^{1,a)}and Shaul Mukamel

^{1,b)}

### Abstract

The excited state dynamics and relaxation of electrons and holes in the photosynthetic reaction center of photosystem II are simulated using a two-band tight-binding model. The dissipative exciton and charge carrier motions are calculated using a transport theory, which includes a strong coupling to a harmonic bath with experimentally determined spectral density, and reduces to the Redfield, the Förster, and the Marcus expressions in the proper parameter regimes. The simulated third order two-dimensional signals, generated in the directions , , and , clearly reveal the exciton migration and the charge-separation processes.

The support of the National Science Foundation Grant No. CHE0745892 and Grant No. DARPA BAA-10-40 QUBE is gratefully acknowledged.

I. INTRODUCTION

II. TIGHT-BINDING TWO-BAND HAMILTONIAN FOR EXCITON AND CHARGE-TRANSFER DYNAMICS

III. MODELING THE ENERGY AND ELECTRON TRANSFER

IV. HAMILTONIAN PARAMETERS FOR THE REACTION CENTER OF PS-II

V. OPTICAL 2D SIGNALS WITH INHOMOGENEOUS BROADENING

VI. SPECTROSCOPY OF THE CT STATES

VII. SUMMARY AND DISCUSSION

### Key Topics

- Excitons
- 37.0
- Charge transfer
- 36.0
- Frenkel excitons
- 30.0
- Absorption spectra
- 13.0
- Excited states
- 12.0

## Figures

Tight-binding model of molecular aggregates. Two molecules are shown. First row: the ground state. Second row: excitation of molecule 2 corresponds to creation of hole and electron on that molecule. Third row: CT state corresponds to creation of hole on molecule 2 and an electron on molecule 1. Electrons are marked by solid circles and holes by open circles.

Tight-binding model of molecular aggregates. Two molecules are shown. First row: the ground state. Second row: excitation of molecule 2 corresponds to creation of hole and electron on that molecule. Third row: CT state corresponds to creation of hole on molecule 2 and an electron on molecule 1. Electrons are marked by solid circles and holes by open circles.

Ground state, donor, and acceptor state potentials along the reaction coordinate. and are defined with respect to the ground state. and are optical absorption reorganization energies. and used in Marcus theory are defined with respect to equilibrium of the donor and the acceptor states.

Ground state, donor, and acceptor state potentials along the reaction coordinate. and are defined with respect to the ground state. and are optical absorption reorganization energies. and used in Marcus theory are defined with respect to equilibrium of the donor and the acceptor states.

Left: the RC of PS-II. Transition dipoles are represented by arrows. Right: the bath spectral density used in the simulations (Refs. 6 and 7).

Left: the RC of PS-II. Transition dipoles are represented by arrows. Right: the bath spectral density used in the simulations (Refs. 6 and 7).

Left: simulated absorption spectra of PS-II RC core at 77 K. Solid black—full model; dotted black—model without CT states. Red curve—square root of pulse power spectrum used in nonlinear optical signal simulations. Vertical lines denote positions of single excitons after reorganization. Contributions of CT states to these eigenstates (from left to right) are 0.94, 0.98, 0.63, 0.07, 0.35, 0, 0.03, 0, and 0. Right: the single-exciton eigenstates below and their reorganization shifts; three additional dark CT states at are not shown. Exciton eigenenergies, , and reorganization-energy shifts, , are shown.

Left: simulated absorption spectra of PS-II RC core at 77 K. Solid black—full model; dotted black—model without CT states. Red curve—square root of pulse power spectrum used in nonlinear optical signal simulations. Vertical lines denote positions of single excitons after reorganization. Contributions of CT states to these eigenstates (from left to right) are 0.94, 0.98, 0.63, 0.07, 0.35, 0, 0.03, 0, and 0. Right: the single-exciton eigenstates below and their reorganization shifts; three additional dark CT states at are not shown. Exciton eigenenergies, , and reorganization-energy shifts, , are shown.

