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Are Exact Exchange-Correlation Potentials Continuous at Atomic Nuclei in Molecules?

Conrad C Moore¹, Viktor N Staroverov¹

¹Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada.

Journal of Chemical Theory and Computation

|October 1, 2024

Summary

This summary is machine-generated.

Exact exchange-correlation potentials in molecules are continuous, despite initial indications of discontinuity near atomic nuclei. This finding resolves a surprising theoretical puzzle in electronic structure calculations.

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Area of Science:

Quantum Chemistry
Computational Physics
Electronic Structure Theory

Background:

The Kohn-Sham (KS) approach is a cornerstone of modern electronic structure theory, enabling practical calculations of molecular properties.
KS exchange-correlation (XC) potentials are central to this method, but their exact form and properties remain an active area of research.
Electronic kinetic energy densities exhibit sharp discontinuities at atomic nuclei, raising questions about the continuity of exact KS potentials.

Purpose of the Study:

To investigate the behavior of exact exchange-correlation potentials near atomic nuclei in molecules.
To determine whether these potentials exhibit discontinuities, as suggested by the properties of kinetic energy densities.
To resolve theoretical ambiguities regarding the continuity of exact KS potentials.

Main Methods:

Analytical deduction of the behavior of relevant electronic quantities near atomic nuclei.
Examination of the contributions to the exchange-correlation potential from interacting and noninteracting kinetic energy densities.
Analysis of the basis-set limit to understand the behavior of exact potentials.

Main Results:

Electronic kinetic energy densities are indeed sharply discontinuous at atomic nuclei.
Potentials derived using Slater-type basis sets show apparent jump discontinuities.
Analytical investigation reveals a nontrivial cancellation of these discontinuities in the basis-set limit.

Conclusions:

Exact Kohn-Sham exchange-correlation potentials are continuous at atomic nuclei.
The apparent discontinuities observed in basis-set calculations do not reflect the behavior of the exact potential.
This resolves a theoretical question concerning the nature of exact exchange-correlation potentials in molecules.