Three-electron coalescence points in two and three dimensions

Abstract

The form of the wave function at three-electron coalescence points is examined for several spin states using an alternative method to the usual Fock expansion. We find that, in two- and three-dimensional systems, the non-analytical nature of the wave function is characterized by the appearance of logarithmic terms, reminiscent of those that appear as both electrons approach the nucleus of the helium atom. The explicit form of these singularities is given in terms of the interelectronic distances for a doublet and two quartet states of three electrons in a harmonic well.

4 pages, 1 figure, accepted for publication as a Communication in the Journal of Chemical Physics

References in corpus (5)

• Jastrow correlation factor for atoms, molecules, and solids
• Two electrons on a hypersphere: a quasi-exactly solvable model
• Ground state of two electrons on a sphere
• Excited states of spherium
• Nodal surfaces and interdimensional degeneracies

Cited by in corpus (5)

• Chemically Accurate Excitation Energies With Small Basis Sets
• Three-body problem in $d$-dimensional space: ground state, (quasi)-exact-solvability
• Three-body problem in 3D space: ground state, (quasi)-exact-solvability
• Quantum Monte Carlo with variable spins: fixed-phase and fixed-node approximations
• Self-Consistent Electron-Nucleus Cusp Correction for Molecular Orbitals