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Communication: Three-electron coalescence points in two and three dimensions.

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Area of Science:

  • Quantum mechanics
  • Atomic physics
  • Computational chemistry

Background:

  • Understanding electron correlation is crucial in atomic and molecular systems.
  • The behavior of wave functions at coalescence points presents unique challenges.

Purpose of the Study:

  • To investigate the wave function's form at three-electron coalescence points.
  • To characterize the non-analytical nature of the wave function in multi-electron systems.

Main Methods:

  • Utilized an alternative method to the standard Fock expansion.
  • Analyzed wave functions in two- and three-dimensional systems.

Main Results:

  • Identified logarithmic terms characterizing wave function singularities.
  • These terms are analogous to those observed near the helium nucleus.
  • Provided explicit forms of singularities in terms of interelectronic distances for specific spin states.

Conclusions:

  • The study elucidates the complex behavior of wave functions at electron coalescence points.
  • Logarithmic singularities are a key feature in three-electron systems.
  • The findings contribute to a deeper understanding of electron correlation in quantum systems.