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## Finite-Field Approach to Solving the Bethe-Salpeter Equation

## Abstract

In this paper, we present a method to compute optical spectra and exciton binding energies of molecules and solids based on the solution of the Bethe-Salpeter equation and the calculation of the screened Coulomb interaction in a finite field. The method does not require either the explicit evaluation of dielectric matrices or of virtual electronic states, and can be easily applied without resorting to the random phase approximation. In addition, it utilizes localized orbitals obtained from Bloch states using bisection techniques, thus greatly reducing the complexity of the calculation and enabling the efficient use of hybrid functionals to obtain single particle wave functions. We report exciton binding energies of several molecules and absorption spectra of condensed systems of unprecedented size, including water and ice samples with hundreds of atoms.

- Authors:

- Univ. of Chicago, IL (United States). Pritzker School of Molecular Engineering
- Univ. of Chicago, IL (United States). Pritzker School of Molecular Engineering, and Dept. of Chemistry
- Univ. of Chicago, IL (United States). Pritzker School of Molecular Engineering; Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division, and Inst. for Molecular Engineering
- Univ. of California, Davis, CA (United States). Dept. of Computer Science
- Univ. of Chicago, IL (United States). Pritzker School of Molecular Engineering, and Dept. of Chemistry; Argonne National Lab. (ANL), Argonne, IL (United States). Materials Science Division, and Inst. for Molecular Engineering

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1530398

- Alternate Identifier(s):
- OSTI ID: 1546405

- Grant/Contract Number:
- AC02-06CH11357

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 122; Journal Issue: 23; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- electron-hole excitation; optical spectra

### Citation Formats

```
Nguyen, Ngoc Linh, Ma, He, Govoni, Marco, Gygi, Francois, and Galli, Giulia. Finite-Field Approach to Solving the Bethe-Salpeter Equation. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.122.237402.
```

```
Nguyen, Ngoc Linh, Ma, He, Govoni, Marco, Gygi, Francois, & Galli, Giulia. Finite-Field Approach to Solving the Bethe-Salpeter Equation. United States. doi:10.1103/PhysRevLett.122.237402.
```

```
Nguyen, Ngoc Linh, Ma, He, Govoni, Marco, Gygi, Francois, and Galli, Giulia. Fri .
"Finite-Field Approach to Solving the Bethe-Salpeter Equation". United States. doi:10.1103/PhysRevLett.122.237402.
```

```
@article{osti_1530398,
```

title = {Finite-Field Approach to Solving the Bethe-Salpeter Equation},

author = {Nguyen, Ngoc Linh and Ma, He and Govoni, Marco and Gygi, Francois and Galli, Giulia},

abstractNote = {In this paper, we present a method to compute optical spectra and exciton binding energies of molecules and solids based on the solution of the Bethe-Salpeter equation and the calculation of the screened Coulomb interaction in a finite field. The method does not require either the explicit evaluation of dielectric matrices or of virtual electronic states, and can be easily applied without resorting to the random phase approximation. In addition, it utilizes localized orbitals obtained from Bloch states using bisection techniques, thus greatly reducing the complexity of the calculation and enabling the efficient use of hybrid functionals to obtain single particle wave functions. We report exciton binding energies of several molecules and absorption spectra of condensed systems of unprecedented size, including water and ice samples with hundreds of atoms.},

doi = {10.1103/PhysRevLett.122.237402},

journal = {Physical Review Letters},

number = 23,

volume = 122,

place = {United States},

year = {2019},

month = {6}

}

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