for singlet states. Doubly excited configurations of type (i)2 → (j′)2 behave like minus states. It is known that an electric dipole transition between states of the same particle−hole symmetry is dipole forbidden. The treatment of the all-trans linear polyenes C2nH2n+2 (n = 3−14) was primarily focused on the determination of the four lowest-lying singlet excited states: 21Ag−, 11Bu−, 11Bu+, and 31Ag−. The state ordering predicted by the MNDO-CAS-CI calculations are shown in Figure 4. The MNDO-CAS-CI calculations predict the 11Bu+ state as an ionic state primarily originating from the 1 → 1′ (HOMO → LUMO) oneelectronic transition (Table 1). The 21Ag− is a covalent state, which comes from the (1)2 → (1′)2 (or (HOMO)2 → (LUMO)2) two-electron transition. The calculations predict the 11Bu− state to be a mixture of one- and two-electron excited

Figure 4. Three lowest singlet electronic excitation energies depending on the number of CC double bonds in the all trans polyene chain calculated by MNDO-CAS-CI method.

configurations 3 → 1′, 1 → 3′, 1;2 → (1′)2, and (1′)2 → 1;2. The 31A g− state is predicted as having mixed multiconfigurational character: double excitations of (1) 2 → (2′)2 and (2)2 → (1′)2 with large fraction of singly and doubly excited configurations 2 → 3′, 3 → 2′ and 1;3 → (1′)2, (1)2 → 1′;3′. The same results follow from CASCI-MRMP calculations.24 For low lying excited states, the MNDO-CAS-CI calculations with active space of 3 highest occupied and 3 lowest unoccupied molecular π orbitals predict the ordering of state energies for the all-trans linear polyenes C2nH2n+2 (n = 3−14) as 21Ag− < 11Bu− < 11Bu+ < 31Ag− (Figure 4). The CASCI-MRMP calculations predict the same ordering only for polyenes 6 < n < 11. The ADC(2)-x79,25 calculation method predicts an energetic ordering of 21Ag− < 11Bu− < 11Bu+ for polyenes 2 < n < 7. The experimental data are in agreement with this ordering.77 However, the energies are underestimated by the MNDO-CAS-CI method. Other methods such as AM1-CASCI focusing on the analysis of the 11Bu+ state and CIS(D) underestimate the excitation energies.76 We can conclude that our results for the excitation energies of the lowest singlet excited states of polyene chains achieved by MNDO-CAS-CI calculations qualitatively are the same as ones achieved using other (sometimes more sophisticated) methods.25,76,77,79 3.3. Excited States Calculations of Lutein. In the case of lutein (Lut QM) calculations by means of MNDO-CAS-CI, we used the same active space as for polyene chains: 3 highest occupied (1, 2, and 3) and 3 lowest unoccupied π orbitals (1′, 2′, and 3′). All of these orbitals are located on the polyene chain, while the 4 and 4′ molecular orbitals are located on the β-ring. The nature of the lowest excited singlet states of Cars is the same as in the polyene chain, and it is mainly determined by the polyene chain. As we have shown, the 3 HOMO and 3 LUMO orbitals are enough for polyene type molecules while using semiempirical methods. The fact that lutein has a β-ring and a ε-ring (Figure 1) connected to the polyene chain leads to a loss of the symmetry. Nevertheless, we assume that the excited states of lutein may be labeled using the same notation 9847



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Table 1. Main Configurations in Wave Function of Polyene Chain and Lutein As Follows from Calculations Using the MNDOCAS-CI Method weights of main configurations of wave functions state

configurationa

polyene (n = 10)

Lut QM cis 1

Lut 1

Lut 2

DefLut 1

DefLut 2

21Ag− 11Bu−b

(1)2 → (1′)2 3 → 1′ 1 → 3′ 1;2 → (1′)2 (1)2 → 1′;2′ 1 → 1′ 1 → 1′

0.58 0.27 0.30 0.31 0.31 0.01 0.61

0.58 0.21 0.28 0.32 0.21 0.31 0.52

0.56 0.27 0.21 0.21 0.32 0.29 0.54

0.57 0.28 0.24 0.25 0.32 0.19 0.58

0.57 0.17 0.26 0.31 0.16 0.39 0.47

0.57 0.27 0.23 0.22 0.33 0.26 0.55

11Bu+

Main configurations in wave function, where HOMO−LUMO is labeled as 1 → 1′. bThe 11Bu− is labeled for polyene chaines, while 11Bu−* is labeled for lutein structures because of 1 → 1′ weights. a

