Efficient and Robust Ab Initio Self-Consistent Field Acceleration Algorithm Based on a Semiempirical Model Hamiltonian

A novel doubly iterative self-consistent field (SCF) approach using a semiempirical model Hamiltonian (denoted as the SMH algorithm) is proposed to accelerate the Hartree–Fock (HF) and density functional theory (DFT) calculations. This method first constructs the Fock matrix exactly in each SCF macroiteration, followed by a few SCF microiterations, where the Fock matrix is incrementally updated using an inexpensive semiempirical approximation. This leads to an improved wave function in each SCF macroiteration with minimal additional cost, and therefore a reduced number of exact Fock builds is required for SCF convergence. The SMH algorithm can be combined with conventional SCF convergence techniques such as level shifting, direct inversion in the iterative subspace (DIIS), and energy-DIIS (EDIIS). When integrated with DIIS, SMH enhances the convergence of simple organic molecules by approximately 10% compared to plain DIIS, with speedups of up to 60% for the more challenging transition metal systems compared to EDIIS + DIIS. Our results show that SMH is a reliable SCF accelerator that seldom deteriorates convergence and is highly robust.