_{2}() with helium

^{1}, Paul J. Dagdigian

^{2,a)}and Millard H. Alexander

^{3,b)}

### Abstract

Following our earlier work on collisions of He with the methylene radical in its excited state [L. Ma, M. H. Alexander, and P. J. Dagdigian, J. Chem. Phys.134, 154307 (2011)]10.1063/1.3575200, we investigate here the analogous relaxation of in its ground electronic state. The molecule is treated as semi-rigid, with fixed bond lengths but a varying bond angle. We use an *ab initio*potential energy surface (PES) which is averaged over the CH_{2} bending angle weighted by the square of the bending wave function. The PES for the interaction of He with CH_{2} in the state is considerably less anisotropic than for interaction with the state since the two 2*p* electrons on the C atom are evenly distributed among the bonding and non-bonding molecular orbitals. We report quantum scattering calculations of state-to-state and total removal cross sections as well as total removal rate constants at room temperature. Because of the less pronounced anisotropy, these cross sections and rate constants are considerably smaller than for collisions of with He. Finally, we investigate the dependence of rotational inelasticity on the bending vibrational quantum number.

This work was supported by the Chemical, Geosciences, and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy (Grant No. DESC0002323). The authors wish to thank Gregory Hall and Tevor Sears for sharing data from their recent experiments on the relaxation of and for their encouragement. We also thank Per Jensen for providing accurate calculated values derived from experimental measurements of the ro-vibrational energies of CH_{2} in the state.

I. INTRODUCTION AND GENERAL CONSIDERATIONS

II. POTENTIAL ENERGY SURFACE

III. SCATTERING CALCULATIONS

IV. RESULTS

A. State-to-state rotationally inelastic collision in the (0,2,0) and (0,3,0) vibrational manifolds

B. Total cross sections and rate constants

C. Variation with bending level

V. DISCUSSION

### Key Topics

- Manifolds
- 25.0
- Anisotropy
- 14.0
- Wave functions
- 11.0
- Ab initio calculations
- 10.0
- Band gap
- 9.0

## Figures

Electron-density contours projected onto the *xy*, *xz*, and *yz* planes for the CH_{2} molecule in its ground electronic state (left contours) and in its excited electronic state (right contours). The geometry is defined in Fig. 1 of Ref. 1.

Electron-density contours projected onto the *xy*, *xz*, and *yz* planes for the CH_{2} molecule in its ground electronic state (left contours) and in its excited electronic state (right contours). The geometry is defined in Fig. 1 of Ref. 1.

(Left-hand panel) The dependence on the bending angle of the energies of the (red curve) and the (blue curve) states of CH_{2}. In both cases the CH_{2} bond lengths are frozen at their equilibrium values [2.031 bohr (Ref. 11)] for the state and [2.101 bohr (Ref. 12)] for the state. The horizontal lines indicate the positions of the vibrational levels, designated (*v* _{ a },*v* _{ b },*v* _{ s }) where the subscripts *a*, *b*, and *s* denote the antisymmetric stretch, the bend, and the symmetric stretch modes, respectively. (Right-hand panel) The dependence of the bending probability (the square of the bending wave function) on the bending angle ρ for the vibrational states (0,0,0) (red) and (0,3,0) (blue). For consistency with the earlier work of Bunker, Hougen, and Johns^{13} the abscissa ρ is the supplement of the bending angle γ.

(Left-hand panel) The dependence on the bending angle of the energies of the (red curve) and the (blue curve) states of CH_{2}. In both cases the CH_{2} bond lengths are frozen at their equilibrium values [2.031 bohr (Ref. 11)] for the state and [2.101 bohr (Ref. 12)] for the state. The horizontal lines indicate the positions of the vibrational levels, designated (*v* _{ a },*v* _{ b },*v* _{ s }) where the subscripts *a*, *b*, and *s* denote the antisymmetric stretch, the bend, and the symmetric stretch modes, respectively. (Right-hand panel) The dependence of the bending probability (the square of the bending wave function) on the bending angle ρ for the vibrational states (0,0,0) (red) and (0,3,0) (blue). For consistency with the earlier work of Bunker, Hougen, and Johns^{13} the abscissa ρ is the supplement of the bending angle γ.

