The Lennard-Jones well depth $\epsilon$ is typically given in energy units ($\mathrm{kJ}$ or $\mathrm{kcal}$; sometimes per mole). Jasper and Miller, however, reported $\epsilon$ values in reciprocal centimeters ($\mathrm{cm^{-1}}$).

Why use $\mathrm{cm^{-1}}$?

  1. It seems unnatural using $hc$ as a conversion factor for a classical description.
  2. Absorption peaks (e.g. in wavenumbers) are not related to the LJ potential well, which is for non-bonded interactions.

Ahren W. Jasper, James A. Miller, Combust. and Flame 2014, 161 (1), 101–110. (preprint pdf)

  • $\begingroup$ Why not? It's just a conversion factor. $\endgroup$ Nov 20, 2016 at 22:41
  • $\begingroup$ @ToddMinehardt it seems unnatural using hc as a conversion factor for a classical description. $\endgroup$
    – Sparkler
    Nov 20, 2016 at 22:44

1 Answer 1


I don't think there's any inherent advantage as one can always convert to another unit. It seems natural to me, however, because chemists generally have a good idea of the energy of vibrational and rotatial states in $cm^{-1}$, so being able to compare the depth of the well with some familiar chemical process is quite nice. For instance, if the well-depth were quite small, one could immediately identify that the system may not spend a lot of time there if it is comparable to the zero-point energy or something similar.

It's similar to how physicists report everything in electron-volts ($eV$). They do it because it's familiar and they have many physical processes they can use as a reference. For instance physicists know that the band gap of semiconductors is between $2-5\ eV$, so it's quite natural to report other energies in the same unit.

  • $\begingroup$ are absorption peaks (e.g. in wavenumbers) related to LJ potential well? (LJ is for non-bonded interactions) $\endgroup$
    – Sparkler
    Nov 21, 2016 at 1:48
  • 1
    $\begingroup$ They are related in some sense. Non-covalent interactions absorb light like covalent bonds do. For instance, a water dimer has intermolecular vibrational normal modes, and these normal modes have a certain energy which corresponds to a frequency of light that might be absorbed when using spectroscopy. These modes can only exist because the water molecules are bound in some potential energy well. If I observed one of the modes were at an energy of $1000\ cm^{-1}$, then I know the well must be deeper than that, and I would express the well-depth in $cm^{-1}$. $\endgroup$
    – jheindel
    Nov 22, 2016 at 2:59

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