(Color online) Structures of candidates for the lowest-energy cluster of . The energy values (in eV) beneath each isomer are the relative energy with respect to the lowest-lying isomer calculated at the corresponding level of DFT. The energy values in black color are based on the PBE/DNP level of theory (Ref. 32). The energy values in parentheses/blue color are based on the PBEPBE/LANL2DZ level of theory (Ref. 33), while the energy values in bracket/red color are based on the single-point-energy calculation at the level of theory (Ref. 33).
(Color online) Histograms of the number of low-energy isomers vs the relative energies (with respect to the lowest-energy isomer calculated at the PBE/DNT level of theory) for , , and . The range of relative energy is set from .
(Color online) A typical spherical-like hollow-cage structure and shell-like flat-cage structure . A flat cage is defined such that besides the overall shape of the cluster is shell-like (or oblate in shape), the Au–Au lines (green lines) connecting through the central region of the cage (in the short-axis direction) are in the range of . Thus, a flat cage may accommodate a small atom such as a hydrogen atom but cannot accommodate another gold atom without major structural distortion. A hollow cage is defined such that the Au–Au lines (green lines) connecting through the central region of the cage are all greater than . Thus the hollow cage can accommodate another gold atom.
Electronic energies (in a.u.) of the leading candidates for the lowest-energy neutral gold clusters calculated at PBEPBE/LANL2DZ and levels of theory. The boldfaced energy values highlight the lowest-energy isomers which can be dependent on the level of theory.
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