Figure 5. In all structures, the lengths of the double bonds are essentially similar. The lengths of single C−C bonds differ

employed for the canonical electronic states of polyene chains. The main difference between Lut QM and polyene chains is in the character of the 11Bu− state wave function. The wave function of the 11Bu− state of lutein has an additional configuration of 1 → 1′ with significant weight. The contribution of this configuration is almost zero (0.01 eV) for 11Bu− state of the polyene chain. The other configurations of the 11Bu− state wave function are similar for Lut QM and polyene chains. Therefore, we labeled this electronic state as 11Bu−* in analogy with the canonical 11Bu− state of a polyene chain (Table 1). The state ordering of 21Ag− < 11Bu−* < 11Bu+ < 31Ag− achieved for Lut QM with respest to excitation energy values is the same as for the polyene chain (Table 1). The excitation energies corresponding to the transition to the 21Ag− state are 2.49 and 2.47 eV for Lut QM cis and trans structures, respectively. The transition energies to the 11Bu−*, 11Bu+, and 31Ag− states are 2.77, 2.85, and 3.47 eV for Lut QM cis and 2.72, 2.82, and 3.35 eV for Lut QM trans, respectively (Figure 2). Both Lut QM cis structures have essentially identical excitation energies (there is a maximum difference of 0.01 eV). The corresponding experimental values are 1.7 and 2.6 eV for 21Ag− and 11Bu+ states, respectively.80 It is worth mentioning that the agreement between experiment and theory for the 21Ag− state is tighter than that of the 11Bu+ state. However, we note that the value of 1.7 eV is taken from transient absorption experiments. It should therefore correspond to the energy following excited state relaxation. Since the methodology we have employed in this work probes only the excitation energies of the vertical transitions, we should expect the calculated 21Ag− to exceed the value of 1.7 eV. Another source of this discrepancy is the fact that we do not account for real environmental effects. The lowest excited states for the polyene chains were labeled as 21Ag−, 11Bu−, 11Bu+, and 31Ag− according C2h point group symmetry, while the lutein states labeling is 21Ag−, 11Bu−*, 11Bu+ ,and 31Ag− (Table 1). Wave functions of the 21Ag−, 11Bu+, and 31Ag− excited states have the same main configurations for both a polyene chain and lutein. The wave functions of 11Bu− state in the polyene chain and 11Bu−* state in lutein have different nature. The 11Bu−* state of lutein has an additional large HOMO−LUMO singly excited configuration weight in wave function, which means the transition to this state from the ground electronic state can be weakly allowed.

Figure 5. Polyene chain C−C bond lengths alternation in various structures (Lut QM cis 1 and pure all trans polyene chain with geometries optimized at the B3LYP/6-311++G(2d,p) level and crystallographic Lut 1 and Lut 2 srtuctures).

more significantly between different structures, while double CC remains the same. The polyene chain has shorter single bonds in the middle of the chain, but bonds 8 and 14 for Lut QM cis are longer by up to 0.05 Å (Figure 5). However, most of the single bonds in the Lut 1 and Lut 2 structures are much longer. A comparison of the dihedral angles in the lutein structure shows that the polyene chain in Lut QM cis is almost planar. The dihedral angles in the polyene chain of Lut 1 and Lut 2 are out of plane by up to ±10°. The Lut QM cis 1 structure possesses the lowest ground state energy. The same result holds for the 21Ag excited state. The ground state energies of Lut 1 and Lut 2 differ hugely (∼0.5 eV) from the ground state energy of Lut QM (Figure 2 inset). This difference may be attributed to the low accuracy of the crystallographic structural data, which gives quite different results in comparison with the conclusions obtained from the quantum mechanical calculations. The Lut QM cis 1 structure was deformed in several ways in accordance with the deformations present in the Lut 1 and Lut 2 structures. Small deformations of Lut QM cis were defined as 50% of the largest deformations present in Lut1 and Lut 2. Six

