Optimized numerical Density Functional Theory calculation of rotationally symmetric jellium model systems

In real space Density Functional Theory calculations, the effective potential depends on the electron density, requiring self-consistent iterations and numerous integrals at each step, making the process timeconsuming. In our research, we propose an optimization method to expedite Density Functional Theory calculations for systems with large aspect ratios, such as metallic nanorods, nanowires, or Scanning Tunneling Microscope tips. This method focuses on employing basis set to expand the electron density, Coulomb potential, and exchange-correlation potential. By precomputing integrals and caching redundant results, this expansion streamlines the integration process, significantly accelerating Density Functional Theory computations. As a case study, we have applied this optimization to metallic nanorod systems of various radii and lengths, obtaining corresponding ground-state electron densities and potentials.