We study the quantum plasmonic features of gold and silver nanoparticles using TD-DFT+TB, a new density functional theory approach to the calculation of excited states, which combines a full DFT ground state with tight-binding approximations in the linear response calculation. In this framework, the optical properties of closed-shell Ag, Au and bimetallic Ag–Au nanoparticles with tetrahedral symmetry (with 20, 56, 120, and 165 atoms) and icosahedral structure (with 13, 55, and 147 atoms) were obtained and compared to full linear response time-dependent density functional theory (TD-DFT) as a reference and also to time-dependent density functional based tight binding (TD-DFTB) as a low-cost alternative approach. We find an excellent agreement of TD-DFT+TB calculated absorption spectra with the TD-DFT reference with errors less than 0.15 eV in peak positions, while TD-DFTB shows larger errors of about 1 eV. The computational cost for the ground state calculation is identical for TD-DFT and TD-DFT+TB, but the excited state calculation becomes about a hundred times faster when applying the TB approximation and is then almost negligible for the overall timing of the calculation. In contrast to TD-DFTB, which can only be applied to element combinations for which a suitable DFTB parametrization is available, TD-DFT+TB can be applied to any combination of elements. To assess the accuracy of TD-DFT+TB for different combinations of atoms, the plasmonic properties of bimetallic clusters with different ratios of Ag and Au atoms were obtained and the trend of energy and intensity reproduced in good agreement with TD-DFT, which is not possible using TD-DFTB with standard parameter sets.

The unique plasmonic character of silver and gold nanoparticles has a wide range of applications, and tailoring this property by changing electronic and geometric structures has received a great deal of attention. Herein, we study the role of the quantum properties in controlling the plasmonic excitations of gold and silver atomic chains and rods. The influence of relativistic effects, scalar as well as spin–orbit, on the intensity and energy of plasmonic excitations is investigated. The intensity quenching and the red shift of energy in the presence of relativistic effects are introduced via the appearance of d orbitals directly in optical excitations in addition to the screening of s-electrons by mixing with the occupied orbitals. For the linear gold system, it will be demonstrated that by increasing the length the relativistic behavior declines and the contribution of d orbitals to the plasmonic excitations evidently decreases. Furthermore, silver atoms are doped in gold chains and rods (with two different arrangements) to realize how gold–silver interactions decrease the relativistic effects and enhance the intensity of collective excitations. Finally, to strengthen the plasmonic behavior of gold, the elongation of chain and doping with suitable atoms such as silver (with the classical plasmonic behavior) can be introduced as the manipulating ways to control the influence of scalar-relativistic and spin–orbit effects and, consequently, reinforce the plasmonic properties.

In the new field of quantum plasmonics, plasmonic excitations of silver and gold nanoparticles are utilized to manipulate and control light–matter interactions at the nanoscale. While quantum plasmons can be described with atomistic detail using Time-Dependent Density Functional Theory (DFT), such studies are computationally challenging due to the size of the nanoparticles. An efficient alternative is to employ DFT without approximations only for the relatively fast ground state calculations and use tight-binding approximations in the demanding linear response calculations. In this work, we use this approach to investigate the nature of plasmonic excitations under the variation of the separation distance between two nanoparticles. We thereby provide complementary characterizations of these excitations in terms of Kohn–Sham single–orbital transitions, intrinsic localized molecular fragment orbitals, scaling of the electron–electron interactions, and probability of electron tunneling between monomers.

The TD-DFT+TB approach is shown to efficiently describe large atomistic models of plasmonic nanocrystals protected with ligands.