The central topic of this article is the examination of the effect of the electron-electron cusp on the convergence of configuration interaction (CI) wave functions. The electron-electron cusp refers to the singularity in the wave function that occurs when two electrons approach each other closely. This singularity arises due to the Coulomb interaction between the two electrons and has been a challenge in quantum mechanical calculations.
In order to address this issue, the authors propose an effective electron-electron interaction that closely reproduces the scattering of the Coulomb interaction but is smooth and finite at zero electron-electron separation. This effective interaction allows for a wave function that is free from the cusp at zero separation. The concept of an effective interaction inspired by the pseudopotential approach for electron-ion interactions has been widely used in quantum mechanics.
To investigate the impact of the electron-electron cusp on the convergence of CI wave functions, the authors perform calculations for He and Be atoms using both the Coulomb electron-electron interaction and the smooth effective electron-electron interaction. By comparing the convergence of the CI expansion for these two interactions, the authors evaluate the significance of considering the electron-electron cusp in CI calculations.
Historically, the electron-electron cusp has been a topic of interest in quantum mechanics, particularly in relation to many-body theories and computational methods. Efforts to accurately describe electron correlations in atoms and molecules have faced challenges due to the singularity at zero electron-electron separation. Advances in computational techniques and approximations have allowed for improved treatments of this phenomenon.
Contemporary research in this area has focused on exploring different approaches to handle the electron-electron cusp and its impact on various quantum mechanical calculations. This article contributes to this ongoing discussion by examining the convergence of CI wave functions with and without considering the cusp, providing insights into its importance or lack thereof in CI calculations to within chemical accuracy.
Abstract: The effect of the electron-electron cusp on the convergence of configuration interaction (CI) wave functions is examined. By analogy with the pseudopotential approach for electron-ion interactions, an effective electron-electron interaction is developed which closely reproduces the scattering of the Coulomb interaction but is smooth and finite at zero electron-electron separation. The exact many-electron wave function for this smooth effective interaction has no cusp at zero electron-electron separation. We perform CI and quantum Monte Carlo calculations for He and Be atoms, both with the Coulomb electron-electron interaction and with the smooth effective electron-electron interaction. We find that convergence of the CI expansion of the wave function for the smooth electron-electron interaction is not significantly improved compared with that for the divergent Coulomb interaction for energy differences on the order of 1 mHartree. This shows that, contrary to popular belief, description of the electron-electron cusp is not a limiting factor, to within chemical accuracy, for CI calculations.