Suppose that I wanna make a program to predict possible forms of carbon's Allotropy.

My idea is to use a structure search program to generate a lot of structures and calculate the Gibbs free energy to determine the stability.

Is there some program available for this sort of job, and if so, is what I described computationally feasible?

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    $\begingroup$ Let me just state the obvious: since an almost infinite number of carbon allotropes exists (if we consider e.g. nanotubes with different chiralities), the task is definitely not feasible as a practical project unless you draw some boundaries on what you consider a new allotrope. Otherwise, software like USPEX (mentioned by Camps) is a good way to go. $\endgroup$
    – Greg
    Feb 15, 2022 at 3:00
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    $\begingroup$ It's even plausible that some unusually large-scale quantum effects (graphene sheets have quite unusual topological properties) will lead to a particular configuration of cross-links having completely different properties, and this will be both very costly to simulate and extremely hard to discover due to the vast space of possible variations. Mesoscopic physics is hard. $\endgroup$ Feb 15, 2022 at 10:35

2 Answers 2


One of the software I know is able to search/generate new structures is USPEX.

From their site, USPEX means:

USPEX (Universal Structure Predictor: Evolutionary Xtallography...and in Russian "uspekh" means "success" - owing to the high success rate and many useful results produced by this method) is a method developed by the Oganov laboratory since 2004. The problem of crystal structure prediction is very old and does, in fact, constitute the central problem of theoretical crystal chemistry. In 1988 John Maddox wrote that:

"One of the continuing scandals in the physical sciences is that it remains in general impossible to predict the structure of even the simplest crystalline solids from a knowledge of their chemical composition solids such as crystalline water (ice) are still thought to lie beyond mortals' ken".

USPEX code solves this problem and allows to predict crystal structure with arbitrary P-T conditions by knowing only chemical composition of the material. Nowdays, it is used by over 7600 researchers worldwide. The First Blind Test of Inorganic Crystal Structure Prediction shows that USPEX outperforms other methods in terms of efficiency and reliability. The method continues to be rapidly developed.

It is developed in Python but needs other codes to optimize/characterize the generated structures. Works with VASP, GULP, LAMMPS, QuantumEspresso and ABINIT and run in any Linux based system.


I will answer this from a "how much time does this cost" perspective. In general, I would say no we cannot predict all possible allotropes because there is always a chance that at higher pressure or higher temperature we form a new crystal. Even if we consider only a single finite temperature and pressure, there is no way to ensure that our unit cell in the calculation is large enough to show the true crystal structure for example. We can always make the cell larger or the true crystal may not even be periodic.

However, in general you should probably expect the simpler crystal structures to be the correct ones and this might not be a practical problem for practical research. This does not mean that we can predict all forms of a given material, even presumably simple ones containing a single element. In general, a scientifically informed guess does tend to allow us to predict the correct structure which is why codes such as USPEX are seen as a success.

  • $\begingroup$ "or the true crystal may not even be periodic." in which case you start running into "fun" results from computability theory (c.f. Wang tiles) $\endgroup$
    – TLW
    Feb 15, 2022 at 5:23

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