We study the electronic and transport properties of two novel molecular wires made of atomic chains of carbon atoms (polyynes) capped with either benzene-thiols or pyridines. While both molecules are structurally similar, the electrical conductance of benzene-thiol-capped chains attached to gold electrodes is found to be much higher than that of pyridine-capped chains. We predict that the conductance is almost independent of molecular length, which suggests that these molecules could be ideal molecular wires for sub-10 nm circuitry. Both systems exhibit negative differential resistance (NDR) but its origin and characteristics depend on the type of molecule. We find a novel type of NDR mechanism produced by the movement of the lowest unoccupied molecular orbital (LUMO) resonance with bias. We also show that by gating the pyridine-capped molecules it is possible to make the NDR disappear and dramatically modify the I-V characteristics and the length dependence.