Contour plot (cm^{−1}) of the dependence on the orientation of the He atom of the –He (left panel) and –He (right panel) PES’s. In both cases the CH_{2}–He distance is frozen at the value corresponding to the global minimum: *R* = 6.95 bohrs for the state and *R* = 4.58 bohrs for the state. Negative contours are indicated in blue, positive in red. The right-hand panel reprinted with permission from L. Ma, M. H. Alexander, and P. J. Dagdigian, J. Chem. Phys.134, 154307 (2011)10.1063/1.3575200. Copyright © 2011, American Institute of Physics.

Contour plot (cm^{−1}) of the dependence on the orientation of the He atom of the –He (left panel) and –He (right panel) PES’s. In both cases the CH_{2}–He distance is frozen at the value corresponding to the global minimum: *R* = 6.95 bohrs for the state and *R* = 4.58 bohrs for the state. Negative contours are indicated in blue, positive in red. The right-hand panel reprinted with permission from L. Ma, M. H. Alexander, and P. J. Dagdigian, J. Chem. Phys.134, 154307 (2011)10.1063/1.3575200. Copyright © 2011, American Institute of Physics.

Dependence of potential energies on ϕ when θ = 90° (motion in the *xy* plane) for the –He (left) and –He (right) systems.

Dependence of potential energies on ϕ when θ = 90° (motion in the *xy* plane) for the –He (left) and –He (right) systems.

Dependence of the largest expansion coefficients *v* _{λμ} on the atom-molecule distance *R*. Over this range the dominant anisotropic terms are *v* _{31}(*R*) and *v* _{20}(*R*).

Dependence of the largest expansion coefficients *v* _{λμ} on the atom-molecule distance *R*. Over this range the dominant anisotropic terms are *v* _{31}(*R*) and *v* _{20}(*R*).

Lower rotational levels of the *ortho* (dashed blue) and *para* (solid red) nuclear spin modifications of in the (0,0,0) and (0,3,0) vibrational manifolds. Each individual level is labelled , where *n* is the rotational angular momentum with *k* _{ a } its (nominal) projection along the principal axis and *k* _{ c }, its (nominal) projection along the prolate axis.

Lower rotational levels of the *ortho* (dashed blue) and *para* (solid red) nuclear spin modifications of in the (0,0,0) and (0,3,0) vibrational manifolds. Each individual level is labelled , where *n* is the rotational angular momentum with *k* _{ a } its (nominal) projection along the principal axis and *k* _{ c }, its (nominal) projection along the prolate axis.

Bar plot of the cross sections for rotationally inelastic scattering of the *n* = 4 and 5, *k* _{ a }=1 levels in the (0,3,0) vibrational manifold of *para* (left figures) and *ortho* (right figures) by collision with He at a collision energy of 300 . Red marks the initial state.

Bar plot of the cross sections for rotationally inelastic scattering of the *n* = 4 and 5, *k* _{ a }=1 levels in the (0,3,0) vibrational manifold of *para* (left figures) and *ortho* (right figures) by collision with He at a collision energy of 300 . Red marks the initial state.

Removal cross sections for –He collisions at 300 cm^{−1} for molecules in different *k* _{ a } = 1 states [*para* in filled circles (red in color) and *ortho* in filled squares (blue in color)] in the (0,3,0) vibrational manifold. The largest set of cross sections refers to transitions out of the *k* _{ a } = 1 stack into both the *k* _{ a } = 0 and 1 levels. The two smaller sets of cross sections refer to total removal into, separately, the *k* _{ a } = 0 and *k* _{ a } = 1 stacks.

Removal cross sections for –He collisions at 300 cm^{−1} for molecules in different *k* _{ a } = 1 states [*para* in filled circles (red in color) and *ortho* in filled squares (blue in color)] in the (0,3,0) vibrational manifold. The largest set of cross sections refers to transitions out of the *k* _{ a } = 1 stack into both the *k* _{ a } = 0 and 1 levels. The two smaller sets of cross sections refer to total removal into, separately, the *k* _{ a } = 0 and *k* _{ a } = 1 stacks.

