Quantitative Symmetry and Chirality of the Molecular Building Blocks of Quartz

We introduce the use of the concept of continuity in symmetry and chirality as a novel descriptor of the structure of the building blocks of materials. These measures are of global nature, and take into account all angles and bond lengths of the molecular building blocks. The particular example we have selected for a detailed analysis is (low) quartz. All of its main building blocks, namely the elementary SiO 4 tetrahedron, the Si(OSi) 4 unit, the silicon atoms tetrahedron SiSi 4, and six of its internal helical structures, were investigated in detail as to their degree of chirality, tetrahedricity content, degree of distortion from C 2 -symmetry, and more. Specific chirality is defined and its value determined for low and high quartz and for cristobalite. The most chiral unit within quartz was found to be a four-SiO 4 segment helix.