Recently, I had to use some ab initio results for a kinetic computation. I was interested in a transition dipole moment of the molecule but none was given. However, there were some “infrared intensities” given in — crazy enougth — km mol^{-1}. I was rather confused about that because, by all convention, this is no unit of an intensity.

[Klippenstein:1996] gives a conversion factor that claims basically:

*A* = 1.25E^{-7} *I*(in km mol^{-1}) *ν*^{2}(in cm^{-1})

where *A* is the Einstein coefficient for spontaneous emission.

I generally do *not* trust such formulas. Furthermore I think they are an unnecessary attack on healthy physical thinking. But how to do better? A colleague found a tutorial of Dunbar where he presented essentially the same formula.

Finally [Neugebauer:2002] could give me deeper insight. The values given as “infrared intensities” seem to be what Neugebauer calls *integrated absorption coefficients*. Using the definitions given in [Neugebauer:2002] it is a simple and straight forward exercise to calculate the Einstein coefficient as

*A* = *I* 8 *π c N _{A}^{-1} (ν/c)^{2}*

In this formula I let *I* be the symbol for the integrated molar absorption coefficient for the sake of continuity.

If one investigates the numerical value of 8 *π c N _{A}*

^{-1}he finds it to be about 1.25115E

^{-14}. The difference of a factor of E

^{7}compared with Klippenstein’s formula is explained by recalling that he is suggesting to use km and cm

^{-2}instead of SI units.

## References

[Klippenstein:1996] Klippenstein et. al. Ion–Molecule Radiative Association Kinetics. *J. Chem. Phys.*, 104(12), 1996.

[Neugebauer:2002] Neugebauer et. al. Raman and IR Spectra for Buckminsterfullerene. *J. Comp. Chem.*, 23(9), 2002.