Bar plot of cross sections for rotationally inelastic scattering from *n* = 4, *k* _{ a } = 1 levels of the *ortho* to final levels with *n* up to 8 in (0,0,0), (0,1,0), and (0,2,0) vibrational states (from top to bottom) by collision with He at a collision energy of 300 cm^{−1}. Red marks the initial level.

Bar plot of cross sections for rotationally inelastic scattering from *n* = 4, *k* _{ a } = 1 levels of the *ortho* to final levels with *n* up to 8 in (0,0,0), (0,1,0), and (0,2,0) vibrational states (from top to bottom) by collision with He at a collision energy of 300 cm^{−1}. Red marks the initial level.

Theoretical and experimental (Ref. 10) total removal rate constants for the *k* _{ a } = 1 levels of *ortho* CH_{2} by collision with He at room temperature. (Note that experimental results were not obtained for all rotational levels). The points designated by filled circles (red in color), corresponding to relaxation of the state, are from calculations reported in Ref. 1, while the points designated by filled squares (blue in color), corresponding to relaxation of the state, are from the calculations reported here. Also shown (open square, green in color) is the calculated relaxation rate of the *n* = 9, *k* _{ a } = 3 level of the (0,2,0) manifold. One spin component of this level is mixed with the *j* = 8, *k* _{ a } = 1 level of the (0,0,0) manifold of the state. The experimentally observed (Ref. 10) relaxation rates of the two mixed levels are shown by the points marked “S” (primarily singlet) and “T” (primarily triplet).

Theoretical and experimental (Ref. 10) total removal rate constants for the *k* _{ a } = 1 levels of *ortho* CH_{2} by collision with He at room temperature. (Note that experimental results were not obtained for all rotational levels). The points designated by filled circles (red in color), corresponding to relaxation of the state, are from calculations reported in Ref. 1, while the points designated by filled squares (blue in color), corresponding to relaxation of the state, are from the calculations reported here. Also shown (open square, green in color) is the calculated relaxation rate of the *n* = 9, *k* _{ a } = 3 level of the (0,2,0) manifold. One spin component of this level is mixed with the *j* = 8, *k* _{ a } = 1 level of the (0,0,0) manifold of the state. The experimentally observed (Ref. 10) relaxation rates of the two mixed levels are shown by the points marked “S” (primarily singlet) and “T” (primarily triplet).

## Tables

Total removal cross sections out of the *n* = 4 and 5, *k* _{ a } = 1 levels in the (0,3,0) vibrational state of *para* and *ortho* by collision with He at a collision energy of 300 cm^{−1}.

Total removal cross sections out of the *n* = 4 and 5, *k* _{ a } = 1 levels in the (0,3,0) vibrational state of *para* and *ortho* by collision with He at a collision energy of 300 cm^{−1}.

Energy gaps for several Δ*n* transitions out of the *n* = 4, *k* _{ a } = 1 (4_{13}) level of *ortho*- in the (*v* _{ s }, *v* _{ b }, *v* _{ a } = 0, 0, 0), (0,1,0), (0,2,0), and (0,3,0) vibrational manifolds.^{a}

Energy gaps for several Δ*n* transitions out of the *n* = 4, *k* _{ a } = 1 (4_{13}) level of *ortho*- in the (*v* _{ s }, *v* _{ b }, *v* _{ a } = 0, 0, 0), (0,1,0), (0,2,0), and (0,3,0) vibrational manifolds.^{a}

Overall inelastic cross sections for transitions out of the *n* = 4, *k* _{ a } = 1 level of *ortho* and *para* , and out of the *j* = 4, *k* _{ a } = 1 level of the (0,0,0) manifold of by collision with He at a collision energy of 300 cm^{−1}.^{a}

Overall inelastic cross sections for transitions out of the *n* = 4, *k* _{ a } = 1 level of *ortho* and *para* , and out of the *j* = 4, *k* _{ a } = 1 level of the (0,0,0) manifold of by collision with He at a collision energy of 300 cm^{−1}.^{a}

Article metrics loading...

Full text loading...

Commenting has been disabled for this content