A Python package for construction and analysis of crystal quotient graphs.

• NumPy
• ASE
• NetworkX 2.5

$ python setup.py install

Currently, there are two scripts in test/: analyze.py and testopt.py.

analyze.py can compute dimensions and multiplicities for all the components in the given structure.

$ python analyze.py <StructureFile> <BondRatio>

StructureFile should be supported by ASE. BondRatio is the criterion to connect atoms. The default value is 1.1.

opt.py firstly finds the optimal quotient graph for the configuration with given coordination numbers (using the method proposed in https://link.aps.org/doi/10.1103/PhysRevB.97.014104). Then the script optimizes the atomic positions and lattice to make the structure fitted to the quotient graph.

$ python opt.py <StructureFile> <Embed>

Embed decides whether the quotient graph is embeded into real space to generate initial structures. The default value is 0 (do not embed).

The structure files are in test/.

The structure COD_7027514.cif contains 2D, 1D, and 0D components.

$ python analyze.py COD_7027514.cif
number of bonds: 80
Number of parallel edges: 0
Number of compenents: 7
Component       Dimension
1               2
2               1
3               1
4               0
5               0
6               0
7               0
Max Dimension: 2

Calculating Multplicities...
Component       Multiplicity
1               1
2               1
3               1
4               1
5               1
6               1
7               1

The structure Cu2O.cif contains two translationally equivalent but disconnected subnets, so its multiplicity is 2.

$ python analyze.py Cu2O.cif
number of bonds: 8
Number of parallel edges: 0
Number of compenents: 1
Component       Dimension
1               3
Max Dimension: 3

Calculating Multplicities...
Component       Multiplicity
1               2

$ python opt.py rand_1.cif
edge ratios: min: 1.3016713493158165, max: 1.8759146848507082, mean: 1.5974768198995881
Optimize the structure using methods in ASE:
          Step     Time          Energy         fmax
graphOpt:    0 20:19:22       17.854404       48.6020
graphOpt:    1 20:19:22        2.999464       16.4721
graphOpt:    2 20:19:23        0.087089        1.2450
graphOpt:    3 20:19:23        0.041000        0.8320
graphOpt:    4 20:19:23        0.006525        0.3127
graphOpt:    5 20:19:23        0.000692        0.1032
graphOpt:    6 20:19:23        0.000000        0.0000
Last loss function: 0.0

rand_1.cif is a random carbon structure. The shortest C-C distance is 1.97 A, which is larger than the typical C-C bond length. In opt.py, coordination numbers of all the atoms are set as 4. The newly generated file end.vasp is the final structure, in which all the coordination numbers become 4 after optimization.

If you are referencing Pycqg in a publication, please cite the following paper:

• Gao, H., Wang, J., Guo, Z. et al. Determining dimensionalities and multiplicities of crystal nets. npj Comput Mater 6, 143 (2020). https://doi.org/10.1038/s41524-020-00409-0

Pycqg is distributed under the terms of the GNU Lesser General Public License 3.