A unifying electron-counting rule for macropolyhedral boranes, metallaboranes, and metallocenes

Area of Science:

• Inorganic Chemistry
• Theoretical Chemistry
• Materials Science

Background:

• Wade's rules are established for predicting the electronic structure of simple boranes.
• Complex polyhedral boranes and metallaboranes present challenges for existing electron-counting methods.
• Metallocenes and condensed polyhedral systems require a more generalized approach.

Purpose of the Study:

• To present a generally applicable electron-counting rule for macropolyhedral boranes, metallaboranes, and metallocenes.
• To demonstrate the rule's ability to predict the stability of diverse and complex cluster compounds.
• To provide a unified framework for understanding the electronic requirements of various polyhedral systems.

Main Methods:

• Development of the mno electron-counting rule based on the number of polyhedra (m), vertices (n), and condensations (o).
• Application of the mno rule to known macropolyhedral boranes, heteroboranes, and metallocenes.
• Analysis of condensation pathways using icosahedral B12 as a model.
• Exploration of the rule's origin using fragment molecular orbital theory.

Main Results:

• The mno rule accurately predicts the electron requirements for stability in macropolyhedral systems, including condensed structures and metallocenes.
• Wade's n + 1 rule is shown to be a special case of the mno rule.
• Examples such as B20H16 and ferrocene are correctly analyzed using the mno rule.
• Fragment molecular orbital analysis confirms the electronic basis for the mno rule, explaining orbital interactions during condensation.

Conclusions:

• The mno rule offers a powerful and general method for predicting the stability of a wide range of polyhedral cluster compounds.
• This rule unifies the understanding of electron counting across different classes of inorganic clusters.
• The findings provide a theoretical basis for designing and synthesizing novel cluster architectures.