Optical spectra of plasmonic Au clusters and nanoparticles obtained using the TDDFT+U method

The description of localized surface-plasmon resonances (LSPRs) in gold clusters has been a long-standing problem for quantum calculations, complicated by the presence of the filled d shell close to the Fermi energy and the resulting strong influence of interband transitions in the visible spectral range. A full quantum-mechanical description that represents the atomistic structure and treats all relevant electrons at the same footing is needed. In this study, we demonstrate that a Hubbard U correction to the 5d electrons in the real-time TDDFT+U approach is able to model the optical response of plasmonic Au clusters and nanoparticles. The corrected LSPR energies show good agreement with "semi-quantal" calculations known to provide reliable plasmon energies, as well as with measurements when the matrix-induced/surface-induced red shifts are taken into account. Our findings establish the RT-TDDFT+U method as a valuable approach for modeling the optical properties of plasmonic Au clusters and nanoparticles, enabling calculations of clusters of up to 923 atoms, representing a 3 nm diameter nanoparticle.