4. STRUCTURAL DEFORMATION OF LUTEIN The C−C bond lengths of the Lut QM cis 1, Lut 1, Lut 2, and polyene n = 10 in the ground electronic states are shown in 9848



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types of deformation similar to those present within the Lut 1 and Lut 2 structures were considered. The first type of Lut 1 and Lut 2 deformations are deformations of the single C−C bonds at the center of the polyene chain (Figure 5). Any deformations smaller than 0.1 Å were neglected. Selected deformations were fixed and all other geometry parameters were optimized. The optimized structures with fixed small (50%) differences in the length of the single/long C−C bonds are denoted ΔLut 1 and ΔLut 2. The same procedures were performed for dihedral angles of the polyene chain (structures ΨLut 1 and ΨLut 2). The DefLut 1 structure was formed by combining deformations ΨLut 1 and ΔLut 1, and the DefLut 2 structure was similarly formed by combining deformations ΨLut 2 and ΔLut 2. All cases show that deformations result in increasing of the ground state energy with respect to that of the Lut QM cis structure (Figure 6). The excited state 21Ag− energy was also obtained as able to increase.

and DefLut 2 structures show that the investigated deformations mainly influence the energy gap between 21Ag− and 11Bu+ states. It is equal to 0.4 eV for Lut QM cis 1 and 0.32 and 0.24 eV for the ΔLut 2 and DefLut 2 structures, respectively. The energy gap between the 21Ag− and 11Bu+ states essentially does not change and is equal to 0.32 eV. It is worth mentioning that the weight of the 1 → 1′ configuration in the 11Bu− state strongly decreases when Lut 2 type deformations take place. As a result of this deformation, we have a less allowable transition from the ground state to the 11Bu− state. Our MNDO-CAS-CI semiempirical investigations show that twisting of the polyene chain affects the energy gap between the 21Ag− and 11Bu+ states, which becomes smaller. These deformations do not have a strong effect on the 21Ag−−11Bu− energy gap for the 50% deformed structures. Similarly, there were no great differences observed between the 21Ag− states of Lut QM and the twisted structures (ΨLut 1 and ΨLut 2). Notably, these results do not allow for a clear identification of an additional ICT state. This question will be discussed later in this article.

5. DISCUSSION AND CONCLUSIONS 5.1. Exited States of Carotenoids. As demonstrated, the MNDO-CAS-CI method implies that the absorption spectrum of the xanthophyll lutein (and by extension, the spectra of all related molecules) display significant sensitivity to geometric distortions to the conjugated chain, which could, in principle, be important when considering the phenomenon of NPQ in higher plants. As mentioned previously, it has been confirmed experimentally that, in addition to the well-known forbidden S1 (21Ag−) and S3 (31A g−) states and allowed S2 (11Bu+) state, Cars possess a poorly understood, low-lying ICT state, which lies, energetically, between the forbidden S1 and allowed S2 states. It was initially thought that the existence of such an ICT state required the presence of an electron-withdrawing carbonyl group within the carotenoid molecular structure, such as that of peridinin.51 However,81 it has been shown that this ICT state is observed for the carbonyl-lacking xanthophylls bound to LHCII, lutein, violaxanthin/zeaxanthin, and neoxanthin. It was suggested that the anisotropic, polar environment within the light-harvesting complex can produce a low-lying ICT state without the need for an electron-withdrawing group. We will direct specific focus on the ICT state that is purportedly an important intermediate state in the NPQ models that rely on lutein-mediated quenching of excitation energy. To this end, we will discuss the dependence of several molecular properties on geometric distortions. All Cars under consideration have some flexibility in the terminal β-rings since the ground state energies are almost the same for at least two of the different β-ring positions.43 Energy barriers between stable structures are typically very high when compared with thermal energies.42 Because of such heterogeneity, the S1 and S2 excited states can also slightly differ for the different configurations. As follows from our quantum chemical studies of the optimized structure, the transition to the first excited state S1, is optically forbidden while the transition to the second state, S2 (11Bu+), is allowed because of the symmetry of the polyene chain.22,27 The state with the energy between S1 and S2 states is of the Bu− symmetry (for lutein, we denote it as 11Bu−*). Indeed, the S1 state as well as the S0 state are of Ag− symmetry, while the S3 state is of the Bu+ symmetry when classified according to the C2h symmetry of the polyene chain.

