Fig. 4: Computed CD spectra for chirality determination.

a Comparing CD spectra of the related Au138 clusters obtained by simplified time-dependent density functional theory (STDDFT) formalism and PBE/SVP level of theory. For the Au138(SH)48 cluster with a Th symmetry, H atoms were placed on preserving the symmetry of the remaining Au138S48 fragment. For the other two clusters, geometry optimizations were performed for the ligands without any constraints on symmetry. All the clusters were generated from the crystal structure of Enantiomer 2. b Mirror-image CD spectra of Au138(SR)48. The optimized enantiomeric structures are depicted in greater detail in Supplementary Fig. 17. Source data are provided as a Source Data file.