^{1}, Toni Kiljunen

^{2}and Mika Pettersson

^{3,a)}

### Abstract

Time-resolved coherent anti-Stokes Raman-scattering (CARS) measurements are carried out to study the interaction between xenon atom and iodine molecule in a solid krypton matrix. Interference between the CARSpolarizations of the “free” and complexed iodine molecules is observed, while the quantum beats of the complex are not detected due to low concentration. Vibrational analysis based on the polarization beats yields accurate molecular constants for the complex. The harmonic frequency of the complex is found to be redshifted by when compared to the free , whereas the anharmonicity is approximately the same. The dephasing rate of the complex is found to be somewhat higher than that of the free iodine molecule in solid Kr, showing that the complexation affects dephasing, although not dramatically. Molecular dynamics simulations are carried out to find the conformation of the complex, and wave packet simulations are used to reproduce the CARS signal to confirm the assignments of the observed beatings as quantum and polarization beats. The results show that the polarization beats are a useful tool for investigating weak interactions in condensed phase.

This work was supported by the Academy of Finland (Decision Nos. 105684 and 110952). The authors thank Pasi Myllyperkiö and Jukka Aumanen for their help in the measurements. Professor Henrik Kunttu and Professor Jouko Korppi-Tommola are thanked for their support to this work. Professor V. A. Apkarian is thanked for many fruitful discussions.

I. INTRODUCTION

II. THEORETICAL BACKGROUND

III. EXPERIMENTAL DETAILS

IV. EXPERIMENTAL RESULTS

V. COMPUTATIONAL METHODS

A. Simulation of TR-CARS signal

B. Molecular dynamics simulation

1. Synopsis of the problem

2. Potential energy surfaces

3. MD method

VI. COMPUTATIONAL RESULTS

A. Vibrational polarization interference in TR-CARS

B. Vibrational energy shifts in the solid

VII. DISCUSSION

A. Assignments

1. A binary complex

2. TR-CARS simulation

3. Quantum and polarization beats

B. Analysis

1. Potential parameters

2. Relative abundances

3. Dephasing rates

4. Possible conformations

5. Heterodyning

VIII. CONCLUSIONS

### Key Topics

- Polarization
- 104.0
- Quantum beats
- 51.0
- Dephasing
- 38.0
- Stimulated Raman scattering
- 33.0
- Molecular dynamics
- 13.0

## Figures

A schematic presentation of the creation of the CARS polarization via the path , where and refer to the ground and excited electronic states of the species, respectively.

A schematic presentation of the creation of the CARS polarization via the path , where and refer to the ground and excited electronic states of the species, respectively.

The effect of Xe concentration on the CARS signal (right side), and the power spectrum (Fourier transform of the signal, left) at .

The effect of Xe concentration on the CARS signal (right side), and the power spectrum (Fourier transform of the signal, left) at .

The spectrum for the wave packet with at . The labels show the vibrational states involved in the generation of a particular peak in the spectrum, with primed numbers referring to the complex, and numbers without prime to the free .

The spectrum for the wave packet with at . The labels show the vibrational states involved in the generation of a particular peak in the spectrum, with primed numbers referring to the complex, and numbers without prime to the free .

The spectrum for the wave packet with at . The labels show the vibrational states involved in the generation of a particular peak in the spectrum, with primed numbers referring to the complex, and numbers without prime to the free .

The spectrum for the wave packet with at . and are the distances in wave numbers from the free quantum beat band, see Eqs. (12) and (13).

The spectrum for the wave packet with at . and are the distances in wave numbers from the free quantum beat band, see Eqs. (12) and (13).

The effect of temperature on the wave packet spectrum. Both the polarization and quantum beat bands are narrowed and shifted with the decreasing temperature.

The effect of temperature on the wave packet spectrum. Both the polarization and quantum beat bands are narrowed and shifted with the decreasing temperature.

The Raman wave packet weights (solid lines) and (dotted lines) for free and complex, respectively. (a) The wave packet is obtained by pulse sequence, where the pulses are centered at 100 and . (b) The wave packet case originates from sequence of pulses at 200 and . Potentials are derived from the present experimental results in Sec. IV.

The Raman wave packet weights (solid lines) and (dotted lines) for free and complex, respectively. (a) The wave packet is obtained by pulse sequence, where the pulses are centered at 100 and . (b) The wave packet case originates from sequence of pulses at 200 and . Potentials are derived from the present experimental results in Sec. IV.

A portion of the lattice atoms in the simulation cube surrounding the impurity iodine molecule. The codoped Xe atom positions are categorized in trapping cases 1–4: (1) A “head-on” position along the molecular axis direction. (2) A “belt” position perpendicular to the molecule. (3) An “ignorant” position 63° off the molecular axis. (4) A “window” position 41° off the axis. The dopant distances to the molecular center are 6.01, 3.47, 4.48, and , respectively. A fcc unit shell is sketched to guide the eye.

