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Symmetry-based crystal structure enumeration in two dimensions



Evan Pretti, Vincent K. Shen, Jeetain Mittal, Nathan Mahynski


The accurate prediction of stable crystalline phases is a long-standing problem encountered in the study of conventional atomic and molecular solids as well as soft materials. One possible solution involves enumerating a reasonable set of candidate structures and then screening them to identify the one(s) with the lowest (free) energy. Candidate structures in this set can also serve as starting points for other routines, such as genetic algorithms, which search via optimization. Here, we present a framework for crystal structure enumeration of two-dimensional systems that utilizes a combination of symmetry- and stoichiometry-imposed constraints to compute valid configurations of particles that tile Euclidean space. With mild assumptions, this produces a computationally tractable total number of proposed candidates, enabling multicomponent systems to be screened by direct enumeration of possible crystalline ground states. The python code that enables these calculations is available at
Journal of Physical Chemistry A


Colloidal crystal, structure prediction, symmetry


Pretti, E. , Shen, V. , Mittal, J. and Mahynski, N. (2020), Symmetry-based crystal structure enumeration in two dimensions, Journal of Physical Chemistry A, [online],, (Accessed April 21, 2024)
Created March 16, 2020, Updated February 23, 2022