Hydrogen molecules (H_{2}) exist in two isomeric forms: para-hydrogen with total nuclear spin *I* = 0 and ortho-hydrogen with *I* = 1.
In the ground electronic and vibrational state¹, the rotational levels of para-H_{2} have even values of the angular momentum *j* while the levels of ortho-H_{2} have odd *j* values.
The ground-state of ortho-H_{2} (*j* = 1) lies 170 K above the ground-state of para-H_{2} (*j* = 0).

In cold environments where the kinetic temperature *T _{k}* is lower than ~50 K and in the absence of radiative pumping, only the ground-state of the two nuclear spin isomers are significantly populated so that only para-H

_{2}(

*j*= 0) and ortho-H

_{2}(

*j*= 1) need to be considered as collision partners. Moreover, the rate coefficients for ortho-H

_{2}(

*j*= 1) are generally larger than those for para-H

_{2}(

*j*= 0), by up to an order of magnitude

At higher kinetic temperatures *T _{k}* < 50 K or in the presence of radiative pumping, H

_{2}molecules in excited levels

*j*= 2, 3, etc. can become significant new colliders. It has been generally found, however, that the dominant collisional rate coefficients for H

_{2}(

*j*> 1) differ by less than 20-30% from those for H

_{2}(

*j*= 1) (e.g. Daniel et al. 2014 and references therein). This result holds for targets in their ground vibrational state and for target rotational levels or kinetic temperatures below ~500 K, i.e. below the opening of the H

_{2}level

*j*= 2 at 510 K. In these conditions, rotation-rotation transfers between the target species and H

_{2}are negligible so that H

_{2}remains mostly in the same rotational state during the collision (i.e.

*j*→

*j*).

**EMAA provides de-excitation rate coefficients (in cm ^{3}s^{-1}) due to collisions with 'para-H_{2}' and 'ortho-H_{2}' which in practice correspond to H_{2} (j = 0 → 0) and H_{2} (j = 1 → 1), respectively (except otherwise stated).**
In order to include excited levels of H

_{2}, rate coefficients for e.g. H

_{2}(

*j*= 2 → 2) can be assumed to be approximately equal to those for H

_{2}(

*j*= 1 → 1).

**Thus, in radiative transfer calculations, the volume density (in cm**A simple solution to estimate the H

^{-3}) affected to the 'para-H_{2}' collider should be that of H_{2}(*j*= 0) while the volume density affected to the 'ortho-H_{2}' collider should be that of the sum of all levels of H_{2}with*j*> 0._{2}level populations is to further assume that these levels are thermalized at the kinetic temperature, with a fixed or thermalized ortho-to-para ratio.

### References

Daniel F., Faure A., Wiesenfeld L., Roueff E., Lis D. C, Hily-Blant P., *MNRAS* **444** 2544-2554 (2014)

Faure A., Lique F., Wiesenfeld L., *MNRAS*** 460** 2103-2109 (2016)

^{1}The first vibrational level of H_{2} opens at 4161.2 cm^{-1}