Accelerated Purification Using Generalized Nonpurifying Intermediate Functions for Large-Scale Self-Consistent Field Calculations

Purification is a widely used technique to calculate idempotent density matrices from a Hamiltonian in large-scale electronic structure calculations. However, the initial guess of a density matrix usually contains large errors, which require many iterations to remove them, using standard recursive schemes such as those derived by McWeeny or Holas. In this Letter, we propose a way to obtain a converged density matrix much more rapidly by removing the stability conditions that the functions have fixed points and vanishing derivatives at 0 and 1, assumptions usually made in most traditional purification methods. That is, by extending the recursive function space, which gives the approximated step function via the generalized nonpurifying intermediate functions, and optimizing them, we reduce the purification cost approximately by a factor of 1.5 compared to grand canonical purification algorithms for the linear alkanes, diamondoid, and a protein endothelin that has a very small band gap.