Efficient Pathways of Excitation Energy Transfer from Delocalized S2

Article pubs.acs.org/JPCB

Efficient Pathways of Excitation Energy Transfer from Delocalized S2 Excitons in the Peridinin−Chlorophyll a−Protein Complex William P. Bricker and Cynthia S. Lo* Department of Energy, Environmental and Chemical Engineering, Washington University, St. Louis, Missouri 63130, United States ABSTRACT: Excitation energy transfer (EET) in peridinin−chlorophyll−protein (PCP) complexes is dominated by the S1 → Qy pathway, but the high efficiencies cannot be solely explained by this one pathway. We postulate that EET from peridinin S2 excitons may also be important. We use complete active space configuration interaction calculations and the transition density cube method to calculate Coulombic couplings between peridinin and chlorophyll a in the PCP complex of the dinoflagellate Amphidinium carterae and compare monomeric and dimeric delocalized peridinin S2 excited states. Our calculations show that the S2 → Qy EET pathway from peridinin to chlorophyll a is the dominant energy transfer pathway from the S2 excited state in PCP, with several values in the sub-picosecond range. This result suggests that the S2 → Qy EET pathway may be responsible for the reported chlorophyll a bleaching signature seen in experiment at around 200 fs, and not the S2 → Qx pathway as previously suggested.

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INTRODUCTION Photosynthetic organisms are known to exhibit extremely high (near 100%) quantum efficiencies1,2 during excitation energy transfer (EET), yet many unresolved questions persist in our understanding of biological light-harvesting processes. Understanding the pathways and efficiencies of EET between pigments embedded in a protein scaffold will enable scientists to harness photosynthetic light-harvesting processes in synthetic organic and biological solar cells. Carotenoid pigments play diverse roles in protein complexes including both light-harvesting and photoprotective functionalities. In densely packed light-harvesting complexes, the interactions between carotenoid and chlorophyll pigments are critical in understanding the inherent high quantum efficiencies. The peridinin−chlorophyll a−protein (PCP) complex in the dinoflagellate Amphidinium carterae, having been successfully crystallized,3 has thus attracted much attention from both experimentalists and theorists, due to its small size, interesting EET properties arising from the unique peridinin carotenoid, and high quantum efficiency (85−95%) for EET from peridinin to chlorophyll a.4−7 Monomer M of the PCP trimer is shown in Figure 1. PCP crystallizes as a protein trimer, with eight peridinin (PID) carotenoids and two chlorophyll a (CLA) pigments per protein monomer. The rate of energy transfer from peridinin to chlorophyll a in A. carterae PCP has been estimated to have a lifetime of 2.3−3.2 ps.6,8−10 The peridinin molecules surrounding the chlorophyll a molecules are excited from the S0 (1A−g ) ground state to the strongly allowed S2 (1Bu+) excited state, and the S0 → S1 (2A−g ) excitation is symmetry forbidden, as is typical in similar polyenes. Additionally, spectroscopic studies by Ilagan et al.11,12 of the high-salt form of PCP13 did not find any significant differences in energy transfer efficiencies from peridinin to chlorophyll a, even though the high-salt form does not contain PIDs 612 and 622. © XXXX American Chemical Society

Figure 1. PCP contains two different pigments, peridinin (PID) and chlorophyll a (CLA), and a lipid molecule, digalactosyl diacyl glycerol (DGD). Peridinin molecules are colored on the basis of their respective geometries, where PID611 and PID621 are blue, PID612 and PID622 are orange, PID613 and PID623 are green, and PID614 and PID624 are yellow. Chlorophyll a molecules are red, DGDs are gray, and the protein backbone is white. This graphic contains all molecules contained in one monomer of the PCP trimer (chain M), and all atomic coordinates are obtained from the Protein Data Bank (PDB ID 1PPR).14 This graphic was generated using VMD.15

Once the S2 state of peridinin is excited, EET to chlorophyll a via the S2 excited state must compete with extremely rapid internal conversion to the S1 state in peridinin. An early (∼200 fs) chlorophyll a bleaching signature has been attributed to excitation via the peridinin S2 → Qx excited state pathway.9,10 On the other hand, the rate of S2 → S1 internal conversion in PCP has been estimated to have a lifetime anywhere from 50 to 200 Received: November 24, 2014 Revised: March 28, 2015

A

DOI: 10.1021/jp511766j J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B fs.4,6,8,10 This internal conversion from S2 to S1 has also been observed in solvent, with lifetimes ranging from 30 to 192 fs, depending on the solvent polarity.6,16 Subsequently, EET from the S1 state in peridinin to chlorophyll a proceeds mainly via the S1 → Qy pathway, which competes with much slower fluorescence to the S0 ground state in peridinin. In this study, we focus on the effect of the S2 excited state on PID → CLA energy transfer to determine the cause of the early (∼200 fs) chlorophyll a bleaching. Additional details on the S2 EET pathways in PCP are depicted in Figure 2.

In the present work, the peridinin S2 excited state is examined further to determine whether delocalized excitonic S2 states are a major factor in the EET pathways from PID to CLA in PCP. As seen in Figure 2, the focus of this study is on the S2 → Qx and S2 → Qy EET pathways. We use a methodology similar to that in our previous study, but additionally compare monomeric peridinin S2 excited states to dimeric delocalized peridinin S2 excitonic states. The dimeric pairs of peridinin studied are those that are shown to be most strongly coupled: PID611 + 612, PID611 + 614, PID612 + 613, PID613 + 614, PID621 + 622, PID621 + 624, PID622 + 623, and PID623 + 624.

