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

Area of Science:

• Chemical Bonding Theory
• Quantum Chemistry
• Computational Chemistry

Background:

• The classification of three-center two-electron (3c2e) bonds into supported or unsupported types, initially proposed for boranes, has been extended to transition metal complexes.
• Distinguishing between supported and unsupported bonds, where terminal atom interactions are negligible in the latter, has relied on qualitative criteria.
• Existing examples of potentially unsupported bonds include Li₂H⁺, Na₂H⁺, B₂H₇⁻, Al₂(CH₃)₇⁻, and [(μ₂-H)Cr₂(CO)₁₀]⁻.

Purpose of the Study:

• To provide a rigorous, quantitative method for classifying 3c2e bonds as supported or unsupported.
• To investigate the nature of chemical bonding in various species using quantum interference principles.
• To apply the Generalized Product Function Energy Partitioning (GFPEP) method, specifically Interference Energy Analysis (IEA), to analyze these bonds.

Main Methods:

• Application of the Generalized Product Function Energy Partitioning (GFPEP) method.
• Detailed Interference Energy Analysis (IEA) to quantify orbital pair interactions within 3c2e bonds.
• Computational study of species including Li₂H⁺, Na₂H⁺, B₂H₇⁻, C₂H₇⁻, Al₂H₇⁻, and [(μ₂-H)Cr₂(CO)₁₀]⁻, and the reaction path Li₂H⁺ → Li₂⁺ + H.

Main Results:

• The IEA revealed that in all studied A-B-C bonds, the interactions between terminal atoms (A-C) are as significant as the interactions involving the central atom (A-B/B-C).
• This indicates that the A-C interactions are not negligible in any of the examined cases.
• The preference for linear geometry in these species is explained by quasi-classical effects, specifically the minimization of electron-electron and nucleus-nucleus repulsions.

Conclusions:

• All investigated three-center two-electron (3c2e) bonds are classified as 'supported' due to significant terminal atom interactions.
• The Interference Energy Analysis (IEA) provides a robust, quantitative framework for understanding and classifying chemical bonds.
• The observed geometries are a consequence of minimizing inter-particle repulsions, supporting a quasi-classical explanation.