Homometric structures

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.

See also

• Patterson function
• Arthur Lindo Patterson