^{1,a)}and S. Ramasesha

^{2,b)}

### Abstract

We have studied the dynamics of excitation transfer between two conjugated polyene molecules whose intermolecular separation is comparable to the molecular dimensions. We have employed a correlated electron model that includes both the charge-charge, charge-bond, and bond-bond intermolecular electron repulsion integrals. We have shown that the excitation transfer rate varies as inverse square of donor-acceptor separation rather than as , suggested by the Förster type of dipolar approximation. Our time-evolution study also shows that the orientational dependence on excitation transfer at a fixed short donor-acceptor separation cannot be explained by Förster type of dipolar approximation beyond a certain orientational angle of rotation of an acceptor polyene with respect to the donor polyene. The actual excitation transfer rate beyond a certain orientational angle is faster than the Förster type of dipolar approximation rate. We have also studied the excitation transfer process in a pair of push-pull polyenes for different push-pull strengths. We have seen that, depending on the push-pull strength, excitation transfer could occur to other dipole coupled states. Our study also allows for the excitation energy transfer to optically dark states which are excluded by Förster theory since the one-photon transition intensity to these states (from the ground state) is zero.

This work was supported in part by DST India (Grant No. SR/S1/IC-08/2008) and J.C. Bose Fellowship. The authors thank Dr. Y. Anusooya Pati for useful discussions and her help with verifying some of the calculations.

I. INTRODUCTION

II. CORRELATED ELECTRONIC MODEL HAMILTONIAN

A. Time evolution of initial donor-acceptor state

III. RESULTS AND DISCUSSION

A. Excitation transfer in unsubstituted polyenes

1. Role of and interactions

2. Orientation dependence of FRET rates

B. Excitation transfer in push-pull polyenes

C. Excitation transfer to optically dark states

IV. CONCLUSIONS

### Key Topics

- Ground states
- 20.0
- Energy transfer
- 19.0
- Excited states
- 19.0
- Carbon
- 7.0
- Electric dipole moments
- 6.0

## Figures

Schematic diagram of Coulomb mechanism suggested by Förster and exchange mechanism suggested by Dexter. The electron repulsion integral (in the charge cloud notation) connects the configuration on the left in (a) with the configuration on the right in (a). Similarly connects the two configurations in (b).

Schematic diagram of Coulomb mechanism suggested by Förster and exchange mechanism suggested by Dexter. The electron repulsion integral (in the charge cloud notation) connects the configuration on the left in (a) with the configuration on the right in (a). Similarly connects the two configurations in (b).

Schematic diagram shows the orientation of an acceptor polyene around the molecular axis of the donor polyene. Polyene with broken lines represents the molecule on the right rotated relative to the molecule on the left. The nonzero value of leads to modeling effects of electron donor and acceptor substitution.

Schematic diagram shows the orientation of an acceptor polyene around the molecular axis of the donor polyene. Polyene with broken lines represents the molecule on the right rotated relative to the molecule on the left. The nonzero value of leads to modeling effects of electron donor and acceptor substitution.

Left and right panels show the projection of initial (solid line) and final (dashed line) wave packets onto the evolved state for (a) a pair of butadienes and (b) a pair of hexatrienes at three sets of interchain distances noted in the upper corner of the panels, respectively, within ZDO approximation.

Left and right panels show the projection of initial (solid line) and final (dashed line) wave packets onto the evolved state for (a) a pair of butadienes and (b) a pair of hexatrienes at three sets of interchain distances noted in the upper corner of the panels, respectively, within ZDO approximation.

The left panel shows the weight of the initial state onto time evolved state for a pair of hexatrienes separated at three different perpendicular distances with the inclusion of -term in the interacting Hamiltonian. The values of are 1.0, 0.8, and 0.66 eV for three perpendicular distances 4, 5, and 6 Å (noted in the upper right corner of the panel), respectively. The corresponding weight of the final state at three different distances is shown in the right panel.

The left panel shows the weight of the initial state onto time evolved state for a pair of hexatrienes separated at three different perpendicular distances with the inclusion of -term in the interacting Hamiltonian. The values of are 1.0, 0.8, and 0.66 eV for three perpendicular distances 4, 5, and 6 Å (noted in the upper right corner of the panel), respectively. The corresponding weight of the final state at three different distances is shown in the right panel.

