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I was looking up the Lennard-Jones parameter $\sigma$ (which, to my understanding, is a measure of molecular size) when I was surprised to discover that the value for the $\ce{N2}$ molecule (3.667 Å) was slightly lower than the value for the $\ce{CH4}$ molecule (3.78 Å). It's my understanding that $\ce{N2}$ molecules are significantly larger than $\ce{CH4}$ molecules, and this is exploited in, for instance, molecular sieves.

My question: is $\sigma$ a reasonable measure of mean atomic radius? And if it isn't, what is a good measure of molecular size, with which I can compare molecules?

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  • $\begingroup$ Chemistry uses mathjax with mhchem package loaded. As chemical formulas shouldn't be slanted, please use mhchem for chemical formulae and equations. $\endgroup$
    – M.A.R.
    Aug 30 '15 at 12:13
  • $\begingroup$ Are you sure you don't mean molecular radius (if such a thing exists) rather than atomic radius. Similarly the title seems out of place. $\endgroup$
    – bon
    Aug 30 '15 at 17:10
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    $\begingroup$ Please be aware that there are actually two different definitions for the Lennard-Jones radius. One is the radius at which the vdW force goes from attractive to repulsive, whereas the other is radius at which the attractive energy is greatest. Both are in common use. While Wikipedia uses different symbols for the two radii, not all sources are as consistent/forthcoming, so be careful when looking up the values. $\endgroup$
    – R.M.
    Aug 30 '15 at 17:36
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Atoms and molecules, as you surely know, are not tiny hard pebbles that you may measure using a slide gauge, unambiguously and with great precision. Instead, they are clouds of electron density with rather fuzzy edges, like things on an out-of-focus photograph. Their apparent size depends on how you define what "edge" is, or how hard you squeeze them. This is one of the reasons why we don't have a single definitive list of atomic radii, but a whole variety thereof.

As to the point of your question, yes, $\sigma$ is a good measure of molecular size. But there are also others, equally good and all subtly different. Which one to use depends on your purpose, and may be a hard problem by itself.

Also, remember that (1) the Lennard-Jones potential is defined for spherically symmetrical objects, which your molecules are not, and (2) even for these objects (atoms) it is but an approximation.

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  • $\begingroup$ Thanks for your answer. Could you suggest a few other measures of molecular size? I'm curious to see how $N_2$ and $CH_4$ compare in other measures. $\endgroup$
    – tom
    Aug 31 '15 at 3:53
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    $\begingroup$ Sure, be my guest. One: parameter b from the van der Waals equation of state. Two: effective area from the Langmuir adsorption isotherm (this one usually works the other way around, but anyway). Three: volume calculated from van der Waals radii and experimental bond lengths, as if the molecules were made of overlapping solid spheres. $\endgroup$ Aug 31 '15 at 6:18

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