In my program Chemcraft, a popular tool is the “Set point group” utility: it symmetrizes the molecule according to a specified point group, and then the symmetry of the molecule is correctly recognized by a program like Gaussian, and this makes the computation faster. Maybe chemists dealing with crystals need something similar?

If I understand correctly, the routine for determining periodic boundary conditions through 3 lattice vectors does not fully describe the crystal symmetry, for example in graphene only 1 symmetry unique carbon atom exists while with cell parameters a=2.4,..beta=90, gamma=120 the program thinks that there are two carbons in the primitive cell. Currently the programs like VASP do not use these additional symmetry constraints? If, nevertheless, they use them, how they can be specified in the input file, and do you think that automatic determination of these constraints by Chemcraft will be useful for its users?

I have found here that the Avogadro and Pymol programs can do that, maybe I will be able to implement a more flexible tool in Chemcraft, and still it is unclear for me, whether these routines in Avogadro and PyMol determine the "full" or "partial" symmetry as I described above.

  • $\begingroup$ Related Physics SE regarding confusion about the unit/primitive cell of graphene. $\endgroup$
    – Tyberius
    Nov 13, 2023 at 17:39
  • $\begingroup$ Hello, I didn't fully understand the reference - it is said that in graphene the green and red atoms are not identical? $\endgroup$
    – Linkey
    Nov 13, 2023 at 19:35
  • $\begingroup$ @Linkey Author of the answer Tyberius linked here. There are two atoms in graphene’s primitive cell. In the photo in the answer, one carbon atom is marked green and the other red. One sits on the lattice point, and the other sits some distance d away from it within the primitive cell. $\endgroup$
    – Roy
    Nov 14, 2023 at 9:29
  • $\begingroup$ If the red and greem carbon atoms are really not identical in the crystal, this means that they have, lets say, different electron densities around them? $\endgroup$
    – Linkey
    Nov 14, 2023 at 11:31

1 Answer 1


Determining space group symmetry is really useful when going between a CIF (which typically only includes the symmetry-unique atoms) and a calculation (which typically includes all atoms in the unit cell).

Many programs, including Avogadro, use the excellent spglib library to determine space groups, generate a primitive unit cell from a "filled" cell, etc. It's very similar to using the various point-group detection and symmetrization routines.

There are a few pitfalls - for one, space group symbols are less standardized than point group symbols. In general, Avogadro 2 uses the "Hall number" internally, which indicates not only the space group symbol, but the setting. This has helped enormously. Even so, I've come across a few weird CIF files recently.

You asked about "full" or "partial" symmetry. I think you mean converting from a primitive to a conventional unit cell and vice versa? Yes, this is an important task (e.g., opening a CIF for silver will only have one atom).

  • $\begingroup$ I didn't fully understand your quesion; however I checked a cif file of graphene and I found that the asymmetric unit contains one carbon atom, while the unit cell contains two carbon atoms. So in "full" symmetry all carbon atoms are identical, while in "partial" symmetry there are two types of carbons. Is this correct? Then, can we say that the space group means the "partial" symmetry, while the crystal system (is it called "singony"?) means the "full" symmetry? $\endgroup$
    – Linkey
    Nov 13, 2023 at 19:41
  • $\begingroup$ I'm not fully understanding your question. A space group implies a particular crystal system. There can sometimes be multiple settings for the same crystal. For example crystallography.net/cod/1200018.html includes one atom in the unit cell for graphite. crystallography.net/cod/1200017.html contains two atoms. You can use JSmol or Mercury to generate larger packings to see they're more-or-less identical. $\endgroup$ Nov 13, 2023 at 21:58
  • $\begingroup$ I checked the cif files provided at this URLs, the first contains two carbon atoms in unit cell while the second contains four carbons. Why at the pictures there is only one carbon atom at first and two at second? Or maybe my visualizer does something wrong? $\endgroup$
    – Linkey
    Nov 14, 2023 at 4:45
  • $\begingroup$ My question was as follows: I suppose that the crystal systems can include symmetry constraints like rotating the atoms around a point, and the space group specified by a,b,c,alpha.. does not describe them? I called using these constraints the "full" symmetry. $\endgroup$
    – Linkey
    Nov 14, 2023 at 4:47
  • $\begingroup$ a, b, c, alpha, beta, gamma do not define a space group. They define lattice parameters that make up a crystal system. Of course it's much better to define the lattice using the 3 lattice vectors or a 3x3 matrix. The space group implies the type of crystal system as well as the transformations / rotations involved in generating any symmetry-defined atoms. $\endgroup$ Nov 14, 2023 at 20:07

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .