Development of Molecular Dynamics Parameters and Theoretical Analysis of Excitonic and Optical Properties in the Light-Harvesting Complex II

Abstract

The light-harvesting complex II (LHCII) in green plants exhibits highly efficient excitation energy transfer (EET). A comprehensive understanding of the EET mechanism in LHCII requires quantum chemical, molecular dynamics (MD), and statistical mechanics calculations that can adequately describe pigment molecules in heterogeneous environments. Herein, we develop MD simulation parameters that accurately reproduce the quantum mechanical/molecular mechanical energies of both the ground and excited states of all chlorophyll (Chl) molecules in membrane embedded LHCII. The present simulations reveal that Chl a molecules reside in more inhomogeneous environments than Chl b molecules. We also find a narrow gap between the exciton energy levels of Chl a and Chl b. In addition, we investigate the nature of the exciton states of Chl molecules, such as delocalization, and analyze the optical spectra of LHCII, which align with experimental results. Thus, the MD simulation parameters developed in this study successfully reproduce the excitonic and optical properties of the Chl molecules in LHCII, validating their effectiveness.

1. Introduction

Green plants, which comprise ∼80% of Earth’s biomass,¹ play a crucial role in autotrophic processes within ecosystems. In photosynthesis, the light-harvesting complex II (LHCII) in photosystem II (PSII) is key to capturing sunlight and efficiently transferring excitation energy to the reaction center (RC). At the RC, water photolysis produces oxygen and electrons, the latter of which are used in the dark reaction to convert carbon dioxide into carbohydrates, storing solar energy vital for life. The light-harvesting process in green plants is notably efficient^2,3 despite various fluctuations that could disrupt the electronic coherence of pigments. LHCII embedded in the thylakoid membrane ensures highly efficient energy transfer, although the precise mechanism remains partially understood.

In order to elucidate the mechanism of excitation energy transfer (EET) dynamics in LHCII, information on its detailed structure and dynamics is crucial. X-ray diffraction and electron microscopy (EM) have revealed the structures of LHCII trimers in photosystems across various plants. For instance, LHCII structures in Spinacia oleracea and Pisum sativum have been analyzed via X-ray diffraction,^4,5 while recent EM studies have provided insights into the entire PSII⁶⁻⁸ and PSI–LHCI–LHCII systems.^9,10 These high-resolution structures show that LHCII comprises various pigments (Figure 1), including chlorophyll a (Chl a), chlorophyll b (Chl b), and carotenoids, arranged to optimize energy transfer and dissipation between these pigments and their light absorption. Additionally, the structural flexibility of LHCII is vital for photoprotection, allowing it to adapt to varying light conditions and dissipate excess energy when needed.^11,12

Figure 1.

LHCII trimer structure in (a) the front view, (b) stromal side view, and (c) lumenal side view. The cyan arrows in (b) and (c) represent the excitonic couplings within clusters, while the yellow arrows in (b) represent excitonic couplings between clusters. The blue and purple spheres represent the magnesium and two nitrogen atoms of each Chl molecules, respectively. The connecting line between the two nitrogen atoms indicates the direction of the Q_y transition dipole moment.

Excitonic and optical properties of LHCII have been investigated using various spectroscopic techniques, including absorption,¹³ linear dichroism (LD),^14,15 circular dichroism (CD),^16,17 and fluorescence (FL) spectroscopies.¹⁸ However, the assignment of energy levels to specific pigments remains challenging owing to structural variations, particularly in mutants. Techniques such as three-pulse photon echo peak shift,¹⁹ pump–probe spectroscopy,²⁰ and two-dimensional electronic spectroscopy²¹⁻²⁵ have further elucidated excitonic properties and energy transfer dynamics of LHCII. For example, Calhoun et al. revealed a narrow energy gap between the excitons of Chl a and Chl b,²¹ while Ramanan et al. explored coherent interactions between low energy Chl molecules in the LHCII trimer,²² and Akhtar et al. investigated the temperature dependence of energy transfer in LHCII.²³ However, analyzing the EET dynamics in detail requires precise information on site energies, exciton couplings, and site energy fluctuations, which are difficult to obtain from experiments alone. Thus, theoretical studies that can accurately provide this information are crucial for an in-depth understanding of the nature of excitonic states and EET dynamics in LHCII.

Determining the properties of EET dynamics in LHCII remains a major challenge for theoretical calculations because it requires accurate electronic structures and fluctuations of Chl molecules. Consequently, many studies rely on fitting experimental spectra to gain insights.^18,26−29 For instance, Novoderezhkin et al. investigated EET dynamics in LHCII based on necessary information obtained by fitting experimental spectral data, including absorption, LD, FL, and transient absorption spectra.^18,26,27 They identified a bottleneck at a604 during energy transfer from lumenal Chl b to Chl a and observed rapid energy transfer from stromal Chl b to Chl a. Additionally, they found that the a610–a611–a612 cluster forms the lowest energy state in LHCII.^30,31

Atomistic approaches,³²⁻³⁸ such as quantum mechanics/molecular mechanics (QM/MM) calculations, provide a direct method to study site energies, transition dipole moments, and excitonic properties of Chl molecules without relying on experimental data. Müh et al. developed a model for LHCII in a dielectric medium that simulates the environments of solutions, proteins, and membranes³² and conducted QM/MM calculations. They carefully determined the protonation states of amino acids, examined environmental effects on site energies and excitonic couplings, and analyzed the calculated absorption, LD, CD, and FL spectra.³³

In QM/MM calculations for photosynthetic systems, such as the LHCII complex, (time-dependent) density functional theory ((TD)DFT) methods are widely used. However, the parameters of the DFT methods, for instance, the value of the range-separated parameter μ for the CAM-B3LYP functional,³⁹ are generally determined using the data of homonuclear diatomic molecules for the first-, second-, and third-row atoms, except rare gas atoms. Therefore, the validity of these calculations must be carefully assessed when applying the (TD)DFT methods to large conjugated systems. Sláma et al. selected the M06-2X functional to accurately describe the electronic states of Chl a and Chl b in LHCII.³⁷ Using the QM/MMpol method,⁴⁰ they analyzed site energies, excitonic properties, and optical spectra for the LHCII trimer. Cignoni et al. improved the accuracy of site energy models for Chl a and Chl b in the CP29 complex using an electrostatic embedding machine learning model.⁴¹ Additionally, Maity et al. used the DFTB–QM/MM–MD method to study excited state energies for Chl a.³⁸ Furthermore, optimization of μ of the CAM-B3LYP functional has demonstrated its ability to reproduce excitation energies for Chl a and Chl b in various solutions with different polarities.⁴²⁻⁴⁴ Using the reparameterized functional, Saito et al. analyzed how the excitation energy of a Chl a varies with the electrostatic (ES) field of a charge positioned at different locations around the Chl a.⁴⁵ In addition, it was also shown that the excitation energies of Chl a and Chl b in solutions can be reproduced using the optimized functional.⁴⁴