Figure 6. Energies of the ground and excited electronic states of Lut QM cis 1 and of its deformed structures. ΔLut 1 and ΔLut 2: structures with fixed small deformations of the lengths of the single/long C−C bonds of the polyene chain similar to ones in crystallographic structures Lut1 and Lut2. ΨLut 1 and ΨLut 2: structures with fixed dihedral angle deformations of the polyene chain similar to ones in crystallographic structures of Lut1 and Lut2. DefLut 1and DefLut 2: structures including both deformations ΔLut and ΨLut as follows from Lut1 and Lut2, correspondingly. All energies are given with respect to the S0 state energy of quantum mechanically optimized structure Lut QM cis 1, all ground state energies were deretmined at the B3LYP/6311++G(2d,p) level. Excited state energies were calculated by adding excitation energies achieved at MNDO-CAS-CI level to the ground state energies of the corresponding structure.

The excited states 11Bu− and 11Bu+ are more sensitive to structural deformations. Results for the Lut 1 and Lut 2 structures show a possible interchange between the 11Bu− and 11Bu+ states, i.e., the 11Bu+ state becoming the lower of the two (Figure 6). The 50% deformations included in the Lut QM structures (ΔLut 1, ΨLut 1, DefLut 1, ΔLut 2, ΨLut 2, and DefLut 2) show that the interchange between excited states is mainly caused by deformations of the C−C single bond lengths. The energies of deformations are quite small, typically reaching 0.01 eV. The collective influence of deformations due to twisting and the single C−C bond lengths on the excited state is about 0.2 eV (Figure 6; Def Lut 1 and Def Lut 2). There is another interesting fact concerning the energy gaps between the 21Ag− state and states 11Bu− and 11Bu+. The energy gap decreases in the Lut 1 and Lut 2 structures with respect to the gap in Lut QM structures (Figure 2). Results for the ΔLut 2 9849



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functions. However, significant changes are only seen for the crystalographic geometries of Lut 1 and Lut 2, and the energetic ordering of these two states is reversed relative to the quantum mechanical structure. The ground state and the excited Ag− states appear to be insensitive to even the relatively severe distortions seen in the crystal structure. This would imply that, while distortions do not result in appreciable mixing between the 21Ag− and 11Bu+ (or 11Bu−) states, they can, in principle, cause significant mixing between the canonical 11Bu− and 11Bu+ states. It should be noted that the semiempirical method (MNDO) coupled with CI within a heavily restricted orbital subspace means that a quantitative analysis of these effects is not possible within this framework. However, qualitatively, these results imply that the wave functions of the singlet Bu states are far more sensitive to bond distortions than those of the singlet Ag states. The transition dipole moments of the 11Bu−* and 11Bu+ excited states are sensitive, to some degree, to distortions to the polyene chain. For the quantum mechanical structure of a linear polyene (n = 10), the 21Ag− has effectively no dipole connection to the ground state. This is expected given that this state possesses both the same inversion symmetry (Ag) and particle−hole symmetry (−) as the ground state. For the same reason, the particle−hole symmetry of the 11Bu− state prevents any dipole connection to the ground state. As expected, the 11Bu+ state is strongly dipole allowed, and as with the 21Ag−, the 31Ag− state is dipole forbidden. We note that our methodology overestimates the transition dipole length of the polyene 11Bu+ state by a factor of 3−4 (|μ| ≈ 49.3 D, compared to the experimental value of ∼14 D), and so, we treat these quantities with caution and use them purely within a comparative context. The 11Ag− → 21Ag− transition of Lut QM, as for 10-polyene, has a vanishing transition dipole moment. However, the 11Bu−* state is now allowed (|μ| ≈ 12.9 D), while the 11Bu+ dipole length is reduced by ∼20% (|μ| ≈ 39.8 D). We note that the magnitude of the transition dipole of the 11Bu−* state is only 30% of that of the 11Bu+ state. At this stage, we must question whether these results are physically meaningful or merely an artifact of the calculation method employed. Physically, the fact that the 11Bu−* state is now allowed implies that the particle− hole symmetry of the state is no longer well-defined as a result of the additional 1 → 1′ component. Conversely, the Ag states are relatively robust with respect to geometric distortion, and their respective inversion and particle−hole symmetries remain relatively well-defined. The 50% twisted deformations suggest that twisting makes the 21Ag− and 11Bu+ gap smaller when compared to the planar case. The 21Ag− and 11Bu−* gap is fixed, but it is different for Lut 1 and Lut 2. However, the Lut 1 and Lut 2 structures are deformed too much for them to be considered physically meaningful, with energy of deformation of up to one electronvolt. This is mainly caused by the distortions to bond lengths in Lut 1 and Lut 2 structures and the distortions most probably are an artifact of the low resolution of the structure. The 50% deformations added to the Lut QM structures show that the interchange between excited states is mainly caused by changes of long C−C (single) bond lengths (Figure 6). It is possible that protein environment may twist the lutein structure and deform long C−C bond of the polyene chain as the characteristic energy of deformation is quite small, about 0.01 eV, and therefore is thermally accessible (Figure 6). Moreover, twisting and long C−C bond deformations together induce

