ElectronâVibrational Coupling and Fluorescence ... - ACS Publications

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The Journal of Physical Chemistry

Electron-Vibrational Coupling and Fluorescence Spectra of Tetra-, Penta- and Hexacoordinated Chlorophylls c1 and c2 Mihajlo Etinski,∗,† Milena Petković,† Miroslav M. Ristić,† and Christel M. Marian‡ Faculty of Physical Chemistry, University of Belgrade Studentski trg 12-16 11000 Belgrade, Serbia, and Institute of Theoretical and Computational Chemistry, Heinrich Heine University D¨ usseldorf, D¨ usseldorf, Universitätsstrasse 1, D-40225 D¨ usseldorf, Germany E-mail: [email protected]

Abstract Chlorophylls (Chls) are a group of pigments related to light absorption, excitation energy and electron transfer in photosynthetic complexes. Given the importance of intramolecular nuclear motion for these electronic processes, many experimental studies were performed in order to relate its coupling to electronic coordinates of these pigments but a detailed analysis is still lacking for isolated Chls c1 and c2 . To gain insight into the intramolecular motion and fluoroscence spectra of these two pigments in tetra, penta- and hexacoodinated states, we performed a quantum chemical study based on density functional theory and multi-mode harmonic approximation with displaced, ∗

To whom correspondence should be addressed University of Belgrade ‡ Heinrich Heine University D¨ usseldorf †

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distorted and rotated normal modes. In order to benchmark the employed methods, we simulated the high-resolution fluorescence spectra of tetracoodinated Chls a, b and d and compared them with available experimental spectra obtained with fluorescence line-narrowing techniques. Although the experimental spectra were obtained for ligand coordinated Chls, qualitatively good agreement was found between the simulated and experimental spectra. Almost all resonances were reproduced in the spectroscopically interesting region from 200 to 1700 cm−1 . The significance of mode distortion and rotation for the simulated spectra is discussed. The fluorescence spectra of Chls c1 and c2 consist of a group of peaks in the 200-450 cm−1 spectral range, a group of weak peaks from 700 to 1000 cm−1 and a large group of strong peaks from 1100 to 1600 cm−1 . Ligand effects are also addressed and a mode is identified as a sensitive probe for the coordination state of Chls c1 and c2 .

Introduction Photosynthesis is a transformation of light into chemical energy. It begins by light harvesting and subsequent charge separation in reaction centers. The principal pigment related to these processes are chlorophylls (Chls). As a part of antenna proteins, they absorb light and transfer excitation energy toward reaction center proteins. In addition, Chls play a role in charge separation and electron transfer. These fascinating electronic processes are consequences of the Chl structure. It is a large heterocyclic macrocycle, tetracoordinated with a magnesium ion, and with a long hydrocarbon chain (phytyl tail) attached to it. Chl is coordinatively unsaturated in vacuum, whereas in solvents the positively charged magnesium center attracts nucleophilic molecules. Thus, solvent molecules can additionally coordinate the magnesium by forming a complex where one or two solvent molecules are located in an axial position relative to the Chl plane. 1 There are several types of Chls depending on the side chains and conjugated electronic π-system of the ring (cf. Figure 1). With respect to the electronic π-system, Chls can be

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classified as chlorin- or porphyrin-type Chls. Chls a, b and d belong to chlorin-type Chls. Chlorin is a porphyrin in which the C17-C18 bond is reduced to a single bond and therefore, it is not aromatic through the entire circumference of the ring. Structural differences between Chls a, b and d concern positions 3 and 7. At position 3, there is a vinyl group in Chls a and b, and a formyl group in Chl d. At position 7, there is a methyl group in Chls a and d, and a formyl group in Chl b. The second group of chlorophylls consists of Chls c1 and c2 , whose aromatic ring is of porphyrin-type. They do not contain a phytyl tail. The difference in their structure is related to the substutient in position 8: Chl c1 has an ethyl group, while Chl c2 has a vinyl group attached to it. Various chemical substitutions enable Chls to absorb light in different spectral regions. The maximum photosynthetic efficiency of plants is ordinarily obtained for red light, the spectral region where Chls a, b and d absorb. But organisms in aqueous enviroment receive more yellow than red light due to preferential absorption of the latter by water. Thus, in order to capture more light, these organisms contain Chl c1 and c2 as accessory pigments for yellow light absorption. 2 In Chls, the fluorescence originates only from the lowest singlet excited Qy state. The nearby Qx state does not contribute to emission. Fluorescence lifetimes amount to several nanoseconds. 3 The room-temperature spectrum has a strong 0-0 transition followed by a vibrational shoulder at ≈ 1200 cm−1 . 3–7 This indicates that the emission takes place from the vibrationally equilibrated electronic state. The shapes of the room-temperature fluorescence spectra do not show any obvious dependence on the Chl’s coordination number, in contrast to the absorption spectra. 4 Due to homogeneous and inhomogeneous broadening, the roomtemperature fluorescence spectra contain limited information about electron-vibrational coupling. In order to reveal vibronic structure of fluorescence spectra, besides cooling a sample one has to excite Chls with a spectrally narrow source within the electronic origin as is done in the fluorescence line-narrowing techniques (FLN and ∆FLN). These techniques are very selective since they provide information only about emitting Chls present in complex enviroment. 4,8–22 Two recent fluorescence line-narrowing studies of isolated chlorin-type Chls in