Although the QM/MM method effectively describes electronic states in the QM region, its direct application to MD simulations is practically challenging owing to the computational time required. Consequently, MD simulations often rely on classical MM force fields, which do not accurately reproduce the potential energy calculated using the QM/MM method. To address this problem, several methods have been developed to bridge the gap between MM and QM/MM energies. For example, Park and Rhee developed a method named interpolation mechanics/molecular mechanics of potential energy surfaces, which accurately reproduces the potential energies calculated using the QM/MM method.⁴⁶ They applied this method to the ground and excited state energies of BChl a in the Fenna–Matthews–Olson (FMO) protein and the light-harvesting 2 complex, as well as to the excitation energies of chromophores in photoactive yellow protein.⁴⁷⁻⁴⁹ Higashi and Saito developed molecular mechanics with Shepard interpolation correction (MMSIC),⁵⁰ an approach that facilitates rapid calculations with QM/MM accuracy, allowing MD simulations to account for environmental effects at each BChl a in the FMO protein. Consequently, MD simulations using the MMSIC method have successfully determined the site energy, coupling, and spectral density of the FMO protein, revealing its EET dynamics.^50,51

Herein, we develop MMSIC parameters for Chl a and Chl b in the LHCII trimer and analyze their site energies, excitonic couplings, and exciton energy levels calculated from the MMSIC–MD simulations. We find that the distribution of site energies for the eight Chl a molecules is broader than that for the six Chl b molecules, indicating that Chl a molecules reside in more inhomogeneous environments, consistent with experimental results.²¹ We examine the nature of the exciton states of LHCII, such as their delocalization. Furthermore, we analyze the absorption, LD, and CD spectra of LHCII, verifying that they align with the experimental and theoretical spectra.^{13,14,17,27,33,37} The present results thus confirm the reliability of the MMSIC parameters determined for the LHCII complex in this study.

This paper is organized as follows: the next section describes the methods developed here. Computational details are provided in Section 3. Section 4 presents and discusses the results obtained in this study, and Section 5 concludes the study.

2. Methods

2.1. Exciton Hamiltonian

The excitonic Hamiltonian H_el of the LHCII system is composed of diagonal and nondiagonal elements,³⁷

1

where ε_i represents the site energy of Chl i, and V_ij represents the excitonic coupling between Chl i and j. The site energies ε_i and excitonic couplings V_ij can be calculated using the QM/MM method. However, owing to the high computational cost of this method, performing long-time MD simulations with the QM/MM method for large systems is not feasible. Therefore, we used an MD method based on MMSIC parameters, which can reproduce QM/MM potentials as developed in the previous study.⁵²

2.2. Site Energies

In the QM/MM method, the total Hamiltonian Ĥ^QM/MM is described using

2

where Ĥ^QM, Ĥ^QM–MM, and Ĥ^MM represent the Hamiltonians for the QM region, QM–MM interactions, and MM region, respectively. Given that the QM–MM interaction can be divided into ES and non-ES interaction parts, the total Hamiltonian can be expressed as⁵²

3

As both Ĥ^QM and Ĥ^QM–MM_ES depend on the electronic wave function, using the eigenfunction ψ of Ĥ^QM + Ĥ^QM–MM_ES, the QM/MM potential energy is given using

4

where R and R^MM represent the coordinates of atoms in the QM region and MM region, respectively. V^QM–MM_non–ES and V^MM denote non-ES QM–MM interactions and MM interactions, respectively. When we use the approximation Ĥ^QM–MM_ES ≃ Q̂^TΦ, the first term in eq 4 becomes

5

where Q̂ and Φ represent the charge operator in the QM region and the ES potential from the MM region, respectively.⁵² Using the point charge approximation, the site–site representation for the second term in eq 5 is,

6

where Q_a is the partial charge at R_a, Q_a = ⟨ψ|Q̂_a|ψ⟩, and Φ_a is the ES potential at R_a from the MM region.

7

Thus, the first term of eq 4 is expressed as the electrostatically embedded QM potential (V^EEQM),⁵²

8

Therefore, eq 4 can be expressed as follows:

9

where Φ is a function of R^MM as shown in eq 7.

In the MMSIC method,⁵² we approximate that V^EEQM as the sum of the MM force field V^MM and the remaining correction term V^SIC:

10

The V^SIC term is evaluated as the weighted sum of the potential correction terms at Shepard point k:

11

where Vk and Wk represent the energy difference between the EEQM and MM methods at Shepard point k and the weight that satisfies the condition ∑NSICkWk = 1, respectively. s(R) denotes the internal coordinates, and the weight Wk is given using

12

where d_k is the generalized distance between the structure and the Shepard point k in the internal coordinate s:

13

where Δϕ^(k) represents the difference of dihedral angles between the sampled structure and Shepard point k, and N^dihed is the number of dihedral angles ϕ_n. V_k is expressed as a second-order Taylor expansion:

14

where Δs^k = s–s^k and ΔΦ^k = Φ–Φ^k represent the differences in the internal coordinates and ES potential between the sampled structure and Shepard point k, respectively. v^k is the difference between the EEQM and MM energies at the geometry of Shepard point k:

15

The vector g^k and matrix h^k are the first and second partial derivatives of V_k, respectively. g^k_s is the gradient of the EEQM and MM energy difference:

16

We define the charge Q_a by taking the partial derivative with respect to Φ_a in eq 6:

17

indicating that the term g^k_Φ is the charge at Shepard point k:

18

h^k_ss is the difference between the Hessian of the EEQM and MM energies:

19

Consequently, the term h^k_ΦΦ is described by the derivatives of the charges Q with respect to the external potential Φ:

20

Because V^EEQM is continuous, h^k_sΦ and h^k_Φ s are identical:

21

The site energy of a Chl molecule in LHCII is the energy difference between the excited (S1) and ground (S0) states:

22

Consequently, the QM/MM site energy is calculated as the difference between V^MMSIC(R, Φ; S1) and V^MMSIC(R, Φ; S0) in this study.

2.3. Excitonic Couplings

The excitonic couplings are described using the site–site interactions of the transition densities ρ^Tr.⁵¹ In the present calculation, the point charge approximation is used for transition densities. Thus, the excitonic coupling V_ij between sites i and j is evaluated as the interaction between transition charges:

23

where N_i denotes the number of atoms in site i, and R_a and Q^Tr_a represent the coordinate and the transition charge of atom a at site i, respectively.

The transition charges Q^Tr are approximated using the Shepard interpolation as follows:

24

where the weight W_k for transition charges is identical to that for energy calculations, i.e., eq 12. Consequently, the transition charges Q^Tr,k(s, Φ) are evaluated using the first-order expansion with respect to s^k and Φ^k:

25

where κ^Tr,k and χ^Tr,k are the partial derivatives of Q^Tr, and Q^Tr,k(s^k, Φ^k) are the transition charges at Shepard point k:

26

and

27

2.4. Exciton Properties

In the exciton representation, exciton state m is expressed as a linear combination of sites:⁵³

28

where N_site and c_i^m denote the number of sites and the eigenvector of state m, respectively.

