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Homometric structures

In chemistry and crystallography, crystal structures that have the same set of interatomic distances are called homometric structures. Homometric structures need not be congruent. Homometric crystal structures produce identical diffraction patterns; therefore, they cannot be distinguished by a diffraction experiment.

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May 27, 2026
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In chemistry and crystallography, crystal structures that have the same set of interatomic distances are called homometric structures.1 Homometric structures need not be congruent (that is, related by a rigid motion or reflection). Homometric crystal structures produce identical diffraction patterns; therefore, they cannot be distinguished by a diffraction experiment.

Recently, a Monte Carlo algorithm was proposed to calculate the number of homometric structures corresponding to any given set of interatomic distances.2

  • Example of two homometric structures (top) formed by the convolution between two non-centrosymmetric structures (bottom) with different orientations.
    Example of two homometric structures (top) formed by the convolution between two non-centrosymmetric structures (bottom) with different orientations.
See also

See also

References

References

  1. Patterson, A.L. (1939). "Homometric Structures". Nature. 143 (3631): 939–940. Bibcode:1939Natur.143..939P. doi:10.1038/143939b0. S2CID 4122325.
  2. Gommes C.J.; Jiao Y; Torquato S (2012). "Density of States for a Specified Correlation Function and the Energy Landscape". Phys. Rev. Lett. 108 (8) 080601. arXiv:1201.1142. Bibcode:2012PhRvL.108h0601G. doi:10.1103/PhysRevLett.108.080601. PMID 22463509. S2CID 166914.