## Hybrid grid/basis set discretizations of the Schrödinger equation

## Abstract

We present a new kind of basis function for discretizing the Schrödinger equation in electronic structure calculations, called a gausslet, which has wavelet-like features but is composed of a sum of Gaussians. Gausslets are placed on a grid and combine advantages of both grid and basis set approaches. They are orthogonal, infinitely smooth, symmetric, polynomially complete, and with a high degree of locality. Because they are formed from Gaussians, they are easily combined with traditional atom-centered Gaussian bases. As a result, we also introduce diagonal approximations that dramatically reduce the computational scaling of two-electron Coulomb terms in the Hamiltonian.

- Authors:

- Univ. of California, Irvine, CA (United States)

- Publication Date:

- Research Org.:
- Univ. of California, Irvine, CA (United States)

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

- OSTI Identifier:
- 1511036

- Alternate Identifier(s):
- OSTI ID: 1414610

- Grant/Contract Number:
- SC0008696; SC008696

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 147; Journal Issue: 24; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
White, Steven R. Hybrid grid/basis set discretizations of the Schrödinger equation. United States: N. p., 2017.
Web. doi:10.1063/1.5007066.
```

```
White, Steven R. Hybrid grid/basis set discretizations of the Schrödinger equation. United States. doi:10.1063/1.5007066.
```

```
White, Steven R. Fri .
"Hybrid grid/basis set discretizations of the Schrödinger equation". United States. doi:10.1063/1.5007066. https://www.osti.gov/servlets/purl/1511036.
```

```
@article{osti_1511036,
```

title = {Hybrid grid/basis set discretizations of the Schrödinger equation},

author = {White, Steven R.},

abstractNote = {We present a new kind of basis function for discretizing the Schrödinger equation in electronic structure calculations, called a gausslet, which has wavelet-like features but is composed of a sum of Gaussians. Gausslets are placed on a grid and combine advantages of both grid and basis set approaches. They are orthogonal, infinitely smooth, symmetric, polynomially complete, and with a high degree of locality. Because they are formed from Gaussians, they are easily combined with traditional atom-centered Gaussian bases. As a result, we also introduce diagonal approximations that dramatically reduce the computational scaling of two-electron Coulomb terms in the Hamiltonian.},

doi = {10.1063/1.5007066},

journal = {Journal of Chemical Physics},

number = 24,

volume = 147,

place = {United States},

year = {2017},

month = {12}

}

Other availability

Cited by: 4 works

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