Can correlation bring electrons closer together?

Abstract

We discuss the exact Coulomb hole for the ground state of the helium atom and helium-like ions. We find that the correlated wavefunction yields a smaller probability of finding the electrons at large separations than does the Hartree–Fock wavefunction, leading to the counterintuitive conclusion that correlation brings distant electrons closer together. This effect becomes less pronounced as the nuclear charge increases.

Keywords:

• Coulomb hole
• intracule
• electron correlation
• helium atom

Acknowledgements

PMWG thanks the APAC Merit Allocation Scheme for a grant of supercomputer time and the Australian Research Council (grant DP0664466) for funding. We thank Andrew Gilbert for pointing out the potential existence of additional holes beyond the secondary one.