Interatomic Repulsion and the Pauli Principle

Abstract

Atoms may repel or attract each other, but bound systems get virtually all of the attention in the classroom. To address the imbalance, instructors can explore the basis of repulsion in a few simple systems and highlight the important role played by the Pauli principle. A good example is the first triplet excited state of H2 wherein both electrons have the same spin. In light of the Hellmann–Feynman theorem, the net interaction is repulsive due to the low electron density that results in the region between the two nuclei. Analogous destabilization occurs in σ-bonding systems involving 3 electrons because two-thirds of the electrons have the same spin. Symmetrical systems like He2+ are exceptions and actually do form bonds because the minority spin is able to delocalize over both centers. In contrast, the ground state of the neutral He2 system entails 2 α and 2 β electrons and is strictly repulsive. Finally, the lowest energy triplet state of ethylene twists toward a D2d structure to avoid a destabilizing interaction akin to that identified in the triplet state of H2.