# A systematic way for the cost reduction of density fitting methods

## Abstract

We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of the computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.

- Authors:

- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest (Hungary)

- Publication Date:

- OSTI Identifier:
- 22415410

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 24; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATIONS; COULOMB FIELD; DENSITY; EFFICIENCY; ELECTRONS; FUNCTIONS; GAIN; INTEGRALS; ITERATIVE METHODS; RANDOM PHASE APPROXIMATION; REDUCTION

### Citation Formats

```
Kállay, Mihály, E-mail: kallay@mail.bme.hu.
```*A systematic way for the cost reduction of density fitting methods*. United States: N. p., 2014.
Web. doi:10.1063/1.4905005.

```
Kállay, Mihály, E-mail: kallay@mail.bme.hu.
```*A systematic way for the cost reduction of density fitting methods*. United States. doi:10.1063/1.4905005.

```
Kállay, Mihály, E-mail: kallay@mail.bme.hu. Sun .
"A systematic way for the cost reduction of density fitting methods". United States.
doi:10.1063/1.4905005.
```

```
@article{osti_22415410,
```

title = {A systematic way for the cost reduction of density fitting methods},

author = {Kállay, Mihály, E-mail: kallay@mail.bme.hu},

abstractNote = {We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of the computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.},

doi = {10.1063/1.4905005},

journal = {Journal of Chemical Physics},

number = 24,

volume = 141,

place = {United States},

year = {Sun Dec 28 00:00:00 EST 2014},

month = {Sun Dec 28 00:00:00 EST 2014}

}