Comparative studies using various quantum chemical methods allow us to conclude that the MNDO-CAS-CI method constitutes a sufficient approach for the calculation of excited state energies and determination of the main configurations of the wave functions of Cars with planar polyene chain structures. Evidently, the excited states of the polyene chains possess an energetic order of 21Ag− < 11Bu− < 11Bu+ < 31Ag− . Lutein structures have an additional 1 → 1′ (HOMO−LUMO) configuration in the 11Bu− state (labeled as11Bu− *) wave function, but the other configurations are the same as for the polyene chain. The variation of the C−C valence bonds lengths in the polyene chains is the main factor responsible for a change in the weighting of the configuration 1 → 1′ in the 11Bu−* state wave function. As a result of these deformations, both the 11Bu−* and 11Bu+ excited states can even be swapped round, but the possibility that this is due to limits in accuracy of the MNDO calculations can not be entirely excluded. It was mentioned54 that the creation of a lowest-lying ICT state requires extensive mixing of the lowest-lying 11Bu+like ionic and 21Ag−-like covalent states to form a new state with extensive bond order reversal and a charge transfer character. However, our calculations imply that the 11Bu−* state wave function of Car includes not only all main configurations similar to 11Bu− state wave function of the polyene chain but also configurations characteristic to 11Bu+ state function. This mixing of covalent and ionic configurations may be a suggestion of the formation of an ICT or S*state. The energy gap between 21Ag− and 11Bu−* is fixed, while the energy gap between 21Ag− and 11Bu+ becomes smaller as a result of twisting deformations, implying that the 11Bu−* state itself is not a good candidate for the elusive S* state. The small energy difference accuracy can suffer from the limitations of semiempirical methods. However, the QM/MM study82 of Cars in LHCII show that the geometry distortions are very sensitive to the chosen functional in DFT. Calculations of excited states in linear polyenes and carotenoids are still a challenging task for the available quantum chemical methods, and semiepirical method is still one of the best ways.80,82 The strong coupling of the 11Bu+ with the dark 11Bu−* state resulting in a crossing was reported.27 Our results confirm such possibility (see Figures 2 and 6) where the swapping between 11Bu+ and 11Bu−* states could be caused by the geometrical deformations. In addition to this, we achieved that the 11Bu−* state was becoming weakly allowed due to such mixing with 11Bu+ state. By examining CI wave function coefficients of our calculated many-body systems, it was found that distortions can, in principle, have a significant impact on the CI composition of the 11Bu− and 11Bu+ states. In fact, the transformation from the all-trans polyene (n = 10) structure to the lutein structure itself involves significant perturbation of the 11Bu− and 11Bu+ wave functions. In particular, the 11Bu− state acquires a more 11Bu+like single HOMO−LUMO excitation character. This implies that the two 11Bu states of lutein (nominally, 11Bu−* and 11Bu+) arise from a mixing of the canonical 11Bu− and 11Bu+ states of the all-trans polyene. The ground and excited 1Ag− wave functions do not differ significantly between all-trans polyene and lutein, implying that the state labels 11Ag−, 21Ag−, and 31Ag− are still appropriate for the quantum mechanical structure of lutein. It appears that even slight distortions to the polyene chain, caused by the continuation of the conjugation path into the βring, can have significant effects on the 11Bu−* and 11Bu+ wave 9850