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COMPUTATIONAL METHODS We present the most relevant details of our computational methodology below, with additional details given in our previous study on PCP.19 To compute EET rates, we use the Förster resonance energy transfer (FRET) model, where VDA is the electronic coupling and JDA is the spectral overlap between donor and acceptor excited states (eq 1): kDA =

2π |VDA|2 JDA ℏ

(1)

The electronic coupling consists of a long-range Coulombic interaction, Vcoul, and a short-range exchange interaction, Vexch (eq 2):

Figure 2. Excitation energy transfer pathways in PCP, with two PID S2 to CLA pathways labeled: k1 (S2 → Qx) and k2 (S2 → Qy). Experimental internal conversion rates are included from S2 → S1, S1 → S0, and Qy → S0. Peridinin is initially excited via the strongly allowed S0 → S2 transition.

VDA = Vcoul + Vexch

(2)

The exchange interaction, Vexch, requires significant atomic orbital (AO) overlap between the donor and acceptor molecules’ transition densities, and so it decays exponentially with distance.20 We therefore assume that Vexch is negligible for this work and set VDA ≈ Vcoul. The typical dipole−dipole FRET electronic coupling21−24 is inappropriate for closely packed donor and acceptor molecules, so the transition density cube (TDC) method is used instead. To accomplish this, a three-dimensional grid of volume elements is created to approximate the transition densities, termed a transition density cube (TDC) and shown in eq 3. The TDCs of the donor and acceptor excited states are then summed over all coordinates to better approximate the Coulombic coupling, VDA, shown in eq 4:25,26

Several computational studies have incorporated various levels of EET theory into an analysis of the PCP complex, which has been facilitated by the availability of a crystal structure of PCP in A. carterae, as determined by X-ray crystallography to a resolution of 2.0 Å.3 Förster resonance energy transfer (FRET) with the ideal dipole approximation (IDA) or a multipole expansion has been used to calculate the electronic interaction between transition dipole moments of donor and acceptor molecules.17 FRET theory for EET is appropriate for systems in which incoherent energy transfer, or “hopping” between donor and acceptor wave functions, occurs. Damjanović et al. and Polı ́vka et al. previously performed FRET studies on PCP, utilizing simple approximations for the electronic interaction.4,18 Our previous study on the PCP complex used complete active space configuration interaction (CAS-CI) quantum mechanical calculations and FRET theory, coupled with the transition density cube (TDC) method, for calculating electronic couplings. We were able to accurately reproduce the lifetime of 2.3−3.2 ps due to S1 → Qy EET.19 Unfortunately, our previous PCP study could not solve the question surrounding the early (∼200 fs) chlorophyll a bleaching signature, which has been previously attributed to the S2 → Qx EET pathway.9,10 We showed that the S2 → Qx EET pathway is relatively inefficient, but because the S2 excited states are strongly coupled, there should be significant delocalization of S2 excited state wave functions.19 In our previous work, we hypothesized that the S2 → Qx EET pathway would account for any PID S2 → CLA energy transfer and, surprisingly, found this pathway too inefficient to fill this role. In our present work, we hypothesize that the delocalization of the S2 excited states will increase the transition dipole moment and, subsequently, the strength of the Coulombic coupling between peridinin S2 and chlorophyll a Qx excited states; thus, excitation energy pathways from the S2 state should be more efficient.

MD,A (x , y , z) = Vδ

∫z

z + δz

∫y

y + δy

∫x

x + δx

ΨGSΨ*ES dx dy dz (3)

VDA =

∑ i,j

MD(i)MA (j) 4π ϵ0rij

(4)

The TDC method, unlike the dipole−dipole method, is valid at all molecular separations and thus well suited for EET in photosynthetic antenna systems, where pigments are tightly packed. The second term in eq 1, JDA, is the spectral overlap between donor and acceptor lineshapes and is equivalent to the expression in eq 5, where A and B are normalization constants, f D is the emission spectra, and ϵA is the absorption molar extinction coefficient: JDA = AB

∫

fD (ν) ϵA (ν) ν3

ν

dν

(5)

Structural Optimization of Peridinin and Chlorophyll a Pigments. We used the atomic coordinates of PCP in A. carterae that were available in the Protein Data Bank (PDB ID 1PPR)14 B


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The Journal of Physical Chemistry B

Table 1. Absorption Properties for Peridinin S2 and Chlorophyll a Qy and Qx Excited States in PCP Using CAS-CI with an Active Space of Four MOs for Monomers and Eight MOs for Dimers Using the MNDO Semiempirical Methoda