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organic solvents revealed frequencies and intensities of major vibronic transitions. 4,20 Rätsep et al. obtained nearly 40 well-resolved vibronic lines of Chl a in the range from 100-1700 cm−1 using the ∆FLN technique at 4.5 K. 4 They found that most of the ground state vibrations are virtually independent of the magnesium coordination. A minor dependence was observed for several modes above 1000 cm−1 . The total inter- and intramolecular linear electron-phonon coupling was estimated to be 0.53 ± 0.07. Telfer et al. measured FLN and resonance Raman spectra of Chls a, b and d. 20 Although these two techniques probe different resonance conditions, their spectra showed remarkable similarity. Telfer et al. used this similarity to assign vibronic transitions associated with vinyl, formyl and keto groups of Chls as well as modes sensitive to coordination state of the magnesium atom. The coordination dependent modes present in FLN spectra for Chls a, b and d in THF were found to be at ≈ 1120, 1290, 1480, 1520 and 1590 cm−1 . To the best of our knowlegde, FLN spectra of Chls c1 and c2 in organic solvents have not been measured. Quantum-chemical studies on Chls’ electronic spectra are scarse and mostly related to Chl a. The majority of the performed studies are related to the computation of vertical 23–30 and adiabatic electronic energies. 6,21,30 In addition, several studies were related to the simulation of the vibronic structure of absorption and emission spectra of Chls and bacteriochlorophylls (BChls). 4,6,21,31–33 Rätsep et al. calculated the vibronic structure of absorption and emission spectra of Chl a. 4 Although they employed a semi-empirical method, the calculated transitions were qualitatively similar to the experimental ones, though with shifted frequencies. Their computed fluorescence spectrum shows two narrow bands in the 500-600 cm−1 spectral region, one at about 700 cm−1 and a series of bands in the 900-1400 cm−1 but fails to reproduce the modes in the 350-450 cm−1 region. In addition, they argued that more realistic modeling of the enviroment is needed in order to reproduce intensities in the 100-200 cm−1 region. In a later study, Rätsep et al. simulated the absorption and emission spectra of BChl a. 21 By testing several computational methods, they concluded that the B3-LYP and CAM-B3-LYP functionals give correct reorganization energies. On the other

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side, the calculated total intramolecular Huang-Rhys factor (0.86) was found to be three times larger than the experimentally determined one (0.29). This discrepancy was explained by taking into account that the major part of the total Huang-Rhys factor comes from the low-frequency modes which are damped in the condensed phase and thus do not contribute to the electron-vibrational coupling. 21 Furthermore, they proposed that intramolecular mode rotation is responsible for the observed asymmetry between absorption and emission spectra. Although significant efforts have been devoted to measure and clarify the vibronic structure of chlorin-type Chls no such studies have been performed for porhyrine-type Chls. In the present contribution we try to shed light on the structure and vibronic fluorescence spectra of Chls c1 and c2 . Since it was demostrated that the increase of the coordination number modifies the vibronic intensities, 4,20 we studied penta- and hexacoordinated Chl-ligand complexes as well as isolated tetracoordinated Chls. It is useful to determine coordinationsensitive modes that can be used to determine the coordination states of Chls c1 and c2 in complex environments where structural data may not be available. In order to bechmark the employed computational methods, we simulated the vibronic fluorescence spectra of tetracoordinated Chl a, b and d and compared them with available experimental FLN spectra.

Computational Details Quantum-Chemical Calculations In order to make the present study computationally feasible, we subsituted the phytyl tail in Chls a, b and d with a methyl group, thus reducing the number of atoms from 137, 136 and 135, to 82, 81 and 80 for Chl a, b and d respectively. Chls c1 and c2 were investigated without modification. Pentacoordinated Chls c1 and c2 were modeled by adding a diethyl ether (Dee) ligand. Chls are pentacoordinated in room-temperature diethyl ether although they can increase 5



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their coordination number at cryogenic temperatures or high pressures. 34 Hexacoordinated Chls are created by binding two pyrimidines (2Pyr). All calculations were performed with the TURBOMOLE program package. 35 We utilized density functional theory (DFT) and time-dependent DFT (TDDFT) with the B3-LYP 36 functional implementation of TURBOMOLE 37,38 for the ground and Qy electronic state optimizations, respectively. It is known that the B3-LYP functional does not correctly describe charge transfer states that exist in chlorophylls 27,39 due to the self-interaction error in the orbital energies obtained in the ground-state DFT calculation. 40 In this study, we limit ourselves to the first (locally) excited singlet state, for which the B3-LYP functional provides the correct energy. Moreover, it was shown that this functional gives the correct reorganization energy for the emission of BChl a. 21 We have not used any symmetry constraints during geometry optimizations. The convergence maximum norm of the Cartesian gradient was set to 10−4 in atomic units. We employed split valence plus polarization (SVP) (Mg, 10s6p/4s2p; C, N, O, 7s4p1d/3s2p1d; H, 4s1p/2s1p) 41 basis sets for the geometry optimization and valence triple-zeta plus polarization (TZVP) (Mg, 14s7p/5s3p; C, N, O, 10s6p1d/4s3p1d; H, 5s1p/3s1p) 42 basis sets for vertical electronic energy calculations. The SNF program 43 was employed for numerical calculations of vibrational frequencies in the harmonic approximation. It is known that the anharmonic coupling is generally particularly strong for low-frequency modes. Furthermore, anharmonic compared to harmonic frequencies are generally shifted to lower values. For the purpose of taking into account anharmonicity, which is very important for Chls’ frequencies, we scaled all harmonic frequencies with factor 0.962. 44,45 The average computing time for the ground and excited state frequency calculations was two and ten days respectively, on eight Intel Xeon CPU 2.66 GHz processors.

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Fluorescence Spectra In this work, we restrict ourselves to harmonic potential energy surfaces. Their normal modes can be calculated using changes in the Cartesian coordinates of the equilibrium geometries of these surfaces. Reimers pointed out an alternative derivation of the normal modes using curvilinear coordinates. 46 He argued that the description of the vibrational motion of large and floppy molecules requires a treatment using curvilinear coordinates because it is dominated by bond-angle and bond-torsion changes that are poorly described with rectilinear motion. Nevertheless, Rätsep et al. found that curvilinear coordinates are not necessary for description of the optical spectra of BChl a 21 since the optimized ground- and excited-state geometries are very similar. Hence, we will use normal modes derived from the Cartesian displacements. Fluorescence is accompanied by a change in the vibrational normal modes. Generally, this means that the normal modes of the ground state are distorted, displaced and rotated relative to the Qy state normal modes. The transformation

Qf = JQi + D

(1)

between the modes is called Duschinsky transformation. 47 Qf and Qi are vectors that contain final and initial modes, respectively, while J and D are the Duschinsky rotational matrix and the mode displacement vector. Huang-Rhys factors Si are related to dimensionless mode displacements Di by Si = Di2 /2 The total Huang-Rhys factor is S =

P

i

(2)

Si . Another useful spectroscopic quantity is the

reorganization energy. It is related to the energy released when a molecule is relaxed to its vibrational ground state. This energy can be calculated using Huang-Rhys factors

λi = h ¯ ω i Si 7


(3)


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and the total reorganization energy λ is a sum of the energies of all modes. The majority of the studies on absorption and fluorescence spectra of Chls assume a Hamiltonian in which potential energy surfaces are displaced but not distorted and rotated. Such Hamiltonian produces mirror symmetry of absorption and fluorescence spectra with respect to the pure electronic 0-0 line position. Furthermore, it simplifies the explanation of low-temperature spectra, since at these temperatures, only 0-1 vibronic transitions are noticeable. Franck-Condon factors for 0-1 transitions, in this case, are related to HuangRhys factors by |h0|1i|2 = Si e−Si .

