Competition between Hückel’s Rule and Jahn–Teller Distortion in Small Carbon Rings: A Quantum Monte Carlo Study

Abstract

Structural properties and energetics of carbon rings are studied with the diffusion Monte Carlo (DMC) method. Our DMC-based geometry optimization reveals that both polyynic C_4<i>n</i> and cumulenic C_{4<i>n</i> + 2} rings exhibit bond length alternations for <i>n</i> ≥ 3, which is understood to be due to Jahn-Teller distortions. The bond length alternation even in a cumulenic (4<i>n</i> + 2) carbon ring was experimentally observed in a recently synthesized C₁₈ molecule. From a comparison of the DMC cohesive energies of C_4<i>n</i> with those of C_{4<i>n</i> + 2}, we present a comprehensive picture of the competition between Hückel's rule and Jahn-Teller distortion in small carbon rings; the former is more dominant than the latter for <i>n</i> < 5 where C_{4<i>n</i> + 2} rings are more stable than C_4<i>n</i>, while C_4<i>n</i> rings are as stable as C_{4<i>n</i> + 2} for <i>n</i> < 5 where dimerization effects due to Jahn-Teller distortion are more important.