Continuum models for metal nanoparticles coupled to real-space real-time time-dependent DFT treatments of molecules

Plasmonic nanoparticle effects on nearby molecules can be treated within the Polarizable Continuum Model (PCM-NP). Numerically, PCM-NP relies on the Boundary Element Method (BEM), whereby nanoparticle polarization due to external electric fields is given in terms of point charges located on its meshed surface. Density Functional Theory (DFT) and time-dependent DFT descriptions for molecules can be performed using a real-space grid. However, combining the standard BEM of PCM-NP with a real-space quantum-mechanical treatment for molecules physisorbed on large nanoparticles (beyond ∼1 nm of radius) quickly faces memory bottlenecks for typical high performance computing architectures. In fact, the 3D spatial grid should be taken large enough to fit the entire NP, in order to interpolate the electrostatic potential at its surface. We propose a new BEM (dubbed dummy-surface BEM or ds-BEM, for short) to handle effectively PCM-NP calculations with a real-space grid and implement it in the widespread Octopus code. Our ds-BEM maps the electrostatic BEM problem from the actual physical interface at the nanoparticle surface to a compact surface around the molecule, which can be embedded in the small-sized real-space grid used in gas-phase calculations. To show the accuracy of ds-BEM results, we benchmark it against standard BEM for real-space and real-time nonequilibrium electronic dynamics of a prototypical system (namely, p-nitroaniline close to a small, gold nanoparticle) computed at the level of time-dependent density functional theory. Absorption and Raman spectra obtained from BEM and ds-BEM show remarkable agreement, opening up the extension of PCM-NP to all property simulations accessible via Octopus.