“…It is shown that different doping atom types and different atomic numbers have different effects on the planar structure of small-sized gold clusters. Our previous work on bromine-atom-doped gold clusters confirmed that, for the ground state clusters, the transition from 2D to 3D structures starts with Au 5 Br ( Zhu et al., 2021 ), while other studies have shown that Au 10 Re ( Sui et al., 2014 ), Au 8 Be ( Chen et al., 2011 ), Au 4 La ( Zhao et al., 2010 ), Au 3 Bi ( Zhang et al., 2019 ), Au 3 C ( Yan et al., 2013 ), Au 9 Mn ( Zhang et al., 2012 ), Au 8 V ( Nhat and Nguyen, 2011 ), Au 11 Sc ( Ge et al., 2010 ), Au 3 Ti, Au 5 Ti and Au 7 Ti ( Toprek and Koteski, 2016 ) are the critical sizes for such 3D "roll-up." The study of doped gold clusters with two same atoms has also been studied, for example, Ca 2 Au n , Be 2 Au n , Cu 2 Au n , Ag 2 Au n , Si 2 Au n , P 2 Au n , Na 2 Au n , Mg 2 Au n .…”