Solution of two-electron Schr?dinger equations using a residual minimization method and one-dimensional basis functions

摘要

Distinctive from conventional electronic structure methods, we solve the Schr?dinger wave equations of the helium atom and its isoelectronic ions by employing one-dimensional basis functions to separate components. We use full two-electron six-dimensional operators and wavefunctions represented with real-space grids where the refinement of the latter is carried out using a residual minimization method. In contrast to the standard single-electron approach, the current approach results in exact treatment of repulsion energy and, hence, more accurate electron correlation within five centihartrees or better included, with moderate computational cost. A simple numerical convergence between the error to accurate results and the grid-spacing size is found. The obtained two-electron Schr?dinger wavefunction that contains vast and elaborating information for the radial correlation function and common one-dimensional functions shows the electron correlation effect on one-electron distributions.