A simultaneous probability density for the intracule and extracule coordinates.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Atomic and Molecular Physics

Background:

• The secondary Coulomb hole is a recently observed phenomenon in electron pair distributions.
• Understanding electron pair behavior requires analyzing both center-of-mass and relative coordinates.

Purpose of the Study:

• Introduce the intex density, X(R,u), for simultaneous probability of electron pair center-of-mass radius (R) and relative separation (u).
• Investigate the origin of the secondary Coulomb hole using the intex density.

Main Methods:

• Developed the intex density by combining intracular and extracular coordinates.
• Compared Hartree-Fock (HF) intex densities with those from explicitly correlated wave functions.

Main Results:

• HF intex densities for helium and heliumlike ions are symmetric, proving 2I(2R)=E(R).
• Explicitly correlated wave functions yield asymmetric intex densities, creating a topologically rich intex correlation hole.
• The probability of large interelectronic separation increases with correlation only when R is near u/2.

Conclusions:

• The intex density provides a novel framework for analyzing electron pair correlations.
• The secondary Coulomb hole arises from the asymmetry introduced by electron correlation effects.
• Electron pair distribution is sensitive to the interplay between center-of-mass radius and relative separation.