(4)

and they can be approximated with Huang-Rhys factors Si for small normal mode displacements. However, a breakdown of the mirror symmetry of the optical spectra was observed for Chl a 4 and BChl a 21 due to Franck-Condon and Herzberg-Teller interactions. It is believed that the Franck-Condon interaction is more important. 21 This indicates that model based on displaced modes is not sufficient to simulate optical spectra but it is necessary to include mode distortion and rotation. In the next section, we will discuss the plausibility of the displaced mode model. Our Chls models have more than 200 normal modes and the explicit calculation of multidimensional Franck-Condon factors becomes computationally extremely demanding. In order to correctly describe the multimode nature of the electronic transition and to take into account the full size of the system, we used a recently developed method 48–50 implemented in the program VIBES 51 for the calculation of one-photon spectra based on the Fourier transformation of the correlation function. The method includes all important normal mode changes (distortion, displacement and rotation) and temperature effects as well. It was succesfully employed to simulate the absorption spectra of free-base porphyrin and chlorin. 50 The vibronic fluorescence spectra were calculated within the Condon approximation for the transition dipole moment. It is not necessary to include Herzberg-Teller coupling since 8


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the transition is electronically allowed and not coupled to the Qx state. In order to obtain converged emission spectra, the correlation function is multiplied with a Gaussian damping function. This gives a finite broadening to spectral lines. The broadening used in this work was set to 5 and 100 cm−1 , respectively, and the correlation function was calculated for 6 and 0.6 ps, respectively. We assume that Chls are in thermal equilibrium with a heat bath, so that the population of the Qy vibronic states is given by the Boltzmann distribution. All spectra were calculated at 10 and 77 K, respectively.

Results and Discussion Optimized Geometries and Energies The Ground State In our previous work on the electronic states of Chls a and b, 30 we compared the optimized B3-LYP/SVP ground-state bond lengths to the crystallographic data. 52,53 Although the employed SVP basis set is rather small, we found excellent agreement between the calculated and the experimental bond lengths. The average bond difference was estimated to be 0.005 and 0.004 ˚ A for Chls a and b, respectively, showing that the B3-LYP functional can provide a good description of the ground state geometry of these biological molecules. Selected bond lengths of the optimized ground state geometries of Chls are listed in Table 1. Comparing them with those computed in previous studies based on density functional theA. Generally, ory 23,26 we find very good agreement with the average discrepancy of 0.01-0.02 ˚ all Chls have similar bond lengths with maximal difference of 0.02 ˚ A , which indicates that ground state geometries are very similar. Exceptions are bonds of side groups and carboncarbon bonds in the five-atom ring with the C17-C18 bond. The single/double character of the C17-C18 bond influences the local aromaticity of the ring and thus modifies nearby bond lengths. This changes the dihedral angle C16-C17-C171-C172 as well, which amounts

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to ≈ 53◦ for Chls a, b and d, and 45◦ for Chls c1 , c2 . On the other side, the dihedral angle C15-C132 -C133 -O is ≈ 73◦ and 46◦ for the first and the second group of Chls, respectively. The magnesium atom is positioned in the Chl’s ring plane, although it is not in the center of the ring. The longest magnesium-nitrogen distance is found for the Mg-N24 bond, and it is significantly longer than the other Mg-N bonds. The average Mg-N distance is 2.07, 2.08 and 2.08 ˚ A for Chls a, b and d respectively. Thus, the peripheral substituents of the chlorine ring do not significantly change the Mg-N distances. This distance is sligthly smaller in the case of the porphyrin-type Chls (2.06 ˚ A). Addition of diethyl ether and two pyrimidine ligands elongates Mg-N bonds of Chls c1 and c2 . In the pentacoordinated state, the Mg-N bonds are 0.02-0.03 ˚ A longer than in the tetracoordinated state while in the hexacoordinated state these bonds are 0.04-0.05 ˚ A longer. Furtheremore, the diethyl ether ligand displaces the magnesium atom out-of-plane while two pyrimidine ligands restrain it in the plane. The elongation of the Mg-N bonds could have an impact on the vibrational frequencies and fluorescence spectra of penta- and hexacoordinated Chls c1 and c2 . Fujiwara and Tasumi 54,55 and later Näveke et al. 56 showed that the frequencies of several modes between 1000 and 1600 cm−1 of Mg and metal-substituted Chls and BChls are linearly dependent on the metal-N bond lengths. More details about the magnesium coordination state and its impact on the vibrational frequencies will be discussed in the next section. Vibrational properties of the ground state of Chl a were computed and analyzed by Hastings and coworkers who studied high intensity bands that correspond to the C=O stretching motion of Chl a in vacuum 57 and in solution. 58 We will briefly analyse the computed frequencies of the five Chls. Concerning Chls a, b and d, the high frequency region 2800-3200 cm−1 corresponds to C-H stretching motions. C=O stretching bands are located between 1740 and 1780 cm−1 , whereas the C-O stretch covers the region 1150-1250 cm−1 . C=C stretching bands are found between 1400 and 1640 cm−1 , while C-C stretches cover a much wider region, some of them being mixed with other types of motion. C-N stretching frequencies are predominantly close to 1350 cm−1 , whereas Mg-N stretching frequencies are mainly located

