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Jacob Katriel¹, H E Montgomery²

¹Department of Chemistry, Technion - Israel Institute of Technology, Haifa 32000, Israel.

The Journal of Chemical Physics

|February 17, 2017

Summary

This summary is machine-generated.

Hund's rules for atomic states show a non-monotonic energy difference (ΔE) with nuclear charge (Z). This explains sign reversals in interelectronic repulsion, unlike monotonic behavior in analogous systems with confining potentials.

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Area of Science:

Atomic Physics
Quantum Chemistry
Theoretical Chemistry

Background:

Hund's rules predict ground state electron configurations based on minimizing interelectronic repulsion.
These rules are typically applied in the weak interelectronic repulsion limit within a common atomic configuration.

Purpose of the Study:

To investigate the asymptotic behavior of energy differences (ΔE) between atomic states governed by Hund's rules.
To analyze how ΔE changes with nuclear charge (Z) in both the high Z (Z→∞) and near-ionization (Z→Z_c) limits.
To understand the implications of this behavior on interelectronic repulsion energies.

Main Methods:

Examined the asymptotic behavior of ΔE as a function of nuclear charge (Z).
Analyzed the ratio ΔEZ² for non-monotonicity and its relation to interelectronic repulsion.
Compared atomic systems with analogous open-shell systems under confining potentials.

Main Results:

The ratio ΔEZ² exhibits non-monotonic behavior, featuring a maximum at intermediate Z.
This non-monotonicity directly explains sign reversals in interelectronic repulsion energy differences.
In contrast, analogous systems with confining potentials show monotonic energy difference functions.

Conclusions:

The interelectronic repulsion energy ordering expected from Hund's rule may not hold universally across isoelectronic sequences due to non-monotonic ΔE.
The monotonic behavior in confined systems suggests a more stable adherence to Hund's rule predictions in those scenarios.
Findings provide deeper insight into electron-electron interactions and their dependence on nuclear charge and confinement.