The inverse participation ratio (IPR) is used to quantify the extent of localization of the exciton states:^53,54

29

If state m is localized at a single site, IPR_m would be equal to 1, whereas IPR_m would be N_site if the exciton state m is delocalized throughout the system.⁵³

2.5. Optical Spectra

The absorption spectrum of the LHCII system is given using⁵⁵

30

where μ^Tr_i(t) represents the transition dipole moment of site i at time t, evaluated using the transition charges as follows:

31

where Q^Tr_a is the transition charge of atom a at site i. U_ij(t) denotes the ij element of the time evolution operator U:⁵⁵

32

where ℏ denotes the Planck constant h divided by 2π and H(t) represents the excitonic Hamiltonian of the LHCII trimer.

The LD spectrum is related to the absorption spectrum as follows:³³

33

where α_∥(ω) and α_⊥(ω) represent the parallel (sum of x and y components) and perpendicular (z component) components of the absorption spectrum, respectively. Here, we assume that the unit vector of the z-axis e_z is the normal vector of the membrane plane. The perpendicular component of the transition dipole moment is defined as μ^Tr_⊥ = e_z^T·μ^Tr. Thus, the LD spectrum is expressed as follows:

34

The CD spectrum of the LHCII system is expressed as follows:

35

where the magnetic transition momentum m_j of site j is defined as follows:⁵⁶

36

Here, c₀ is the speed of light, and R_j denotes the coordinates of the magnesium atom at site j.

3. Computational Details

3.1. LHCII Structure

The present system consisted of an LHCII complex trimer embedded in a membrane of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) that is surrounded by water molecules on both the stromal and lumenal sides. The LHCII trimer was composed of subunits B, F, and G from the X-ray crystal structure of spinach (Spinacia oleracea, PDB code: 1RWT) as shown in Figure 1.⁴ Each monomeric subunit of the LHCII complex contained 218 amino acid residues, 14 Chls (eight Chl a and six Chl b), and four carotenoids (two luteins, one violaxanthin, and one neoxanthin). In addition, a lipid (1,2-dipalmitoyl-phosphatidyl-glycerole, PG) coordinated to a611 was included. A β-nonyl-glucoside observed in each X-ray structure monomer as crystallization detergent, was omitted from this calculation. Glutamic and aspartic acids, arginine, and lysine were assigned default protonation states at physiological pH. His-120 was protonated on both δ and ϵ-nitrogens with a charge of +1 owing to its strong hydrogen bond with Asp-111, consistent with the study by Müh et al.³² The other two histidines, His-68 and His-231, were neutral, with δ-nitrogen atoms protonated and ϵ-nitrogen atoms coordinated to magnesium cations at a603 and a614. Consequently, one monomer of the LHCII complex had a net charge of −11, and 33 sodium cations were added to neutralize the total charge of the system, which contains 152,099 atoms.

3.2. Equilibrium Classical MD Simulations

The ff14SB,⁵⁷ lipid14,⁵⁸ and TIP3P⁵⁹ force fields were employed for the protein, POPC membrane, and water, respectively. The SHAKE algorithm was applied to bonds involving hydrogen atoms, e.g., the hydrogen atoms in TIP3P water. The general Amber force field (GAFF)⁶⁰ was employed for PG molecules, and parameters from Joung and Cheatham⁶¹ were used for the sodium cations. For carotenoids, Chl a, and Chl b, bond and angle parameters were obtained from GAFF, while charges in the MM region were replaced by the RESP⁶² charges derived from QM/MM calculations. Furthermore, Lennard-Jones parameters developed by Åqvist⁶³ were applied to magnesium cations in Chl a and Chl b. Classical MD simulations were conducted using the Amber 22 package.⁶⁴ Initially, a 5 ns isothermal–isobaric MD simulation was performed at 300 K and 1 bar with the MM force field to relax the surface tension and determine the system volume. The simulation time step was set at 2 fs, with periodic boundary conditions applied to the system, and long-range ES interactions calculated using the particle mesh Ewald method. The final system box dimensions were 132.5 Å × 132.5 Å × 82.7 Å, as derived from the equilibrium result.

3.3. Shepard Points for MMSIC–MD Simulations

We performed QM/MM calculations to determine the parameters for the MMSIC method. To reduce computational costs, the 8-ethyl and 17-propionate groups in Chl a and Chl b in LHCII were truncated to methyl groups, and link hydrogen atoms were added at the QM–MM boundary, as in our previous study.⁴⁴ The QM–MM interactions for valence bonds at the QM–MM boundary were evaluated using the link atom method.⁶⁵ The truncated groups of Chl a and Chl b were treated as part of the MM region, with GAFF parameters and RESP charges applied to the atoms in these truncated groups. These parameters were retained during the MMSIC simulations. Consequently, the QM region consisted of 70 and 69 atoms for Chl a and Chl b, respectively. In our previous study,⁴⁴ the default range-separated parameter μ = 0.33 Bohr^–1 of the CAM-B3LYP³⁹ functional was optimized to μ_a = 0.137 Bohr^–1 and μ_b = 0.142 Bohr^–1 for Chl a and Chl b, respectively, to reproduce their excitation energies. Thus, the CAM-B3LYP hybrid density functional with the optimized range-separated parameter was used in the QM/MM calculations. The GAFF force field provided the MM parameters for the atoms of Chl a and Chl b in the QM region to evaluate non-ES QM–MM energy. During the development of the MMSIC parameters for b601 and a604, the distances between nitrogen on the chlorin ring and nearby hydrogen atoms were often too short. To address this, LJ parameters from the GLYCAM06g force field⁶⁶ (R* = 0.2 Å and ϵ = 0.03 kcal/mol) were added for interactions between a604 and nearby hydrogen atoms of water and between b601 and the hydroxyl group of the neoxanthin.⁵⁰ The tolerance of the QM/MM geometry optimization was set to 0.0005 hartree/Bohr. Parameters for the charges Q_a, first- and second-order derivatives (g and h in eq 14) of the ES potential, and EEQM energies of the geometries were calculated using a modified version of GAMESS.^67,68 The initial Shepard point for each Chl molecule was based on the structure optimized at the last data of the classical MD simulation. After generating the initial Shepard point for a Chl molecule, we performed a 100 ps MMSIC–MD simulation treating this Chl molecule as the QM region at 300 K with a 0.5 fs time step using the Amberplus program.⁶⁹ One hundred configurations saved every 0.5 ps over the last 50 ps were used to estimate energy differences between the MMSIC and EEQM methods. These energy differences were evaluated using the mean unsigned error (MUE). If the energy differences exceeded 2 kcal/mol, which corresponds to ∼3% of the thermal vibrational energy in the S0 state of the QM region, the structure with the largest error was added to the Shepard points. The same threshold value was used to determine the MMSIC parameters of the FMO protein.⁵⁰ The iteration was repeated until the energy difference between the MMSIC and EEQM methods was less than 2 kcal/mol. As shown below in Section 4, using this threshold value, the error in the site energy between the MMSIC and QM/MM methods can be accurately determined to be ∼0.2 kcal/mol. As shown in Figure S1, dihedral angles involving the 3-vinyl and the 13²-methylester groups of Chl molecules were used for the Shepard points. Owing to the symmetrical structure of the methyl group, coordinates and dihedral angles associated with methyl hydrogens were excluded from Shepard point weight calculations. Site energies of Chl molecules were obtained from MMSIC energy differences between their S1 and S0 states. For simplicity, herein, ligand molecules were excluded from the QM region, with their quantum effects on the site energies accounted for by introducing a correction term, i.e., the difference in QM/MM energies with and without the ligand molecule in the QM region. In addition, previous studies have shown that hydrogen bonds (HBs) formed between a Chl molecule and neighboring molecules have a substantial influence on the site energy.^42,44 Therefore, an HB correction was also applied to the site energy, as performed in previous studies. Considering these corrections, the total energy correction for the excitation energy of site i is given as follows:

37

where ΔE_i,lig and ΔE_i,HB(ζ) represent the corrections for the ligand effect and the HB effect of the formyl group (only on Chl b, ζ = formyl) or keto group (on both Chl a and Chl b, ζ = keto) for site i, respectively. The individual correction term is calculated as

38

where η represents the group of a correction term, i.e., lig, HB(keto), or HB(formyl), and E^large_i and E^small_i represent the QM/MM site energies with and without η in the QM region for site i, respectively. The ensemble for the calculation of ΔE_i,η was obtained from a 100 ps MMSIC–MD simulation of each specific site to evaluate the correction terms in the QM region. The difference between total correction energies calculated by considering all the groups in the QM region and those obtained by directly summing all individual correction energies was less than 10 cm^–1.⁴⁴ This HB correction method has successfully reproduced the absolute values of site energies for BChl a in the FMO protein and Chl a and Chl b in solution.^44,50 Therefore, herein, the total correction energy was obtained by summing these individual correction energies.

Previous studies have shown that excitation energies calculated with CAM-B3LYP are overestimated using the QM/MM method,^42,44 although they can qualitatively reproduce the experimental excitation energies of Chl a and Chl b in various solutions. To evaluate the absolute values of all Chl molecules in LHCII, the calculated site energies were corrected using the average difference between experimental and calculated excitation energies for Chl a and Chl b in solutions:

39

where E^expr_a,k, E^QM/MM_a,k, E^expr_b,k, and E^QM/MM_b,k represent the experimental and calculated QM/MM excitation energies of Chl a and Chl b in solution k (ethanol, diethyl ether, and acetone), respectively.⁴⁴ The shift ΔE^expr–calc between E^expr and E^QM/MM was −2095.6 cm^–1 to reproduce the absolute values of the excitation energies of Chl a and Chl b in several solutions. Consequently, the absolute value of the site energy ε_i of Chl i was finally calculated as

40

The standard deviations (STDs) of site energies were obtained from their distributions. Using these STDs, the reorganization energies of Chl a and Chl b in LHCII were calculated as follows:

41

where β and δE_n represent the inverse temperature 1/(k_BT) and the STD of the excitation energy at site n, respectively. The reorganization energies are crucial properties for site-dependent spectral densities and indispensable for understanding EET dynamics.

3.4. MMSIC–MD Simulations

Starting from the last configuration of the classical MD equilibrium simulation, we performed a 2 ns MMSIC–MD simulation for equilibration under NVT conditions at 300 K using a time step of 0.5 fs. All 42 Chl molecules in the LHCII trimer were treated as the QM region. After equilibration, a 2 ns MMSIC–MD simulation production run was conducted. Two independent MMSIC–MD simulations were performed, generating a total of 8 × 10⁷ configurations over 4 ns. The S0 and S1 state energies, along with the transition charges of the 4 ns MMSIC–MD simulations, were saved and used to calculate the site energies and excitonic couplings and conduct spectroscopic analyses.

It is known that transition dipole moments of Chl a are generally overestimated in TDDFT calculations.⁷⁰ Therefore, we rescaled the transition charges and excitonic couplings. Knox provides the experimental values of the transition dipole moments of Chl a and Chl b in different environments.⁷¹ Based on Knox’s model, we determined the scaling factors for Chl a and Chl b:

42

and

43

where μ^Tr_expr, μ^Tr_calc, and f^scale present the experimental and calculated transition dipole moments of Chl a and Chl b molecules in a vacuum, and the scaling factor for the calculated transition charges, respectively. Herein, the scaling factors for Chl a and Chl b were found to be 0.863 and 1.030, respectively. We implemented a distance cutoff of 30 Å for excitonic couplings in the excitonic Hamiltonian, excluding excitonic couplings between sites separated by more than this distance. Site energies ε_i and excitonic couplings V_ij in the Hamiltonian H^el were given using eqs 40 and 43, respectively.

3.5. Optical Spectra

Using the excitonic Hamiltonian and transition dipoles calculated from the MMSIC–MD simulations with 42 sites, we analyzed the absorption, LD, and CD spectra of LHCII using the time correlation function. The time evolution operator U at time t = nΔt was evaluated using the product of exp(−iH(t)Δt/ℏ) over time,⁵⁵ i.e.,

44

For the LD spectrum, the unit normal vector was determined as the average of 14 normal vectors, each derived from three magnesium cations in the corresponding Chl molecules of the LHCII trimer:

45

where R_i(k) represents the coordinate of the magnesium cation at site i in monomer k of the LHCII trimer.

4. Results and Discussion

4.1. MMSIC Modeling

Table 1 and Figure S1 present the number of Shepard points, N^SIC derived from eq 11, for each Chl molecule and the geometries of these Shepard points for all Chl a and Chl b molecules, respectively. In our previous study, we applied the MMSIC method to bacteriochlorophyll a (BChl a) molecules in the FMO protein.⁵⁰ We found that describing the conformational fluctuations of Chl molecules in LHCII requires more Shepard points than for BChl a in the FMO protein. This is owing to the substantial fluctuations of 3-vinyl and 13²-ester groups of most Chl a molecules and some Chl b molecules caused by their exposure to the solvent and membrane environment, requiring many Shepard points to accurately describe their rotations. Additionally, the fluctuation of the 3-vinyl group in a604 is caused by the nearby flexible neoxanthin, indicating large fluctuations of the Chl molecules in LHCII.

Table 1. Number of the Shepard Points (N^SIC) and Mean Unsigned Errors (MUEs) between Potential Energies in the S0 and S1 States and the Site Energies Calculated from the MMSIC and EEQM Methods (in kcal/mol), and those Calculated from the MM and EEQM Methods.