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between approximately 1000 and 1300 cm−1 . A similar behavior is found in Chls c1 and c2 , with additional appearance of O-H stretching frequencies above 3560 cm−1 . The complete list of the ground state frequencies is given is Supplementary Information. The Qy State In order to compare geometry changes upon excitation to the first excited singlet state, we present differences between Qy and ground state bond lengths in Table 1. These differences clearly show that most of the bonds do not change their lengths upon electronic excitation to the first excited electronic state. This very moderate geometry change has important consequences on the fluorescence spectrum. The largest bond length changes are observed for Chl a and b, and the smallest for Chls c1 and c2 . The changes are usually in the range of 0.01 ˚ A. There are a few with variations up to 0.02 ˚ A: C1-C2, C4-C5, C1-N21 (Chl a), C1-C2, C4-C5 (Chl b), C1-N21, C133 -O (Chl d), C9-C10 (Chls c1 ·2Pyr and c2 ·2Pyr). Interestingly, there is only one bond that changes its length in all considered Chls: C4-C5. In the chlorintype Chls, the average Mg-N distance decreases in the Qy state. Particularly, the N22-Mg and N24-Mg bonds shrink their lengths, while two other Mg-N bond lengths elongate or remain constant depending on the Chl species. In Chl c1 , the average Mg-N distance does not change but in the penta- and hexacoordinated states it is slightly longer than in the ground state. A similar behaviour is found for Chl c2 as well. In addition to the transition between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), HOMO→LUMO, the Qy state involves the HOMO-1→LUMO+1 transition. 59 The orbitals related to these transitions in Chl c1 and its complexes are shown in Figure 2. The orbitals for other examined Chls are given in SI. All orbitals are of π character. Their electron densities are delocalized on the macrocycle as well as on the side groups but not on the magnesium atom. The substantial electron density on magnesium atom appears in higher energy orbitals. The fact that there is no electron density on the magnesium atom in the frontier orbitals indicates that these orbitals

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are not affected strongly by solvent coordination. As can be seen from the Figure 2, this is partially true because only the HOMO changes upon coordination of the Chl c1 . The HOMO gradually loses the electron density on the atoms C13 and C4 upon the increase of the coodination number. Hence, due to the contribution of the HOMO, various coordination states have sligthly different electron density in the Qy state. The orbitals can be divided into two groups according to the electronic structure of the Chls: in one group are orbitals of chlorin-type Chls a, b and d, in other group are orbitals of porphyrin-type Chls c1 and c2 . The transition from the HOMO to the LUMO mainly involves a decrease of electron density on atom C7 and an increase on atoms N22, N24 and C10 for the chlorine-type Chls and a decrease of electron density on atom C16 accompanied by an increase on atoms C13, C131 and C3 for the porphyrin-type Chls. On the other side, transition from HOMO-1 to LUMO+1 involves a loss of electron density on atoms N24 and N22 and a gain on atoms C7 and C8 for the chlorine-type Chls and a shift of the electron density on atom C3 to atom C2 for the porphyrin-type Chls. The Qy oscillator strengths, electronic adiabatic energies together with zero-point corrected values are presented in Table 2. It can be seen that the computed oscillator strengths of Chl c1 and c2 are an order of magnitude smaller than the ones of Chl a, b and d and that they decrease upon coordination. The largest oscillator strengths have Chls a (0.261) and d (0.248). The Qy adiabatic energies are in the range 2.04-2.16 eV. Correction for zero-point vibrational motion lowers these energies by ≈ 0.1 eV. We nicely reproduce the experimental ordering of the Qy state energies. In order to obtain quantitive agreement between calculated and experimental energies, it is necessary to include ligands in the calculation as can be seen from the excellent agreement between the computed and experimental energy of the hexacoordinated Chl c2 . Neglect of ligands blue-shifts 0-0 energies by ≈ 0.15 eV.

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Huang-Rhys Factors and Reorganization Energies Quantities that essentially contribute to the spectral line shape are normal mode displacements. They are related to the Huang-Rhys factors by equation 2. Complete lists of the Huang-Rhys factors for all examined Chls are provided in the SI and their sum S is given in Table 3. Chls a and b have the same value ≈ 0.8 for S while Chl d has two and a half times lower value of ≈ 0.3. Thus, Chl d is less vibronically active than Chls a and b. The tetracoordinated Chls c1 and c2 have the total Huang-Rhys factor ≈ 0.8 and 0.6 respectively. Addition of ligands increases the values almost by a factor of two. This increase is expected since the presence of ligands creates slightly different geometry distortions in the ground and Qy states (cf. Table 1.). In addition, displacements of the ligand atoms contribute to the S as well. Moreover, for both Chls in the hexacoordinated state, the total Huang-Rhys factor is larger than in the pentacoordinated state. The computed value of the total Huang-Rhys factor for Chl a is larger than the experimentally determined value which is ≈ 0.3. 4,6,21 Nevertheless, similar computed values of S were also found for BChl a. 21 As proposed by Ra¨tsep et al., 21 the discrepancy between the computed and experimental values stems from the fact that gas-phase models overestimate displacements of low-frequency modes (tail torsion and bending, out-of-plane bending combined with methyl group rotation). These modes are damped in the condensed phase. In order to estimate the total Huang-Rhys factor in the condensed phase, we divided the Huang-Rhys factors into two groups: factors due to low-frequency modes up to 200 cm−1 , and those due to modes above this value (cf. Table 3). The former group has Huang-Rhys factors of the order of 0.1 and it contributes 50-70% to the S for Chls a, b and d, while for Chls c1 and c2 the contribution is 80% regardless of the coordination state. The sum of the Huang-Rhys factors for the modes above 200 cm−1 is in the range of 0.13-0.30. These values could be an estimate of S in the condensed phase. Ten ground state modes with the largest Huang-Rhys factors for the Qy →S0 transition in the spectroscopically interesting range between 200 and 1700 cm−1 are compiled in Tables 4, 5 and 6. The approximate assignment of modes is given as well. Usually, many atoms 13



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contribute to a mode. Hence, in order to simplify the assignment only the main vibrational types are given. The modes with the largest Huang-Rhys factors are mainly related to C-C, C-N stretching and out-of-plane and in-plane bending. Same strongly displaced modes are present in Chls a and d, though with different Huang-Rhys factors. Thus, it is expected that their fluorescence spectra will be similar. On the other hand, Chl b has different distribution of the Huang-Rhys factors in comparison to Chls a and d. The porphyrin-type Chls have more strongly displaced low-frequency modes ( from 200 to ≈ 350 cm−1 ) than chlorin-type Chls. These modes include in-plane and out-of-plane modes as well as modes due to Mgumbrella motion. Ligand coordination changes these mode frequencies only by up to 2-3 cm−1 . In addition, coordination can shift frequencies to the red or blue side. Surprisingly, the Huang-Rhys factors can change even by an order of magnitude. Hence, coordination effects are more readily observable in the vibronic peak intensities than in their frequency shifts. Since the difference between Chls c1 and c2 lies in the single/double bond character of the C81 -C82 bond, large differences in the distribution of the Huang-Rhys factors is not expected. Nevertheless, there are exceptions like for instance the out-of-plane mode at ≈ 310 cm−1 . In the case of tetracoordinated Chl c1 , its Huang-Rhys factor is almost five times larger than in Chl c2 . The mode that changes its displacement most upon the change of coordination number from five to six is the Mg-N24 stretching mode computed at 1341 cm−1 and 1339 cm−1 for the penta- and hexacoordinated Chls c1 and c2 , respectively. It is presented in Figure 3. The Huang-Rhys factor of this mode increases from 0.0043 to 0.0116 for Chl c1 and from 0.0010 to 0.0072 for Chl c2 . Due to a large change of the Huang-Rhys factor, we propose that this mode could be used as a probe for the coordination state of porhyrin-type Chls. In addition to mode displacements, the transition from the Qy to the ground state is followed by frequency changes and reorientation of the normal modes. Figures 3.-11. in the SI depict the expansion of the Qy normal modes in the basis of the ground state normal modes. The ground and Qy state modes are presented on the y and x axes, respectively. The

