Geometric Quantification of Chirality in Ligand-Protected Metal Clusters

Abstract

Chirality has been found as a relevant property of nanomaterials, including ligand-protected metal clusters and nanorods. This property not only is crucial in nanotechnology developments related to asymmetric catalysis and chiroptical phenomena but also generates fundamental questions on the existence of chirality at the nanoscale. In fact, X-ray total structure determination, electron diffraction studies, NMR, and circular dichroism spectroscopies as well as theoretical calculations performed on gold clusters protected with thiolate or phosphine ligands have confirmed the existence of chiral structures in the size range of 18–144 Au atoms. In this work, we realize a comparative analysis of the degree or amount of chirality existing in chiral ligand-protected gold clusters (LPGC), through a geometric quantification, using the Hausdorff chirality measure (HCM). The calculated HCM values provide a quantitative framework to compare, classify, and gain insight into the origin of chirality. Interestingly, thes...