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Hund's multiplicity rule: from atoms to quantum dots
Y Sajeev1, M Sindelka, N Moiseyev
1Schulich Faculty of Chemistry and Minerva Center for Nonlinear Physics of Complex Systems, Technion-Israel Institute of Technology, Haifa 32000, Israel.
The Journal of Chemical Physics
|February 20, 2008
Summary
This study revisits Hund's multiplicity rule, showing that angular electronic correlation isn't needed to explain singlet and triplet states in helium and quantum dots. Calculations confirm the triplet state is lower in energy, aligning with older explanations.
Area of Science:
- Quantum mechanics
- Atomic physics
- Condensed matter physics
Background:
- The textbook explanation of Hund's multiplicity rule, based on the Pauli principle, was shown to be incorrect in 1965.
- Subsequent analyses suggest that angular electronic correlation is necessary for accurate calculations, a complexity often included in modern textbooks.
Purpose of the Study:
- To investigate the validity of the argument requiring angular electronic correlation for Hund's rule.
- To explore the applicability of this argument to two-electron systems like helium and quantum dots (QDs).
Main Methods:
- Utilizing mean-field approximation for calculations.
- Analyzing the energy differences between singlet and triplet excited states.
- Comparing results for helium and two-electron spherical QDs.
Main Results:
- The mean-field approximation successfully explains the energy differences between singlet and triplet states without angular electronic correlation.
- Calculations for both helium and QDs demonstrate this finding.
- The triplet state of the QD was found to be lower in energy than the singlet state due to reduced electronic repulsion.
Conclusions:
- Angular electronic correlation is not essential for understanding Hund's multiplicity rule in these systems.
- The findings support the original, simpler explanation of Hund's rule based on the Pauli principle and reduced electronic repulsion.
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