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state with an appreciable CT component. As we have already discussed, even the rather strong dihedral and bond distortions implied by the crystallographic structures of Lut 1 and Lut 2 do not result in mixing between these two states. In fact, the 21Ag− state in particular appears to be rather resistant to the effects of geometric distortion. The ICT state may be a separate electronic state entirely. We do note that lutein possesses a slightly allowed state, 11Bu−*, that differs significantly from the canonical 11Bu− state of the linear polyenes. Although the character of this new state is sensitive to distortions in the conjugated chain, it is present even in the quantum mechanical structure in which it lies between the vertical S1 (21Ag−) and S2 (11Bu+) states. However, this state does not possess the largely ionic character that we would expect of an ICT state. This is confirmed by the fact that, in our calculations, this state does not have a large static dipole moment. We may therefore conclude from these results that geometric distortions to the xanthophyll conjugated structure, imposed by the protein/cofactor environment, are not responsible for the ICT state observed during NPQ in plant light-harvesting complexes. In solution, low-lying carotenoid ICT states are observed only for carotenoids containing electron-withdrawing side groups such as carbonyl. In lutein, there is no such group associated with the conjugated chain. Since distortions have been shown to be an unlikely cause of the low-lying lutein ICT state observed in plant light-harvesting complexes, we may, tentatively, discuss other possible causes. It is possible that a low-lying ICT state could be the result of the specific solvent environment of the luteins with the light-harvesting complexes. As seen from the crystal structure, each lutein has a highly specific and anisotropic local environment, with the end group associated with charged aspartates. Figure 7 shows Lut 1 in red

only small changes to the various state energies, which are up to 0.02 eV (Figure 6 Def Lut 1 and Def Lut 2). The deformation of dihedral angles in the polyene chain does not appear to have a significant perturbative effect on the excited states. The ground state (S0) energy is, however, evidently sensitive to deformations of the Lutein structure, which can push it up by about 0.5 eV. However, it is worthwhile to mention that the ground state energy increases by only 0.03 eV for Lut QM structures with 50% deformations of Lut 1 and Lut 2 type. The major Lut 1 and Lut 2 deformations are the twisting of dihedral angles along the polyene chain and changes in the lengths of the long C−C bonds. Small stretching of the single C−C bonds lengths increases alternation of the bond lengths and thus changes the energy gaps between states. It is therefore no surprise to see that changes to the alternating bond lengths, as seen in the Lut1 and Lut2 structures, change the energy of the ground state by up to 0.5 eV. However, the influences of small deformations, twisting and C−C stretching, are comparable to room temperature thermal energies (0.01 eV). At this point, we should discuss the likelihood of the geometric distortions observed in the crystal structure being physically realistic. The resolution of the crystal structure is 2.72 Å, and so, we may conclude that the dihedral distortions studied here, which are responsible for the overall shape of the molecule are physically realistic. However, given that the structure is partially determined by force field modeling, there is some uncertainty over whether the bond length distortions are real or an artifact of the particular force field used in determining the structure. However, the discussion of how these states is still useful as we have shown that C−C stretching is thermally accessible at room temperature and so is likely to have some effect on the lutein electron spectrum. 5.2. Origin of the ICT State. For the crystallographic structure of Lut 1, the 11Ag− → 11Bu−* and 11Ag− → 11Bu+ transitions have a transition dipole strength of ∼20.1 D and ∼36.7 D, respectively. This further illustrates the fact that the particle−hole symmetry of these states is not well-defined as we see further mixing of the original 11Bu−* and 11Bu+ polyene states. As before, the excited Ag states have negligible connection to the ground state. Similar results are also found for the Lut 2 crystallographic structure. Although distortions do seem to result in mixing of the 11Bu− and11Bu+ states, we may argue that these states are not very well-defined even for lutein in an idealized all-trans conformation. It has been proposed that the ICT state is a 21Ag− state that has acquired a large static dipole moment. As was mentioned previously, our calculations indicate that geometric distortions have little effect on the character of the 21Ag− state wave function. The 21Ag− state retains its doubly excited (covalent) character throughout and therefore has a vanishing static electric dipole moment in all cases. We can therefore conclude that, if the elusive ICT is in fact a strongly dipolar 21Ag− state, it is highly unlikely that geometric distortions could generate this state. Another possibility that the ICT state is a quantum mechanical mixture of the canonical 21Ag− state and a 11Bu−like state54 requires that the ICT state observed in carbonylcontaining polyenes be a mixture of the 21Ag− and a 11Bu−-like states. Unlike these carbonyl-containing polyenes, our model system (lutein) lacks an oxygen-withdrawing group directly attached to the conjugated chain. We wished to test whether geometric distortions could, in principle, produce such a mixed

