Counterintuitive Coulomb hole around the bond midplane

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• The Coulomb hole describes the depletion of electron density around a reference electron due to electron-electron repulsion.
• Understanding the Coulomb hole is vital for accurate electronic structure calculations and predicting chemical properties.

Purpose of the Study:

• To investigate the spatial distribution and characteristics of the Coulomb hole in chemical bonds.
• To explore the relationship between the Coulomb hole, Fermi hole, and exchange-correlation hole.
• To evaluate the accuracy of approximate density functional theory (DFT) methods in describing the Coulomb hole.

Main Methods:

• Analysis of electron density and pair density.
• Examination of the Fermi hole and exchange-correlation hole.
• Comparison with results from approximate DFT methods (e.g., generalized gradient approximation).

Main Results:

• The Coulomb hole is localized around nuclear sites, not the bond midplane, splitting into two distinct regions.
• Positive values ('Coulomb heap') can occur when the Fermi hole is deeper than the exchange-correlation hole.
• Left-right correlation contracts electron density towards nuclei, depleting the bond center.

Conclusions:

• The spatial distribution of the Coulomb hole is more complex than previously assumed, localized near atomic nuclei.
• Correlation effects on one-electron density significantly influence the Coulomb hole's behavior.
• Accurate description of the Coulomb hole requires advanced theoretical methods beyond current approximate DFT.