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I am looking for numbers which tell you something about the 3D shape of the molecule, and is also easily calculated.

One of these is the acentricity factor. I am aware of this one. My problem is you calculate acentricit, from thermochemical data, which are usually hard to find, and can contain a great degree of experimental errors.

A more suitable quantity would be constructed from the groups of the molecule. Is there such a thing? Or what are other quantifiers of molecular shape other than acentricit, factor?

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    $\begingroup$ This sounds like it could be a bit of an XY problem. What are you actually trying to do? $\endgroup$ – Aesin Mar 20 '16 at 19:06
  • $\begingroup$ I am planning to relate some physical-chemical properties of large sets of molecules to their shapes. For example, trying to find a qualitative picture of what is the effect of the molecular shape on the critical temperature. I am also planning to characterize the efficiency of currently used descriptor calculation methods. $\endgroup$ – Ezze Mar 20 '16 at 19:16
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    $\begingroup$ So you already know a bunch of descriptors, and we should figure out ones you may not know... Wouldn't it be helpful if you mention which ones you know? Also, it is nice to have an argument behind using a descriptor, not just some random parameter you tried and seemed to wok ona limited number of molecules. $\endgroup$ – Greg Mar 21 '16 at 5:59
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There are lots of descriptors of molecular size and shape that come to mind:

  • Moments of inertia (e.g., how different are they)
  • Radii (e.g., enclosing the molecule in a best-fit box)
  • Surface area or polar surface area (there are existing group-based methods)
  • Volume (e.g., of the van der Waals surface)

Some people have also used 3D shape descriptors like "spectrophores".

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    $\begingroup$ Both the absolute magnitudes and relative values of the moments of inertia contain useful information, I think. Absolute values give overall size, whereas the relative values (ratios close to $1$, or very different) give symmetry/asymmetry. The moments can't capture convexity or concavity, though. $\endgroup$ – hBy2Py Mar 20 '16 at 21:29
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    $\begingroup$ I haven't seen any good measures of convexity or concavity, but those would likely be nice too. $\endgroup$ – Geoff Hutchison Mar 20 '16 at 23:44

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