Electron Correlation inC4N+2Carbon Rings: Aromatic versus Dimerized Structures

The electronic structure of ${\mathrm{C}}_{4N+2}$ carbon rings exhibits competing many-body effects of Hückel aromaticity, second-order Jahn-Teller (SOJT), and Peierls instability at large sizes. This leads to possible ground state structures with aromatic, bond angle, or bond length alternated geometry. Highly accurate quantum Monte Carlo results indicate the existence of a crossover between ${\mathrm{C}}_{10}$ and ${\mathrm{C}}_{14}$ from bond angle to bond length alternation. The aromatic isomer is always a transition state. The gap opening mechanism is the SOJT effect, which coalesces with the Peierls regime as $N\to \infty$.