# 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 gauge-fixing matrix. The resulting projected commutator-DIIS method (PC-DIIS) only operates on matrices of the same dimension as that consists of Kohn–Sham orbitals. The cost of the method is comparable to that of standard charge mixing schemes used in large basis set calculations. The PC-DIIS method is gauge-invariant, which guarantees that its performance is invariant with respect to any unitary transformation of the Kohn–Sham orbitals. Wemore »

- Authors:

- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1480243

- Grant/Contract Number:
- [DMS-1652330]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Theory and Computation

- Additional Journal Information:
- [ Journal Volume: 13; Journal Issue: 11]; Journal ID: ISSN 1549-9618

- Publisher:
- American Chemical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Hu, Wei, Lin, Lin, and Yang, Chao. Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations. United States: N. p., 2017.
Web. doi:10.1021/acs.jctc.7b00892.
```

```
Hu, Wei, Lin, Lin, & Yang, Chao. Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations. United States. doi:10.1021/acs.jctc.7b00892.
```

```
Hu, Wei, Lin, Lin, and Yang, Chao. Fri .
"Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations". United States. doi:10.1021/acs.jctc.7b00892. https://www.osti.gov/servlets/purl/1480243.
```

```
@article{osti_1480243,
```

title = {Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations},

author = {Hu, Wei and Lin, Lin and Yang, Chao},

abstractNote = {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 gauge-fixing matrix. The resulting projected commutator-DIIS method (PC-DIIS) only operates on matrices of the same dimension as that consists of Kohn–Sham orbitals. The cost of the method is comparable to that of standard charge mixing schemes used in large basis set calculations. The PC-DIIS method is gauge-invariant, which guarantees that its performance is invariant with respect to any unitary transformation of the Kohn–Sham orbitals. We demonstrate that the PC-DIIS method can be viewed as an extension of an iterative eigensolver for nonlinear problems. We use the PC-DIIS method for accelerating Kohn–Sham density functional theory calculations with hybrid exchange–correlation functionals, and demonstrate its superior performance compared to the commonly used nested two-level SCF iteration procedure. Furthermore, we demonstrate that in the context of ab initio molecular dynamics (MD) simulation with hybrid functionals one can extrapolate the gauge-fixing matrix to achieve the goal of extrapolating the entire density matrix implicitly along the MD trajectory. Here, numerical results indicate that the new method significantly reduces the number of SCF iterations per MD step, compared to the commonly used strategy of extrapolating the electron density.},

doi = {10.1021/acs.jctc.7b00892},

journal = {Journal of Chemical Theory and Computation},

number = [11],

volume = [13],

place = {United States},

year = {2017},

month = {9}

}

*Citation information provided by*

Web of Science

Web of Science