^{1}, Toni Kiljunen

^{2}, Henrik Kunttu

^{2}and Jussi Eloranta

^{3,a)}

### Abstract

Electron spin resonance(ESR) measurements were carried out to study the rotation of methyl radicals in a solid argon matrix at temperatures. The radicals were produced by dissociating methane by plasma bursts generated either by a focused laser radiation or a radio frequency discharge device during the gas condensation on the substrate. The ESR spectrum exhibits axial symmetry at the lowest temperature and is ascribed to ground state molecules with symmetric total nuclear spin function . The hyperfine anisotropy was found to be , whereas that of the value was . The anisotropy is observed for the first time in Ar and is manifested by the splitting of the low-field transition. Elevation of temperature leads reversibly to the appearance of excited state contribution having antisymmetric . As a function of the sample temperature, the relative intensities of symmetric and antisymmetric spin states corresponding to ground and excited rotor states, respectively, proton hyperfine and electron -tensor components, and spin-lattice relaxation rates were determined by a numerical fitting procedure. The experimental observations were interpreted in terms of a free rotation about the axis and a thermal activation of the -type rotations above . The ground and excited rotational state energy levels were found to be separated by and to exhibit significantly different spin-lattice coupling. A crystal field model has been applied to evaluate the energy levels of the hindered rotor in the matrix, and crystal field parameter , corresponding to a effective potential barrier for rotation of the axis, was obtained.

One of the authors (T.K.) was supported by the Academy of Finland (Decision No. 105684). Professor T. Momose at UBC, CA is thanked for providing his FORTRAN code for evaluation of the symmetry-adapted crystal field states. Dr. M. Fushitani at IMS Okazaki, Japan is thanked for advice.

I. INTRODUCTION

II. EXPERIMENTAL DETAILS

III. EXPERIMENTAL RESULTS

IV. THEORETICAL METHODS

A. Rotational Hamiltonian

B. interaction

V. THEORETICAL RESULTS

VI. DISCUSSION

A. Experiments

B. Modeling

VII. CONCLUSIONS

### Key Topics

- Anisotropy
- 21.0
- Electron paramagnetic resonance spectroscopy
- 21.0
- Tunneling
- 14.0
- Ground states
- 12.0
- Nuclear spin
- 10.0

## Figures

The ESR spectrum of in solid Ar, obtained at , consists of the lines of the symmetric spin state and exhibits axial asymmetry as manifested by the splitting in panel (a) and the well-matching simulation result shown on top of the experimental lines. The anisotropy for the axial hyperfine and -tensor parameters are and , respectively. The panels [(a), (b), (c), and (d)] corresponding to transitions at four nuclear spin orientations, , , , and , respectively, are recorded separately due to the low modulation frequency of . The modulation amplitude was . The magnetic field sweep was wide ( data points) for each transition and the central is shown in each panel. The signal intensities are scaled to the same level in each of the panels.

The ESR spectrum of in solid Ar, obtained at , consists of the lines of the symmetric spin state and exhibits axial asymmetry as manifested by the splitting in panel (a) and the well-matching simulation result shown on top of the experimental lines. The anisotropy for the axial hyperfine and -tensor parameters are and , respectively. The panels [(a), (b), (c), and (d)] corresponding to transitions at four nuclear spin orientations, , , , and , respectively, are recorded separately due to the low modulation frequency of . The modulation amplitude was . The magnetic field sweep was wide ( data points) for each transition and the central is shown in each panel. The signal intensities are scaled to the same level in each of the panels.

The portion of the ESR spectrum of in Ar at temperatures. The transition of the antisymmetric spin state emerges to the high magnetic field side of the symmetric spin state transition line as the temperature is elevated. The frequency fluctuation of the microwave source is compensated by shifting the resonance positions to the same magnetic field value in the panels. The noise is reduced by presenting wide running averages of the original data (using 27 data point smoothing).

The portion of the ESR spectrum of in Ar at temperatures. The transition of the antisymmetric spin state emerges to the high magnetic field side of the symmetric spin state transition line as the temperature is elevated. The frequency fluctuation of the microwave source is compensated by shifting the resonance positions to the same magnetic field value in the panels. The noise is reduced by presenting wide running averages of the original data (using 27 data point smoothing).

