The shape and symmetry of polyhedra are two key notions commonly used in the description of the principal structural features of individual molecules and solid-state structures. The establishment of stereochemical rules that rationalize the adoption of a certain structure by a set of atoms or molecules is often based on the comparison of this structure with a reference archetypical structure with a higher symmetry. For this purpose it is very useful to dispose of mathematical tools such as continuous shape and symmetry measures (CShM and CSM, respectively) that allow the quantification of the shape and symmetry content for a given polyhedral structure or some of its representative fragments. After a brief introduction to the mathematical formalism of CShMs and CSMs, in this communication I will discuss how temperature lowers the symmetry in the C4H4, B6H6, C8H8, B12H12, and C20H20 molecules with cages having the shape of platonic polyhedra. In a second part of the communication I will show how changes in temperature, pressure and the presence of defects affect the local tetrahedral symmetry in simple solids with the diamond structure (carbon, silicon, and germanium) as well as in other lower symmetry tetrahedral polymorphs of carbon and amorphous phases of carbon and silicon.

Effect of temperature on the symmetry of molecules and solids: A continuous symmetry measures study

254th National Meeting (2017)

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