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largest mode rotation occurs in the range 900-1700 cm−1 , where C-C stretching frequencies are positioned. On the other side, high-frequency modes such as C-H stretching modes are generally not significantly altered. Contributions of the Qy modes in the expansion of the ten ground-state modes with the largest Huang-Rhys factors are given in Tables 4, 5 and 6. Many of these modes are not dominated by a single vibration and moreover, there are several modes with three or more contributions. Since the modes with the largest HuangRhys factors determine the fluorescence spectra, this has important consequences on its shape. We present a detailed discussion of mode mixing in the next subsection. Reorganization energies of Chl modes are generally below 20 cm−1 except for a few modes. The modes with the largest reorganization energies mainly consist of stretching modes in the range 900-1600 cm−1 as well as C-H stretching modes around 2900 cm−1 . In the spectral range 200-1700 cm−1 these are: 1313 (C-N stretching) and 1528 cm−1 (C-C stretching) for Chl a, 1251 (C-C, C-N stretching) and 1473 cm−1 (C-C stretching) for Chl b, 1528 (C-C stretching) and 1316 cm−1 (C-N, C-C stretching) for Chl d. For porphyrin-type Chls these modes are ≈ 1326 (C-N, C-C stretching) and ≈ 1352 cm−1 (C-C stretching). The total reorganization energy is insensitive to the contribution from low-frequency modes (cf. Table 3). Although these modes have large displacements, their energies are low and consequently their contribution to the total reorganization energy is small. The total reorganization energies for Chls are in the range of 140-398 cm−1 . The smallest value is found for Chl c2 while the largest value is computed for Chl b. Ligand coordination increases the reorganization energies as expected.

Fluorescence Spectra Chls a, b and d Shown in Figure 4 are simulated and experimental fluoroscence spectra of Chls a, b and d at 77 K. The experimental spectra of hexacoordinated Chls were obtained by Hartzler et al. 7 in toluene/pyridine solution. A Gaussian damping of 100 cm−1 was used. The general structure 15



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of the spectra is similar, but it is obvious that there are minor differences in the vibronic structure. The spectra are dominated by the 0-0 transition. In addition, there are two small peaks in the region of C-C, C-N stretching (∼ 1300 cm−1 for Chls a and b and ∼ 1200 cm−1 for Chl d) as well as C-H stretching (∼ 3000 cm−1 for Chls a, b and d). Their relative intensities are computed to be 0.10 and 0.11 (for Chl a), 0.14 and 0.06 (for Chl b) and 0.05 and 0.02 (for Chl d), respectively. We find that the experimental peak in the C-H stretching region is much weaker than the computed one. This indicates that our displacements of high-frequency modes are overestimated. The experimental peak corresponding to C-C and C-N stretching motion appears at smaller energies (1100-1200 cm−1 ) than ours. This is due to the neglect of the ligands in our model since in this region there are coordination-sensitive modes whose displacements are underestimated. Neverthless, the relative intensity of this peak (0.10, 0.10 and 0.07 for Chls a, b and d respectively) is in reasonable agreement with the computed value. Large broadening hides detailed vibronic structure of the fluorescence spectrum. In order to benchmark our methods, we therefore computed high-resoulution spectra at 10 K with the 5 cm−1 broadening. Let us more closely compare the spectroscopically important range from 200 to 1700 cm−1 of the computed spectra for which there are experimental spectra obtained by line-narrowing techniques. The simulated spectra together with the digitalized experimental spectra are presented in Figure 5. The experimental spectra include the ∆FLN spectrum of Chl a measured by Rätsep et al. in 1-propanol at 4.5 K 4 and the FLN spectra of Chls a, b and d measured by Telfer et al. in THF at 4 K. 20 THF provides two axial ligands to the central Mg atom while 1-propanol provides one ligand. Unfortunately, the part of the FLN spectra below ≈ 700 cm−1 is not available. Although we used a simplified theoretical model in our study and did not realistically model the complex surroundings of the chlorin-type Chls (bulk solvent-Chl interaction and axial coordination), the simulated peaks reasonably well match the peaks observed in FLN and ∆FLN spectra (cf. Figure 5). Most of the computed peaks can be related to experimental ones. A broad substructure in

16


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the simulated spectra observed in the range 200-500 cm−1 comes from low-frequency modes (ω200 ) and reorganization energy in cm−1 (λ). Table 4: Ten ground state modes of Chls a, b and d between 200 and 1700 cm−1 with highest Huang-Rhys factors for the Qy →S0 transition, their approximate assignment and the Qy modes contributions (>10%). Table 5: Ten ground state modes of Chls c1 , Chls c1 ·Dee, Chls c1 ·2Pyr between 200-1700 cm−1 with highest Huang-Rhys factors for the Qy →S0 transition, their approximate assignment and the Qy mode contributions (>10%). Table 6: Ten ground state modes of Chls c2 , Chls c2 ·Dee, Chls c2 ·2Pyr between 200 and 1700 cm−1 with highest Huang-Rhys factors for the Qy →S0 transition, their approximate assignment and the Qy mode contributions (>10%).

