_{2}(

*ã*) with helium

^{1}, Millard H. Alexander

^{1,2,a)}and Paul J. Dagdigian

^{3,b)}

### Abstract

Rotationally inelastic collisions of the CH2 molecule in its electronic state have been investigated. We have determined a potential energy surface (PES) for the interaction of rigid CH2(ã), frozen at its equilibrium geometry, with a helium atom, using a coupled-cluster method that includes all single and double excitations, as well as perturbative contributions of connected triple excitations [RSSCD(T)]. The PES is quite anisotropic, due to lack of electron density in the unoccupied CH2 non-bonding orbital perpendicular to the molecular plane. Quantum scattering calculations have been carried out to compute state-to-state rotational energy transfer and elastic depolarization cross sections at collision energies up to 2400 cm^{−1}. These cross sections were thermally averaged to derive room-temperature rate constants. The total removal and elastic depolarization rate constants for the ortho k a = 1 levels agree well with recent experimental measurements by Hall, Sears, and their co-workers. We observe a strong even–odd alternation in the magnitude of the total rate constants which we attribute to the asymmetry splitting of the k a = 1 levels.

This work was supported by the Chemical, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy, under Grant No. DESC0002323. The authors are grateful to Gregory Hall, Trevor Sears, and Hua Gen Yu for their encouragement and for sharing their unpublished rate constants and the results of earlier, unpublished calculations of the CH_{2}(*ã*)–He potential energy surface.

I. INTRODUCTION

II. POTENTIAL ENERGY SURFACE

III. SCATTERING CALCULATIONS

IV. RESULTS

A. State-to-state rotationally inelastic collisions

B. Overall rotational relaxation

C. Elastic depolarization

V. DISCUSSION

### Key Topics

- Elasticity
- 34.0
- Elastic collisions
- 14.0
- Anisotropy
- 13.0
- Band gap
- 10.0
- Angular momentum
- 9.0

## Figures

Body-frame coordinate system used to specify the orientation of the helium atom with respect to the center of mass of the CH2(ã) molecule. The body-frame z axis is defined to lie along the a inertial axis of the molecule. The molecule lies in the xz-plane. Note that the origin is at the center of mass, which is displaced toward negative x by 0.19 bohr from the C atom

Body-frame coordinate system used to specify the orientation of the helium atom with respect to the center of mass of the CH2(ã) molecule. The body-frame z axis is defined to lie along the a inertial axis of the molecule. The molecule lies in the xz-plane. Note that the origin is at the center of mass, which is displaced toward negative x by 0.19 bohr from the C atom

Dependence of the potential energy (in cm^{−1}) on the orientation of the helium with respect to the CH2(ã) molecule for an atom–molecule separation R = 4.58 bohr.

Dependence of the potential energy (in cm^{−1}) on the orientation of the helium with respect to the CH2(ã) molecule for an atom–molecule separation R = 4.58 bohr.

Contour plot of the highest-occupied molecular orbital (3a 1) of the CH2(ã) molecule. This is the higher in energy of the two bonding molecular orbitals (1b 2 and 3a 1).

Contour plot of the highest-occupied molecular orbital (3a 1) of the CH2(ã) molecule. This is the higher in energy of the two bonding molecular orbitals (1b 2 and 3a 1).

Dependence on the He–CH2(ã) distance of the larger of the expansion coefficients v λμ [defined in Eq. (1) ].

Dependence on the He–CH2(ã) distance of the larger of the expansion coefficients v λμ [defined in Eq. (1) ].

Dependence of the potential energy for the interaction of CH2(ã) with helium upon the angle ϕ for θ = 90° at several values of the atom–molecule separation R (given in bohr). The motion shown here corresponds to rotation of the He atom in the xy-plane in Fig. 1 .

Dependence of the potential energy for the interaction of CH2(ã) with helium upon the angle ϕ for θ = 90° at several values of the atom–molecule separation R (given in bohr). The motion shown here corresponds to rotation of the He atom in the xy-plane in Fig. 1 .

Rotational levels of ortho (solid) and para (dashed) of CH2(ã) with energies less than 500 cm^{−1}. The levels are grouped by column according to the value of the prolate-limit body-frame projection quantum number k a . The individual rotational levels are labeled by the total angular momentum j and by its projections along the a and c inertial axes: k a and k c .

Rotational levels of ortho (solid) and para (dashed) of CH2(ã) with energies less than 500 cm^{−1}. The levels are grouped by column according to the value of the prolate-limit body-frame projection quantum number k a . The individual rotational levels are labeled by the total angular momentum j and by its projections along the a and c inertial axes: k a and k c .

Bar plot of the cross sections for rotationally inelastic scattering of para CH2(ã) in the j = 4 and 5, k a = 1 levels by collision with He at a collision energy of 300 cm^{−1}. The initial level is denoted by a dark box.

Bar plot of the cross sections for rotationally inelastic scattering of para CH2(ã) in the j = 4 and 5, k a = 1 levels by collision with He at a collision energy of 300 cm^{−1}. The initial level is denoted by a dark box.

Bar plot of the cross sections for rotationally inelastic scattering of ortho CH2(ã) in the j = 4 and 5, k a = 1 levels by collision with He at a collision energy of 300 cm^{−1}. The initial level is denoted by a dark box.

