A Hückel Study of the Effect of a Molecular Resonance Cavity on the Quantum Conductance of an Alkene Wire

Abstract

We use simple Hückel theory to examine the interference effects on conductance of a “lollypop” side-chain connected to a wire acting as a . We find a clear signature of interference. This is due to the ballistic conductance of these systems and the fact that the voltage bias is not too large (less than about 1eV); at higher voltages the summations in the transmission probability over energies mask the interference. The interference is strongest for small systems. We show that gating effects are enhanced by the presence of the loop, where the electronic wavefunctions can experience a large accumulated change in phase. The interference pattern can be summarized, for a lead with a stick-wire side-group, as dependent on an interference index, I = mod(S,2) + mod(L,4), defined in terms of the stick length S and the loop length L. If I is zero (or 4) then the interference pattern is purely constructive and the conductance is high; if I is 2 then the interference is destructive and conductance is low.

Keywords: Physical Chemistry > Theoretical Chemistry, physchem/0312003