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The plasmon excitations in small metal-atom clusters have been extensively investigated in recent years, and most of the efforts are focused on freestanding clusters. However, freestanding clusters are inherently unstable and have to be stabilized by interacting with a two-dimensional or three-dimensional substrate; hence, the effects of substrates should be taken into account in the calculations of electronic excitations. With the use of the random-phase approximation, we extensively investigate the polarization effects of substrates on the plasmon resonances of small Na chains on Si surfaces. Our results show that due to the polarization effects of Si substrates, the redshifts of plasmon peaks appear in both longitudinal and transverse absorption spectra, and the strengths of the main plasmon resonant peaks have some variation; in particular, the strength gets a very large enhancement when the external field is applied in the direction perpendicular to the surface of Si. In addition, we study the formation mechanism of the end mode and the central mode of transverse-plasmon excitations and show that the two modes are caused by electron-electron interactions, which reflects the collective excitations induced by the interactions.

Impurity doping in atomic chains provides a potentially effective way to adjust its electronic excitation. Recently, it was reported that doping transition-metal atoms into small gold atomic chains induces a local dipolar plasmon mode which corresponds to charge oscillations around the impurity atoms, whereas our studies indicate that such a local mode does not exist. In this paper, using time-dependent density functional theory, we extensively investigate the excitation properties of plasmons in doped gold nanostructures. Our results show that all the plasmon peaks are affected by impurity, and the corresponding plasmon modes mutate into different forms compared to pure gold atomic chains. The propagation of charge oscillations in some plasmon modes is blocked in the doped chain, so that the charges oscillate mainly in half of the chain. Furthermore, the $5d$ electrons of gold atoms reduce the energies and intensities of plasmon resonances for both the transverse and longitudinal modes, and cause the end and center features of the induced charge distributions to nearly vanish in the transverse plasmon modes.

In the presence of a nonlocal potential in molecular device systems, generally the charge conservation cannot be satisfied, and in literatures the modifications of the conventional definition of current were given to solve this problem. We demonstrate that, however, the nonconservation is not due to the invalidation of the conventional definition of current, but originates respectively from the improper approximations to electron-electron interactions and the inappropriate definition of current using pseudo wave functions in pseudopotential implementations. In this work, we propose a nonlocal-potential formulation of the interactions to fulfill the charge conservation and also give a discussion about the calculation of current when the pseudopotential is involved. As an example of application of our formulation, we further present the calculated results of a double-barrier model., Comment: 8 pages, 6 figures