# Hyperfine excitation of ^{13}CN by para-H_{2} (Flower et al, 2015)

**Display rate coefficients as :**
**Display rate coefficients graphically :**
**Data information :**
- 13CN initial level labelled from 2 to 146
- 13CN final level labelled from 1 to 145
- H2 initial level labelled from 1 to 1
- H2 final level labelled from 1 to 1
- 16 temperatures between 5 K and 80 K
- Units : cm
^{3} s^{-1}

N/A

The 2D PES used was adapted from the

^{12}CN-H

_{2} 4D PES described in Kalugina et al, 2012, 2013.

The calculation of the 4D PES assumes that both

^{12}CN and H

_{2} are rigid rotors. For H

_{2}, the bond distance is fixed to the value averaged over the fundamental vibration mode, i.e. r

_{HH} = 1.4487 a

_{0}. For CN, the equilibrium distance is taken, i.e. r

_{CN} = 2.2144 a

_{0} (this value was also assumed when building the

^{13}CN-H

_{2} PES). The reactive channel towards HCN + H is ignored, given that this reaction have an activation energy of at least 1100 cm

^{-1} (Ter Horst et al, 1996).

The

^{12}CN-H

_{2} 4D PES was calculated at the RCCSD(T) / aug-cc-pVTZ level of theory. The basis was supplemented with mid bond functions. The basis set superposition error (BSSE) was corrected at all geometries with the Boys and Bernardi counterpoise procedure (Boys and Bernardi 1970). The AVTZ + bond functions was found to reproduce higher basis sets calculations (i.e. AV5Z) within ~1-2 cm

^{-1} in the potential well.

The calculations were performed at regularly spaced distances in the range 4-16 a

_{0}. At each distance, the angular dependence was sampled on a predefined grid for the 3 angles that describe the 4D PES. A 2D PES is then built from the 4D PES by averaging the ab initio points over the two angles that describe the H

_{2} rotation. At this point, the coordinates of the ab initio points were modified to account for the shift of mass center between the

^{12}CN-H

_{2} and

^{13}CN-H

_{2} systems. The new 2D PES specific to

^{13}CN-H

_{2} was then fitted with a 9-term angular expansion over Legendre polynomials, thanks to the fitting procedure described by Werner et al, 1989. The fit was performed accounting for all the ab initio points calculated up to 16 a

_{0}. Above this intermolecular distance, the anisotropic terms with

were damped exponentially to zero while the first three terms were extrapolated with R

^{-6} and R

^{-7} dependences.

### References :

None

Close-coupling (CC) calculations were performed by solving the nuclear spin-free coupled set of differential equations. The CC calculations consider explicitely the fine structure.

Hyperfine structure (due to both

^{13}C and N) cross sections were obtained through a recoupling technique, in a two step procedure. First, CC calculations were performed just taking into account the fine structure energy levels of

^{13}CN, which leads to obtain the scattering matrix elements

. The hyperfine structure is subsequently introduced and the scattering matrix elements are recoupled according to the methodology described by Corey & McCourt 1983.

### References :

None

not specified

not specified

The methodology used typically allows the determination of rate coefficients with a few percent accuracy, with respect to the PES used.

In the current case, an additional source of error comes from the PES, which is not specifically tailored for ^{13}CN (the bond length used corresponds to the ^{12}CN bond length averaged over the fundamental mode of vibration). This typically induces uncertainties of a few 10% (see e.g. scribano et al, 2010).

Additionally, the dynamical calculations neglect the j=2 state of H_{2} and it was shown by Kalugina et al. 2013 that in the particular case of CN-H2 collisions, this induces uncertainties around 30% in rate coefficients.

## Presentation

Hyperfine de-excitation rate coefficients are provided for the first 146 hyperfine levels of ^{13}CN (up to N=12) in collision with para-H_{2}, for temperatures in the range 5-80K.

## References

* NB : the main reference is displayed in red*
**PDF Version**
## Collision history

**Status** |
**Version** |
**Date** |

Collision added into the database |
1 |
2016-03-16 |

Documentation modified |
2 |
2016-03-17 |