In summary, we have developed a fully first-principles-based conductance model for single-molecule junctions using a modified tunneling equation. Results from our model for benzene-1,4thiol and benzene-1,4-diamine junctions containing gold electrodes agree well with experimental results. We attribute the better accuracy of our model to the use of a range-separated hybrid functional as well as to the calculation of an ab initio effective mass of the transporting charge. Further, we have applied our model to junctions not only within the well-studied gold electrode system but also to less studied junction electrode materials such as silver and copper. Our work highlights the importance of describing the atomistic and quantum-mechanical nature of the molecule-electrode realistically to capture the electrical and mechanical properties of single-molecule junctions. Future work will employ this tunneling model with ab initio molecular dynamics to investigate conductance fluctuations in single-molecule junctions.