Figure 7. Lut1 (in red) with its local binding pocket in LHCII shown in green.

with part of its local binding pocket in LHCII shown in green (apart from oxygen and nitrogen atoms, which are shown in red and blue, respectively). A schematic representation of the monomeric LHCII protein is shown in pale blue. The structure of LHCII shows many charged groups (such as aspartates, glutamates, etc.), and it is possible that charge neutralization, due to protonation during the proton-driven switch to the NPQ state, could have a strong influence on the position of 9851



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(14) Pascal, A. A.; Liu, Z. F.; Broess, K.; van Oort, B.; van Amerongen, H.; Wang, C.; Horton, P.; Robert, B.; Chang, W. R.; Ruban, A. Nature 2005, 436, 134−137. (15) Ruban, A. V.; Pascal, A. A.; Robert, B.; Horton, P. J. Biol. Chem. 2001, 276, 24862−24870. (16) Ilioaia, C.; Johnson, M. P.; Liao, P. N.; Pascal, A. A.; van Grondelle, R.; Walla, P. J.; Ruban, A. V.; Robert, B. J. Biol. Chem. 2011, 286, 27247−27254. (17) Valkunas, L.; Trinkunas, G.; Chmeliov, J.; Ruban, A. V. Phys. Chem. Chem. Phys. 2009, 11, 7576−7584. (18) Ruban, A. V.; Pascal, A.; Lee, P. J.; Robert, B.; Horton, P. J. Biol. Chem. 2002, 277, 42937−42942. (19) Lampoura, S. S.; Barzda, V.; Owen, G. M.; Hoff, A. J.; van Amerongen, H. Biochemistry 2002, 41, 9139−9144. (20) Bode, S.; Quentmeier, C. C.; Liao, P. N.; Hafi, N.; Barros, T.; Wilk, L.; Bittner, F.; Walla, P. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 12311−12316. (21) Muller, M. G.; Lambrev, P.; Reus, M.; Wientjes, E.; Croce, R.; Holzwarth, A. R. ChemPhysChem 2010, 11, 1289. (22) Polivka, T.; Sundström, V. Chem. Rev. 2004, 104, 2021−2071. (23) Tavan, P.; Schulten, K. J. Chem. Phys. 1986, 85, 6602−6609. (24) Kurashige, Y.; Nakano, H.; Nakao, Y.; Hirao, K. Chem. Phys. Lett. 2004, 400, 425−429. (25) Starcke, J. H.; Wormit, M.; Schirmer, J.; Dreuw, A. Chem. Phys. 2006, 329, 39−49. (26) Wu, W.; Danovich, D.; Shurki, A.; Shaik, S. J. Phys. Chem. A 2000, 104, 8744−8758. (27) Ostroumov, E.; Muller, M. G.; Marian, C. M.; Kleinschmidt, M.; Holzwarth, A. R. Phys. Rev. Lett. 2009, 103, 108302−4. (28) Polivka, T.; Zigmantas, D.; Herek, J. L.; He, Z.; Pascher, T.; Pullerits, T.; Cogdell, R. J.; Frank, H. A.; Sundström, V. J. Phys. Chem. B 2002, 106, 11016−11025. (29) Niedzwiedzki, D.; Koscielecki, J. F.; Cong, H.; Sullivan, J. O.; Gibson, G. N.; Birge, R. R.; Frank, H. A. J. Phys. Chem. B 2007, 111, 5984−5998. (30) Cong, H.; Niedzwiedzki, D. M.; Gibson, G. N.; Frank, H. A. J. Phys. Chem. B 2008, 112, 3558−3567. (31) Niedzwiedzki, D. M.; Sullivan, J. O.; Polivka, T.; Birge, R. R.; Frank, H. A. J. Phys. Chem. B 2006, 110, 22872−22885. (32) Gradinaru, C. C.; Kennis, J. T. M.; Papagiannakis, E.; van Stokkum, I. H. M.; Cogdell, R. J.; Fleming, G. R.; Niederman, R. A.; van Grondelle, R. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 2364−2369. (33) Papagiannakis, E.; Kennis, J. T. M.; van Stokkum, I. H. M.; Cogdell, R. J.; van Grondelle, R. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 6017−6022. (34) Papagiannakis, E.; Das, S. K.; Gall, A.; van Stokkum, I. H. M.; Robert, B.; van Grondelle, R.; Frank, H. A.; Kennis, J. T. M. J. Phys. Chem. B 2003, 107, 5642−5649. (35) Polivka, T.; Balashov, S. P.; Chabera, P.; Imasheva, E. S.; Yartsev, A.; Sundström, V.; Lanyi, J. K. Biophys. J. 2009, 96, 2268− 2277. (36) Fujiwara, M.; Yamauchi, K.; Sugisaki, M.; Yanagi, K.; Gall, A.; Robert, B.; Cogdell, R.; Hashimoto, H. Phys. Rev. B 2008, 78, 161101− 4. (37) Christensson, N.; Polivka, T.; Yartsev, A.; Pullerits, T. Phys. Rev. B 2009, 79, 245118−14. (38) Papagiannakis, E.; Stokkum, I. H. M.; Vengris, M.; Cogdell, R. J.; Grondelle, R.; Larsen, D. S. J. Phys. Chem. B 2006, 110, 5727−5736. (39) Polivka, T.; Sundström, V. Chem. Phys. Lett. 2009, 477, 1−11. (40) Savolainen, J.; Buckup, T.; Hauer, J.; Jafarpour, A.; Serrat, C.; Motzkus, M.; Herek, J. L. Chem. Phys. 2009, 357, 181−187. (41) Buckup, T.; Savolainen, J.; Wohlleben, W.; Herek, J. L.; Hashimoto, H.; Correia, R. R. B.; Motzkus, M. J. Chem. Phys. 2006, 125, 194505−7. (42) Frank, H. A.; Bautista, J. A.; Josue, J.; Pendon, Z.; Hiller, R. G.; Sharples, F. P.; Gosztola, D.; Wasielewski, M. R. J. Phys. Chem. B 2000, 104, 4569−4577. (43) Rechthaler, K.; Köhler, G. Chem. Phys. 1994, 189, 99−116. (44) Rettig, W. Angew. Chem., Int. Ed. 1986, 25, 971−988.

