Conductance through analytic constrictions

We study the dependence of the intrinsic conductance of a nanocontact on its shape by using the recursion-transfer-matrix method. Hour-glass, torus, and spherical shapes are defined through analytic potentials, the latter two serving as rough models for ring-like and spherical molecules, respectively. The sensitivity of the conductance to geometric details is analyzed and discussed. Strong resonance effects are found for a spherical contact weakly coupled to electron reservoirs.