Fig. 5

Comparison of the spectrum of vibrational frequencies, or density of states (vDOS) of C₁−Au₆₀, I−Au₆₀, and I−Au₇₂ clusters. a For the compact structure (see Fig. 1h), the vDOS resembles that of the incipient 3D lattice of bulk FCC gold, i.e., acoustic (to ~80 cm⁻¹) and optical (>80 cm⁻¹) phonons. b, c The spectra of the chiral-icosahedral shells (Fig. 1e, g) differ qualitatively from the spectra of the compact structure, showing a quasi-continuum of shape-deformation modes in the 20–60 cm⁻¹ range, and then a highly structured pattern of higher frequency modes reflective of the quasi-2D lattice (including its topological defects). The extreme simplicity (regularity or sparseness) in the case of I−Au₆₀, in b, reflects the 60-fold equivalence of all atomic sites. The large solitary spike, at the highest frequency ~190 cm⁻¹, provides a quantitative measure of its enhanced rigidity