Bar plot of the cross sections for rotationally inelastic scattering of ortho CH2(ã) in the j = 4 and 5, k a = 1 levels by collision with He at a collision energy of 300 cm^{−1}. The initial level is denoted by a dark box.

Bar plot of the cross sections for rotationally inelastic scattering of ortho CH2(ã) in the j = 4, k a = 1 level by collision with He at a collision energy of 300 cm^{−1}, plotted here against the energy gap, with ΔE = E(j a ^{′},k a ^{′}) – E(j a ka). The square at 0 cm^{−1} denotes the initial level.

Bar plot of the cross sections for rotationally inelastic scattering of ortho CH2(ã) in the j = 4, k a = 1 level by collision with He at a collision energy of 300 cm^{−1}, plotted here against the energy gap, with ΔE = E(j a ^{′},k a ^{′}) – E(j a ka). The square at 0 cm^{−1} denotes the initial level.

(a) Rotationally inelastic total removal cross section for the lower k a = 1 ortho and para rotational levels of CH2(ã) in collisions with He at a collision energy of 300 cm^{−1}. (b) Similar plot but for the rotationally inelastic total removal rates constants at 298 K.

(a) Rotationally inelastic total removal cross section for the lower k a = 1 ortho and para rotational levels of CH2(ã) in collisions with He at a collision energy of 300 cm^{−1}. (b) Similar plot but for the rotationally inelastic total removal rates constants at 298 K.

Dependence upon the collision energy of the state-to-state integral cross sections for rotational transitions out of the lowest levels of the (a) para [000] and (b) ortho [101] nuclear spin modifications of CH2(ã) in collisions with helium. Only the dominant transitions are plotted.

Dependence upon the collision energy of the state-to-state integral cross sections for rotational transitions out of the lowest levels of the (a) para [000] and (b) ortho [101] nuclear spin modifications of CH2(ã) in collisions with helium. Only the dominant transitions are plotted.

Dependence upon the collision energy of the rotationally inelastic total removal cross sections for the k a = 1 (a) para and (b) ortho levels of CH2(ã) in collisions with helium. The value of the angular momentum j is indicated beside each curve.

Dependence upon the collision energy of the rotationally inelastic total removal cross sections for the k a = 1 (a) para and (b) ortho levels of CH2(ã) in collisions with helium. The value of the angular momentum j is indicated beside each curve.

Dependence upon the collision energy of the K = 2 elastic depolarization cross sections for the k a = 1 (a) para and (b) ortho levels of CH2(ã) in collisions with helium. The value of the angular momentum j is indicated beside each curve.

Dependence upon the collision energy of the K = 2 elastic depolarization cross sections for the k a = 1 (a) para and (b) ortho levels of CH2(ã) in collisions with helium. The value of the angular momentum j is indicated beside each curve.

Computed rate constants for elastic depolarization of the rank K = 1 and 2 multipoles (orientation and alignment, respectively) of the (a) para and (b) ortho k a = 1 levels of CH2(ã) in collisions with helium.

Computed rate constants for elastic depolarization of the rank K = 1 and 2 multipoles (orientation and alignment, respectively) of the (a) para and (b) ortho k a = 1 levels of CH2(ã) in collisions with helium.

Elastic depolarization cross sections of the j = 1–3 rotational levels of ortho and para CH2(ã) in collisions with helium at a collision energy of 300 cm^{−1}. For each value of j, the levels (labeled also by k a and k c , see Fig. 6 ) are ordered in increasing energy from left to right.

Elastic depolarization cross sections of the j = 1–3 rotational levels of ortho and para CH2(ã) in collisions with helium at a collision energy of 300 cm^{−1}. For each value of j, the levels (labeled also by k a and k c , see Fig. 6 ) are ordered in increasing energy from left to right.

Rate constants for collisional removal by rotational transitions and for elastic depolarization of alignment (K = 2) for CH2(ã) ortho k a = 1 levels in collisions with helium. The theoretical values were computed in the present study, while the experimental values were taken from the investigation by Hall, Sears, and their co-workers [Ref. 21 ]. The j = 8 level of this manifold is known to be strongly perturbed by a vibration-rotation level of the ^{3} B 1 state (Ref. 20 ). The labels S and T denote the experimentally observed rate constants for the two perturbed levels of predominantly singlet and triplet character, respectively.

Rate constants for collisional removal by rotational transitions and for elastic depolarization of alignment (K = 2) for CH2(ã) ortho k a = 1 levels in collisions with helium. The theoretical values were computed in the present study, while the experimental values were taken from the investigation by Hall, Sears, and their co-workers [Ref. 21 ]. The j = 8 level of this manifold is known to be strongly perturbed by a vibration-rotation level of the ^{3} B 1 state (Ref. 20 ). The labels S and T denote the experimentally observed rate constants for the two perturbed levels of predominantly singlet and triplet character, respectively.

## Tables

Overall inelasticity of j = 4, k a = 1 and j = 5, k a = 1 rotational levels of ortho and para CH2(ã) in collisions with helium at a collision energy of 300 cm^{−1}.

Overall inelasticity of j = 4, k a = 1 and j = 5, k a = 1 rotational levels of ortho and para CH2(ã) in collisions with helium at a collision energy of 300 cm^{−1}.

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