Representation of the Kato electron-electron cusp condition by wavelet-based density-operator expansions

János Pipek, Szilvia Nagy

Research output: Contribution to journalArticle

Abstract

Since Kato proved his singularity condition for Coulomb potentials in 1957, there has been interest in the creation of wave functions that meet the prescriptions of the cusp conditions, necessary for high-precision quantum-mechanical calculations. It is well known, that wave-function expansions based on Slater determinants of one-electron functions are poorly convergent with respect to satisfying the electron-electron cusp condition. In this contribution we show that with the wavelet expansion of density operators even the local form of the electron-electron cusp condition is easily representable by Slater determinants of one-electron wavelet functions with a proper asymptotics of the expansion coefficients, which is explicitly calculated for Haar wavelets.

Original languageEnglish
Number of pages1
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume64
Issue number5
DOIs
Publication statusPublished - Jan 1 2001

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cusps
operators
expansion
electrons
determinants
wave functions
Coulomb potential
coefficients

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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AB - Since Kato proved his singularity condition for Coulomb potentials in 1957, there has been interest in the creation of wave functions that meet the prescriptions of the cusp conditions, necessary for high-precision quantum-mechanical calculations. It is well known, that wave-function expansions based on Slater determinants of one-electron functions are poorly convergent with respect to satisfying the electron-electron cusp condition. In this contribution we show that with the wavelet expansion of density operators even the local form of the electron-electron cusp condition is easily representable by Slater determinants of one-electron wavelet functions with a proper asymptotics of the expansion coefficients, which is explicitly calculated for Haar wavelets.

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