Overcoming Computational Bottlenecks in Quantum Hydrodynamics: A Volume-Based Integral Formalism for Spherical Nanoparticles.

Mesoscopic models of the optical response of metals have emerged as fundamental building blocks in quantum plasmonics, in principle overcoming the computational bottlenecks of ab initio techniques by implementing aspects of the atomistic description of the metal in otherwise classical calculations. Nonetheless, even these approaches are eventually hindered by demanding computations due to a sophisticated material response. Here, this issue is addressed for the advanced self-consistent hydrodynamic Drude model (SC-HDM), which captures both nonlocal electron dynamics and electron spill-out, through a volume integral equation (VIE) method. Adopting an IE-based method shifts perspective from the commonly employed differential equation (DE)-based ones, demonstrating significant computational efficiency. The VIE approach is a valuable methodological scaffold: it addresses SC-HDM and simpler models, but can also be adapted to more advanced ones. For spherical nanoparticles (NPs), using the inherent symmetries, similar performance for three increasingly complicated material models is achieved, breaking the taboo that increased sophistication in the material response requires taxing simulations. Mesoscopic material-response functions can be readily extracted from the VIE implementation, thus circumventing the need for lengthy microscopic calculations. This method opens a new way of modeling quantum hydrodynamic NPs and will serve as an essential benchmarking tool for recipes addressing more complicated geometries.