^{1,a)}, Joshua P. Martin

^{1}, Joshua P. Darr

^{1}, W. Carl Lineberger

^{1,b)}and Robert Parson

^{1,c)}

### Abstract

We report the collaborative experimental and theoretical study of the time-resolved recombination dynamics of photodissociated clusters. Excitation of the bare anionic chromophore to the dissociative state yields only and Br products. Interestingly, however, the addition of a few solvent molecules promotes recombination of the dissociating chromophore on the ground state, which correlates asymptotically with and I products. This process is studied experimentally using time-resolved, pump-probe techniques and theoretically via nonadiabaticmolecular dynamics simulations. In sharp contrast to previous studies where more kinetic energy was released to the photofragments, the observed recombination times increase from picoseconds to nanoseconds with increasing cluster size up to . The recombination times then drop dramatically back to picoseconds for cluster sizes . This trend, seen both in experiment and theory, is explained by the presence of a solvent-induced well on the state, the depth of which directly corresponds to the asymmetry of the solvation about the chromophore. The results seen for both the branching ratios and recombination times from experiment and theory show good qualitative agreement.

We gratefully acknowledge support from the National Science Foundation, Awards CHE0809391 and PHY 0551010, and the Air Force Office of Scientific Research, Award FA9550-06-1-0066. We also thank Dr. Joseph Fowler, Dr. Nikki Delaney, Dr. James Faeder, and Dr. Paul Maslen for their discussions on all aspects of this work.

I. INTRODUCTION

II. METHODS

A. Experimental apparatus

1. Laser system

2. Methodology

B. Electronic structure

C. Molecular dynamics

D. Minimum energy structures

E. Trajectory methods

III. RESULTS

A. Photofragment branching ratios

B. Near-IR time-resolved studies

1. Experimentally observed absorption recovery dynamics of ,

2. Simulated absorption recovery dynamics of ,

IV. DISCUSSION

V. SUMMARY AND CONCLUSIONS

### Key Topics

- Carbon dioxide
- 112.0
- Solvents
- 58.0
- Ground states
- 23.0
- Excited states
- 13.0
- Non adiabatic reactions
- 12.0

## Figures

Potential energy curves for the six lowest spin-orbit states of .

Potential energy curves for the six lowest spin-orbit states of .

Exemplar calculated minimum energy structures for , . The pattern of filling is first around the bond, next the Br end at , and then the I end at .

Exemplar calculated minimum energy structures for , . The pattern of filling is first around the bond, next the Br end at , and then the I end at .

Sequential binding energies for calculated minimum energy clusters of (squares), (circles), and (triangles).

Sequential binding energies for calculated minimum energy clusters of (squares), (circles), and (triangles).

Average for 100 configurations of in the ground state at 60 K. Error bars represent one standard deviation of the mean.

Average for 100 configurations of in the ground state at 60 K. Error bars represent one standard deviation of the mean.

Calculated photoabsorption spectrum for .

Calculated photoabsorption spectrum for .

Near-IR (790 nm) branching ratios for . The theoretical simulated results (dashed line) are based on an “infinite” timescale. The experimental results (solid line) are from Sanford *et al.* (Ref. 19).

Near-IR (790 nm) branching ratios for . The theoretical simulated results (dashed line) are based on an “infinite” timescale. The experimental results (solid line) are from Sanford *et al.* (Ref. 19).

Transient illustrating the absorption recovery of . The circles represent the experimental data, and the dotted line is the result of a single exponential fit. The black line is used to guide the eye.

Transient illustrating the absorption recovery of . The circles represent the experimental data, and the dotted line is the result of a single exponential fit. The black line is used to guide the eye.

Absorption recovery transient for (dashed line and squares) and (solid line and circles). The lines are shown to guide the eye.

Absorption recovery transient for (dashed line and squares) and (solid line and circles). The lines are shown to guide the eye.

Cartoon illustrating the origin of the overshoot of the asymptote for the absorption recovery of . The ground-state potential is a Morse potential obtained using the experimentally determined parameters for the equilibrium bond length and vibrational frequency (Refs. 52 and 53). The excited-state potential is also a model Morse potential with the well depth chosen to match the experimentally determined value (Ref. 54) and the equilibrium bond length adjusted to illustrate the origin of the overshoot. The arrow labeled represents the transition giving rise to the overshoot of the asymptote, and the arrow labeled represents the transition giving rise to the asymptotic signal. Note the break in the energy scale along the axis.

