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Efficient Evaluation of Nonlocal Pseudopotentials via Euler Exponential Spline Interpolation
Author(s) -
Lee HeeSeung,
Tuckerman Mark E.,
Martyna Glenn J.
Publication year - 2005
Publication title -
chemphyschem
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.016
H-Index - 140
eISSN - 1439-7641
pISSN - 1439-4235
DOI - 10.1002/cphc.200500123
Subject(s) - pseudopotential , reciprocal lattice , linear scale , euler's formula , scaling , atomic orbital , exponential function , fourier transform , electronic structure , basis set , basis function , mathematics , physics , chemistry , computational chemistry , mathematical analysis , quantum mechanics , electron , geometry , density functional theory , geodesy , diffraction , geography
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 NM log M ∼ N 2 log N , 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 N log N 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 p th‐order spline.