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We present a general analytical formula and an ab initio study of quantuminterference in multi-branch molecules. Ab initio calculations are used toinvestigate quantum interference in a benzene-1,2-dithiolate (BDT) moleculesandwiched between gold electrodes and through oligoynes of various lengths. Weshow that when a point charge is located in the plane of a BDT molecule and itsposition varied, the electrical conductance exhibits a clear interferenceeffect, whereas when the charge approaches a BDT molecule along a line normalto the plane of the molecule and passing through the centre of the phenyl ring,interference effects are negligible. In the case of olygoynes, quantuminterference leads to the appearance of a critical energy $E_c$, at which theelectron transmission coefficient $T(E)$ of chains with even or odd numbers ofatoms is independent of length. To illustrate the underlying physics, we derivea general analytical formula for electron transport through multi-branchstructures and demonstrate the versatility of the formula by comparing it withthe above ab-initio simulations. We also employ the analytical formula toinvestigate the current inside the molecule and demonstrate that large countercurrents can occur within a ring-like molecule such as BDT, when the pointcharge is located in the plane of the molecule. The formula can be used todescribe quantum interference and Fano resonances in structures with branchescontaining arbitrary elastic scattering regions connected to nodal sites.

Quantum Interference in Single Molecule Electronic Systems