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The commutator direct inversion of the iterative subspace (commutator DIIS orC-DIIS) method developed by Pulay is an efficient and the most widely usedscheme in quantum chemistry to accelerate the convergence of self consistentfield (SCF) iterations in Hartree-Fock theory and Kohn-Sham density functionaltheory. The C-DIIS method requires the explicit storage of the density matrix,the Fock matrix and the commutator matrix. Hence the method can only be usedfor systems with a relatively small basis set, such as the Gaussian basis set.We develop a new method that enables the C-DIIS method to be efficientlyemployed in electronic structure calculations with a large basis set such asplanewaves for the first time. The key ingredient is the projection of both thedensity matrix and the commutator matrix to an auxiliary matrix called thegauge-fixing matrix. The resulting projected commutator-DIIS method (PC-DIIS)only operates on matrices of the same dimension as the that consists ofKohn-Sham orbitals. The cost of the method is comparable to that of standardcharge mixing schemes used in large basis set calculations. The PC-DIIS methodis gauge-invariant, which guarantees that its performance is invariant withrespect to any unitary transformation of the Kohn-Sham orbitals. We demonstratethat the PC-DIIS method can be viewed as an extension of an iterativeeigensolver for nonlinear problems. We use the PC-DIIS method for acceleratingKohn-Sham density functional theory calculations with hybridexchange-correlation functionals, and demonstrate its superior performancecompared to the commonly used nested two-level SCF iteration procedure.

Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations