^{1}, Valentina A. Mikhailova

^{1}and Anatoly I. Ivanov

^{1,a)}

### Abstract

A theoretical description of photoinduced charge transfer involves explicit treating both the optical formation of the nuclear wave packet on the excited free energy surface and its ensuing dynamics. The reaction pathway constitutes two-stage charge transfer between three centers. Manifestations of fractional charge transfer at first stage are explored. An expression for time dependent rate constant of photoinduced charge transfer is found in the framework of the linear dielectric continuum model of the medium. The model involves both the intramolecular vibrational reorganization and the Coulombic interaction of the transferred charge with the medium polarization fluctuations and allows to express the rate in terms of intramolecular reorganization parameters and complex dielectricpermittivity. The influence of the vibrational coherent motion in the locally excited state on the charge transfer dynamics has been explored. The dependence of the ultrafast photoinduced charge transfer dynamics on the excitation pulse carrier frequency (spectral effect) has been investigated. The spectral effect has been shown to depend on quantity of the fractional charge.

The authors are grateful to Eric Vauthey (University of Geneva) for helpful comments. This work was supported by the Russian Foundation for Basic Research grants (Grant No. 05-03-32680).

I. INTRODUCTION

II. THE ULTRAFAST PCT MODEL AND POPULATION DYNAMICS OF THE CHARGE SEPARATED STATE

III. CHARGE TRANSFER GEOMETRY AND ITS INFLUENCE ON PARAMETERS OF DIABATIC FREE ENERGY SURFACES

IV. RESULTS OF NUMERICAL INVESTIGATIONS OF THE SPECTRAL EFFECT AND THEIR INTERPRETATION

A. Photoinduced charge transfer dynamics

B. The model including an inertial and a few overdamped modes

C. The model including an underdamped mode

V. CONCLUSIONS

### Key Topics

- Charge transfer
- 60.0
- Dielectrics
- 18.0
- Solvents
- 18.0
- Excited states
- 16.0
- Free energy
- 11.0

## Figures

The geometry of the charge transfer. The quantities , , and are the radii of the cavities around the sites , , and , respectively. , , and are the site-to-site distances and is the angle between the directions of the two charge transfer steps.

The geometry of the charge transfer. The quantities , , and are the radii of the cavities around the sites , , and , respectively. , , and are the site-to-site distances and is the angle between the directions of the two charge transfer steps.

(a) Dependence of the angle on the angle for different values of . (b) Dependence of the reorganization energy, , on the angle for different values . (c) Dependence on the angle . Here is the solution of Eq. (34) at . The parameters used are , , , , and (acetonitrile).

(a) Dependence of the angle on the angle for different values of . (b) Dependence of the reorganization energy, , on the angle for different values . (c) Dependence on the angle . Here is the solution of Eq. (34) at . The parameters used are , , , , and (acetonitrile).

Time dependencies of the charge transfer rate constant, (in ), for single Debye mode model with relaxation time : (1) , (2) , and (3) . The wave packet is produced at (solid lines) and at (dashed lines). The parameters used are , , , , , , , , , and .

Time dependencies of the charge transfer rate constant, (in ), for single Debye mode model with relaxation time : (1) , (2) , and (3) . The wave packet is produced at (solid lines) and at (dashed lines). The parameters used are , , , , , , , , , and .

Configurations of the electronic terms. The solid circles , , and are the equipotential curves of the ground, the locally excited, and the charge transferred states, correspondingly. and are the reaction coordinates of the optical transition and the charge transfer, respectively. The crossing line between the terms and is labeled as for Marcus normal region and for the Marcus inverted region. The dashed circles are the equipotential curves of charge transferred state for . The crossing line between the terms and is labeled as for Marcus normal region and for the Marcus inverted region. The shaded ellipses show the initial positions and the forms of the wave packets produced by the pump pulses with the frequencies at half the absorbtion band maximum.

Configurations of the electronic terms. The solid circles , , and are the equipotential curves of the ground, the locally excited, and the charge transferred states, correspondingly. and are the reaction coordinates of the optical transition and the charge transfer, respectively. The crossing line between the terms and is labeled as for Marcus normal region and for the Marcus inverted region. The dashed circles are the equipotential curves of charge transferred state for . The crossing line between the terms and is labeled as for Marcus normal region and for the Marcus inverted region. The shaded ellipses show the initial positions and the forms of the wave packets produced by the pump pulses with the frequencies at half the absorbtion band maximum.

Logarithm of effective rate constant (in ) as a function of delta for single Debye mode model with relaxation time : (1) , (2) , and (3) . The wave packet is produced at (solid lines) and at (dashed lines). The parameters used are , , , , , , , , , and .

Logarithm of effective rate constant (in ) as a function of delta for single Debye mode model with relaxation time : (1) , (2) , and (3) . The wave packet is produced at (solid lines) and at (dashed lines). The parameters used are , , , , , , , , , and .

Logarithm of the thermal rate constant (in ) vs fractional charge, , for single Debye mode model with relaxation time : (1) , ; (2) , ; (3) , ; and (4) , . The parameters used are , , , , , , , , and .

Logarithm of the thermal rate constant (in ) vs fractional charge, , for single Debye mode model with relaxation time : (1) , ; (2) , ; (3) , ; and (4) , . The parameters used are , , , , , , , , and .

Free energy dependencies of the spectral effect for the three-mode model, Eq. (44): (1) , (2) , and (3) . The fraction of the charge transferred is equal to (a) 0.2 and (b) 0.8. The other parameters used are , , , , , , , , , , , and .

Free energy dependencies of the spectral effect for the three-mode model, Eq. (44): (1) , (2) , and (3) . The fraction of the charge transferred is equal to (a) 0.2 and (b) 0.8. The other parameters used are , , , , , , , , , , , and .

Free energy dependencies of the spectral effect for single Debye mode model: (solid lines) and (dashed lines). (1) , (2) , and (3) . The other parameters used are , , , , , , , and .

Free energy dependencies of the spectral effect for single Debye mode model: (solid lines) and (dashed lines). (1) , (2) , and (3) . The other parameters used are , , , , , , , and .

Dependencies of the spectral effect on the angle, , for the three-mode model: (a) and (b) . The fraction of the charge transferred is equal to (1) , (2) , (3) , and (4) . The other parameters used are , , , , , , , , , , , and .

Dependencies of the spectral effect on the angle, , for the three-mode model: (a) and (b) . The fraction of the charge transferred is equal to (1) , (2) , (3) , and (4) . The other parameters used are , , , , , , , , , , , and .

Free energy dependencies of the spectral effect for the model including an underdamped mode, Eq. (45): (1) , , ; (2) , , ; and (3) , , . The fraction of the charge transferred is equal to (a) and (b) . The other parameters used are , , , , , , , , , , and .

Free energy dependencies of the spectral effect for the model including an underdamped mode, Eq. (45): (1) , , ; (2) , , ; and (3) , , . The fraction of the charge transferred is equal to (a) and (b) . The other parameters used are , , , , , , , , , , and .

Trajectories of the wave packet maximum for the model accounting for the underdamped mode. The time dependencies of and are pictured as solid and dotted curves, respectively. The straight lines stand for the position of the term crossing for different values of the free energy . The solid lines correspond to the maxima of the spectral effect and the dashed lines correspond to the minima of the spectral effect pictured in Fig. 10. (1) , (2) , and (3) . The other parameters used are , , , , , , , , , , , , , , , and .

Trajectories of the wave packet maximum for the model accounting for the underdamped mode. The time dependencies of and are pictured as solid and dotted curves, respectively. The straight lines stand for the position of the term crossing for different values of the free energy . The solid lines correspond to the maxima of the spectral effect and the dashed lines correspond to the minima of the spectral effect pictured in Fig. 10. (1) , (2) , and (3) . The other parameters used are , , , , , , , , , , , , , , , and .

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