Temperature dependence of the ESR spectrum parameters of in Ar obtained from numerical analysis. Top panel: intensity ratio of the symmetric and antisymmetric nuclear spin states compared to the gas phase rotational energy level distribution. The fit gives a slope of corresponding to the energy separation of the ground and first excited states. Lower two panels: isotropic hyperfine coupling constants and transition linewidths for the and nuclear spin states.

Temperature dependence of the ESR spectrum parameters of in Ar obtained from numerical analysis. Top panel: intensity ratio of the symmetric and antisymmetric nuclear spin states compared to the gas phase rotational energy level distribution. The fit gives a slope of corresponding to the energy separation of the ground and first excited states. Lower two panels: isotropic hyperfine coupling constants and transition linewidths for the and nuclear spin states.

Plot of the inverse of the electron spin-lattice relaxation time vs the sample temperature for the radical isolated in Ar crystal. The linear regression fits for the four lower-temperature and four higher-temperature points have a crossing at .

Plot of the inverse of the electron spin-lattice relaxation time vs the sample temperature for the radical isolated in Ar crystal. The linear regression fits for the four lower-temperature and four higher-temperature points have a crossing at .

(Color online) A methyl molecule occupying a substitutional site of the fcc crystal of solid Ar. The rotational axes perpendicular to the molecular plane and along one of the C–H bonds of the molecule are shown. The present configuration represents a , orientation of the molecule with respect to the crystalline cage. Two solvation shells, i.e., the 12 nearest-neighbor and 6 second-nearest Ar atoms are represented by the large circles. The crystal field axis system is designated as , , and .

(Color online) A methyl molecule occupying a substitutional site of the fcc crystal of solid Ar. The rotational axes perpendicular to the molecular plane and along one of the C–H bonds of the molecule are shown. The present configuration represents a , orientation of the molecule with respect to the crystalline cage. Two solvation shells, i.e., the 12 nearest-neighbor and 6 second-nearest Ar atoms are represented by the large circles. The crystal field axis system is designated as , , and .

Left panel: rotational energy levels of methyl radical in cubic crystal lattice (solid lines) as a function of crystal field parameter . The potential minimum at ⟨100⟩ and saddle point at ⟨110⟩ are drawn with dashed lines. Right panel: the energy spectrum scaled with respect to the ground state. Arrows are drawn to show the energy separation extracted from the experiment.

Left panel: rotational energy levels of methyl radical in cubic crystal lattice (solid lines) as a function of crystal field parameter . The potential minimum at ⟨100⟩ and saddle point at ⟨110⟩ are drawn with dashed lines. Right panel: the energy spectrum scaled with respect to the ground state. Arrows are drawn to show the energy separation extracted from the experiment.

Rotational energy levels of methyl radical in cubic crystal lattice as a function of crystal field parameter , when the potential strength is fixed to either (left panel) or to (right).

Rotational energy levels of methyl radical in cubic crystal lattice as a function of crystal field parameter , when the potential strength is fixed to either (left panel) or to (right).

(Color online) Rotational potential energy landscape for in the 18-atom Ar cage calculated with Table I parameters by Eq. (9). The angle corresponds to rotation about the axis of the molecule, and for each , a 0°-180° rotation about the axis along the C–H bond indicated in Fig. 5 is carried out.

(Color online) Rotational potential energy landscape for in the 18-atom Ar cage calculated with Table I parameters by Eq. (9). The angle corresponds to rotation about the axis of the molecule, and for each , a 0°-180° rotation about the axis along the C–H bond indicated in Fig. 5 is carried out.

Potential energy cuts for - and -type rotations. The two cuts and the with can be read directly from Fig. 8, whereas the thick solid line maps the rotation with axis locked in orientation.

Potential energy cuts for - and -type rotations. The two cuts and the with can be read directly from Fig. 8, whereas the thick solid line maps the rotation with axis locked in orientation.

## Tables

Buckingham model parameters used in Eq. (9) for the interaction. The attractive well depth parameter (implicit in ) is also given.

Buckingham model parameters used in Eq. (9) for the interaction. The attractive well depth parameter (implicit in ) is also given.

Potential energy extrema for the crystal field (CF) model at , and the pair-potential (PP) evaluation of interaction in the 18-atom cage.

Potential energy extrema for the crystal field (CF) model at , and the pair-potential (PP) evaluation of interaction in the 18-atom cage.

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