Model DFT exchange holes and the exact exchange hole: Similarities and differences

Area of Science:

• Quantum chemistry
• Computational physics
• Electron interaction modeling

Background:

• Exchange and correlation holes are fundamental quantum concepts explaining electron interactions.
• The exact exchange hole, derived from first principles, is crucial but often approximated in density functional theory (DFT).

Purpose of the Study:

• To develop and implement an algorithm for calculating the spherically averaged exact exchange hole.
• To assess the accuracy of popular approximate exchange hole models against the exact exchange hole.
• To investigate molecular correlation effects using the exact exchange hole.

Main Methods:

• Algorithm development for computing the spherically averaged exact exchange hole using molecular orbitals in Gaussian basis functions.
• Incorporation of a novel recursive relation for Bessel function averages and asymptotic expressions.
• Comparative analysis of popular model exchange holes against the exact exchange hole for atoms and molecules (H2, Cr2).

Main Results:

• Successful implementation of an algorithm for the exact exchange hole computation.
• Identification of BR89 as a moderately suitable model for atomic point-wise accuracy among tested models.
• Analysis of deviations revealed insights into left-right static correlation in stretched molecules.

Conclusions:

• The developed algorithm provides a rigorous tool for studying electron interactions.
• Current approximate exchange holes, including popular models, require significant improvement for accurate atomic and molecular correlation descriptions.
• Further development of exchange hole models is necessary for advancing quantum chemical calculations.