Small molecules may adsorb strongly in metal-organic frameworks (MOFs) through interactions with under-coordinated open metal sites (OMS) that often exist within these structures. Among adsorbates, CO is attractive to study both for its relevance in energy-related applications and for its ability to engage in both σ-donation and π-backbonding interactions with the OMS in MOFs. Concomitant with strong adsorption, structural changes arise due to modifications of the electronic structure of both the adsorbate and adsorbent. These structural changes affect the separation performance of materials, and accurately capturing these changes and the resulting energetics is critical for accurate predictive modeling of adsorption. Traditional approaches to modeling using classical force fields typically do not capture or account for changes at the electronic level. To characterize the structural and energetic effects of the local structural changes, we employed density functional theory (DFT) to study CO adsorption in M-MOF-74s. M-MOF-74s feature OMS at which CO is known to adsorb strongly and can be synthesized with a variety of divalent metal cations with distinct performance in adsorption. We considered M-MOF-74s with a range of metals of varied d-band occupations (Mg (3d0), Mn (3d5), Ni (3d8), and Zn (3d10)) with various structural constraints ranging from geometrically constrained adsorbent and adsorbate ions to fully optimized geometries to deconvolute the relative contributions of various structural effects to the adsorption energetics and binding distances observed. Our data indicate that the most significant structural changes during adsorption correlate with the greatest π-backbonding behaviors and commensurately result in a sizable binding energy change observed for CO adsorption. The insights built from this work are relevant to two longstanding research challenges within the MOF community: rational design of materials for separations and the design of force fields capable of accurately modeling adsorption.