and chose monomer M for our study.3 We added hydrogen atoms to the crystal structures of the peridinin (PID) and chlorophyll a (CLA) pigments and the digalactosyl diacyl glycerol (DGD) lipids. The protein structure was also appropriately protonated. Hydrogen atoms were added to the structure of pigments, lipids, and protein using Maestro 9.0 software.27 We optimized the geometry of all of the hydrogen atoms using the MOZYME routine28,29 found in the MOPAC 2012 software package,30 coupled with the semiempirical MNDO31,32 method. After optimization, a Mulliken population analysis33 of the entire complex was performed, so that reasonable partial charges of the environment surrounding the PCP pigments could be retained during the upcoming singlemolecule excited state calculations. These initial calculations provided us with ground state geometries for the eight peridinin and two chlorophyll a pigments, as well as an accurate electrostatic environment surrounding each pigment. Calculation of Excited State Properties. For excited state calculations, we used complete active space configuration interaction (CAS-CI),34,35 which includes all configuration state functions (CSFs), such as single, double, triple, and higher excitation determinants. Prior to calculating excited state properties based on the ground and excited state structures, we performed a further optimization step to prepare the ground state geometry for calculation of vertical excitation energies using CAS-CI. It has been shown that geometries obtained from X-ray crystal structures may not be completely physically realistic for immediate use in quantum mechanical modeling, particularly the smallest bond lengths, whereas the distortion of the dihedral angles in the crystal structure should be fairly accurate.36 Thus, the ground state CAS-CI wave functions (S0) were optimized after the dihedral angles of all of the heavy atoms in peridinin and chlorophyll a had been frozen, as well as the angles and bond lengths of the heavy atoms along the peridinin polyene chain. In this study, excited state wave functions remained unoptimized due to computational limitations, and emission properties were estimated from the ground-state geometries. The CAS-CI calculations were performed with a background electrostatic interaction,37 using the partial charges obtained from the previous Mulliken analysis of the entire PCP monomer M complex. For the optimization and excited state calculations, we used an active space of four (monomer) or eight (dimer) molecular orbitals, performed with the MNDO semiempirical method. In our previous work, we used an active space of six molecular orbitals for all calculations, so the resulting excited state properties of monomeric peridinins shown here are not exactly the same as those previously computed.19 This change, however, is necessary because an active space of eight MOs is the maximum computationally allowable in the MOPAC 2012 software; thus we can only use four MOs for our current monomeric S2 calculations to maintain consistency in size with our dimeric S2 calculations. The results of these excited state calculations performed with CAS-CI and the MNDO method are compared in Table 1. Calculation of Transition Densities. The MOPAC 2012 software used for the quantum mechanical calculations outputs transition dipole moments, so EET using the dipole−dipole approximation can be modeled using the publicly available version of the software. EET calculations using the transition density cube (TDC) method, however, require the actual transition density of the excited state, which is not available by default. To calculate the TDC of the donor and acceptor wave

absorption properties ES

E (eV)

μ12 (D)

S (%)

D (%)

PID611 PID612 PID613 PID614 PID621 PID622 PID623 PID624

S2 S2 S2 S2 S2 S2 S2 S2

2.44 2.43 2.38 2.37 2.61 2.49 2.51 2.64

14.82 14.20 14.41 14.47 15.99 14.33 16.38 15.13

84.33 79.94 82.88 79.85 97.08 84.15 95.64 95.87

14.00 18.06 15.15 18.05 2.37 14.10 3.64 3.53

PID611 + 612(1) PID611 + 612(2) PID611 + 614(1) PID611 + 614(2) PID612 + 613(1) PID612 + 613(2) PID613 + 614(1) PID613 + 614(2) PID621 + 622(1) PID621 + 622(2) PID621 + 624(1) PID621 + 624(2) PID622 + 623(1) PID622 + 623(2) PID623 + 624(1) PID623 + 624(2)

S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2

2.43 2.50 2.32 2.46 2.38 2.45 2.34 2.49 2.50 2.65 2.59 2.82 2.48 2.53 2.45 2.65

8.81 18.65 12.44 15.10 9.03 17.78 12.87 14.06 10.79 18.85 14.39 15.71 8.20 19.96 13.39 15.69

84.50 75.47 72.93 78.34 80.16 73.71 76.79 75.25 86.73 89.00 94.79 93.36 83.67 85.80 82.65 87.54

10.02 15.15 19.46 12.49 14.12 17.12 16.43 15.18 7.80 5.04 3.54 1.80 9.18 8.85 12.91 6.02

CLA601

Qy Qx Qy Qx

2.16 2.26 2.14 2.27

3.54 1.06 3.38 1.14

95.45 79.89 95.75 80.46

3.89 15.45 3.76 14.67

molecule

CLA602 a

Single (S) and double (D) excitation percentages shown. The magnitude of the S2 transition dipole moment of peridinin in solvent has been estimated at 10.6−12.4 D.4,40.

functions, we utilized an external Python code, written for our previous work on PCP.19 In this code, the transition density at each predetermined grid point is calculated using Pμν, the transition density matrix in atomic orbital (AO) basis, as shown in eq 6. The transition dipole moment is approximated from this transition density cube using ri, the transition dipole moment operator, as shown in eq 7. Mnm(x , y , z) = Vδ ∑ Pμνϕμ(x , y , z)ϕν*(x , y , z) μν

μnm ≈

∑ rM i nm(i) i

(6)

(7)

To check the accuracy of the external transition density code, we used eq 7 to back-calculate the transition dipole moment from the TDC files of the excited state transitions. All TDCs are calculated using an 8 × 10−3 Å3 volumetric grid size (5 grid points per Å), which we previously showed to have an average relative error below 0.1%.19 Modeling of Excitation Energy Transfer. To calculate the spectral overlap integral, JDA, we fitted ν0 to Gaussian-type functions, as shown in eq 8, where ν0 values are the vertical C


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Figure 3. Transition densities of the eight peridinin molecules in PCP vertically excited from the ground state geometries to the dimeric S2 delocalized excited states. Transition densities of the S0 → S2 delocalized excited states in dimeric (a, b) PID611 + 612, (c, d) PID613 + 614, (e, f) PID621 + 622, (g, h) PID623 + 624, (i, j) PID611 + 614, (k, l) PID612 + 613, (m, n) PID621 + 624, and (o, p) PID622 + 623. These images were generated using VMD, with a density isovalue of 0.00005.15

excitation energies, Γ0 are the full width at half-maximum (fwhm) values for the Gaussian line shape function, and A and B are the normalization constants for the Gaussian lineshapes in eq 5. ⎛ ⎛ ν − ν0 ⎞2 ⎞ ⎜ ϵA (ν), fD (ν) ≈ exp⎜ − 2.773⎜ ⎟⎟ ⎝ Γ0 ⎠ ⎟⎠ ⎝