		⟨|VMMSIC – VEEQM|⟩			⟨|VMM – VEEQM|⟩
site	NSIC	S0	S1	Eex	S0	S1	Eex
a602	9	0.89	0.91	0.33	5.84	5.87	1.03
a603	8	1.04	1.09	0.19	6.01	6.17	0.91
a604	9	1.29	1.26	0.28	5.75	5.86	0.91
a610	1	0.89	0.92	0.19	5.57	5.53	0.80
a611	7	1.24	1.27	0.29	6.55	6.54	1.31
a612	9	0.87	0.89	0.20	5.49	5.71	1.05
a613	1	1.06	1.00	0.22	5.49	5.59	0.90
a614	9	0.88	0.88	0.17	5.69	5.96	0.93
b601	6	1.01	1.00	0.28	6.69	6.49	0.96
b605	9	0.97	0.96	0.22	6.00	5.92	0.93
b606	3	0.80	0.82	0.17	6.47	6.44	0.94
b607	4	0.98	0.97	0.24	5.51	5.48	0.84
b608	7	0.93	0.97	0.20	5.84	5.81	1.05
b609	6	1.34	1.37	0.24	6.03	6.06	0.89
avg. (Chl a)		1.02	1.03	0.23	5.80	5.90	0.98
avg. (Chl b)		1.01	1.02	0.23	6.10	6.03	0.93
avg. (all)		1.01	1.02	0.23	5.90	5.96	0.96

We then compared the energies of the S0 and S1 states of Chl a calculated using the MMSIC and MM methods with those from the EEQM method. Figure 2a and b show a narrow diagonal distribution for the S0 and S1 states, respectively, indicating that the energies calculated using the MMSIC method for both states well reproduce those calculated using the EEQM method. In contrast, the energy distributions of these states calculated using the MM and EEQM methods, as shown in Figure 2c and d, are broad and deviate from the diagonal line, especially at high and low energies. The MUEs between the MMSIC and EEQM methods were ∼1 kcal/mol, while those between the MM and EEQM methods were ∼6 kcal/mol, as shown in Table 1.

Figure 2.

Comparison of the MMSIC and EEQM energies (top) and the MM and EEQM energies (bottom) for all Chl a molecules in LHCII, based on 500 configurations obtained from the MMSIC–MD simulations. Blue and red points represent the energies of the ground (S0) and excited (S1) states, respectively.

Figure S2 shows a comparison of the MMSIC and MM energies of the S0 and S1 states with EEQM energies for Chl b. Similar to Chl a, the MMSIC method reproduces the EEQM energies for both states of Chl b, with a small MUE (an average of ∼1 kcal/mol). In contrast, the comparison of the energies of the MM and EEQM methods for the S0 and S1 states of Chl b shows a broad off-diagonal distribution (∼6 kcal/mol), similar to the results for Chl a.

We examined the reproducibility of the site energies, which is defined as the energy difference between the S1 and S0 states. The average MUEs for site energies of Chl a and Chl b calculated from the MMSIC and MM methods are ∼0.2 and ∼1.0 kcal/mol, respectively (Table 1). The apparently small MUE for site energies calculated using the MM method is owing to the elimination of the energy discrepancies between the S0 and S1 states. The average values and fluctuations of site energies in the S0 state are required to study EET dynamics of LHCII. Thus, a proper description of the dynamics in the S0 state is indispensable. The present results demonstrate that the MMSIC method can accurately calculate the energies of the S0 and S1 states and site energies for all Chl molecules in LHCII. Furthermore, the calculation speed for the energy and force of the S0 state using the MMSIC method is ∼2 million times faster than that of the QM/MM method. As a result, the MMSIC method enables efficient MD simulations while maintaining the accuracy of the QM/MM method.

4.2. Site Energies

Figure 3 and Table 2 show site energies from the present and previous studies.^27,32,37 First, we found that the energy difference between the average site energies of Chl a and Chl b in LHCII (∼500 cm^–1) is larger than that between the average excitation energies of Chl a and Chl b in solutions (∼380 cm^–1).⁴⁴ This result indicates that Chl molecules in LHCII are more inhomogeneous than those in solutions. Consistent with current and previous studies,^27,32,37 site a610 is identified as the lowest energy site. The intramolecular structure of Chl molecules reveals that the low site energy of a610 results from the destabilization of the S0 state owing to distortions in rings A and D, caused by the presence of the rigid lutein molecule near the 17-propionate group of ring A. Distortions in ring D are also found in a611 and a613, although the destabilization of their S0 states is minor. We also find that the chlorin ring of a604 is distorted by neoxanthin near the nitrogen atoms. This structural distortion destabilizes the S0 state of a604, lowering the excitation energy by about 100 cm^–1.

Figure 3.

Comparison of site energies for 14 Chls relative to a610 calculated from the present and previous studies. The blue, green, yellow, and red lines represent site energies calculated by Novoderezhkin et al.,²⁷ Müh et al.,³² Sláma et al.,³⁷ and the present study, respectively.

Table 2. Averages and Standard Deviations of the Site Energies and Reorganization Energies for Chl a and Chl b in LHCII^a.

site	Novoderezhkin et al.27	Müh et al.32	Sláma et al.37	this study	STD	λ
a602	15087	14850	14858	14735	244.5	143.4
a603	15222	14860	15004	14888	258.4	160.1
a604	15310	14920	15072	14858	252.7	153.1
a610	15038	14780	14857	14709	221.7	117.9
a611	15100	14930	14998	14813	251.1	151.2
a612	15082	14960	15067	15086	235.0	132.4
a613	15150	14870	14974	14902	230.4	127.3
a614	15249	14980	15075	14963	224.6	121.0
b601	15849	15415	15491	15411	255.0	155.9
b605	15681	15555	15324	15240	245.2	144.2
b606	15745	15395	15261	15335	241.3	139.6
b607	15635	15305	15303	15437	250.7	150.7
b608	15689	15175	15224	15308	245.7	144.8
b609	15597	15635	15418	15463	234.1	131.4

^aUnits are cm^–1.

We also examined the environmental effects on site energies. Figure 4 shows the energy shifts caused by environmental ES interactions. As shown by the green bar, the site energies of all Chl b molecules decrease by more than 50 cm^–1 owing to environmental ES interactions, although the magnitude of the energy change depends on the site. In contrast, the environmental ES interactions have a highly varied effect on Chl a, as shown by the blue bar in Figure 4: site energies for a604, a612, and a614 increase, while those for a603, a610, and a613 decrease. The site energy of a604 increases by ∼20 cm^–1 owing to the environmental ES interactions. However, as shown above, the distortion of the chlorin ring reduces its site energy. As a result, we find that the site energy of a604 is lower than that of a613 and a614. Unlike a604 and a610, a612 has no significant intramolecular structural distortion. Its site energy increases owing to the environmental ES interactions, resulting in the highest site energy among the eight Chl a molecules. In addition, as shown in Section 4.3, the strong excitonic coupling between a611 and a612 further raises the exciton level involving a612. The variation in environmental ES interactions increases the site energy differences among Chl a molecules, with the site energy difference between the highest (a612) and lowest (a610) sites for Chl a being ∼340 cm^–1, whereas that between the highest (b609) and lowest (b605) sites for Chl b being ∼270 cm^–1. In addition, this increase in site energy for a612 and decrease for b605 owing to environmental ES interactions narrow the energy difference between a612 and b605 to ∼150 cm^–1. These results show that Chl a molecules are in more intramolecularly and intermolecularly inhomogeneous environments than Chl b.

