Tube-like Gold Clusters M<sub>2</sub>@Au<sub>17</sub><sup><i>q</i></sup> (M = W, Mo; <i>q</i> = 0, ±1): Structure, Electronic\nProperty, and Optical Nonlinearity

Density functional\ntheory (DFT) calculations are carried out to\ndetermine the geometries and electronic and nonlinear optical (NLO)\nproperties of the doubly doped gold clusters in three charge states\nM<sub>2</sub> @ Au<sub>17</sub><sup><i>q</i></sup> with M = W, Mo and <i>q</i> =\n0, ±1. At their lowest-lying equilibrium structures, the impurities\nthat are vertically encapsulated inside a cylindrical gold framework,\nsignificantly enhance the stability and modify properties of the host.\nThe presence of M<sub>2</sub> units results in the formation of a\ntube-like ground state, which is identified for the first time for\ngold clusters. Having 30 itinerant electrons, the electron shell of\nM<sub>2</sub>@Au<sub>17</sub><sup>–</sup> can be described as 1S<sup>2</sup>1P<sup>6</sup>1D<sup>10</sup>2S<sup>2</sup>{1F<sub><i>xz</i><sup>2</sup></sub><sup>2</sup>1F<sub><i>yz</i><sup>2</sup></sub><sup>2</sup>}1F<sub><i>z</i><sup>3</sup></sub><sup>2</sup>{1F<sub><i>xyz</i></sub><sup>2</sup>1F<sub><i>z</i>(<i>x</i><sup>2</sup>–<i>y</i><sup>2</sup>)</sub><sup>2</sup>}{1F<sub><i>y</i>(3<i>x</i><sup>2</sup><i>–y</i><sup>2</sup>)</sub>,1F<sub><i>x</i>(<i>x</i><sup>2</sup><i>–</i>3<i>y</i><sup>2</sup>)</sub>}. The species\nis thus stabilized upon doping, but it is not a magic cluster. The\noptical transitions are shifted to the lower-energy region upon doping\nMo and W atoms into Au<sub>17</sub><sup><i>q</i></sup>. The static and dynamic NLO properties of\nM<sub>2</sub>@Au<sub>17</sub><sup><i>q</i></sup> are also computed and compared to those\nof the pure Au<sub>19</sub><sup><i>q</i></sup> (having the same number of atoms) and an external\nreference molecule, i.e., para-nitroaniline (<i>p</i>-NA).\nFor hyperpolarizabilities, the doped clusters possess smaller values\nthan those of their pure counterparts but much larger values than\nthe <i>p</i>-NA. Of the doubly doped systems, the neutral\nM<sub>2</sub>@Au<sub>17</sub> exhibits particularly high first and\nsecond hyperpolarizability tensors. The doped cluster units can also\nbe used as building blocks for the design of gold-based nanowires\nwith outstanding electronic and optical characteristics.