We used dispersion-corrected density-functional theory to perform an in silico search over a series of primary alkylamines, including linear, branched, and cyclic molecules, to identify capping molecules for shape-selective Cu nanocrystal synthesis. We identify several attributes associated with successful capping agents. Generally, molecules with good geometric matching to the Cu surfaces possessed the strongest molecule-surface chemical bonds. However, non-bonding van der Waals interactions and molecular packing constraints can play a more significant role in determining the overall binding energy, the surface coverage, and the likely efficacy of the capping molecule. Though nearly all the molecules exhibited stronger binding to Cu(100) than to Cu(111), all predicted Wulff shapes are primarily {111}-faceted, based on ab initio thermodynamics calculations. From predicted capping-molecule densities on Cu(100) and Cu(111) for various solution environments, we identified several candidate molecules to produce {100}- or {111}-faceted nanocrystals with kinetic shapes, based on synthesis conditions used to grow Cu nanowires with ethylenediamine capping agent. Our study reveals the complexity of capping-molecule binding and important considerations that go into the selection of a successful capping agent.