such a state. Additionally, protein conformation changes could result in significant changes to the local environment of lutein in LHCII. In particular, Wentworth et al.83 observed significant changes in the relative orientation of the two luteins in LHCII during switching between fluorescent and dissipative states. However, significant work is needed in order to clarify this issue, and we intend to perform the investigation of such a mechanism, that is a topic of future theoretical work. Of specific interest is the aspartic acid residues, which are each closely associated with the ε-ends of both luteins in LHCII (and in the minor antenna complex CP29). According to the electrostatic modeling,79 these residues are unlikely to be protonated under physiological conditions and so carry a negative charge. We conjecture that the presence of significant charge anisotropy within the locality of lutein, coupled with the highly specific solvent environment, may explain the presence of the low-lying lutein ICT state observed in plant LHCII complex. We must note at this point that, since we have neglected any electrostatic interactions with the protein, this point is highly speculative in nature.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: mindaugas.macernis@ff.vu.lt. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported partly by the European Social Grant under the Global Grant Measure (to L.V. and M.M.), UK EPSRC grant EP/H024697/1, and The Royal Society International Joint Project Grant 2009/R4. The public access supercomputer from the High Performance Computing Center (HPCC) of the Lithuanian National Center of Physical and Technology Sciences (NCPTS) at Vilnius University was used.

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