37



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Table 1: The S0 and difference between the S0 and Qy (∆Qy ) bond lengths in ˚ A. bond C1-C2 C2-C3 C3-C4 C4-N21 C4-C5 C5-C6 C6-N22 C6-C7 C7-C8 C8-C9 C9-N22 C9-C10 C10-C11 C11-N23 N23-C14 C14-C13 C13-C12 C12-C11 C13-C131 C131 -C132 C132 -C15 C15-C14 C15-C16 C17-C18 C18-C19 C19-C20 C20-C1 C19-N24 N21-Mg N22-Mg N23-Mg N24-Mg C3-C31 C31 -C32 C31 =O C2-C21 C18-C181 C1-N21 C16-N24 C7-C71 C71 =O C8-C81 C81 -C82 C12-C121 C131 =O C132 -C133 C133 =O C133 -O O-C134 C16-C17 C17-C171 C171 -C172 C172 -C173 C173 =O C173 -O O-C174

Chl S0 1.46 1.39 1.46 1.38 1.39 1.41 1.36 1.45 1.38 1.46 1.38 1.41 1.40 1.39 1.33 1.42 1.39 1.46 1.46 1.58 1.54 1.42 1.39 1.55 1.53 1.39 1.41 1.36 2.03 2.08 2.02 2.16 1.46 1.35 / 1.50 1.54 1.36 1.38 1.50 / 1.50 1.54 1.50 1.21 1.52 1.21 1.34 1.43 1.53 1.55 1.53 1.52 1.21 1.35 1.43

a ∆Qy -0.02 0.01 0.01 -0.01 0.02 -0.01 0.01 0.01 0.00 0.01 -0.01 0.00 0.01 0.00 0.01 0.01 0.00 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 -0.01 0.01 0.01 0.00 0.01 -0.01 0.00 -0.01 -0.01 0.00 / 0.00 0.00 0.02 0.00 0.00 / 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 0.00

Chl S0 1.46 1.38 1.47 1.38 1.39 1.42 1.36 1.45 1.40 1.44 1.38 1.41 1.40 1.39 1.33 1.43 1.39 1.46 1.47 1.58 1.54 1.42 1.38 1.55 1.53 1.39 1.41 1.36 2.03 2.09 2.02 2.16 1.46 1.34 / 1.50 1.54 1.36 1.38 1.46 1.22 1.50 1.54 1.50 1.21 1.52 1.21 1.34 1.43 1.52 1.55 1.53 1.52 1.21 1.35 1.43

b ∆Qy -0.02 0.01 0.01 -0.01 0.02 -0.01 0.01 0.01 -0.01 0.01 0.00 0.01 0.00 0.00 0.01 0.00 0.00 0.00 -0.01 0.00 -0.01 0.00 0.01 0.00 -0.01 0.00 0.01 0.01 0.01 -0.01 0.01 -0.01 0.00 0.01 / 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Chl S0 1.45 1.39 1.46 1.37 1.40 1.41 1.36 1.46 1.38 1.46 1.37 1.41 1.40 1.39 1.33 1.43 1.39 1.46 1.47 1.58 1.54 1.41 1.39 1.55 1.53 1.39 1.41 1.36 2.04 2.08 2.02 2.16 1.47 / 1.22 1.50 1.54 1.36 1.37 1.50 / 1.50 1.54 1.50 1.21 1.52 1.21 1.34 1.43 1.52 1.55 1.53 1.52 1.21 1.35 1.43

d ∆Qy 0.00 0.01 0.00 0.00 0.01 -0.01 0.01 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 -0.01 0.00 -0.01 0.01 0.00 0.00 -0.01 0.01 0.00 0.00 0.00 -0.01 0.00 -0.01 -0.01 / 0.00 0.00 0.00 -0.02 0.01 0.00 / 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Chl S0 1.46 1.39 1.47 1.36 1.40 1.41 1.36 1.46 1.38 1.46 1.37 1.40 1.41 1.38 1.34 1.43 1.39 1.46 1.46 1.58 1.54 1.41 1.41 1.38 1.45 1.41 1.40 1.37 2.04 2.08 2.02 2.11 1.46 1.35 / 1.50 1.50 1.37 1.38 1.50 / 1.50 1.54 1.50 1.21 1.53 1.20 1.35 1.43 1.47 1.46 1.35 1.48 1.21 1.35 /

c1 ∆Qy -0.01 0.00 0.00 0.00 0.01 -0.01 0.01 0.00 0.00 0.00 0.00 0.01 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.01 -0.01 0.01 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 / 0.00 0.00 0.01 0.01 0.00 / 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 /

38

Chl c1 ·Dee S0 ∆Qy 1.46 -0.01 1.39 0.01 1.47 0.00 1.36 0.00 1.41 0.01 1.41 0.00 1.36 0.01 1.46 0.00 1.38 0.01 1.47 0.00 1.37 0.00 1.41 0.00 1.41 0.01 1.37 0.01 1.34 0.00 1.43 0.00 1.39 0.01 1.47 -0.01 1.46 -0.01 1.59 0.00 1.54 -0.01 1.41 0.01 1.42 0.00 1.39 0.00 1.46 -0.01 1.42 -0.01 1.41 0.01 1.36 0.01 2.06 0.01 2.11 0.00 2.04 0.01 2.14 -0.01 1.46 -0.01 1.35 0.00 / / 1.50 0.00 1.50 0.00 1.36 0.01 1.37 0.01 1.50 0.00 / / 1.46 0.00 1.34 0.01 1.50 0.00 1.21 0.00 1.52 0.00 1.20 0.00 1.35 0.00 1.43 0.00 1.47 0.00 1.46 -0.01 1.35 0.00 1.48 0.00 1.21 0.00 1.35 0.00 / /


Chl c1 ·2Pyr S0 ∆Qy 1.46 -0.01 1.38 0.01 1.47 0.00 1.36 0.00 1.40 0.01 1.41 0.00 1.36 0.01 1.46 0.00 1.38 0.01 1.47 0.00 1.37 0.00 1.40 0.02 1.41 0.00 1.38 0.01 1.34 0.00 1.43 0.00 1.39 0.00 1.46 0.00 1.46 0.00 1.59 0.00 1.53 0.00 1.41 0.01 1.41 0.00 1.38 0.01 1.45 0.00 1.41 0.01 1.40 0.01 1.36 0.01 2.07 0.00 2.12 0.01 2.05 0.00 2.15 0.00 1.46 0.01 1.35 0.00 / / 1.50 0.00 1.50 0.00 1.37 0.01 1.38 0.00 1.50 0.00 / / 1.46 0.00 1.34 0.01 1.50 -0.01 1.21 0.00 1.52 0.00 1.20 0.00 1.35 0.00 1.43 0.00 1.47 0.00 1.46 -0.01 1.35 0.00 1.48 0.00 1.21 0.00 1.35 0.00 / /

