Diffuse reflectance infrared (IR) spectroscopy was used to study the structure and dynamics of H2 and CO2 adsorbed within the isostructural metal–organic frameworks M2L (M = Mg, Mn, Fe, Co, Zn; L = 2,5-dioxidobenzene-1,4-dicarboxylate) referred to as M-MOF-74 and CPO-27-M. Cluster models of the primary adsorption site were excised from periodic models that were optimized using plane-wave density functional theory at the Perdew–Burke–Ernzerhof (PBE) level. Models incorporating an adsorbed H2 or CO2 were optimized using dispersion-corrected density functional theory (DFT), and the anharmonic vibrational frequencies of the adsorbate were calculated using the discrete variable representation method. The calculated vibrational frequency shifts reveal the same trend among the M2L materials as those observed experimentally and provide insight into the origins of these shifts. Our experimental spectra of adsorbed CO2 confirm a unique blue shift of the ν3 mode for molecules adsorbed in Mg2L, while the frameworks assembled from transition metals induce a red shift. By shifting the focus to the CO2 local vibrational modes, a deeper insight into the influence of “back bonding” (metal d-electron density donation into CO2 π* orbitals) is revealed; for Mg2L there is a near-complete cancellation of the opposing local mode contributions to the observed frequency shift. Additional spectral features in the CO2 ν3 region are assigned to (1) the ν3 mode of the 13CO2 isotopologue, (2) a combination mode involving a ν2 excitation, and (3) librational sidebands arising from center-of-mass motion of the adsorbed molecule on the surface. Interestingly, below 100 K we observe the appearance of a new band that is distinct from the primary ν3 band observed at room temperature. This band is attributed to an alternate, localized orientation of CO2 adsorbed to the metal site, which is supported by the DFT model.