Exciton population dynamics when all states are initially equally populated, (the three high-energy, CT states are not shown). The states are numbered by their energy ; color code is the same as in Fig. 4.

Exciton population dynamics when all states are initially equally populated, (the three high-energy, CT states are not shown). The states are numbered by their energy ; color code is the same as in Fig. 4.

2D photon echo (rephasing) signal. Left—full model, middle—Frenkel model (no CT states), and right—the difference. Each plot is scaled according to Eq. (51) and normalized [Eq. (50)] as follows: for left and middle columns, is the maximum at zero delay time; for the right column, is the maximum of each signal.

2D photon echo (rephasing) signal. Left—full model, middle—Frenkel model (no CT states), and right—the difference. Each plot is scaled according to Eq. (51) and normalized [Eq. (50)] as follows: for left and middle columns, is the maximum at zero delay time; for the right column, is the maximum of each signal.

Time dependence of integrated amplitudes in regions A–C and their cross-peaks (marked by squares in Fig. 6). The traces are shifted vertically to make the initial amplitude 0.

Time dependence of integrated amplitudes in regions A–C and their cross-peaks (marked by squares in Fig. 6). The traces are shifted vertically to make the initial amplitude 0.

The three components contributing to the 2D spectra at two delay times. The amplitudes of the ESE and ESA components have been multiplied by the factors given in each panel. The signal is scaled according to Eq. (51) and [Eq. (50)] is the maximum of each plot.

The three components contributing to the 2D spectra at two delay times. The amplitudes of the ESE and ESA components have been multiplied by the factors given in each panel. The signal is scaled according to Eq. (51) and [Eq. (50)] is the maximum of each plot.

2D photon echo (nonrephasing) signal . Left—full model, middle—Frenkel model (no CT states), and right—the difference. The signal is scaled according to Eq. (51) and normalized [Eq. (50)] as follows: for left and middle columns, is the maximum at zero delay time; for the right column, is the maximum of the signal of each plot.

2D photon echo (nonrephasing) signal . Left—full model, middle—Frenkel model (no CT states), and right—the difference. The signal is scaled according to Eq. (51) and normalized [Eq. (50)] as follows: for left and middle columns, is the maximum at zero delay time; for the right column, is the maximum of the signal of each plot.

The three components contributing to the 2D spectra at two delay times. The numbers inside the plots are the relative amplitudes of the component, compared to GSB. Each plot is scaled according to Eq. (51) and normalized [ in Eq. (50)] to the maximum.

The three components contributing to the 2D spectra at two delay times. The numbers inside the plots are the relative amplitudes of the component, compared to GSB. Each plot is scaled according to Eq. (51) and normalized [ in Eq. (50)] to the maximum.

2D double-quantum-coherence signals. Left—full model, middle—Frenkel exciton model (no CT states), and right—the difference. Each plot is scaled according to Eq. (51) and normalized [ in Eq. (50)] to the maximum.

2D double-quantum-coherence signals. Left—full model, middle—Frenkel exciton model (no CT states), and right—the difference. Each plot is scaled according to Eq. (51) and normalized [ in Eq. (50)] to the maximum.

The two pathways of the signals and their corresponding Feynman diagrams. Each plot is scaled according to Eq. (51) and normalized [ in Eq. (50)] to the maximum.

The two pathways of the signals and their corresponding Feynman diagrams. Each plot is scaled according to Eq. (51) and normalized [ in Eq. (50)] to the maximum.

## Tables

Single-exciton Hamiltonian in calculated using 2.9 resolution structure parameters (Ref. 3) [Protein Data Bank (PDB) database file 3BZ1.pdb]. The intermolecular dipole-dipole interactions were computed using transition dipole directions taken from Ref. 27 and transition amplitudes and .

Single-exciton Hamiltonian in calculated using 2.9 resolution structure parameters (Ref. 3) [Protein Data Bank (PDB) database file 3BZ1.pdb]. The intermolecular dipole-dipole interactions were computed using transition dipole directions taken from Ref. 27 and transition amplitudes and .

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