We present a general analytical formula and an ab initio study of quantum
interference in multi-branch molecules. Ab initio calculations are used to
investigate quantum interference in a benzene-1,2-dithiolate (BDT) molecule
sandwiched between gold electrodes and through oligoynes of various lengths. We
show that when a point charge is located in the plane of a BDT molecule and its
position varied, the electrical conductance exhibits a clear interference
effect, whereas when the charge approaches a BDT molecule along a line normal
to the plane of the molecule and passing through the centre of the phenyl ring,
interference effects are negligible. In the case of olygoynes, quantum
interference leads to the appearance of a critical energy Ec, at which the
electron transmission coefficient T(E) of chains with even or odd numbers of
atoms is independent of length. To illustrate the underlying physics, we derive
a general analytical formula for electron transport through multi-branch
structures and demonstrate the versatility of the formula by comparing it with
the above ab-initio simulations. We also employ the analytical formula to
investigate the current inside the molecule and demonstrate that large counter
currents can occur within a ring-like molecule such as BDT, when the point
charge is located in the plane of the molecule. The formula can be used to
describe quantum interference and Fano resonances in structures with branches
containing arbitrary elastic scattering regions connected to nodal sites.Comment: 12 pages, 11 figure
