How do we Treat Electron Correlation in Small Carbon Rings?

Abstract

In addition to linear-geometry triplet states, small even-numbered carbon clusters C-2n adopt cyclic geometries with singlet electronic states. Small in this context means up to twenty atoms or thereabouts. According to both theory (such as coupled-cluster methods) and experiment clusters with 4n + 2 atoms form D(2n+1)h SYMInetry rings with 4n + 2 equal bonds and alternating bond angles, whereas those with 4n atoms form C-2nh symmetry rings with alternating bonds and angles. Higher symmetry forms are assumed to be transition states between these structures. However, coupled-cluster calculations yield multiple negative eigenvalues of the Hessian for these high-symmetry structures, and attempts to follow some of the negative eigenvalue directions downhill lead to inconclusive results. In addition, multiconfigurational reference calculations predict quite different results, in which the high-symmetry structures are genuine transition states, but the downhill direction leads to bond-alternating structures for the 4n + 2 atom rings, instead of the expected angle-alternating structures. We shall review computational results in this area and discuss whether any method currently feasible for systems like this can yield reliable results.