Cartoon illustrating the origin of the overshoot of the asymptote for the absorption recovery of . The ground-state potential is a Morse potential obtained using the experimentally determined parameters for the equilibrium bond length and vibrational frequency (Refs. 52 and 53). The excited-state potential is also a model Morse potential with the well depth chosen to match the experimentally determined value (Ref. 54) and the equilibrium bond length adjusted to illustrate the origin of the overshoot. The arrow labeled represents the transition giving rise to the overshoot of the asymptote, and the arrow labeled represents the transition giving rise to the asymptotic signal. Note the break in the energy scale along the axis.

Ground-state recombination dynamics for . The stepped line represents theoretical results, , and the dots represent experimental data, . The dotted and dashed-dotted-dashed lines represent single exponential fits to the experimental and simulated data, respectively, see Eq. (2).

Ground-state recombination dynamics for . The stepped line represents theoretical results, , and the dots represent experimental data, . The dotted and dashed-dotted-dashed lines represent single exponential fits to the experimental and simulated data, respectively, see Eq. (2).

Comparison of experimental and theoretical ground-state recombination times. The solid line and diamonds represent the experimental data, and the dashed line and triangles represent the results of the theoretical calculations. The lines connecting the data points correspond to the fast component of the absorption recovery in cases where the recovery was best fit to a biexponential function. The data points not connected by a line correspond to the slow component of the absorption recovery.

Comparison of experimental and theoretical ground-state recombination times. The solid line and diamonds represent the experimental data, and the dashed line and triangles represent the results of the theoretical calculations. The lines connecting the data points correspond to the fast component of the absorption recovery in cases where the recovery was best fit to a biexponential function. The data points not connected by a line correspond to the slow component of the absorption recovery.

Visual representation of the solvent coordinate, , using clusters. is defined by the change in energy when the charge is transferred from the bromine atom to the iodine atom as shown on the left and right sides of the figure, respectively. A symmetric solvent configuration (top) corresponds to a small . An asymmetric solvent configuration (bottom) corresponds to large values of .

Visual representation of the solvent coordinate, , using clusters. is defined by the change in energy when the charge is transferred from the bromine atom to the iodine atom as shown on the left and right sides of the figure, respectively. A symmetric solvent configuration (top) corresponds to a small . An asymmetric solvent configuration (bottom) corresponds to large values of .

Plot of solute internuclear distance vs solvent coordinate, , for a trapped trajectory for . The green line represents trajectory dynamics on the state shown in Fig. 1.

Plot of solute internuclear distance vs solvent coordinate, , for a trapped trajectory for . The green line represents trajectory dynamics on the state shown in Fig. 1.

Plot of solute internuclear distance vs solvent coordinate, , for a relaxed trajectory for . Black, red, and green represent trajectory dynamics on the , , and states, respectively, as seen in Fig. 1.

Plot of solute internuclear distance vs solvent coordinate, , for a relaxed trajectory for . Black, red, and green represent trajectory dynamics on the , , and states, respectively, as seen in Fig. 1.

Plot of solute internuclear distance vs solvent coordinate, , for 2 ns trajectories for that end with the product in the ground state. Black, red, and green represent trajectory dynamics on the , , and states, respectively, as seen in Fig. 1.

Plot of solute internuclear distance vs solvent coordinate, , for 2 ns trajectories for that end with the product in the ground state. Black, red, and green represent trajectory dynamics on the , , and states, respectively, as seen in Fig. 1.

Average solvent coordinate, , of the excited-state well in trajectory simulations. Error bars represent one standard deviation of the mean.

Average solvent coordinate, , of the excited-state well in trajectory simulations. Error bars represent one standard deviation of the mean.

Comparison of single and biexponential fits to the ground-state recombination trajectories of . The solid line represents the theoretical results. The dotted and dashed lines are single and biexponential fits, respectively. The corresponding constants are also labeled. The ensemble is composed of one hundred 3 ns trajectories.

Comparison of single and biexponential fits to the ground-state recombination trajectories of . The solid line represents the theoretical results. The dotted and dashed lines are single and biexponential fits, respectively. The corresponding constants are also labeled. The ensemble is composed of one hundred 3 ns trajectories.

## Tables

Summary of energetics from *ab initio* calculations (energies in eV).

Summary of energetics from *ab initio* calculations (energies in eV).

Properties of minimal energy clusters of from 80 K trajectory ensembles.

Properties of minimal energy clusters of from 80 K trajectory ensembles.

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