# Are there computational methods for the determination of the point group symmetry of a molecule of a given geometry?

I am aware that there exists a flowchart about how to determine the point group of a molecule with a given geometry, such as given in the diagram available in ChemLibre Texts. If we just look at the geometry visually or having it pictured in mind, it wouldn't be difficult to follow this flowchart. But I would like to automate this procedure inside my electronic-structure code.

Is there a well-established computational method to determine, e.g. how many rotational axes of symmetry a molecule has? Is it possible to perform this identification generally, that is, in a way in which I don't need to write a function or routine dedicated for each symmetry type? References are much appreciated.

• I found a reference here pubs.acs.org/doi/10.1021/ci990322q, I haven't read it but although the title says 'simple' I've heard many anecdotes including here that symmetry is not implemented correctly i.e. it is hard to do right. – Cody Aldaz Jul 28 '20 at 4:18
• In your linked Quora question, the deficiency in symmetry handling refers to Orca. Or does Orca use the method in the cited paper? – nougako Jul 28 '20 at 4:49
• There is a big difference between determining the point group and actually exploiting it in the evaluation of the integrals etc. My last knowledge (which is 6 years old) was that ORCA made no attempt at that exploitation, but that may have changed in the meantime. As an aside, while symmetry can be useful, almost all of biochemistry and a lot of other chemistry is actually $C_1$. – TAR86 Jul 28 '20 at 5:19

In order to get this question answered there are a variety of algorithms for determining symmetry.

Here is what I've found

Simple Algorithms for Determining the Molecular Symmetry -- not open access

New computer program to calculate the symmetry of Molecules -- open access and with some matlab code snippets

I've also found this link to a Researchgate page

This lists software that can identify the symmetry for you including:

1. chemcraft
2. GaussView
3. symmol
4. 3dmolsym
5. Jmol

Symmol was linked to the source code so if you can read Fortran you could translate their algorithms to suit your own needs.

• Shall CFOUR, MOLPRO, MRCC and most other quantum chemistry codes be added to that list too? – Nike Dattani Jul 28 '20 at 19:57
• They could be, I think the ones in the list are stand alone tho, so that's why I didn't bother mentioning others – Cody Aldaz Jul 28 '20 at 19:59