### Abstract

An Euler exponential spline (EES) based formalism is employed to derive new expressions for the electron-atom nonlocal pseudopotential interaction (NL) in electronic structure calculations performed using a plane wave basis set that can be computed more rapidly than standard techniques. Two methods, one that is evaluated by switching between real and reciprocal space via fast Fourier transforms, and another that is evaluated completely in real space, are described. The reciprocal-space or g-space-based technique, NLEES-G, scales as NMlogM-N^{2}logN, where N is the number of electronic orbitals and M is the number of plane waves. The real-space based technique, NLEES-R, scales as N^{2}. The latter can potentially be used within a maximally spatially localized orbital method to yield linear scaling, while the former could be employed within a maximally delocalized orbital method to yield NlogN scaling. This behavior is to be contrasted with standard techniques, which scale as N^{3}. The two new approaches are validated using several examples, including solid silicon and liquid water, and demonstrated to be improvements on other, reduced-order nonlocal techniques. Indeed, the new methods have a low overhead and become more efficient than the standard technique for systems with roughly 20 or more atoms. Both NLEES methods are shown to work stably and efficiently within the Car-Parrinello ab initio molecular dynamics framework, owing to the existence of p-2 continuous derivatives of a pth-order spline.

Original language | English (US) |
---|---|

Pages (from-to) | 1827-1835 |

Number of pages | 9 |

Journal | ChemPhysChem |

Volume | 6 |

Issue number | 9 |

DOIs | |

State | Published - Sep 5 2005 |

### Fingerprint

### Keywords

- Ab initio calculations
- Molecular dynamics
- Silicon
- Splines
- Water

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*ChemPhysChem*,

*6*(9), 1827-1835. https://doi.org/10.1002/cphc.200500123

**Efficient evaluation of nonlocal pseudopotentials via euler exponential spline interpolation.** / Lee, Hee Seung; Tuckerman, Mark; Martyna, Glenn J.

Research output: Contribution to journal › Article

*ChemPhysChem*, vol. 6, no. 9, pp. 1827-1835. https://doi.org/10.1002/cphc.200500123

}

TY - JOUR

T1 - Efficient evaluation of nonlocal pseudopotentials via euler exponential spline interpolation

AU - Lee, Hee Seung

AU - Tuckerman, Mark

AU - Martyna, Glenn J.

PY - 2005/9/5

Y1 - 2005/9/5

N2 - An Euler exponential spline (EES) based formalism is employed to derive new expressions for the electron-atom nonlocal pseudopotential interaction (NL) in electronic structure calculations performed using a plane wave basis set that can be computed more rapidly than standard techniques. Two methods, one that is evaluated by switching between real and reciprocal space via fast Fourier transforms, and another that is evaluated completely in real space, are described. The reciprocal-space or g-space-based technique, NLEES-G, scales as NMlogM-N2logN, where N is the number of electronic orbitals and M is the number of plane waves. The real-space based technique, NLEES-R, scales as N2. The latter can potentially be used within a maximally spatially localized orbital method to yield linear scaling, while the former could be employed within a maximally delocalized orbital method to yield NlogN scaling. This behavior is to be contrasted with standard techniques, which scale as N3. The two new approaches are validated using several examples, including solid silicon and liquid water, and demonstrated to be improvements on other, reduced-order nonlocal techniques. Indeed, the new methods have a low overhead and become more efficient than the standard technique for systems with roughly 20 or more atoms. Both NLEES methods are shown to work stably and efficiently within the Car-Parrinello ab initio molecular dynamics framework, owing to the existence of p-2 continuous derivatives of a pth-order spline.

AB - An Euler exponential spline (EES) based formalism is employed to derive new expressions for the electron-atom nonlocal pseudopotential interaction (NL) in electronic structure calculations performed using a plane wave basis set that can be computed more rapidly than standard techniques. Two methods, one that is evaluated by switching between real and reciprocal space via fast Fourier transforms, and another that is evaluated completely in real space, are described. The reciprocal-space or g-space-based technique, NLEES-G, scales as NMlogM-N2logN, where N is the number of electronic orbitals and M is the number of plane waves. The real-space based technique, NLEES-R, scales as N2. The latter can potentially be used within a maximally spatially localized orbital method to yield linear scaling, while the former could be employed within a maximally delocalized orbital method to yield NlogN scaling. This behavior is to be contrasted with standard techniques, which scale as N3. The two new approaches are validated using several examples, including solid silicon and liquid water, and demonstrated to be improvements on other, reduced-order nonlocal techniques. Indeed, the new methods have a low overhead and become more efficient than the standard technique for systems with roughly 20 or more atoms. Both NLEES methods are shown to work stably and efficiently within the Car-Parrinello ab initio molecular dynamics framework, owing to the existence of p-2 continuous derivatives of a pth-order spline.

KW - Ab initio calculations

KW - Molecular dynamics

KW - Silicon

KW - Splines

KW - Water

UR - http://www.scopus.com/inward/record.url?scp=24944515724&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944515724&partnerID=8YFLogxK

U2 - 10.1002/cphc.200500123

DO - 10.1002/cphc.200500123

M3 - Article

VL - 6

SP - 1827

EP - 1835

JO - ChemPhysChem

JF - ChemPhysChem

SN - 1439-4235

IS - 9

ER -