Converging TDDFT calculations in 5 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 re-tuning the empirical scaling factor and the angular momenta of a minimal auxiliary basis. The final preconditioner produced includes up to $d$-functions in the auxiliary basis and is named "rid". The rid preconditioner converges excitation energies and polarizabilities in 5-6 iterations on average, a factor of 2-3 faster than the conventional diagonal preconditioner, without changing the converged results. Thus, the rid preconditioner is a broadly applicable and efficient preconditioner for TDDFT calculations.