Understanding the molecular details of CO2-sorbent interactions is critical for the design of better carbon-capture systems. Here we report crystallographic resolution of CO2 molecules and their binding domains in a metal-organic framework functionalized with amine groups. Accompanying computational studies that modeled the gas sorption isotherms, high heat of adsorption, and CO2 lattice positions showed high agreement on all three fronts. The modeling apportioned specific binding interactions for each CO2 molecule, including substantial cooperative binding effects among the guest molecules. The validation of the capacity of such simulations to accurately model molecular-scale binding bodes well for the theory-aided development of amine-based CO2 sorbents. The analysis shows that the combination of appropriate pore size, strongly interacting amine functional groups, and the cooperative binding of CO2 guest molecules is responsible for the low-pressure binding and large uptake of CO2 in this sorbent material.