The weight of initial (left) and final (right) wave packets onto the evolved state for a pair of hexatrienes separated at a perpendicular distance of 4 Å with inclusion of both and in the interacting Hamiltonian.

The weight of initial (left) and final (right) wave packets onto the evolved state for a pair of hexatrienes separated at a perpendicular distance of 4 Å with inclusion of both and in the interacting Hamiltonian.

The figure shows the weight of the initial wave packet in the time evolved state at a different angle of orientation of the acceptor butadiene with respect to donor butadiene when they are separated at 4 Å in collinear geometry. The angles of orientation are given inside each panel.

The figure shows the weight of the initial wave packet in the time evolved state at a different angle of orientation of the acceptor butadiene with respect to donor butadiene when they are separated at 4 Å in collinear geometry. The angles of orientation are given inside each panel.

Decay time of the weight of the initial state as a function of the orientational angle . The solid line corresponds to the elapsed decay time of the initial state within the dipole-dipole interaction approximation and the dashed line corresponds to the same from wave packet dynamics.

Decay time of the weight of the initial state as a function of the orientational angle . The solid line corresponds to the elapsed decay time of the initial state within the dipole-dipole interaction approximation and the dashed line corresponds to the same from wave packet dynamics.

The left panel shows the projection of the initial state (solid line) and the final state (dashed line) for small before crossover. The right panel shows the projection of initial state (solid line) and final state (dashed line) for large after crossover. Both panels correspond to the geometry where the donor (acceptor) site of one butadiene molecule is directly above the donor (acceptor) site of the other butadiene molecule.

The left panel shows the projection of the initial state (solid line) and the final state (dashed line) for small before crossover. The right panel shows the projection of initial state (solid line) and final state (dashed line) for large after crossover. Both panels correspond to the geometry where the donor (acceptor) site of one butadiene molecule is directly above the donor (acceptor) site of the other butadiene molecule.

Evolution of initial and final states for a pair of butadienes with donor sites of one molecule directly above the acceptor site of the other. Three values of are considered. The left panel shows the weight of the initial state and the right panel shows the weight of the final states whose labels are shown in the boxes. Larger contributions arise from other transition dipole coupled excited singlet states.

Evolution of initial and final states for a pair of butadienes with donor sites of one molecule directly above the acceptor site of the other. Three values of are considered. The left panel shows the weight of the initial state and the right panel shows the weight of the final states whose labels are shown in the boxes. Larger contributions arise from other transition dipole coupled excited singlet states.

Time evolution of the weight of different states for a pair of butadiene molecules. The Hamiltonian has and at a short distance of separation 4 Å. The left panel shows the weight of the initial state and the right panel shows the weight of the final state . state is the two-photon state.

Time evolution of the weight of different states for a pair of butadiene molecules. The Hamiltonian has and at a short distance of separation 4 Å. The left panel shows the weight of the initial state and the right panel shows the weight of the final state . state is the two-photon state.

Same as in Fig. 10 for a pair of hexatriene molecules.

Same as in Fig. 10 for a pair of hexatriene molecules.

## Tables

The decay time (time taken for the weight of the initial wave packet to reach zero for the first time) for three sets of donor-acceptor separations . and correspond to this time for a pair of butadienes and a pair of hexatrienes, respectively.

The decay time (time taken for the weight of the initial wave packet to reach zero for the first time) for three sets of donor-acceptor separations . and correspond to this time for a pair of butadienes and a pair of hexatrienes, respectively.

Comparison of the ratio of the decay times of the weight of the initial wave packet to the square of the ratio of corresponding donor-acceptor distances.

Comparison of the ratio of the decay times of the weight of the initial wave packet to the square of the ratio of corresponding donor-acceptor distances.

Excitation energies and magnitude of transition dipole matrix elements for butadienes and hexatrienes as a function of push-pull strength. are the first three singlet states. and energies are in eV and transition dipole moments are in debye.

Excitation energies and magnitude of transition dipole matrix elements for butadienes and hexatrienes as a function of push-pull strength. are the first three singlet states. and energies are in eV and transition dipole moments are in debye.

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