Magnus Method for Electronic Structure Calculations at Extreme Conditions

Quantum mechanical methods for High Energy Density (HED) applications solve the Kohn-Sham or Dirac-Kohn-Sham equations. At extreme conditions, numerical solvers are pushed to their limits at high energies or large volumes where the solutions are highly oscillatory, not solvable on a reasonable spatial grid using traditional methods. To address this, we employ the Magnus method to solve the radial Dirac equations efficiently and accurately for such conditions without any limitations. The ability to obtain solutions for complex energies allows us to use Green's function techniques which are then used to improve the stability and efficiency for highly oscillatory states of an atom-in-jellium code for a broad range of densities and temperatures, as needed in the construction of equations of state for HED conditions.