Converging Time-Dependent Density Functional Theory Calculations in Five Iterations with Minimal Auxiliary Preconditioning

Eigenvalue problems and linear systems of equations involving large symmetric matrices are commonly solved in quantum chemistry using Krylov space methods, such as the Davidson algorithm. The preconditioner is a key component of Krylov space methods that accelerates convergence by improving the quality of new guesses at each iteration. We systematically design a new preconditioner for time-dependent density functional theory (TDDFT) calculations based on the recently introduced TDDFT-ris semiempirical model by retuning the empirical scaling factor and the angular momenta of a minimal auxiliary basis. The final preconditioner produced includes up to