A portion of the lattice atoms in the simulation cube surrounding the impurity iodine molecule. The codoped Xe atom positions are categorized in trapping cases 1–4: (1) A “head-on” position along the molecular axis direction. (2) A “belt” position perpendicular to the molecule. (3) An “ignorant” position 63° off the molecular axis. (4) A “window” position 41° off the axis. The dopant distances to the molecular center are 6.01, 3.47, 4.48, and , respectively. A fcc unit shell is sketched to guide the eye.

Potential energy surfaces for (upper half) and (lower half) as a function of parallel and perpendicular distances and between the rare gas atom and the middle of the bond . The contour level step is .

Potential energy surfaces for (upper half) and (lower half) as a function of parallel and perpendicular distances and between the rare gas atom and the middle of the bond . The contour level step is .

(a) The CARS signal simulated for the 2–6 wave packet with 15% complex concentration. The decay is due to the multiplication by . A portion of the experimental signal is overlaid for comparison. (b) The FFT power spectra obtained from the traces in (a) for the polarization beat region. (c) The FFT power spectra in the fundamental region. (d) The FFT power spectra in the first overtone region. The experimental spectrum is the same as in Fig. 3.

(a) The CARS signal simulated for the 2–6 wave packet with 15% complex concentration. The decay is due to the multiplication by . A portion of the experimental signal is overlaid for comparison. (b) The FFT power spectra obtained from the traces in (a) for the polarization beat region. (c) The FFT power spectra in the fundamental region. (d) The FFT power spectra in the first overtone region. The experimental spectrum is the same as in Fig. 3.

(a) The CARS signal simulated for the 8–9 wave packet with 1:4 complex:free concentration ratio. The decay is due to the multiplication by . A portion of the experimental signal is shown for comparison. (b) The FFT power spectra obtained from the traces in (a) for the fundamental region. The simulation (solid line) reproduces the experimental (dashed) peak locations: the polarization peaks at and , and the fundamental (8–9) at . The weak contribution from the pure complex (dash-dotted peak) is plotted as the FFT *amplitude* (instead of power) to illustrate the amplification effect. (c) The FFT power spectra in the polarization beat region. The shift of the peak to slightly higher frequency as compared with the experiment is visible also in the time domain plot (a). See Fig. 5 for labeling.

(a) The CARS signal simulated for the 8–9 wave packet with 1:4 complex:free concentration ratio. The decay is due to the multiplication by . A portion of the experimental signal is shown for comparison. (b) The FFT power spectra obtained from the traces in (a) for the fundamental region. The simulation (solid line) reproduces the experimental (dashed) peak locations: the polarization peaks at and , and the fundamental (8–9) at . The weak contribution from the pure complex (dash-dotted peak) is plotted as the FFT *amplitude* (instead of power) to illustrate the amplification effect. (c) The FFT power spectra in the polarization beat region. The shift of the peak to slightly higher frequency as compared with the experiment is visible also in the time domain plot (a). See Fig. 5 for labeling.

## Tables

Wave numbers (in ) for quantum and polarization beat bands for the superposition from both the experiments and the Morse oscillator fits [Eqs. (14) and (15)]. A “-” sign indicates that the peak is not visible in the spectrum.

Wave numbers (in ) for quantum and polarization beat bands for the superposition from both the experiments and the Morse oscillator fits [Eqs. (14) and (15)]. A “-” sign indicates that the peak is not visible in the spectrum.

Wave numbers (in ) for quantum and polarization beat bands for the superposition from both the experiments and the Morse oscillator fits [Eqs. (14) and (15)]. A “-” sign indicates that the peak is not visible in the spectrum.

Dephasing rates (in ) for free and complex at and , calculated from the frequency-domain fits. (No value: The band needed for analysis is either missing or too weak in the spectrum).

Dephasing rates (in ) for free and complex at and , calculated from the frequency-domain fits. (No value: The band needed for analysis is either missing or too weak in the spectrum).

The difference of solvation energies (in ) of with . The complex case labels are defined in Fig. 8. The two lattice constants and used in geometry optimization are 5.67 and , respectively. Standard deviations for the well depth averages are given in parentheses.

The difference of solvation energies (in ) of with . The complex case labels are defined in Fig. 8. The two lattice constants and used in geometry optimization are 5.67 and , respectively. Standard deviations for the well depth averages are given in parentheses.

The shifts of the fundamental vibrational transition frequencies for the complex cases from the pure values. The negative values correspond to redshifted frequencies. All values in .

The shifts of the fundamental vibrational transition frequencies for the complex cases from the pure values. The negative values correspond to redshifted frequencies. All values in .

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