What is the exchange-repulsion energy? Insight by partitioning into physically meaningful contributions

Exchange repulsion, the dominant repulsive contribution to intermolecular interaction energies, is caused by the Pauli principle, which enforces that electrons with the same spin must not be located at the same place. Starting from the Heitler-London expression of the exchange-repulsion energy, Exr, we investigate how it can be partitioned into physically relevant and comprehensible contributions. We demonstrate that a division of Exr into a positive kinetic and a negative potential part is possible. However, these contributions correlate only poorly with the actual exchange-repulsion energy. A meaningful partitioning of Exr is derived, where the kinetic energy contribution belongs to a term that vanishes for exact Hartree-Fock wave functions. The remaining pure potential energy terms are distinguished into an exchange integral contribution, Exi, as well as contributions to the repulsion-energy with two, three and four orbital indices (Exr2, Exr3, and Exr4). Qualitative explanations of these terms and their physical origin are proposed. The forms, relationships and absolute sizes of the four parts of Exr suggest an intuitive partitioning of the exchange-repulsion energy into orbital-pair contributions. Insight into the analytic form and quantitative size of the contributions to Exr is provided by considering the 3Sigma+u (1sigma g 1sigma u) state of the H2 molecule, the water dimer, as well as an argon atom interacting with Cl2 and N2. It is demonstrated that Exr is best described as a contribution due to the potential energy and that its leading contribution, Exr2, provides an intuitive qualitative and quantitative approach towards the exchange-repulsion energy.