Efficient and Robust\nAb Initio Self-Consistent Field\nAcceleration Algorithm Based on a Semiempirical Model Hamiltonian

A novel doubly iterative self-consistent field (SCF)\napproach using\na semiempirical model Hamiltonian (denoted as the SMH algorithm) is\nproposed to accelerate the Hartree–Fock (HF) and density functional\ntheory (DFT) calculations. This method first constructs the Fock matrix\nexactly in each SCF macroiteration, followed by a few SCF microiterations,\nwhere the Fock matrix is incrementally updated using an inexpensive\nsemiempirical approximation. This leads to an improved wave function\nin each SCF macroiteration with minimal additional cost, and therefore\na reduced number of exact Fock builds is required for SCF convergence.\nThe SMH algorithm can be combined with conventional SCF convergence\ntechniques such as level shifting, direct inversion in the iterative\nsubspace (DIIS), and energy-DIIS (EDIIS). When integrated with DIIS,\nSMH enhances the convergence of simple organic molecules by approximately\n10% compared to plain DIIS, with speedups of up to 60% for the more\nchallenging transition metal systems compared to EDIIS + DIIS. Our\nresults show that SMH is a reliable SCF accelerator that seldom deteriorates\nconvergence and is highly robust.