Chiral indices of crystalline surfaces as a measure of enantioselective potential

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, I_C (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 I_C=0, but we find that surfaces of intrinsically chiral crystals [e.g., quartz (1 0 1)] may also display I_C=0, depending on the surface atoms selected. Of 14 surfaces modeled, I_C is greatest for chiral faces of achiral crystals: the (2 1 4) scalenohedral faces of calcite (I_C=2.60 Å), the (1 1 0) faces of diopside (I_C=1.54 Å), and the (6 4 3) faces of FCC metals such as copper and platinum (I_C=1.29 Å).