Supported or unsupported three-center two-electron bonds? A criterion based on Interference Energy Analysis

The classification of three-center two-electron (3c2e) bonds into supported (closed) or unsupported (open) was proposed by Lipscomb in his work on boranes and extended to transition metal complexes by Bau and co-workers. The species in which the interactions of the terminal atoms are negligible are called "unsupported bonds." Examples of chemical species that are said to exhibit such bonds are Li₂H⁺, Na₂H⁺, B₂H₇ ^-, Al₂(CH₃)₇ ^-, and [(μ₂-H)Cr₂(CO)₁₀]^- although the general criterion for distinguishing these types of bonds is somewhat qualitative. Besides providing a unifying view of the nature of the chemical bond, in terms of quantum interference among electronic states, the Generalized Product Function Energy Partitioning method through the Interference Energy Analysis (IEA) is also potentially capable of providing a rigorous ground to the concept of supported bonds by looking at the specific interference energies between the orbital pairs associated with the bond. The IEA was performed in the species Li₂H⁺, Na₂H⁺, B₂H₇ ^-, C₂H₇ ^-, Al₂H₇ ^-, and [(μ₂-H)Cr₂(CO)₁₀]^-, as well as along the reaction path Li₂H⁺ → Li₂ ⁺ + H. The results shown that in all studied A-B-C bonds, the A-C interactions are as important as the A-B/B-C ones, leading to the conclusion that all studied 3c2e bonds are "supported," in the sense that the A-C interaction is not negligible. The particularity of those species in preferring linear geometry is completely explained by quasi-classical effects, more specifically, by minimization of the electron-electron and nucleus-nucleus repulsions.