To calculate the electronic coupling term, VDA, we constructed a TDC file (in Gaussian cube file format) for the fluorescence transition density of the donor molecules, and the absorption transition density for the acceptor molecules, from their respective transition density matrix elements using the external Python code.19 The electronic coupling between these excited state transitions was estimated using the TDC method,25,26 because the dipole−dipole electronic coupling, or ideal dipole approximation (IDA), is inappropriate in closely packed pigments.21−24

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Absolute values for ν0 are shown in Table 1, and although these are close to experimental values, they are not quite good enough to calculate an accurate spectral overlap integral. We instead retain the energy differences between distinct peridinin S2 excited states, as these are influenced by the differing pigment geometries and protein electrostatic environments, but populate these energies around the following average excited state values for ν0 and Γ0 taken from experiment: ν0(S2,Abs) = 20661 cm−1, ν0(S2,Em) = 19170 cm−1, ν00(Qy,Abs) = 14993 cm−1, ν01(Qy,Abs) = 16219 cm−1, ν0(Qx,Abs) = 16000 cm−1, Γ0(S2,Abs) = 4315 cm−1, Γ0(S2,Em) = 3709 cm−1, Γ00(Qy,Abs) = 270 cm−1, Γ01(Qy,Abs) = 270 cm−1, Γ0(Qx,Abs) = 1025 cm−1, f 00(Qy,Abs) = 1.00, and f 01(Qy,Abs) = 0.18. Peridinin S2 and chlorophyll a parameters were estimated from spectra in PCP, and fwhm values were estimated from experimental spectra and previous FRET studies.3−6,8−10,16,38,39 For the chlorophyll a Qy absorption excited state in particular, we included an additional vibronic band, ν01, in addition to the main vibronic transition, ν00. This is due to data in solvent suggesting a vibrational band ∼1200 cm−1 from the main peak.39 The chlorophyll a Qy spectral line shape is modeled using a Gaussian sum, shown in eq 9. In this equation, n is the number of vibronic bands, f i is the oscillator strength of the vibronic band, and f max is the largest oscillator strength of the excited state absorption band. n

ϵA (ν) ≈

∑ i

fi fmax

⎛ ⎛ ν − ν0i ⎞2 ⎞ ⎜ exp⎜ −2.773⎜ ⎟⎟ ⎝ Γ0i ⎠ ⎟⎠ ⎝

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RESULTS AND DISCUSSION

Using CAS-CI with the MNDO semiempirical method, we calculated absorption properties for the peridinin S2 excited state, and the chlorophyll a Qy and Qx excited states, as shown in Table 1. In the monomeric peridinin S2 excited state calculations, energies and transition dipole moments are relatively similar. In the dimeric peridinin S2 excited state calculations, the energies between pairs of S2 states are split, and the strength and directionality of the transition dipole moments are distinct as wellespecially in the PID611 + 612, PID612 + 613, PID621 + 622, and PID622 + 623 pairs. The S2 excited states can be identified from their S1 counterparts by analyzing the percentage of single and double excitation character of each excited state. All S2 excited states, both monomeric and dimeric, are shown to have >70% single excitation character. In Figure 3, the transition densities of the 16 dimeric delocalized S2 excited states of peridinin are visualized using the calculated TDC files. It is immediately clear that the level of delocalization in each pair of peridinin molecules is distinct. Pairs PID611 + 612 and PID621 + 622 show nearly complete delocalization of S2 wave functions, but the rest of the dimer pairs have greater localization of wave functions on one peridinin molecule while still being slightly delocalized. This is also shown by comparing the transition dipole moments of some

(9) D


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The Journal of Physical Chemistry B monomeric S2 excited states (PID611, PID612, PID613, and PID614) to those of some of the dimeric S2 excited states (PID611 + 612 and PID613 + 614) in Figure 4. All of the

Table 2. Coulombic Couplings (VDA) between Monomeric (a) Peridinin and Chlorophyll a Qx, (b) Peridinin and Chlorophyll a Qy, and (c) Peridinin and Peridinin Using CASCI with the MNDO Semiempirical Method and an Active Space of Four MOsa donor

acceptor


CLA601 CLA601 CLA601 CLA601 CLA602 CLA602 CLA602 CLA602


CLA601 CLA601 CLA601 CLA601 CLA602 CLA602 CLA602 CLA602



VDA (cm−1)

ΔE (cm−1)

(a) S2 → Qx

Figure 4. Transition dipole moment vectors for monomeric and dimeric peridinin S2 excited state calculations. Shown are monomeric transition dipole moment vectors for PID611 (blue arrow), PID612 (orange arrows), PID613 (green arrow), and PID614 (yellow arrow) and dimeric transition dipole moments for PID611 + 612 and PID613 + 614 (black arrows). In (a) we compare monomeric and dimeric transition dipole moment vectors for dimer pair PID611 + 612, and in (b) we compare monomeric and dimeric transition dipole moment vectors for dimer pair PID613 + 614. This graphic was generated using VMD.15

14.0 22.2 21.0 4.22 5.82 20.2 0.650 24.4 (b) S2 → Qy 223 108 69.6 212 239 74.0 76.4 182 (c) S2 → S2 485 247 264 298 549 230 291 372

3170 3170 3170 3170 3170 3170 3170 3170 4177 4177 4177 4177 4177 4177 4177 4177 1491 1491 1491 1491 1491 1491 1491 1491

These are compared to estimated ΔE values between donors and acceptors.

