^{1}, Evgeny Popov

^{2}, Henrik Kunttu

^{1}and Jussi Eloranta

^{2,a)}

### Abstract

Electron spin resonance(ESR) measurements were carried out to study the rotation of methyl radicals in a solid krypton matrix at temperature range. The radicals were produced by dissociating methane by plasma bursts generated by a focused excimer laser radiation during the krypton gas condensation on the substrate. The ESR spectrum exhibits only isotropic features at the temperature range examined, and the intensity ratio between the symmetric and antisymmetric spin state lines exhibits weaker temperature dependence than in a solid argon matrix. However, the general appearance of the methyl radical spectrum depends strongly on temperature due to the pronounced temperature dependency of the state linewidths. The rotational energy level populations are analyzed based on the static crystal field model, pseudorotating cage model, and quantum chemical calculations for an axially symmetric, planar rotor. Crystal field strength parameter values of in Ar and in Kr match most closely the experimentally observed rotational energy level shifts from the gas phase value. In the alternative model, considering the lattice atom movement in a pseudorotating cage, the effective lowering of the rotational constants and to 80%–90% leads to similar effects.

T.K. was supported by the Academy of Finland Decision No. 124974 and J.E. was supported by the Petroleum Research Fund (PRF No. 47789-GB6) administered by the American Chemical Society.

I. INTRODUCTION

II. EXPERIMENTAL DETAILS

III. THEORETICAL MODELS

A. Crystal field model

B. Pseudorotation

C. Potential functions

IV. EXPERIMENTAL RESULTS

V. THEORETICAL RESULTS

VI. DISCUSSION

VII. CONCLUSIONS

### Key Topics

- Electron paramagnetic resonance spectroscopy
- 27.0
- Anisotropy
- 11.0
- Nuclear spin
- 7.0
- Solid hydrogen
- 7.0
- Linewidths
- 6.0

## Figures

The resonance portion of the ESR spectrum of in solid Kr at temperatures. The -line transition of the asymmetric nuclear spin state is labeled by E and the symmetric nuclear spin state -line by A above the top panel. The frequency fluctuation of the microwave source is compensated by shifting the resonance positions to the same magnetic field value.

The resonance portion of the ESR spectrum of in solid Kr at temperatures. The -line transition of the asymmetric nuclear spin state is labeled by E and the symmetric nuclear spin state -line by A above the top panel. The frequency fluctuation of the microwave source is compensated by shifting the resonance positions to the same magnetic field value.

Linewidths for the -and -lines as obtained from the component are shown. The -lines exhibit strong broadening when temperature is decreased.

Linewidths for the -and -lines as obtained from the component are shown. The -lines exhibit strong broadening when temperature is decreased.

The broad transition under the sharp pair of and resonance lines is shown at . The maximum and minimum of the broad transition are indicated by the arrows. The intensity, as well as the linewidth, is tenfold with respect to the signal originating from well-ordered lattice sites.

The broad transition under the sharp pair of and resonance lines is shown at . The maximum and minimum of the broad transition are indicated by the arrows. The intensity, as well as the linewidth, is tenfold with respect to the signal originating from well-ordered lattice sites.

Calculated pair potentials for the interaction in three orientations as illustrated in the inset: Rg approaching the C atom from above the molecular plane (solid), in-plane toward a H atom (dashed) or between two C–H bonds (dotted). The curves were obtained with the RHF-UCCSD(T) method using Dunning basis sets and counterpoise correction for the BSSE.

Calculated pair potentials for the interaction in three orientations as illustrated in the inset: Rg approaching the C atom from above the molecular plane (solid), in-plane toward a H atom (dashed) or between two C–H bonds (dotted). The curves were obtained with the RHF-UCCSD(T) method using Dunning basis sets and counterpoise correction for the BSSE.

Angular dependence of the caged interaction calculated after relaxing the nearest 18 Kr atom positions. The energy minimum in each contour plot panel locates the orientation of the rotation axis during the lattice geometry optimization. Color scales are quantified in and represent the low barriers in the case of nearest-neighbor distance set initially for the Kr lattice. The top left panel shows the dependence of the potential barrier height on the variation in .

Angular dependence of the caged interaction calculated after relaxing the nearest 18 Kr atom positions. The energy minimum in each contour plot panel locates the orientation of the rotation axis during the lattice geometry optimization. Color scales are quantified in and represent the low barriers in the case of nearest-neighbor distance set initially for the Kr lattice. The top left panel shows the dependence of the potential barrier height on the variation in .

Dependence of the rotational energy level separation from the ground state on the crystal field strength parameter for gas phase fixed rotational constants.

Dependence of the rotational energy level separation from the ground state on the crystal field strength parameter for gas phase fixed rotational constants.

The intensity ratio between the spin-symmetric and antisymmetric states is constructed for several cases. The rotational energy level populations and for the and , respectively, appear as in the EPR spectrum. The nonlinearity in the plot against inverse temperature indicates the deviation from the two-level model. Top: The experimental solid Ar and Kr values are compared to curves obtained by downscaling of the rotational constants by 90% and 80%, respectively, corresponding to the pseudorotating cage model. The gas phase (unscaled and , ) result is given by the dashed curve. Bottom: Comparison to the crystal field model. The curves are plotted for the parameter or that best fit the experiments in Ar and Kr.

The intensity ratio between the spin-symmetric and antisymmetric states is constructed for several cases. The rotational energy level populations and for the and , respectively, appear as in the EPR spectrum. The nonlinearity in the plot against inverse temperature indicates the deviation from the two-level model. Top: The experimental solid Ar and Kr values are compared to curves obtained by downscaling of the rotational constants by 90% and 80%, respectively, corresponding to the pseudorotating cage model. The gas phase (unscaled and , ) result is given by the dashed curve. Bottom: Comparison to the crystal field model. The curves are plotted for the parameter or that best fit the experiments in Ar and Kr.

## Tables

Experimental population ratios in solid Kr (present) and Ar (Ref. 12).

Experimental population ratios in solid Kr (present) and Ar (Ref. 12).

Summary of the pair interaction data used in the evaluations of potential barriers for rotation. The atom-molecule potentials are obtained from the present RHF-UCCSD(T) calculations, while the Rg-Rg is taken from Ref. 42. The Rg is assigned values of 1, 2, or 3 according to the number of equal H atoms within the molecule (see Fig. 4): Labels 1 and 2 are the in-plane components, while Rg3 aligns with the surface normal. is the plane averaged potential that accounts for the free rotation about the axis.

Summary of the pair interaction data used in the evaluations of potential barriers for rotation. The atom-molecule potentials are obtained from the present RHF-UCCSD(T) calculations, while the Rg-Rg is taken from Ref. 42. The Rg is assigned values of 1, 2, or 3 according to the number of equal H atoms within the molecule (see Fig. 4): Labels 1 and 2 are the in-plane components, while Rg3 aligns with the surface normal. is the plane averaged potential that accounts for the free rotation about the axis.

Temperature dependence of some computed population ratios (beyond the two-level approximation) as seen in the ESR spectra. The scalings correspond to the pseudorotating cage model, while CF labels the static crystal field model in Eq. (2).

Temperature dependence of some computed population ratios (beyond the two-level approximation) as seen in the ESR spectra. The scalings correspond to the pseudorotating cage model, while CF labels the static crystal field model in Eq. (2).

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