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My book says that only the Van der Waal's radius of noble gases can be measured as these gases generally do not form compounds (except Xenon.) Then why can't we just calculate the atomic radii by computation, say solving the Schrödinger equation? Can't we make computer simulation models of isolated atoms of noble gases?

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    $\begingroup$ We can all right, but that's not what is called a measurement. $\endgroup$ – Ivan Neretin Jul 16 '17 at 6:39
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    $\begingroup$ @IvanNeretin Agreed, then can't we accept the simulated model results as excatly as a measurement? $\endgroup$ – Apoorv Potnis Jul 16 '17 at 6:45
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    $\begingroup$ What's to accept and what for? We won't be needing those radii anytime soon. And in any case, the book says nothing about that. It just says they can't be measured, which is true. $\endgroup$ – Ivan Neretin Jul 16 '17 at 6:50
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    $\begingroup$ You can experimentally measure the atomic radii using x-ray crystallography. All form crystals except helium. $\endgroup$ – porphyrin Jul 16 '17 at 8:52
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    $\begingroup$ @porphyrin Solid helium has a hexagonal crystal structure. Also there is no such thing as an "atomic radius", that is a catch-all term for vdW radius, ionic radius, covalent radius, metallic radius. en.wikipedia.org/wiki/Atomic_radius $\endgroup$ – Karl Jul 16 '17 at 14:33
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Covalent radius is measured as the distance ($r_\text{cov} = d/2$) between the nuclei of two bonded atoms (covalent). But, if you try to do the same for noble gases/inert gases (good luck!), as they have fully filled $np$ orbitals, they will repel each other, hence the closest distance between the two atoms is taken (high pressure, low temperature) as the van der Waals radius.

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    $\begingroup$ This does not answer my question. I was asking why we do not accept values produced by simulation models. $\endgroup$ – Apoorv Potnis Jul 16 '17 at 8:14
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    $\begingroup$ @ApoorvPotnis Noble gases have no covalent radius, because they do not form bonds. You cannot calculate something that does not exist. $\endgroup$ – Karl Jul 16 '17 at 14:46
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    $\begingroup$ @ApoorvPotnis It is pointless to compare the 95% electron propability radii of single, isolated atoms. What kind of scientific question would you want to answer with that information? You can't even prove that your calculation is correct! The values here en.wikipedia.org/wiki/Atomic_radius#Calculated_atomic_radii are interesting from a didactic point of view, but nothing more. $\endgroup$ – Karl Jul 16 '17 at 15:30
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    $\begingroup$ They are scientifically useless, because they do not appear in measureable reality! You cannot use those values to prove or predict anything, you cannot even prove the values themselves by some independent means. So why bother? It's unscientific. A nice mathematical excercise, didactically helpful, most likely correct, but, by all relevant criteria, unscientific. en.wikipedia.org/wiki/Falsifiability $\endgroup$ – Karl Jul 16 '17 at 17:11
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    $\begingroup$ You could do a calculation for a noble gas and get the radial distribution of the wave function (or derived from this the electron density). But this will be a distribution function of the radius. There is no atomic radius where the electron density suddenly stops. You could ask for characteristic points (like maximum, expectation value, where the density is below a certain threshold, where the integrated density/probability exceeds 90%, ...), but those would be arbitrary decisions. $\endgroup$ – Feodoran Jul 17 '17 at 7:29

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