Figure 4.

Environmental ES interactions at each Chl molecule in LHCII.

Figure 5 shows the site energy distributions of Chl a and Chl b calculated from the 4 ns MMSIC–MD simulations and Table 2 shows the STDs of site energies and the reorganization energies (eq 41) for Chl molecules in LHCII. It was found that site energy distributions for some BChl a sites, i.e., sites 2, 5, and 8, considerably deviate from a Gaussian distribution in the FMO protein.⁵⁰ However, the site energy distributions for all Chl a and Chl b in LHCII are well represented by Gaussian distributions. The STDs of the site energies for individual Chl a and Chl b molecules in LHCII, ranging from ∼220 to ∼260 cm^–1, are larger than those for Chl a and Chl b in solutions (∼90 to ∼125 cm^–1)⁴⁴ and BChl a in the FMO protein (from ∼145 to ∼250 cm^–1).⁵¹ The high STDs for Chl molecules in LHCII are consistent with the large number of Shepard points required for these molecules. In addition, the variance in site energy fluctuations between LHCII and the FMO protein implies that LHCII acts as a coarse scaffold where its Chl molecules are exposed to the solution and membrane environment and show noticeable fluctuations. In contrast, the FMO protein served as a container that suppresses fluctuations in BChl a molecules. The STD of a site energy is related to the reorganization energy, λ, as shown in eq 41. Our previous study highlighted the critical role of site-specific reorganization energies in efficient EET within the FMO protein.⁵¹ Therefore, it is of interest to see how the large reorganization energies affect EET dynamics in LHCII.

Figure 5.

Site energy distributions of Chl a (a) and Chl b (b) in LHCII calculated from the MMSIC–MD simulations. The energy distributions are arranged according to site energies and offset by 1.0 × 10^–3 for clarity.

We have thus far discussed the average site energies. The broadening of the site energy distributions caused by structural fluctuations and environmental heterogeneity can change the order of two sites. Therefore, we analyzed the probabilities of the site energy level exchanges (Table S1) and each site being the highest or lowest site of Chl a/b or in clusters (Table S2) using 4 ns MMSIC simulations. Table S1 shows that site energy level exchanges occur during the simulations. However, it is found that the probability being a612 the highest energy Chl a is the highest (∼36%), which is more than twice as large as that of the second highest energy site, a614 (∼17%). Additionally, the probability of b605 being the lowest energy Chl b is ∼31%, which is approximately 10% higher than that of b608. Furthermore, for Chl a on the lumenal side, the probability of a604 being the lowest energy Chl a is over 43%. These results indicate that individual Chl molecules exhibit significant fluctuations in site energies. Nevertheless, the overall picture derived from the average site energies remains appropriate.

We also analyzed the correlation of the site energy fluctuations between different sites using ⟨δε_iδε_j⟩. We find the correlation is significantly small, only 1/40 of the smallest fluctuation of site energy, ⟨δε²_a614⟩ (Table S3). The present result is similar to the result in the FMO protein, where the largest ⟨δε_iδε_j⟩is only 1/20 of the smallest site energy fluctuation.⁵¹

4.3. Exciton Properties

The excitonic couplings for all 42 Chl a and Chl b molecules in the LHCII trimer were obtained from the 4 ns MMSIC–MD simulations. Tables 3 and S4 present the intramonomeric and intermonomeric Hamiltonians of the LHCII trimer complex, respectively. Consistent with previous studies,^27,32 we found five clusters in LHCII: a602–a603, a610–a611–a612, b601′–b608–b609, a613–a614, and a604–b605–b606–b607, where b601′ denotes b601 present in an adjacent monomer. Figure 6 shows the 15 highest intramonomeric couplings, indicating that the excitonic couplings calculated in this study are in good agreement with previous results, especially those from refs (27,32), and (72). Figure 6 further demonstrates strong couplings in pairs such as b601–a602, a603–b609, b608–a610, a604–b606, a613–a614, a610–a611, and a611–a612. The three couplings, b601–a602, a603–b609, and b608–a610, are considered to strengthen interactions among the three clusters on the stromal side, i.e., a602–a603, a610–a611–a612, and b601′–b608–b609 (Figure 1b).^27,32 The two couplings a610–a611 and a611–a612 are related to the cluster a610–a611–a612. In particular, the coupling a610–a611 was found to decrease the energy of the lowest exciton state (m = 1) by 25 cm^–1, in which a610 is involved. Additionally, the coupling a611–a612 was found to increase the energy of the exciton state m = 8 related to a612 by 50 cm^–1, in which a612 is strongly involved, decreasing the energy gap between Chl a and Chl b. Thus, these two couplings increased the width of the eight exciton states for Chl a and decreased the gap between the excitons of Chl a and Chl b. The couplings a604–b606 and a613–a614 are located in lumenal side clusters, specifically, a604–b605–b606–b607 and a613–a614 (Figure 1c), respectively, with the former involved in the coupling between Chl a and Chl b on the lumenal side. The present analysis also reveals that pairs a603–b609, a604–b606, and a611–a612 show large couplings owing to the aligned orientation of the transition dipole moments of their respective Chl molecules. Similarly, although the a610–a611 is separated by 18.3 Å, the orientation of the transition dipole moments of the two Chl molecules is aligned, making the coupling in this pair also relatively strong. We analyzed the fluctuations in excitonic couplings. As shown in Table S5, the fluctuations in excitonic couplings, i.e.,⟨δV²_ij⟩, are small, different from those in the site energies.

Table 3. Intramonomer Hamiltonian of LHCII (in cm^–1) from the MMSIC–MD Simulation^a.

