# Is there a Python module for calculating Ovality of a molecule?

Ovality gives a measure of how the shape of a molecule approaches a sphere (at one extreme) or a cigar shape (at the other). Ovality is described by a ratio of volume to area (see https://en.wikipedia.org/wiki/Ovality). So, it is basically "just" about intersecting Van-der-Waals spheres. Although this sounds simple, it can get pretty complicated.

There is a nice paper from M. Petitjean explaining how to get correct values of Van-der-Waals volumes and surfaces (see https://hal.archives-ouvertes.fr/hal-01955983). According to this paper, inacceptable approximations have been used in the past. I can follow this paper to a certain extent, but when it comes to implementing this in Python it would exceed my mathematical and programming knowledge.

Therefore my question:

Is there maybe already a Python module which can calculate Ovality from a given molecular structure? Input would be: atom types, atom positions, and Van-der-Waals radii of the atoms.

I'm already using RDKit and maybe it can do it, and I just haven't found this feature. Thank you for any hints.

I guess there was need for clarification:

The ovality (O), a parameter used as shape descriptor, is defined as the ratio between actual surface and minimum surface for the same volume (the surface of a sphere with a volume that equals the actual volume) (see https://www.sciencedirect.com/topics/chemistry/molecular-size)

For this, the van-der-Waals surface and the van-der-Waals volume of the molecule need to be calculated, basically by intersecting spheres with different sizes at different positions.

• It may be too crude a method, but why not start by calculating moments of inertia assuming all masses are the same. This will give you a prolate or oblate spheroid from which you can get area & volume etc. and is simple to calculate. May 26 '20 at 16:28
• You are looking for the terms oblate (round & flat) and prolate (rugby ball). You usually quantify their shape with the aspect ratio.
– Karl
May 26 '20 at 19:52
• @Karl and porphyrin, I would like to calculate the van-der-Waals-surface and the van-der-Waals-volume of a given molecule. How could "moments of inertia" with a crude approximation and the terms "oblate" and "prolate" help me achieving this? May 26 '20 at 20:45
• Because I have never heard the term "ovality", and suspect that you may find other literature with more common search terms, which also don´t exclude the oblate part of molecules? Spheroid might also be a good search term.
– Karl
May 27 '20 at 7:00
• @Karl, ok, I see. Sorry, I was not aware that "ovality" is not such a common term. I will update the question. May 27 '20 at 8:04