Illusory Connection between Cross-Conjugation and Quantum Interference

Quantum interference, be it destructive or constructive, has a substantial influence on the magnitude of molecular conductance, and consequently there is significant interest in predicting these effects. It is commonly thought that cross-conjugated paths result in suppressed conductance due to destructive quantum interference. Using Hückel theory and density functional theory calculations we investigate systems that break this cross-conjugation rule of thumb. We predict and rationalize how a class of conjugated molecules containing closed loops can exhibit destructive interference despite being linearly conjugated and exhibit constructive interference despite being cross-conjugated. The arguments build on the graphical rules derived by Markussen et al. [ Nano Lett. 2010, 10, 4260] and the hitherto neglected effects of closed loops in the molecular structure. Furthermore, we identify the 1,3 connected azulene molecule as belonging to the closed-loop class and argue that this explains recent measurements of its electrical conductance.