^{1,2}, Thierry Stoecklin

^{1,a)}, Philippe Halvick

^{1}, Marie-Lise Dubernet

^{3,4}and Sarantos Marinakis

^{3}

### Abstract

Owing to its large dipole, astrophysicists use carbon monosulfide (CS) as a tracer of molecular gas in the interstellar medium, often in regions where H_{2} is the most abundant collider. Predictions of the rovibrational energy levels of the weakly bound complex CS-H_{2} (not yet observed) and also of rate coefficients for rotational transitions of CS in collision with H_{2} should help to interpret the observed spectra. This paper deals with the first goal, i.e., the calculation of the rovibrational energy levels. A new four-dimensional intermolecular potential energy surface for the H_{2}-CS complex is presented. *Ab initio*potential energy calculations were carried out at the coupled-cluster level with single and double excitations and a perturbative treatment of triple excitations, using a quadruple-zeta basis set and midbond functions. The potential energy surface was obtained by an analytic fit of the *ab initio* data. The equilibrium structure of the H_{2}-CS complex is found to be linear with the carbon pointing toward H_{2} at the intermolecular separation of 8.6 *a* _{o}. The corresponding well depth is −173 cm^{−1}. The potential was used to calculate the rovibrational energy levels of the *para*-H_{2}-CS and *ortho*-H_{2}-CS complexes. The present work provides the first theoretical predictions of these levels. The calculated dissociation energies are found to be 35.9 cm^{−1} and 49.9 cm^{−1}, respectively, for the *para* and *ortho* complexes. The second virial coefficient for the H_{2}-CS pair has also been calculated for a large range of temperature. These results could be used to assign future experimental spectra and to check the accuracy of the potential energy surface.

I. INTRODUCTION

II. THEORY

A. Potential energy surface

B. Bound states calculations

C. Second virial coefficient

III. RESULTS AND DISCUSSION

A. Potential energy surface

B. Rovibrational bound states

C. Second virial coefficient

IV. CONCLUSION

### Key Topics

- Bound states
- 23.0
- Polymers
- 7.0
- Potential energy surfaces
- 7.0
- Ab initio calculations
- 5.0
- Carbon
- 5.0

## Figures

Set of body fixed coordinates used to describe the diatom-diatom system. The azimuthal angle *φ* is undefined when *θ* _{1} or *θ* _{2} is equal to 0° or 180°.

Set of body fixed coordinates used to describe the diatom-diatom system. The azimuthal angle *φ* is undefined when *θ* _{1} or *θ* _{2} is equal to 0° or 180°.

Contour plot of the rigid rotor PES for *θ* _{1} = 0°. The contour lines are equally spaced by 10 cm^{−1}.

Contour plot of the rigid rotor PES for *θ* _{1} = 0°. The contour lines are equally spaced by 10 cm^{−1}.

Contour plot of the rigid rotor PES for *θ* _{2} = 0°. The contour lines are equally spaced by 10 cm^{−1}.

Contour plot of the rigid rotor PES for *θ* _{2} = 0°. The contour lines are equally spaced by 10 cm^{−1}.

Contour plot of the rigid rotor PES for *θ* _{2} = 180°. The contour lines are equally spaced by 10 cm^{−1}.

Contour plot of the rigid rotor PES for *θ* _{2} = 180°. The contour lines are equally spaced by 10 cm^{−1}.

Contour plot of the rigid rotor PES for *φ* = 0° and *R* relaxed. The contour lines are equally spaced by 10 cm^{−1}. The optimised values of *R* span the range [7.10,9.77] *a* _{ o }.

Contour plot of the rigid rotor PES for *φ* = 0° and *R* relaxed. The contour lines are equally spaced by 10 cm^{−1}. The optimised values of *R* span the range [7.10,9.77] *a* _{ o }.

Cross second virial coefficient calculated with the present PES.

Cross second virial coefficient calculated with the present PES.

## Tables

Calculated rovibrational bound states of *p*H_{2}-CS for *J* ≤ 2. For each state, we report the energy in cm^{−1}, the total rotational quantum number *J*, the parity ɛ, the CS rotational quantum number *j* _{2}, the orbital quantum number *L*, and the percentage weight (*w*) of the leading basis set function. For some states, several basis functions need to be given in order to distinguish them from lower states with same *J* and *ɛ*.

Calculated rovibrational bound states of *p*H_{2}-CS for *J* ≤ 2. For each state, we report the energy in cm^{−1}, the total rotational quantum number *J*, the parity ɛ, the CS rotational quantum number *j* _{2}, the orbital quantum number *L*, and the percentage weight (*w*) of the leading basis set function. For some states, several basis functions need to be given in order to distinguish them from lower states with same *J* and *ɛ*.

Calculated energies (cm^{−1}) of the rovibrational bound states of *o*H_{2}-CS for *J* ≤ 2, along with the associated quantum numbers (*J*, *ɛ*).

Calculated energies (cm^{−1}) of the rovibrational bound states of *o*H_{2}-CS for *J* ≤ 2, along with the associated quantum numbers (*J*, *ɛ*).

Energy spacing (cm^{−1}) between *p*H_{2}-CS bound states associated with two successive values of *j* _{2} for *L* = 0.

Energy spacing (cm^{−1}) between *p*H_{2}-CS bound states associated with two successive values of *j* _{2} for *L* = 0.

Energy spacing (cm^{−1}) between *para* bound levels associated with successive values of *L*. *B* _{rel} is the rotational constant of the two-body system H_{2} + CS calculated from the spacing.

Energy spacing (cm^{−1}) between *para* bound levels associated with successive values of *L*. *B* _{rel} is the rotational constant of the two-body system H_{2} + CS calculated from the spacing.

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