A Hückel study of the effect of a molecular resonance cavity on the quantum conductance of an alkene wire

We use Hückel theory to examine interference effects on conductance of a wire when a `lollypopʹ side-chain is bonded to it, acting as a resonance cavity. A clear signature of interference is found at these ballistic conducting systems, stronger in small systems. Gating effects are enhanced by the presence of the loop, where the electronic wavefunctions can experience large changes in phase. Using an `interference indexʹ, I=mod(S,2)+mod(L,4), where S,L are stick and loop lengths, respectively, we conclude that interference is constructive (destructive) and conductance high (low) when I=0,4(I=2).