Tube-like Gold Clusters M₂@Au₁₇^<i>q</i> (M = W, Mo; <i>q</i> = 0, ±1): Structure, Electronic Property, and Optical Nonlinearity

Density functional theory (DFT) calculations are carried out to determine the geometries and electronic and nonlinear optical (NLO) properties of the doubly doped gold clusters in three charge states M₂ @ Au₁₇ ^<i>q</i> with M = W, Mo and <i>q</i> = 0, ±1. At their lowest-lying equilibrium structures, the impurities that are vertically encapsulated inside a cylindrical gold framework, significantly enhance the stability and modify properties of the host. The presence of M₂ units results in the formation of a tube-like ground state, which is identified for the first time for gold clusters. Having 30 itinerant electrons, the electron shell of M₂@Au₁₇ ^- can be described as 1S²1P⁶1D¹⁰2S²{1F _{<i>xz</i> ²} ²1F _{<i>yz</i> ²} ²}1F _{<i>z</i> ³} ²{1F _<i>xyz</i> ²1F _{<i>z</i>(<i>x</i> ²-<i>y</i> ²)} ²}{1F _{<i>y</i>(3<i>x</i> ² <i>-y</i> ²)},1F _{<i>x</i>(<i>x</i> ² <i>-</i>3<i>y</i> ²)}}. The species is thus stabilized upon doping, but it is not a magic cluster. The optical transitions are shifted to the lower-energy region upon doping Mo and W atoms into Au₁₇ ^<i>q</i> . The static and dynamic NLO properties of M₂@Au₁₇ ^<i>q</i> are also computed and compared to those of the pure Au₁₉ ^<i>q</i> (having the same number of atoms) and an external reference molecule, i.e., para-nitroaniline (<i>p</i>-NA). For hyperpolarizabilities, the doped clusters possess smaller values than those of their pure counterparts but much larger values than the <i>p</i>-NA. Of the doubly doped systems, the neutral M₂@Au₁₇ exhibits particularly high first and second hyperpolarizability tensors. The doped cluster units can also be used as building blocks for the design of gold-based nanowires with outstanding electronic and optical characteristics.