Open-shell spherical aromaticity: the 2N2 + 2N + 1 (with S = N + ½) rule

Area of Science:

• Theoretical Chemistry
• Quantum Chemistry
• Aromaticity Theory

Background:

• Baird's rule extended Hückel's 4N + 2 rule to triplet states.
• Hirsch's rule addresses aromaticity in spherical systems.
• The need to understand aromaticity in open-shell spherical compounds.

Purpose of the Study:

• To extend the 2(N + 1)(2) Hirsch rule to open-shell spherical compounds.
• To identify criteria for aromaticity in these systems.
• To provide theoretical evidence for the proposed aromaticity rule.

Main Methods:

• Theoretical extension of the Hirsch rule.
• Analysis of electronic configurations in spherical systems.
• Correlation of electron counts and spin states with aromaticity.

Main Results:

• The study successfully extends the Hirsch rule to open-shell spherical species.
• Evidence suggests aromaticity in systems with 2N(2) + 2N + 1 electrons and S = N + ½.
• Aromaticity is linked to a half-filled last energy level with all others fully-filled.

Conclusions:

• The extended Hirsch rule provides a new criterion for aromaticity in open-shell spherical compounds.
• Specific electronic configurations (2N(2) + 2N + 1 electrons, S = N + ½) are indicative of aromaticity.
• This work contributes to a deeper understanding of aromaticity beyond planar systems.