Quantum Mechanical Identification of Quadrupolar Plasmonic Excited States in Silver Nanorods

Quadrupolar plasmonic modes in noble metal nanoparticles have gained interest in recent years for various sensing applications. Although quantum mechanical studies have shown that dipolar plasmons can be modeled in terms of excited states where several to many excitations contribute coherently to the transition dipole moment, new approaches are needed to identify the quadrupolar plasmonic states. We show that quadrupolar states in Ag nanorods can be identified using the semiempirical INDO/SCI approach by examining the quadrupole moment of the transition density. The main longitudinal quadrupolar states occur at higher energies than the longitudinal dipolar states, in agreement with previous classical electrodynamics results, and have collective plasmonic character when the nanorods are sufficiently long. The ability to identify these states will make it possible to evaluate the differences between dipolar and quadrupolar plasmons that are relevant for sensing applications.