a

can be modeled using FRET, due to large ΔE values, even though the Coulombic couplings for S2 → Qy are relatively strong. On the other hand, S2 → S2 excited states are strongly coupled and would require an excitonic description for calculating accurate EET properties. Therefore, it is unsurprising that the dimeric peridinin S2 excited state calculations show significant delocalization, especially in pairs PID611 + 612 and PID621 + 622. The values for ΔE in Table 2 are estimated as the average donor/ acceptor energy gap on the basis of the spectral overlap energy and fwhm values under Computational Methods. The four dimer pairs (PID611 + 612, PID613 + 614, PID621 + 622, PID623 + 624) that are also the closest by physical distance will be considered for further analysis, along with four additional pairs (PID611 + 614, PID612 + 613, PID621 + 624, and PID622 + 623) that have relatively large Coulombic couplings. The questions to be addressed include (1) do the delocalized S2 excitons actually enhance EET to the chlorophyll a molecules and (2) can a fast EET pathway (∼200 fs) be identified from PID → CLA? Both of these questions can be answered by analyzing the FRET Coulombic couplings and lifetimes of EET in Tables 3 and 5. All FRET calculations are performed according to the information contained under Computational Methods, using the CAS-CI method34,35 with the semiempirical MNDO basis set31,32 found in the MOPAC 2012 software package.30 For monomeric pigment calculations, an active space of four molecular orbitals (MOs) is used, and for dimeric pigment

monomeric S2 transition dipole moments are pointing roughly along the polyene backbone of their respective peridinin molecules, but the dimeric S2 transition dipole moments have a different character. In the PID611 + 612 dimer, the dimeric transition dipole moments take on character from both monomeric excited states. In contrast, in the PID613 + 614 dimer, the dimeric transition dipole moments are virtually identical in direction to the monomeric transition dipole moments. Note that the absolute directions of the monomeric transition dipole moments are arbitrary, meaning that some of the dimeric transition dipole moment vectors are in opposite absolute directions, but still corresponding to the same excited state wave functions. Thus, in peridinin S2 excited states, the extent of delocalization can be ascertained qualitatively by comparing the direction of the transition dipole moment vectors of the monomeric and dimeric S2 excited state calculations. Some of this behavior is explained by the calculated Coulombic couplings shown in Table 2, where the Coulombic couplings between monomeric donor and acceptor molecules are compared to respective energy gaps between excited states. For FRET theory to be applicable, it has been shown that the ΔE > 5VDA criterion is adequate. Otherwise, it is likely that some degree of excitonic coupling and delocalization of excited states will occur, and FRET will not be an adequate description of EET in this system.41 In Table 2, both S2 → Qx and S2 → Qy pathways E


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Table 3. Comparison of Lifetimes (τDA) and Efficiencies (ΦDA) of S2 → Qx and S2 → Qy EET Using TDC Coulombic Couplings (VDA) between Monomeric Peridinin and Chlorophyll a CAS-CI with the MNDO Semiempirical method and an Active Space of Four MOs for Peridinin and Chlorophyll aa variable JDA donor

acceptor

VDA (eV)

−1

JDA (eV )

constant JDA

τDA (ps)

ΦDA (%)

τDA (ps)

ΦDA (%)

51.0 19.1 15.5 359 235000 122 10.4 15800 6850 61.2 4.83 1180 1460 37.1 43900 117

0.39 1.04 1.27 0.06 0.00 0.16 1.88 0.00 0.00 0.33 3.97 0.02 0.01 0.54 0.00 0.17

73.5 29.5 32.9 812 68900 116 8.12 3270 9860 94.7 10.3 2670 427 35.3 34300 24.3

0.27 0.67 0.60 0.02 0.00 0.17 2.40 0.01 0.00 0.21 1.91 0.01 0.05 0.56 0.00 0.82

30.17 10.00 6.61 41.74 0.00 0.03 0.17 0.00 0.00 0.01 0.34 0.02 6.71 2.74 2.29 1.72

0.736 3.14 7.57 0.818 12500 633 88.9 987 17800 2490 157 3090 0.641 6.69 6.27 1.11

21.37 5.98 2.57 19.65 0.00 0.03 0.22 0.02 0.00 0.01 0.13 0.01 23.78 2.90 3.09 15.26

S 2 → Qx

PID611 PID612 PID613 PID614 PID621 PID622 PID623 PID624 PID611 PID612 PID613 PID614 PID621 PID622 PID623 PID624

CLA601 CLA601 CLA601 CLA601 CLA601 CLA601 CLA601 CLA601 CLA602 CLA602 CLA602 CLA602 CLA602 CLA602 CLA602 CLA602

−1.74 × 10−3 −2.75 × 10−3 2.60 × 10−3 −5.23 × 10−4 −5.69 × 10−5 −1.38 × 10−3 5.23 × 10−3 −2.61 × 10−4 −1.50 × 10−4 −1.53 × 10−3 −4.66 × 10−3 2.89 × 10−4 −7.22 × 10−4 −2.51 × 10−3 8.06 × 10−5 −3.03 × 10−3

0.678 0.728 0.999 1.065 0.138 0.449 0.367 0.098 0.678 0.728 0.999 1.065 0.138 0.449 0.367 0.098

PID611 PID612 PID613 PID614 PID621 PID622 PID623 PID624 PID611 PID612 PID613 PID614 PID621 PID622 PID623 PID624


−2.77 × 10−2 −1.34 × 10−2 8.63 × 10−3 −2.63 × 10−2 −2.12 × 10−4 −9.43 × 10−4 2.52 × 10−3 −7.55 × 10−4 −1.78 × 10−4 4.76 × 10−4 1.90 × 10−3 4.27 × 10−4 −2.96 × 10−2 −9.17 × 10−3 −9.48 × 10−3 2.25 × 10−2

0.296 0.325 0.498 0.545 0.043 0.175 0.137 0.029 0.296 0.325 0.498 0.545 0.043 0.175 0.137 0.029

S 2 → Qy 0.463 1.80 2.83 0.279 54200 672 121 6350 11200 1430 58.5 1060 2.78 7.11 8.53 7.15