Chl S0 1.46 1.39 1.47 1.37 1.40 1.41 1.37 1.46 1.38 1.47 1.37 1.40 1.41 1.38 1.34 1.43 1.39 1.46 1.46 1.58 1.53 1.41 1.41 1.38 1.45 1.41 1.40 1.37 2.04 2.09 2.02 2.11 1.46 1.35 / 1.50 1.50 1.37 1.38 1.50 / 1.46 1.34 1.50 1.21 1.53 1.20 1.35 1.43 1.47 1.46 1.35 1.48 1.21 1.35 /

c2 ∆Qy -0.01 0.00 -0.01 0.00 0.01 0.00 0.00 -0.01 0.01 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.01 0.01 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.01 0.00 0.00 / 0.00 0.00 0.00 0.00 0.00 / 0.00 0.01 -0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 /

Chl c2 ·Dee S0 ∆Qy 1.46 -0.01 1.39 0.01 1.47 0.00 1.36 0.00 1.41 0.01 1.41 0.00 1.36 0.01 1.46 0.00 1.38 0.01 1.47 0.00 1.37 0.00 1.41 0.00 1.41 0.01 1.37 0.01 1.34 0.00 1.43 0.00 1.39 0.01 1.47 -0.01 1.46 -0.01 1.59 0.00 1.54 -0.01 1.41 0.01 1.42 0.00 1.39 0.00 1.46 -0.01 1.42 -0.01 1.41 0.01 1.36 0.01 2.06 0.01 2.11 0.00 2.04 0.01 2.14 -0.01 1.46 -0.01 1.35 0.00 / / 1.50 0.00 1.50 0.00 1.36 0.01 1.37 0.01 1.50 1.50 / / 1.46 0.00 1.34 0.01 1.50 0.00 1.21 0.00 1.52 0.00 1.20 0.00 1.35 0.00 1.43 0.00 1.47 0.00 1.46 -0.01 1.35 0.00 1.48 0.00 1.21 0.00 1.35 0.00 / /

Chl c2 ·2Pyr S0 ∆Qy 1.46 -0.01 1.38 0.01 1.47 0.00 1.36 0.00 1.40 0.01 1.41 0.00 1.36 0.01 1.46 0.00 1.38 0.01 1.47 0.00 1.37 0.00 1.40 0.02 1.41 0.00 1.38 0.01 1.34 0.00 1.43 0.00 1.39 0.00 1.46 0.00 1.46 0.00 1.59 0.00 1.53 0.00 1.41 0.01 1.41 0.00 1.38 0.01 1.45 0.00 1.41 0.01 1.40 0.01 1.36 0.01 2.07 0.00 2.12 0.01 2.05 0.00 2.15 0.00 1.46 0.00 1.35 0.00 / / 1.50 0.00 1.50 0.00 1.37 0.01 1.38 0.00 1.50 0.00 / / 1.46 0.00 1.34 0.01 1.50 -0.01 1.21 0.00 1.52 0.00 1.20 0.00 1.35 0.00 1.43 0.00 1.47 0.00 1.46 -0.01 1.35 0.00 1.48 0.00 1.21 0.00 1.35 0.00 /

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Table 2: The oscillator strengths (f ) for the Qy →S0 transition, electronic (∆Ee ) and zeropoint energy corrected (∆E00 ) adiabatic energies of the Qy state in eV.

a

Chl f ∆Ee ∆E00 Exp. a 0.261 2.09 2.00 1.86a b 0.156 2.12 2.04 1.87b d 0.248 2.05 1.97 1.76b ,1.77c c1 0.035 2.16 2.08 c1 ·Dee 0.029 2.14 2.06 c1 ·2Pyr 0.014 2.04 1.95 c2 0.015 2.16 2.06 c2 ·Dee 0.014 2.13 2.04 c2 ·2Pyr 0.006 2.04 1.95 1.94d in room temperature diethyl ether and in room temperature pyridine 4 b in room temperature pyridine 3 c in diethyl ether at 77 K 5 d in room temperature tetrahydrofuran 3

39



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Table 3: The total Huang-Rhys factor (S), its value for modes above 200 cm−1 (S>200 ) and reorganization energy in cm−1 (λ). Chl a b d c1 c1 ·Dee c1 ·2Pyr c2 c2 ·Dee c2 ·2Pyr

S S>200 0.791 0.242 0.798 0.292 0.293 0.149 0.802 0.181 1.482 0.278 1.504 0.296 0.613 0.129 0.927 0.170 1.198 0.257

40

λ 309 335 151 231 398 391 140 203 338


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Graphical TOC Entry R

3

R

7

N Mg N

N R

8

N R

17

O O

O

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Table 4: Ten ground state modes of Chls a, b and d between 200 and 1700 cm−1 with highest Huang-Rhys factors for the Qy →S0 transition, their approximate assignment and the Qy modes contributions (>10%). ω 1000*Si 1528 7.8 1313 27.8 1214 5.5 1192 6.4 1136 4.7 962 8.6 734 5.5 382 4.6 342 7.1 240 16.0 ω 1000*Si 1473 9.7 1331 10.5 1278 8.6 1251 14.1 1216 8.7 1127 5.9 745 6.7 544 6.6 236 9.8 228 8.7 ω 1000*Si 1528 9.4 1316 10.4 1238 3.8 1215 4.4 1157 4.9 1135 7.1 963 5.8 829 4.0 256 5.6 232 3.9

