Comparison and convergence of optical absorption spectra of noble metal nanoparticles computed using linear-response and real-time time-dependent density functional theories

The real-time time-dependent density functional theory (RT-TDDFT) is rapidly gaining prominence as an alternative approach to capture optical properties of molecular systems, which warrants the necessity to benchmark the traditional linear response (LR) method and the RT approach. We calculate the absorption spectra of noble metal nanoparticles with a variety of sizes and shapes to demonstrate the consistency of the two methods over a broad range of energy. The RT spectrum obtained using a grid-based basis set with pseudopotentials achieves results in good agreement with the LR spectrum obtained with large QZ4P atom-centered basis sets. Factors that lead to convergence of the spectra are considered. In addition, the real-time variation of the electron density is visualized to show the collective oscillation of electron density for the plasmon modes of noble metal nanoparticles. The RT approach is most useful when calculating wide absorption spectra of larger gold or silver nanoparticles.