With the aid of the Friedel sum rule, we perform first-principles calculations of conductances through monatomic Na wires, taking into account the sharp tip geometry and discrete atomic structure of electrodes. We find that conductances $\left(G\right)$ depend on the number $\left(L\right)$ of atoms in the wires; $G$ is $G_0({=2e}^2/h)$ for odd $L$, independent of the wire geometry, while $G$ is generally smaller than $G_0$ and sensitive to the wire structure for even $L$. This even-odd behavior is attributed to the charge neutrality and resonant character due to the sharp tip structure. We suggest that similar even-odd behavior may appear in other monovalent atomic wires.

• Received 7 December 2000

DOI:https://doi.org/10.1103/PhysRevLett.87.096803