0.000000125 are Not a Coincidence

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) ν2(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 NA-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 NA-1 he finds it to be about 1.25115E-14. The difference of a factor of E7 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.

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