Collectivity of plasmonic excitations in small sodium clusters with ring and linear structures

The collectivity of the electronic motion in finite systems is studied by using both the linear response density functional theory (LRDFT) and the collectivity index defined by the transition density matrix. We demonstrate a collectivity analysis on the size-dependent peaks of electronic excitations of small sodium clusters (rings and linear chains). We find the excitation-mode dependence of the collectivity and large collectivities for the higher-energy plasmonic excitations. The collectivity analysis also clarifies the existence of the nondipolar collective motion at the energies very close to the higher-energy plasmonic excitations. The importance of the nondipolar motion is pointed out in light of nano-optics.