Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations

Abstract

The commutator direct inversion of the iterative subspace (commutator DIIS or C-DIIS) method developed by Pulay is an efficient and the most widely used scheme in quantum chemistry to accelerate the convergence of self consistent field (SCF) iterations in Hartree-Fock theory and Kohn-Sham density functional theory. 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 used for 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 efficiently employed in electronic structure calculations with a large basis set such as planewaves for the first time. The key ingredient is the projection of both the density matrix and the commutator matrix to an auxiliary matrix called the * To whom correspondence should be addressed

Subspace Methods for Nonlinear Optimization

“…Then, a new Hamiltonian matrix is obtained Hk = ∑ m−1 j=0 c j H k−j . Since an explicit storage of the density matrix can be prohibitive, the projected C-DIIS in [61] uses projections of the density and commutator matrices so that the sizes are much smaller.…”

Numerical methods for Kohn–Sham density functional theory

“…Recently, a new method, called the projected commutator DIIS (PC-DIIS) method, has been introduced so that the C-DIIS method can be used for Kohn–Sham DFT calculations with non-local functionals performed with a large basis set (Hu, Lin and Yang 2017 b ). Since it is not possible to explicitly store or mix the density matrices in such calculations, it is tempting to perform the DIIS procedure on the orbital matrix .…”

A DFT Study on the Adsorption of H2S and SO2 on Ni Doped MoS2 Monolayer

“…The double numerical plus polarization (DNP) was chosen as the basis set, the density functional semi-core pseudopotential (DSPP) was applied in core treatment, and the Monkhorst-pack k point mesh of 5 × 5 × 1 was employed [ 32 , 33 ]. The self-consistent (SCF) field tolerance was set to 1 × 10 −6 Ha, and the DIIS size was set to 6 to speed up the convergence of SCF [ 34 ].…”