Effects of shape and dopant on structural, optical absorption, Raman, and vibrational properties of silver and copper quantum clusters：A density functional theory study

We investigate the effects of shape and single-atom doping on the structural, optical absorption, Raman, and vibrational properties of Ag₁₃, Ag₁₂Cu₁, Cu₁₃, and Cu₁₂Ag₁ clusters by using the (time-dependent) density functional theory. The results show that the most stable structures are cuboctahedron (COh) for Ag₁₃ and icosahedron (Ih) for Cu₁₃, Ag₁₂Cu _1core, and Cu₁₂Ag _1sur. In the visible-near infrared optical absorption, the transitions consist of the interband and the intraband transitions. Moreover, red shifts are observed as follows: 1) clusters change from Ag₁₂Cu _1core to Ag₁₃ to Ag₁₂Cu _1sur with the same motifs, 2) the shapes of pure Ag₁₃ and Ag₁₂Cu _1core clusters change from COh to Ih to decahedron (Dh), 3) the shape of Ag₁₂Cu _1sur clusters changes from Ih to COh to Dh, and 4) the shapes of pure Cu₁₃ and Cu₁₂Ag₁ clusters change from Ih to Dh to COh. All of the Raman and vibrational spectra exhibit many significant vibrational modes related to the shapes and the compositions of the clusters. The ranges of vibrational spectra of Ag₁₃, Ag₁₂Cu₁ or Cu₁₃, and Cu₁₂Ag₁ clusters become narrower and the vibrational intensities increase as the shape of the clusters changes from Ih to Dh to COh.