Spectral overlap integrals (JDA) are also shown. The constant JDA term is equal to 0.471 eV−1 for S2 → Qx and 0.186 eV−1 for S2 → Qy. The shortest lifetime from donor to acceptor is highlighted for each distinct pathway. a

acceptor and donor pairs are located on adjacent tetramers, for S2 → Qx transfer, the respective transition densities are in the highest coincidence and, thus, have the largest Coulombic couplings. Unfortunately, these transfer pathways are still too slow to compete with the ultrafast S2 → S1 internal conversion. The delocalized S2 excitons in Table 4 do not enhance the efficiency of the S2 → Qx EET pathway, but they do appear to lend a greater consistency to the reported Coulombic couplings (VDA), FRET lifetimes (τDA), and efficiencies (ΦDA). It is not clear, however, whether this effect arises from the distinct transition dipoles from monomer to dimer or from the distinct excited state energies of the delocalized excited states, which directly affect the value of the spectral overlap integral (JDA). The two fastest EET pathways in the delocalized model are attributed to PID623 + 624(1) → CLA601 and PID612 + 613(1) → CLA602, which have Coulombic couplings of VDA = −4.74 × 10−3 and 3.57 × 10−3 eV, respectively. Nevertheless, neither monomeric nor dimeric S2 → Qx EET pathways are efficient enough to contribute to the fast chlorophyll a bleaching signature.

calculations, an active space of eight MOs is used. For the spectral overlap calculations, variable JDA integrals were calculated using the methodology presented under Computational Methods and compared to constant JDA integrals performed using ν0 and Γ0 values from spectra. We had expected that JDA integrals should be distinct between different donor/acceptor pairs, but our calculations indicate a broad range of potential spectral overlap integrals. Thus, the true in vivo spectral density of these donor/ acceptor pairs in PCP is likely bracketed between the extremes calculated for variable JDA versus constant JDA. Peridinin S2 to Chlorophyll a Qx Energy Transfer. In our previous study, the S2 → Qx EET pathway was analyzed in PCP, with the reported efficiencies much too low to explain the fast (∼200 fs) chlorophyll a bleaching from experiment.19 In the current study, the S2 → Qx EET pathway is again studied with FRET values reported in Tables 3 and 4. Again, we report no fast S2 → Qx pathways, with the highest efficiency being 3.97% and the fastest lifetime being 4.83 ps. Interestingly, the fastest S2 → Qx EET pathways are from PID613 → CLA602 and PID623 → CLA601, as well as their related dimer pairs. Whereas the fastest F


Article


Table 4. Comparison of Lifetimes (τDA) and Efficiencies (ΦDA) of S2 → Qx EET Using TDC Coulombic Couplings (VDA) between Dimeric Peridinin and Monomeric Chlorophyll a Using CAS-CI with the MNDO Semiempirical Method and an Active Space of Four MOs for Monomeric Chlorophyll a and Eight MOs for Dimeric Peridinina JDA = 0.471 eV−1

variable JDA JDA (eV−1)

τDA (ps)

ΦDA (%)

τDA (ps)

ΦDA (%)



−1.41 × 10 2.65 × 10−3 −2.40 × 10−5 −8.09 × 10−4 −3.55 × 10−3 −1.34 × 10−3 8.22 × 10−4 1.94 × 10−3 8.54 × 10−4 −5.21 × 10−4 −2.83 × 10−4 3.30 × 10−5 1.81 × 10−3 5.07 × 10−3 4.74 × 10−3 −2.65 × 10−4

0.837 0.474 1.448 0.648 1.100 0.691 1.314 0.519 0.467 0.104 0.192 0.009 0.618 0.357 0.736 0.107

63.3 31.5 126000 248 7.55 84.1 118 53.4 138 2250 6790 Inf 51.7 11.4 6.34 13900

0.32 0.63 0.00 0.08 2.58 0.24 0.17 0.37 0.14 0.01 0.00 0.00 0.39 1.72 3.06 0.00

112 31.7 388000 341 17.6 123 329 58.9 137 499 2772 205000 67.9 8.65 9.91 3160

0.18 0.63 0.00 0.06 1.12 0.16 0.06 0.34 0.15 0.04 0.01 0.00 0.29 2.26 1.98 0.01



−1.19 × 10−3 1.06 × 10−3 2.69 × 10−4 −2.72 × 10−5 3.57 × 10−3 −3.27 × 10−3 −1.63 × 10−3 −4.74 × 10−3 2.02 × 10−3 −1.83 × 10−3 −4.01 × 10−3 1.18 × 10−3 −2.00 × 10−3 1.50 × 10−3 8.62 × 10−4 2.89 × 10−3

0.837 0.474 1.448 0.648 1.100 0.691 1.314 0.519 0.467 0.104 0.192 0.009 0.618 0.357 0.736 0.107

88.9 197 1000 219000 7.49 14.2 30.1 8.98 54.8 300 34.0 8620 42.2 131 192 118

0.22 0.10 0.02 0.00 2.60 1.39 0.66 2.18 0.36 0.07 0.59 0.00 0.47 0.15 0.10 0.17

158 198 3080 302000 17.5 20.9 84.0 9.90 54.4 66.6 13.9 159 55.4 99.2 300 26.7

0.13 0.10 0.01 0.00 1.13 0.95 0.24 1.98 0.37 0.30 1.42 0.13 0.36 0.20 0.07 0.74

donor

acceptor

VDA (eV) −3

a

Spectral overlap integrals (JDA) are also shown. The shortest lifetime from donor to acceptor is highlighted for each distinct pathway. Lifetimes >1 μs are marked as Inf.

