Visualizing the Origin of the Exchange Energy

Surusch Djalali^{1, 2}, Amitabh Banerji³, Martin Kleinschmidt⁴, Peter Gilch^1, and Lena Halbrügge^{3, 5,}

¹Institut für Physikalische Chemie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany

²Present address: Department of Biomolecular Systems, Max-Planck-Institute of Colloids and Interfaces, Am Mühlenberg 1, 14476 Potsdam, Germany

³Institut für Chemiedidaktik, Universität Potsdam, Didaktik der Chemie, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany

⁴Institut für Theoretische Chemie und Computerchemie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany

⁵Present address: Institut für Organische Chemie und Makromolekulare Chemie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany

Cite this paper

Surusch Djalali, Amitabh Banerji, Martin Kleinschmidt, Peter Gilch and Lena Halbrügge. Visualizing the Origin of the Exchange Energy. World Journal of Chemical Education. 2023; 11(4):141-148. doi: 10.12691/WJCE-11-4-3

Abstract

Atoms and molecules with two unpaired electrons can adopt singlet and triplet spin multiplicities. The implications of this are far reaching. For instance, the properties of molecular oxygen with its triplet ground state cannot be understood if this is not considered. In the design of emitters for OLEDs, the energy gap between singlet and triplet excitations is of utmost importance. This energy gap equals twice the exchange energy. Because of this relevance, the exchange energy is treated in textbooks and courses on physical and quantum chemistry. The treatments are commonly based on the quantum mechanical formalism and leave the students wondering why the exchange energy is non-zero. Here, the formalism is briefly re-iterated. Then wavefunctions for singlet and triplet states with identical configurations are visualized relying on the well-known particle-in-a-box model. The visualization shows that in the triplet state the electrons “automatically” avoid each other. This lowers the triplet energy compared to the singlet one. Some short comings of this didactic approach are also discussed.

Keywords

upper-division undergraduate, chemistry bachelor programs in Europe, physical chemistry, quantum chemistry, photochemistry, exchange energy, particle-in-a-box model

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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