Bulk-like Compressibility of the Au-Au Metallic Bond in the Atomically Precise $\mathrm{Au}_{25}$ Cluster

Abstract

We present a high-pressure single-crystal X-ray diffraction study of the atomically precise $\mathrm{Au}_{25}(\mathrm{PET})_{18}^{q}$ cluster ($q=-1,0$) up to 10 GPa under strictly hydrostatic conditions. Our crystallographic analysis provides direct evidence for the pressure-induced phase transitions previously suggested by spectroscopic studies. Structural refinements reveal that the cluster accommodates compression through the reorganization of the flexible ligand shell and secondary distortions of the staple motifs, while the $\mathrm{Au}_{13}$ icosahedral core remains intact. Notably, the internal Au-Au distances exhibit a monotonic contraction that quantitatively mirrors the compressibility of bulk gold. This invariant rigidity at the sub-nanometer scale demonstrates that the fundamental stiffness of the metallic bond is preserved regardless of size. Our findings reconcile previous contradictions in the elasticity of metal nanostructures by isolating the intrinsic mechanical response of the gold kernel from extrinsic structural and experimental artifacts.