^{1,a)}and Millard H. Alexander

^{2,b)}

### Abstract

Transport properties for collisions of methylene, in both its ground and low-lying electronic states, with helium have been computed using recently computed high-quality * ab initio * potential energy surfaces (PESs). Because of the difference in the orbital occupancy of the two electronic states, the anisotropies of the PESs are quite different. The CH_{2}( )–He PES is very anisotropic because of the strong interaction of the electrons on the helium atom with the unoccupied CH_{2} orbital perpendicular to the molecular plane, while the anisotropy of the CH_{2}( )–He PES is significantly less since this orbital is singly occupied in this case. To investigate the importance of the anisotropy on the transport properties, calculations were performed with the full potential and with the spherical average of the potential for both electronic states. Significant differences (over 20% for the state at the highest temperatures considered) in the computed transport properties were found.

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.

I. INTRODUCTION

II. CALCULATION OF TRANSPORT PROPERTIES

III. SCATTERING CALCULATIONS

IV. RESULTS

V. DISCUSSION

### Key Topics

- Transport properties
- 48.0
- Anisotropy
- 20.0
- Diffusion
- 13.0
- Ab initio calculations
- 9.0
- Elasticity
- 8.0

## Figures

Dependence of the effective total cross sections [panels (a) and (b)] and [panels (c) and (d)] for collisions of CH_{2} in its [panels (b) and (d)] and [panels (a) and (c)] states with helium as a function of the collision energy. Red curves: 0_{00} level; blue curves: 8_{08} level. The black curves were computed with the spherical average (*V* _{00} term in the angular expansion) of the respective PESs. Also included in panels (a) and (b) is the elastic contribution to the effective total cross section for the 0_{0} level, computed with the full PES.

Dependence of the effective total cross sections [panels (a) and (b)] and [panels (c) and (d)] for collisions of CH_{2} in its [panels (b) and (d)] and [panels (a) and (c)] states with helium as a function of the collision energy. Red curves: 0_{00} level; blue curves: 8_{08} level. The black curves were computed with the spherical average (*V* _{00} term in the angular expansion) of the respective PESs. Also included in panels (a) and (b) is the elastic contribution to the effective total cross section for the 0_{0} level, computed with the full PES.

State-dependent collision integrals in units of 10^{−11} cm^{3} s^{−1} as a function of the rotational angular momentum *j* for –He at a temperature of 300 K. Red and blue symbols denote *ortho* and *para* levels, respectively. In panels (a) and (b), levels with different values of the body-frame projection quantum number are denoted by the following symbols: *k* _{ a } = 0, circles; *k* _{ a } = 1, plus signs; *k* _{ a } = 2, diamonds; *k* _{ a } = 3, upward-pointing triangles; *k* _{ a } = 4, downward-pointing triangles; *k* _{ a } = 5, left-pointing triangle; *k* _{ a } = 6, right-pointing triangle; *k* _{ a } = 7, squares.

State-dependent collision integrals in units of 10^{−11} cm^{3} s^{−1} as a function of the rotational angular momentum *j* for –He at a temperature of 300 K. Red and blue symbols denote *ortho* and *para* levels, respectively. In panels (a) and (b), levels with different values of the body-frame projection quantum number are denoted by the following symbols: *k* _{ a } = 0, circles; *k* _{ a } = 1, plus signs; *k* _{ a } = 2, diamonds; *k* _{ a } = 3, upward-pointing triangles; *k* _{ a } = 4, downward-pointing triangles; *k* _{ a } = 5, left-pointing triangle; *k* _{ a } = 6, right-pointing triangle; *k* _{ a } = 7, squares.

The collision integrals Ω^{(1, 1)} and Ω^{(2, 2)} as a function of temperature, computed for the –He systems. The full PES and the spherical average of the PES was employed for both electronic states.

The collision integrals Ω^{(1, 1)} and Ω^{(2, 2)} as a function of temperature, computed for the –He systems. The full PES and the spherical average of the PES was employed for both electronic states.

Differential cross section for elastic –He collisions at a relative translational energy of 300 cm^{−1}: Blue, full PES for the 0_{0} initial level; red, spherically averaged potential. The inset shows the angle-dependent contribution to the *Q* ^{(1)} effective elastic cross section for the two potentials; the area under a curve multiplied by 2π equals the effective elastic cross section.

Differential cross section for elastic –He collisions at a relative translational energy of 300 cm^{−1}: Blue, full PES for the 0_{0} initial level; red, spherically averaged potential. The inset shows the angle-dependent contribution to the *Q* ^{(1)} effective elastic cross section for the two potentials; the area under a curve multiplied by 2π equals the effective elastic cross section.

Diffusion coefficients for the –He systems, computed with the full PESs and their isotropic, spherical averages.

Diffusion coefficients for the –He systems, computed with the full PESs and their isotropic, spherical averages.

Diffusion coefficients for the CH_{2}–He system: Black and red lines, quantum scattering calculations using *ab initio* CH_{2}–He PES for the and states, respectively; blue and green lines, classical scattering calculations using Lennard-Jones 12-6 and 9-6 potentials, respectively.

Diffusion coefficients for the CH_{2}–He system: Black and red lines, quantum scattering calculations using *ab initio* CH_{2}–He PES for the and states, respectively; blue and green lines, classical scattering calculations using Lennard-Jones 12-6 and 9-6 potentials, respectively.

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