# A Finite Field Approach to Solving the Bethe Salpeter Equation.

## Abstract

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:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science - Office of Basic Energy Sciences - Materials Sciences and Engineering Division - Midwest Integrated Center for Computational Materials (MICCoM); Swiss National Science Foundation (SNSF)

- OSTI Identifier:
- 1530398

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 122; Journal Issue: 23

- 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.
```*A 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.
```*A 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 .
"A Finite Field Approach to Solving the Bethe Salpeter Equation.". United States. doi:10.1103/PhysRevLett.122.237402.
```

```
@article{osti_1530398,
```

title = {A 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 = {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}

}