Chl a Qy modes contributions 1509 (39%), 1517 (28%) 1309 (50%), 1293 (19%) 1208 (87%) 1222 (34%), 1201 (26%), 1107 (37%), 1062 (12%), 960 (88%) 725 (71%), 730 (18%) 378 (87%), 368 (11%) 339 (98%) 239 (55%), 237 (42%) Chl b assignment Qy modes contribution C-C stretching 1444 (6%), 1470 (80% ) C-N, C-C stretching 1326 (28%), 1333 (58%) C-N stretching 1184 (12%), 1281 (30%), C-C, C-N stretching 1247 (91%) 2 3 C13 -C13 stretching 1211 (45%), 1218 (21%), C-N stretching 1066 (10%), 1101 (10%), out-of-plane bending 739 (74%), 743 (13%) N21-Mg-N23 in-plane bending 541 (94%) out-plane bending 233 (89%) out-plane bending 226 (97%) Chl d assignment Qy modes contribution C-C stretching 1506 (32%), 1446 (25%), C-N, C-C stretching 1312 (72%) C-C stretching 1240 (82%) C132 -C133 stretching 1209 (81%), 1219 (12%) C-N, C-C stretching 1146 (34%), 1100 (21%), C-N stretching 1130 (40%), 1119 (18%) C-C stretching 960 (88%) out-of-plane bending 817 (45%), 825 (41%) in-plane bending 253 (99%) N-Mg-N out-of-plane bending 228 (96%) assignment C-C stretching C-N stretching C132 -C133 stretching C-N, Mg-N21 stretching C-N stretching C-C stretching out-of-plane bending out-of-plane bending in-plane bending in-plane bending

42


1180 (18%) 1118 (11%), 1082 (10%)

1283 (23%) 1241 (13%), 1246 (11%) 1122 (43%)

1517 (11%), 1478 (10%)

1181 (15%)

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Table 5: Ten ground state modes of Chls c1 , Chls c1 ·Dee, Chls c1 ·2Pyr between 200-1700 cm−1 with highest Huang-Rhys factors for the Qy →S0 transition, their approximate assignment and the Qy mode contributions (>10%). ω 1000*Si 1548 4.9 1513 4.5 1352 7.9 1326 13.4 1125 5.5 1103 5.1 465 6.7 310 20.2 268 6.4 260 8.7 ω 1000*Si 1546 6.0 1351 8.3 1324 19.8 1270 6.0 464 8.8 316 6.7 308 10.2 271 9.8 260 13.3 239 10.1 ω 1000*Si 1349 9.7 1344 6.8 1339 7.2 1323 11.0 1271 11.1 462 7.4 310 14.4 274 16.0 239 9.8 215 12.6

Chl c1 assignment Qy modes contribution C-C stretching 1527 (39%), 1517 (37%), 1501 (10%) C-C stretching 1527 (36%), 1517 (20%), 1445 (19%) C-C, Mg-N stretching 1345 (46%), 1326 (16%), 1348 (13%) C-N, C-C stretching 1277 (17%), 1325 (10%) Mg-N stretching 1114 (54%), 1122 (22%) Mg-N stretching 1095 (65%), 1096 (23%) in-plane bending 460 (51%), 458 (42%) Mg-N-C out-of-plane bending 309 (98%) Mg-N-C out-of-plane bending 262 (65%), 257 (17%), 270 (16%) in-plane bending 257 (79%), 262 (20%) Chl c1 ·Dee assignment Qy modes contribution C-C stretching 1519 (77%) C-C stretching 1345 (76%) C-N stretching 1289 (28%), 1327 (24%) vinyl group 1277 (52%), 1272 (42%) in-plane bending 459 (85%) Mg umbrella motion 314 (90%) Mg-N-C out-of-plane bending 307 (98%) Mg-N-C out-of-plane bending 266 (67%), 273 (29%) Mg-N-C out-of-plane bending 257 (86%), 250 (11%) in-plane bending 236 (91%) Chl c1 ·2Pyr assignment Qy modes contribution C-C stretching 1345 (59%), 1345 (28%) C-C stretching 1345 (43%), 1345 (24%), 1335 (22%) Mg-N24 stretching 1340 (38%), 1330 (15%) C-N stretching 1323 (39%), 1298 (13%) vinyl group 1276 (65%), 1273 (13%), 1273 (11%) in-plane bending 457 (87%) Mg-N-C out-of-plane bending 309 (95%) Mg-N-C out-of-plane bending 273 (89%) in-plane bending 238 (98%) Mg-N–C out-of-plane bending 212 (96%)

43



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Table 6: Ten ground state modes of Chls c2 , Chls c2 ·Dee, Chls c2 ·2Pyr between 200 and 1700 cm−1 with highest Huang-Rhys factors for the Qy →S0 transition, their approximate assignment and the Qy mode contributions (>10%). ω 1000*Si 1559 3.2 1321 3.3 1126 3.8 1103 3.3 309 4.2 300 11.4 290 4.0 285 3.7 268 13.9 204 4.2 ω 1000*Si 1351 6.4 1323 7.9 1101 4.4 470 6.5 362 4.9 301 7.7 287 9.1 276 5.2 268 11.9 207 4.9 ω 1000*Si 1552 6.0 1349 7.7 1339 11.6 1321 8.4 1271 11.6 362 7.9 302 15.3 270 12.6 241 12.8 217 11.4

Chl c2 assignment Qy modes contribution C12-C13 stretching 1543 (71%), 1551 (18%) C-C, C-N stretching 1305 (65%), 1318 (15%), Mg-N stretching 1126 (40%), 1119 (36%), Mg-N(21,24) stretching 1095 (61%) N-Mg-N out-of-plane bending 305 (98%) out-of-plane bending 295 (95%) Mg-N-C out-of-plane bending 287 (76%), 289 (22%) Mg-N-C out-of-plane bending 280 (83%) in-plane bending 267 (95%) Mg umbrella motion 201 (53%), 199 (44%) Chl c2 ·Dee assignment Qy modes contribution C-C stretching 1345 (41%), 1347 (29%), C-C, C-N stretching 1320 (35%), 1251 (14%) Mg-N(21,24) stretching 1093 (86%) in-plane bending 460 (69%), 470 (37%) out-of-plane bending 358 (98%) out-of-plane bending 299 (69%), 294 (27%) Mg-N-C out-of-plane bending 281 (80%) Mg-N-C out-of-plane bending 275 (58%), 273 (37%) in-plane bending 266 (91%) Mg umbrella motion 204 (99%) Chl c2 ·2Pyr assignment Qy modes contribution C-C stretching 1526 (73%) C-C stretching 1345 (67%), 1351 (19%) Mg-N24 stratching 1329 (29%), 1338 (15%) C-C, C-N stretching 1322 (30%), 1296 (12%), vinyl group in position 3 1275 (88%) in-plane bending 358 (88%), 357 (10%) out-of-plane bending 298 (98%) Mg-N-C out-of-plane bending 269 (86%), 265 (10%) in-plane bending 240 (99%) Mg umbrella motion 215 (93%)

44


1320 (11%) 1129 (15%)

1351 (10%)

1371 (11%), 1284 (11%)

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