Chl	a602	a603	a604	a610	a611	a612	a613	a614	b601	b605	b606	b607	b608	b609
a602	14,734	29	8	–9	0	14	–4	1	74	0	7	9	–8	–33
a603	29	14,888	–1	12	–1	0	3	–8	–8	0	–5	9	5	98
a604	8	–1	14,858	–2	–4	2	2	–4	0	7	114	33	–5	3
a610	–9	12	–2	14,709	–42	34	9	0	–6	0	–2	1	78	–2
a611	0	–1	–4	–42	14,813	129	–3	0	32	0	0	0	7	5
a612	14	0	2	34	129	15,086	2	0	3	0	3	3	–1	0
a613	–4	3	2	9	–3	2	14,902	–50	–11	0	2	3	0	–3
a614	1	–8	–4	0	0	0	–50	14,963	3	0	0	–4	0	0
b601	74	–8	0	–6	32	3	–11	3	15,411	0	0	0	0	0
b605	0	0	7	0	0	0	0	0	0	15,240	25	–8	–7	–1
b606	7	–5	114	–2	0	3	2	0	0	25	15,335	33	–5	14
b607	9	9	33	1	0	3	3	–4	0	–8	33	15,437	–5	–4
b608	–8	5	–5	78	7	–1	0	0	0	–7	–5	–5	15,308	36
b609	–33	98	3	–2	5	0	–3	0	0	–1	14	–4	36	15,463

^aOff-diagonal coupling elements are scaled using eq 43.

Figure 6.

Comparison of the 15 largest intramonomeric couplings. The blue, green, yellow, pink, and red lines represent the exciton couplings calculated by Novoderezhkin et al.,²⁷ Müh et al.,³² Sláma et al.,³⁷ Frähmcke and Walla,⁷² and the present study, respectively.

The exciton energy levels calculated from the Hamiltonian of the LHCII trimer are presented in Table 4. Figure 7 shows the exciton energy levels obtained from experimental and theoretical studies.^21,27,32,37 In all cases, the lowest exciton state is primarily assigned to a610. Herein, the highest exciton state involving Chl a is assigned to a612, consistent with the results of Sláma et al.³⁷ For Chl b, the lowest and highest exciton states are mainly assigned to b605 and b609, respectively, which is in agreement with Schlau-Cohen et al.²⁴ and Müh et al.³² Thus, the detailed assignments of exciton states vary among studies, mainly owing to differences in the site energies of Chl a and Chl b depending on the calculations and models used.

Table 4. Energy Levels, Site Probabilities, and Principal Monomer Probabilities for Each Exciton State.

m	1	2	3	4	5	6	7	8	9	10	11	12	13	14
ϵm	14,665	14,717	14,786	14,830	14,863	14,895	14,991	15,139	15,230	15,311	15,358	15,393	15,449	15,520
a610	0.688	0.052	0.216	0.008	0.005	0.013	0.000	0.001	0.000	0.014	0.002	0.001	0.000	0.000
a602	0.054	0.851	0.010	0.022	0.004	0.042	0.001	0.000	0.000	0.000	0.000	0.011	0.000	0.002
a611	0.189	0.013	0.601	0.010	0.008	0.037	0.000	0.138	0.000	0.000	0.000	0.003	0.000	0.001
a604	0.000	0.003	0.007	0.632	0.075	0.230	0.001	0.000	0.005	0.005	0.028	0.001	0.012	0.000
a613	0.000	0.000	0.009	0.084	0.643	0.029	0.232	0.000	0.000	0.000	0.000	0.001	0.000	0.000
a603	0.011	0.063	0.058	0.190	0.032	0.565	0.051	0.000	0.000	0.001	0.002	0.007	0.000	0.020
a614	0.000	0.000	0.001	0.014	0.225	0.050	0.710	0.000	0.000	0.000	0.000	0.000	0.000	0.000
a612	0.044	0.001	0.089	0.001	0.001	0.006	0.000	0.854	0.001	0.001	0.000	0.001	0.000	0.000
b605	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.001	0.872	0.030	0.055	0.001	0.040	0.000
b608	0.011	0.001	0.004	0.000	0.000	0.000	0.000	0.001	0.004	0.811	0.105	0.017	0.017	0.029
b606	0.000	0.000	0.000	0.035	0.006	0.010	0.000	0.000	0.098	0.085	0.472	0.020	0.263	0.011
b601	0.001	0.010	0.002	0.000	0.000	0.000	0.001	0.004	0.000	0.002	0.028	0.723	0.002	0.228
b607	0.000	0.000	0.000	0.001	0.001	0.001	0.000	0.000	0.018	0.006	0.284	0.027	0.661	0.001
b609	0.001	0.006	0.001	0.003	0.001	0.017	0.003	0.000	0.000	0.045	0.022	0.189	0.004	0.708
Pmainm	0.872	0.700	0.950	0.924	0.950	0.925	0.930	0.992	0.994	0.998	0.906	0.719	0.997	0.767

Figure 7.

Experimental and calculated exciton energy levels of LHCII (in cm^–1). The purple line represents the experimental results from Calhoun et al.,²¹ and the blue, green, yellow, and red lines represent the calculated results from Novoderezhkin et al.,²⁷ Müh et al.,³² Sláma et al.,³⁷ and the present study, respectively. Solid and dotted lines represent excitons mainly involving of Chl a and Chl b, respectively.

We then analyzed the energy widths of exciton states mainly related to Chl a and Chl b, i.e., m = 1 to 8 and 9 to 14. The energy width of the exciton states related to Chl b in this study (∼290 cm^–1) aligns with experimental results²¹ and calculated results by Novoderezhkin et al.²⁷ and Sláma et al.³⁷ In contrast, the energy width of the exciton states related to Chl a (∼470 cm^–1) is broader than that related to Chl b. This broad energy width of the exciton states related to Chl a, consistent with experimental results²¹ and findings from Sláma et al.,³⁷ reflects the more heterogeneous environments for Chl a compared to Chl b. Furthermore, the energy gap between the highest exciton level of Chl a and the lowest exciton level of Chl b obtained in this study is ∼90 cm^–1, which is close to the experimental result (∼80 cm^–1).²¹

The delocalization of exciton states was then examined using the IPR defined in eq 29. As shown in Table 4 and Figure 8, the six lowest energy exciton states and exciton state m = 11 are relatively delocalized (IPR > 2). Here, exciton states 1 and 3 are delocalized within the a610–a611–a612 cluster owing to a610–a611 coupling. Schlau-Cohen et al. also reported delocalization of these two lowest states.²⁴ Exciton states 2 and 6 are also delocalized by the a602–a603 coupling. In addition, exciton state 11, consisting of the a604–b605–b606–b607 cluster, is the most delocalized state. Sláma et al. similarly identified high delocalization in exciton states involving b605–b606–b607.³⁷ In contrast to these delocalized states, exciton states 8, 9, and 10 are localized at sites a612, b605, and a608, respectively.

Figure 8.

IPR for each exciton state of LHCII.

We analyzed the extent to which the exciton state m is localized within a monomer using the following equation:

46

where k^main indicates the monomer with the highest probability. Table 4 shows that most exciton states are localized within a single monomer. However, exciton states 2, 12, and 14 are delocalized across different monomers with probabilities ranging from 0.2 to 0.3. Specifically, exciton state 2 is delocalized across different monomers owing to the of a602′–a603 coupling, while exciton states 12 and 14 are delocalized owing to the b601′–b609 coupling.

