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The electron-electron counterbalance hole, a quantum mechanical effect, is proven to exist in all two-electron systems with spatial inversion symmetry. This finding applies to both approximate and exact wave functions in both position and momentum space.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Many-Electron Systems

Background:

  • Spatial inversion symmetry is a fundamental property in quantum mechanics.
  • The electron-electron counterbalance hole describes a phenomenon where electrons with parallel spins avoid opposite positions in symmetric systems.
  • Previous work identified this hole for specific Hartree-Fock orbitals.

Purpose of the Study:

  • To generalize the existence of the electron-electron counterbalance hole.
  • To demonstrate its presence in all two-electron systems with spatial inversion symmetry.
  • To explore its validity in both position and momentum space.

Main Methods:

  • Theoretical analysis of two-electron systems.
  • Investigation of wave functions with spatial inversion symmetry.
  • Examination of both approximate and exact wave functions.

Main Results:

  • The electron-electron counterbalance hole is universally present in two-electron systems with spatial inversion symmetry.
  • This holds true for any wave function with even inversion parity.
  • The phenomenon is confirmed in both position and momentum representations.

Conclusions:

  • The electron-electron counterbalance hole is a robust feature in symmetric two-electron systems.
  • This generalized finding has implications for understanding electron correlation.
  • The study also discusses potential extensions to larger electron systems.