Peridinin S2 to Chlorophyll a Qy Energy Transfer. On the other hand, the S2 → Qy EET pathways, reported in Tables 3 and 5, show much larger Coulombic couplings, shorter lifetimes, and higher efficiencies. In fact, seven separate pathways are shown to have lifetimes under 1 ps when using a variable JDA integral: PID611 → CLA601 (463 fs), PID614 → CLA601 (279 fs), PID611 + 612(2) → CLA601 (851 fs), PID611 + 614(1) and PID611 + 614(2) → CLA601 (448 and 773 fs, respectively), PID612 + 613(1) → CLA601 (987 fs), and PID613 + 614(1) → CLA601 (202 fs). These seven pathways have efficiencies of 30.17, 41.74, 19.02, 30.88, 20.55, 16.85, and 49.73%, respectively. The very large Coulombic couplings from S2 → Qy (due in part to the relatively large transition dipole moments of the peridinin S2 and chlorophyll a Qy excited states), along with a large enough spectral overlap, can clearly result in extremely fast EET pathways and may explain the fast chlorophyll a bleaching signature near 200 fs. Using the constant spectral overlap integral of JDA = 0.186 eV−1, we observe seven sub-picosecond lifetimes, although none are as fast as the variable JDA lifetime of PID613 + 614(1) → CLA601.

The spectroscopic studies by Ilagan et al.11,12 on the high-salt form of PCP (HSPCP)13 showed that the removal of PID612 and PID622 from the structure did not have a noticeable effect on the rates and efficiencies of energy transfer from peridinin to chlorophyll a in PCP. Here, the fastest routes of EET from S2 → Qy are from the PID611 and PID614 monomeric pigments to CLA601 and from the PID621 and PID624 monomeric pigments to CLA602. There would be no PID611 + 612 or PID621 + 622 S2 delocalization in an analogous study on HSPCP, because PID612 and PID622 are missing, but delocalization may occur with another peridinin pigment, such as PID611 + 614 or PID621 + 624, both of which yield very strong Coulombic couplings as well. Thus, removal of PID612 and PID622 in our current model would not remove the fastest routes of EET from S2 → Qy in PCP, but it would remove the most strongly coupled peridinin S2 dimers, possibly resulting in distinct population dynamics of peridinin S2 excited states between the main-form and high-salt PCP complexes. The differences between monomeric peridinin S2 excited states and delocalized peridinin S2 excitons are subtle for the S2 → Qy EET pathway. The magnitude of the largest S2 transition G


Article


Table 5. Comparison of Lifetimes (τDA) and Efficiencies (ΦDA) of S2 → Qy EET Using TDC Coulombic Couplings (VDA) between Monomeric Chlorophyll a and Dimeric Peridinin Using CAS-CI with the MNDO Semiempirical Method and an Active Space of Four MOs for Monomeric Chlorophyll a and Eight MOs for Dimeric Peridinina JDA = 0.186 eV−1

variable JDA JDA (eV−1)

τDA (ps)

ΦDA (%)

τDA (ps)

ΦDA (%)



5.62 × 10 2.56 × 10−2 −1.64 × 10−2 −2.21 × 10−2 −1.36 × 10−2 −8.22 × 10−3 2.64 × 10−2 6.69 × 10−3 8.46 × 10−4 −5.59 × 10−4 −7.89 × 10−4 5.95 × 10−5 6.49 × 10−4 2.61 × 10−3 2.38 × 10−3 4.81 × 10−4

0.391 0.188 0.866 0.279 0.571 0.303 0.743 0.210 0.184 0.031 0.631 0.000 0.263 0.132 0.329 0.032

8.51 0.851 0.448 0.773 0.987 5.11 0.202 11.1 794 10700 2670 Inf 948 117 56.1 14200

2.30 19.02 30.88 20.55 16.85 3.76 49.73 1.77 0.03 0.00 0.01 0.00 0.02 0.17 0.36 0.00

17.90 0.858 2.08 1.16 3.03 8.33 0.807 12.6 787 1800 904 159000 1340 83.0 99.3 2440

1.11 18.90 8.75 14.72 6.20 2.34 19.85 1.57 0.03 0.01 0.02 0.00 0.01 0.24 0.20 0.01



3.22 × 10−4 −3.46 × 10−4 4.93 × 10−4 7.69 × 10−6 −1.51 × 10−3 1.18 × 10−3 1.51 × 10−4 1.96 × 10−3 −4.34 × 10−3 −3.05 × 10−2 1.79 × 10−2 3.39 × 10−2 −1.28 × 10−2 −2.49 × 10−3 −1.18 × 10−2 −2.12 × 10−2

0.391 0.188 0.866 0.279 0.571 0.303 0.743 0.210 0.184 0.031 0.631 0.000 0.263 0.132 0.329 0.032

2590 4680 497 Inf 80.8 249 6160 129 30.1 3.61 5.18 Inf 2.43 127 2.29 7.27

0.01 0.00 0.04 0.00 0.25 0.08 0.00 0.15 0.66 5.25 3.72 0.00 7.59 0.16 8.04 2.68

5440 4710 2320 Inf 248 406 24600 146 29.9 0.605 1.76 0.490 3.44 90.6 4.05 1.25

0.00 0.00 0.01 0.00 0.08 0.05 0.00 0.14 0.67 24.83 10.22 29.00 5.50 0.22 4.71 13.79

donor

acceptor

VDA (eV) −3

a

Spectral overlap integrals (JDA) are also shown. The shortest lifetime from donor to acceptor is highlighted for each distinct pathway. Lifetimes >1 μs are marked as Inf.

