Efficient evaluation of nonlocal pseudopotentials via euler exponential spline interpolation

Hee Seung Lee, Mark Tuckerman, Glenn J. Martyna

Research output: Contribution to journalArticle

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-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.

Original languageEnglish (US)
Pages (from-to)1827-1835
Number of pages9
JournalChemPhysChem
Volume6
Issue number9
DOIs
StatePublished - Sep 5 2005

Fingerprint

splines
Splines
pseudopotentials
interpolation
Interpolation
evaluation
Atoms
orbitals
Silicon
plane waves
Fast Fourier transforms
Electronic structure
Molecular dynamics
Railroad cars
scaling
Derivatives
Electrons
Water
Liquids
atoms

Keywords

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

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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

In: ChemPhysChem, Vol. 6, No. 9, 05.09.2005, p. 1827-1835.

Research output: Contribution to journalArticle

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