Representation of the Kato electron-electron cusp condition by wavelet-based density-operator expansions - art. no. 052506

Since Kato proved his singularity condition for Coulomb potentials in 1957, there has been interest in the creation of wave functions that meet the pr escriptions of the cusp conditions, necessary for high-precision quantum-me chanical calculations. It is well known. that wave-function expansions base d on Slater determinants of one-electron functions are poorly convergent wi th respect to satisfying the electron-electron cusp condition. In this cont ribution we show that with the wavelet expansion of density operators even the local form of the electron-electron cusp condition is easily representa ble by Slater determinants of one-electron wavelet functions with a proper asymptotics of the expansion coefficients, which is explicitly calculated f or Haar wavelets.