Towards the description of charge transfer states in solubilised LHCII using subsystem DFT

Abstract

Light harvesting complex II (LHCII) in plants and green algae have been shown to adapt their absorption properties, depending on the concentration of sunlight, switching between a light harvesting and a non-harvesting or quenched state. In a recent work, combining classical molecular dynamics (MD) simulations with quantum chemical calculations (Liguori et al. in Sci Rep 5:15661, 2015) on LHCII, it was shown that the Chl611-Chl612 cluster of the terminal emitter domain can play an important role in modifying the spectral properties of the complex. In that work the importance of charge transfer (CT) effects was highlighted, in re-shaping the absorption intensity of the chlorophyll dimer. Here in this work, we investigate the combined effect of the local excited (LE) and CT states in shaping the energy landscape of the chlorophyll dimer. Using subsystem Density Functional Theory over the classical [Formula: see text]s MD trajectory we look explicitly into the excitation energies of the LE and the CT states of the dimer and their corresponding couplings. Upon doing so, we observe a drop in the excitation energies of the CT states, accompanied by an increase in the couplings between the LE/LE and the LE/CT states facilitated by a shorter interchromophoric distance upon equilibration. Both these changes in conjunction, effectively produces a red-shift of the low-lying mixed exciton/CT states of the supramolecular chromophore pair.

Keywords: Charge transfer; Chromophore; Diabatic; Exciton.

Fig. 1

Excitation energy transfer and electron transfer are represented in the monomer coordinate system. The red arrows represents Förster (Förster 1948) energy transfer flow, whereas the green arrows represent the Marcus (Marcus and Sutin 1985) electron transfer between pigments A and B. Vertical excitation processes are represented with broken arrows. The ground, local excited and ionized potential surfaces of the corresponding pigments A and B are shown in black, red and green (denoted by ${\mathrm{\Psi }}_i^{A/B}$) respectively in the increasing order of energy. ${\lambda }_i^{A/B}$ denotes the reorganization energy associated with the electronic transition

Fig. 2

The ground state, ${\mathrm{\Phi }}_{\text{GS}}$, two locally excited states, ${\mathrm{\Phi }}_{A^{\ast }B}$ and ${\mathrm{\Phi }}_{A{B}^{\ast }}$, and two CT states, ${\mathrm{\Phi }}_{\text{CT1}}$ , ${\mathrm{\Phi }}_{\text{CT2}}$ along with the distribution of electrons, where each fragment is considered as a two-level two electron system, are shown. $a^{†}$ and a are the corresponding creation and annihilation operators, and i, j and a, b represent occupied and unoccupied orbitals of the fragments A and B, respectively

Fig. 3

Structure of a the Hamiltonian matrix, ${\mathbf{H}}^{\text{dia}}$, and b the Overlap matrix, ${\mathbf{S}}^{\text{dia}}$ which is used in this work. LE represents the locally excited states on pigment A and B, and CT the, non-local charge transfer states. The ${\mathbf{H}}_{\text{LE}}^{\text{dia}}$, ${\mathbf{H}}_{\text{CT}}^{\text{dia}}$ and ${\mathbf{H}}_{\text{LE}-\text{CT}}^{\text{dia}}$ blocks, constructed following Table 1 are shown in green, blue and orange, respectively. We assume zero coupling (white areas) between the CT states of different polarity

Fig. 4

Workflow for the calculation of charge transfer (CT) state energies using frozen density embedding (FDE)

Fig. 5

The 4 LE and 2 CT diabatic states of the Chla612–Chla611 dimer are shown for the initial and final (left and right of the split on x-axis) parts of the trajectory. For comparison we also show with black dotted lines the lowest six states obtained in a supramolecular calculations . All units are in eV. Also shown in boxes are the two structures of the Chla612–Chla611 dimer from the beginning (left) and end (right) of the trajectory

Fig. 6

The effect of the DRF environment on the 4 LE states and 2 CT states in the snapshots taken from the first and last sets of the trajectory (left and right of the split on the x-axis). Bold lines denote DRF environment and dotted lines denote vacuum calculation for the Chla612–Chla611 dimer. All units are in eV

Fig. 7

The absolute LE/LE couplings between $Q_y$ and $Q_x$ ($V_{\mathit{Qy}}$ and $V_{\mathit{Qx}}$) (upper panel) and the LE/CT couplings corresponding to hole and electron transfer (lower panel, see text for notations) from the first and last set of frames (left and right of the split on x-axis) of the trajectory are shown. All units are in eV

Fig. 8

The difference of the LE/LE couplings involving $Q_y$ and $Q_x$ ($V_{\mathit{Qy}}$ and $V_{\mathit{Qx}}$, upper panel) and LE/CT couplings (lower panel, see text for notations) between DRF and vacuum ($V_{\text{DRF}}-V_{\text{VAC}}$), $\mathrm{\Delta }\text{Couplings}$, for the first and last set of frames (left and right of the split on x-axis) of the trajectory are shown. All units are in eV

Fig. 9

The six adiabatic states labelled E1–E6 are shown in bold in increasing order of their energy from the beginning and the end (left and right of the split on x-axis) of the trajectory. Also shown in dotted lines are the lowest six supramolecular states. All units are in eV