# Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions

## Abstract

Jastrow correlation factors play an important role in quantum Monte Carlo calculations. Together with an orbital based antisymmetric function, they allow the construction of highly accurate correlation wave functions. In this paper, a generic expansion of the Jastrow correlation function in terms of polynomials that satisfy both the electron exchange symmetry constraint and the cusp conditions is presented. In particular, an expansion of the three-body electron-electron-nucleus contribution in terms of cuspless homogeneous symmetric polynomials is proposed. The polynomials can be expressed in fairly arbitrary scaling function allowing a generic implementation of the Jastrow factor. It is demonstrated with a few examples that the new Jastrow factor achieves 85%–90% of the total correlation energy in a variational quantum Monte Carlo calculation and more than 90% of the diffusion Monte Carlo correlation energy.

- Authors:

- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen (Germany)
- (JARA-HPC), 52056 Aachen (Germany)

- Publication Date:

- OSTI Identifier:
- 22416167

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 8; Other Information: (c) 2015 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; CORRELATION FUNCTIONS; DIFFUSION; ELECTRON CORRELATION; ELECTRON EXCHANGE; ELECTRONS; MONTE CARLO METHOD; POLYNOMIALS; SYMMETRY; THREE-BODY PROBLEM; VARIATIONAL METHODS; WAVE FUNCTIONS

### Citation Formats

```
Lüchow, Arne, E-mail: luechow@rwth-aachen.de, Jülich Aachen Research Alliance, Sturm, Alexander, Schulte, Christoph, and Haghighi Mood, Kaveh.
```*Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions*. United States: N. p., 2015.
Web. doi:10.1063/1.4909554.

```
Lüchow, Arne, E-mail: luechow@rwth-aachen.de, Jülich Aachen Research Alliance, Sturm, Alexander, Schulte, Christoph, & Haghighi Mood, Kaveh.
```*Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions*. United States. doi:10.1063/1.4909554.

```
Lüchow, Arne, E-mail: luechow@rwth-aachen.de, Jülich Aachen Research Alliance, Sturm, Alexander, Schulte, Christoph, and Haghighi Mood, Kaveh. Sat .
"Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions". United States.
doi:10.1063/1.4909554.
```

```
@article{osti_22416167,
```

title = {Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions},

author = {Lüchow, Arne, E-mail: luechow@rwth-aachen.de and Jülich Aachen Research Alliance and Sturm, Alexander and Schulte, Christoph and Haghighi Mood, Kaveh},

abstractNote = {Jastrow correlation factors play an important role in quantum Monte Carlo calculations. Together with an orbital based antisymmetric function, they allow the construction of highly accurate correlation wave functions. In this paper, a generic expansion of the Jastrow correlation function in terms of polynomials that satisfy both the electron exchange symmetry constraint and the cusp conditions is presented. In particular, an expansion of the three-body electron-electron-nucleus contribution in terms of cuspless homogeneous symmetric polynomials is proposed. The polynomials can be expressed in fairly arbitrary scaling function allowing a generic implementation of the Jastrow factor. It is demonstrated with a few examples that the new Jastrow factor achieves 85%–90% of the total correlation energy in a variational quantum Monte Carlo calculation and more than 90% of the diffusion Monte Carlo correlation energy.},

doi = {10.1063/1.4909554},

journal = {Journal of Chemical Physics},

number = 8,

volume = 142,

place = {United States},

year = {Sat Feb 28 00:00:00 EST 2015},

month = {Sat Feb 28 00:00:00 EST 2015}

}