Coulombic coupling over monomeric PID621, due to the larger transition dipole moment of the delocalized excited state. Therefore, the delocalized PID621 + 624(2) excited state improves the efficiency of the S2 → Qy pathway when compared to monomeric S2 states as well as using constant spectral overlap integrals. Spectral overlaps when calculated separately for each donor/acceptor pair range from 0.000 to 0.866 eV−1, whereas the constant spectral overlap integral is 0.186 eV−1. These spectral overlap integrals are estimated on the basis of average values taken from experimental spectra, as well as the relative excited state energies taken from CAS-CI/MNDO calculations. Unfortunately, it remains unknown from experiment which peridinin molecules in PCP contribute to a higher (or lower) spectral overlap with the chlorophyll a pigments so, again, the true values likely lie between those calculated for variable and constant JDA spectral overlaps. Much discussed in the literature surrounding PCP is the intramolecular charge transfer (ICT) behavior of the peridinin S1 excited state and, to a lesser extent, the S 2 excited state.5,10,16,38,42−47 The ICT properties are inherently included in the TDC formalism for calculating Coulombic couplings and

dipole moments for the most delocalized pairs, PID611 + 612, PID612 + 613, PID621 + 622, and PID622 + 623, is larger than those of the monomeric S2 excited states. This effect leads to one of the largest Coulombic couplings between PID and CLA: −3.05 × 10−2 eV from PID621 + 622(2) → CLA602. (The Coulombic coupling of PID621 + 624(2) → CLA602 is slightly larger at 3.39 × 10−2 eV.) This may be due specifically to the PID621 monomeric S2 excited state, which has the largest Coulombic coupling with CLA602, at −2.96 × 10−2 eV. In the variable spectral overlap model, the shortest lifetime improves from 279 to 202 fs for PID614 → CLA601 and PID613 + 614(1) → CLA601, respectively. This effect can be attributed to the increased spectral overlap integral in the dimeric calculation, as the calculated Coulombic couplings between the two pathways are nearly identical. The calculated lifetimes for the S2 excited states using the constant spectral overlap term are more consistent than those using the variable spectral overlap terms. In the constant spectral overlap model, the shortest lifetime improves from 641 to 490 fs for PID621 → CLA602 and PID621 + 624(2) → CLA602, respectively. In comparison, the dimeric PID621 + 622(2) excited state actually has an increased H



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thus are included in this study involving the monomeric and dimeric S2 excited states of peridinin. It is possible, though, that an additional ICT state exists between the S1 and S2 excited states of peridinin and that the purely ICT state could be responsible for the fast bleaching characteristic of chlorophyll a in PCP. We do not calculate any additional ICT excited states using the MNDO/CAS-CI methodology, but it is possible that these excited states could show up in a dynamical study of PCP. Also, any intermolecular charge transfer excited states involving peridinin and chlorophyll a or more than two peridinin molecules are not calculated in this current study. Computational limitations involving the size of the active space for MNDO/ CAS-CI calculations are currently prohibitive toward larger molecular complexes.

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Article

AUTHOR INFORMATION

Corresponding Author

*(C.S.L.) Phone: (314) 935-8055. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Sergei Tretiak and Christopher Duffy for useful discussions relating to excitation energy transfer, Brent Krueger for assistance with the TDC code, and James Stewart for assistance with the MOPAC code. This material was based on work supported as part of the Photosynthetic Antenna Research Center (PARC), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award DE-SC 0001035. This work was also performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Los Alamos National Laboratory (Contract DE-AC52-06NA25396) and Sandia National Laboratories (Contract DE-AC0494AL85000).

CONCLUSIONS

We have extended our previous theoretical work on the PCP complex to examine the peridinin S2 exciton in more detail, utilizing a combination of FRET dynamics with semiempirical configuration interaction excited state calculations and a methodology for determining highly accurate Coulombic couplings using the TDC method. We used both a monomeric and a dimeric model for the S2 excited states, to compare EET properties between peridinin S2 and chlorophyll a. We show that strong Coulombic couplings between the nine studied dimer pairs of peridinin S2 excitons, especially PID611 + 612, PID611 + 614, PID621 + 622, and PID621 + 624, lead to delocalization of the respective S2 exciton wave functions over the dimer pairs studied. In our FRET analysis, we again show that the S2 → Qx EET pathway is inefficient for both monomeric and dimeric S2 excitons, but instead see that the S2 → Qy EET pathway is relatively efficient. This may explain the fast chlorophyll a bleaching signature due to several sub-picosecond lifetimes (e.g., 202 fs for PID613 + 614(1) → CLA601 using a variable spectral overlap integral and 490 fs for PID621 + 624(2) → CLA602 using a constant spectral overlap integral.) Although it seems from these data that the nature of the fast chlorophyll a bleaching signature is due to the S2 → Qy EET pathway, as opposed to the S2 → Qx EET pathway, questions persist that cannot be answered using the static FRET analysis performed here. The significance of the delocalized S2 excitons in the overall efficiency of the PCP complex may be such that a FRET analysis is not always valid for modeling peridinin to peridinin energy transfer from the strongly coupled S2 excitons. Also, the current computational limitation to delocalization over only a pair of peridinin molecules may be problematic, as delocalization effects in PCP may be important over the entire protein monomer. A coherent energy transfer study of the S2 excitons in PCP using a Redfield model could elucidate the population dynamics within the complex. In addition, the spectral characteristics of the excited states could be analyzed in more detail using a dynamic quantum mechanical (QM)/molecular mechanical (MM) simulation, to incorporate the real effects of the surrounding protein environment into the energy transfer calculations and eliminate the need to estimate a spectral term for each pigment in both FRET and Redfield theories. All of these are likely subjects of future work on this complex. Nevertheless, the focus here on delocalized S2 states and the relatively efficient S2 → Qy EET pathway may help researchers understand the remaining keys to the high efficiency in the PCP complex.

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REFERENCES

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Efficient Pathways of Excitation Energy Transfer from Delocalized S2

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