4.4. Optical Spectra

Finally, we validated the present MMSIC model by comparing experimental and calculated spectra of LHCII. Figure 9 shows the absorption, LD, and CD spectra, i.e., eqs 30, 34, and 35, calculated from the 4 ns MMSIC–MD simulations of the LHCII trimer at 300 K.

Figure 9.

Absorption (a), LD (b), and CD (c) spectra of LHCII. The red solid represents spectra calculated at 300 K in this study, while the black dashed and black dotted lines correspond to experimental data at 77 K (refs (13,14), and (16)) and 300 K (refs (13,15), and (17)), respectively.

The calculated and experimental absorption spectra are presented in Figure 9a. The calculated absorption spectrum shows the peaks at ∼14,700 and ∼15,400 cm^–1. This shows that the present method using the developed parameters can adequately reproduce the experimental absorption spectrum.¹³ We also analyzed the absorption spectrum for each Chl molecule given using

47

Notably, U_ii(t) considers all couplings between sites through the Hamiltonian and eigenfunction from time 0 to t. As shown in Figure S4a, these peaks at ∼14,700 and ∼15,400 cm^–1 are attributed to Chl a and Chl b, respectively. Figure S4a also shows shoulders at 15,100 and 14,750 cm^–1 in the spectra of a611 and a612 and at 15,450 and 14,850 cm^–1 in the spectra of a604 and b606, indicating strong coupling between sites.

Figure 9b shows the calculated and experimental LD spectra of LHCII. The calculated LD spectrum features a positive peak at ∼14,750 cm^–1 and a negative peak at ∼15,150 cm^–1. These results align well with the results of Müh and Renger³³ at 77 K and with the experimental LD spectrum at 77 K, where the positive and negative peaks are observed at ∼14,750 and ∼15,200 cm^–1, respectively.¹⁴ We analyzed the LD spectra derived from individual Chl molecules given using

48

As shown in Figure S4b, the narrow positive peak at ∼14,750 cm^–1 results from the cancellation of positive peaks from a610, a611, and a602 with negative peaks from a604 and a613. Conversely, the weak negative peak at ∼15,150 cm^–1 likely arises from the cancellation of negative peaks from b605 and b607 with positive peaks from b601, b608, and b609. Despite this, there are some discrepancies between the calculated and experimental LD spectra¹⁵ at 300 K. The experimental LD spectrum shows broad positive peaks at ∼14,800 and ∼15,300 cm^–1.¹⁵

The experimental and calculated CD spectra of LHCII are shown in Figure 9c. The calculated spectrum features negative peaks at ∼14,800 and ∼15,500 cm^–1, along with a positive peak between ∼14,900 and ∼15,400 cm^–1. We examined the contributions of individual Chl molecule couplings to the CD spectrum, given as follows:

49

Figure S4c shows that the negative peak at ∼14,800 cm^–1 in the CD spectra primarily owing to contributions from a611–a612, a613–a614, a602–a610, and b608–a610, while the other negative peak at ∼15,500 cm^–1 mainly results from b609–b601′. In addition, the positive peak between ∼14,900 and ∼15,400 cm^–1 is attributed to contributions from a611–a612, a613–a614, b609–b601′, and b608–a610. The results align well with those calculated by Müh and Renger³³ and Sláma et al.,³⁷ although all calculated CD spectra show broader positive spectra compared to the experimental spectra at 77 and 300 K.^16,17 The discrepancies between calculated and experimental LD and CD spectra may be owing to the fact that the time scale used, i.e., 4 ns, is insufficient to capture the slow fluctuations observed in single-molecule spectroscopy.^73,74 However, Figure 9 demonstrates that the parameters developed for the MMSIC–MD simulations of the LHCII trimer in this study can reasonably reproduce the three experimental spectra, supporting the reliability of these parameters.

5. Conclusions

Herein, we developed parameters for the MMSIC–MD simulations for LHCII, providing an atomistic description with faster computation than the QM/MM method. This approach enables a detailed elucidation of the excitonic and optical properties of Chl molecules in the LHCII trimer, as summarized below.

We found that the average energy difference between the excitation energies of Chl a and Chl b in LHCII is greater than that observed in solutions. Environmental ES interactions reduce the site energies of all Chl b molecules, whereas Chl a molecules experience more diverse effects. In addition, some Chl a site energies decrease owing to their intramolecular structural distortions, suggesting that Chl a molecules are in a more inhomogeneous intramolecular and intermolecular environment than Chl b. For example, the reduced site energy of a610, which is the lowest site energy, is attributed to both intramolecular distortions and stabilization by ES interactions. Furthermore, the reorganization energies of Chl a and Chl b in LHCII are generally higher than those of BChl a in the FMO protein, indicating more fluctuations in Chl a and Chl b in LHCII.

We also investigated exciton properties, including exciton energy levels, excitonic couplings, and delocalizations. Strong intercluster couplings on the stromal side facilitate connections between three clusters: a602–a603, a610–a611–a612, and b601′–b608–b609.³² The a611–a612 coupling increases the energy of the exciton state 8, which is the highest exciton level of Chl a, leading to a small energy gap between the highest exciton level of Chl a and the lowest exciton level of Chl b in LHCII, consistent with experimental result.²¹ We found that several excitons, e.g., exciton states 1, 3, and 11, are delocalized within monomers, while other states, such as exciton states 2, 12, and 14, are delocalized among monomers.

Finally, we calculated the absorption, LD, and CD spectra of the LHCII trimer, finding that these spectra calculated with the parameters developed in this study align well with previous theoretical results and closely reproduce experimental spectra at 77 K. The experimental spectra at 300 K are not fully reproduced, possibly because the slow fluctuations of LHCII at high temperatures may not have been sufficiently sampled in the 4 ns simulation conducted in this study. Nonetheless, the parameters successfully show reasonable reproducibility, suggesting their reliability.

In conclusion, this study provides detailed insights into the excitonic states of LHCII, such as energy levels, fluctuations, and couplings. These properties are crucial in influencing the EET dynamics, highlighting the importance of understanding their roles in photosynthetic efficiency in green plants.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.4c01214.

• Figures for the comparison of the MMSIC and EEQM energies and the MM and EEQM energies for all Chl b; the geometries of the Shepard points for Chl a and Chl b; the site energies with and without the environmental effects for Chl a and Chl b in LHCII; the detail contributions of absorption, LD, and CD spectra of LHCII; and tables for the probability that the site energy of site j is higher than that of site i; the probability that site i is the highest or lowest energy site; the correlation of the site energy fluctuations between sites i and j; the intermonomer excitonic couplings; the fluctuation of the intra- and intermonomer excitonic couplings in the LHCII trimer (PDF)

The authors declare no competing financial interest.

Special Issue

Published as part of Journal of Chemical Theory and Computationspecial issue “Developments of Theoretical and Computational Chemistry Methods in Asia.”