6
$\begingroup$

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)

$\endgroup$
  • $\begingroup$ Why not? It's just a conversion factor. $\endgroup$ – Todd Minehardt Nov 20 '16 at 22:41
  • $\begingroup$ @ToddMinehardt it seems unnatural using hc as a conversion factor for a classical description. $\endgroup$ – Sparkler Nov 20 '16 at 22:44
4
$\begingroup$

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.

| improve this answer | |
$\endgroup$
  • $\begingroup$ are absorption peaks (e.g. in wavenumbers) related to LJ potential well? (LJ is for non-bonded interactions) $\endgroup$ – Sparkler Nov 21 '16 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 '16 at 2:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.