Chiral crystal surfaces lack mirror or glide plane symmetry. Nevertheless, some chiral surfaces deviate more significantly from an achiral configuration, and thus possess greater enantioselective potential, than others. We describe a procedure to calculate chiral indices, IC (in Å), of any two-dimensional (2D) periodic atomic surface based on atomic displacements from ideal mirror or glide plane symmetry. We define a 2D unit cell parallel to the surface, identify coordinates of atoms associated with that surface unit cell, and employ minimization procedures to determine the positions and orientations of best-fit pseudo-mirror and pseudo-glide plane operators perpendicular to that surface. Achiral surfaces invariably have IC=0, but we find that surfaces of intrinsically chiral crystals [e.g., quartz (1 0 1)] may also display IC=0, depending on the surface atoms selected. Of 14 surfaces modeled, IC is greatest for chiral faces of achiral crystals: the (2 1 4) scalenohedral faces of calcite (IC=2.60 Å), the (1 1 0) faces of diopside (IC=1.54 Å), and the (6 4 3) faces of FCC metals such as copper and platinum (IC=1.29 Å).
- Chiral indices
- Crystalline surfaces
- Enantioselective potential
ASJC Scopus subject areas
- Process Chemistry and Technology
- Physical and Theoretical Chemistry