## 3 Case Studies
### Carbon Monoxide Adsorption in Zeolites  
As a first example of gas adsorption in zeolites as studied by VTIR spectroscopy (combined with periodic DFT calculations) let us consider the case of CO adsorption in ferrierite, which is a medium pore zeolite having the framework topology depicted in Figure 2. Representative variable-temperature FT-IR spectra (in the C-O stretching region) of carbon monoxide adsorbed on a thin self-supported wafer of Na-FER having a Si:Al ratio of 8:1 are shown in Figure 3, experimental details can be found elsewhere [92]. It is important to remark, however, that surface coverage (\(\theta\)) should be always kept small enough to avoid formation of dicarbonyl species [93,94], which would otherwise complicate application of the VTIR method. Main IR absorption bands are seen at 2158 and 2175 cm\({}^{-1}\), both of them showing a hypsochromic shift of the C-O stretching frequency (2143 cm\({}^{-1}\) for free CO) as expected for an adsorption carbonyl species (Na\({}^{+}\cdots\)CO) having the dipolar CO molecule interacting through the carbon atom with a positively charged adsorption site [95,96]. By contrast, formation of an isocarbonyl complex (Na\({}^{+}\cdots\)OC) is expected to bring about a bathochromic shift of the C-O stretching mode [97,78,97], as actually shown by the very weak IR absorption band peaking at about 2115 cm\({}^{-1}\). This isocarbonyl species is, however, a very minor feature, which will not be give further consideration herein. After computer resolution and determination of the integrated absorbance of the bands at 2158 and 2175 cm\({}^{-1}\) in Figure 3, for the whole set of IR spectra experimentally recorded, the corresponding plots of the left-hand side of Equation (5) against the reciprocal of the temperature (van't Hoff plots) shown in Figure 4 were obtained. In each case, the needed value of \(A_{\rm M}\) was obtained by refining the corresponding experimental one following the iteration procedure described elsewhere [38]. From those linear van't Hoff plots, the value of the corresponding standard adsorption enthalpy resulted to be \(\Delta H^{0}=-34.6\) kJ mol\({}^{-1}\) for the adsorbed species giving rise to the band at 2158 cm\({}^{-1}\), and \(\Delta H^{0}=-30.5\) kJ mol\({}^{-1}\) for that one peaking at 2175 cm\({}^{-1}\), which coincide (within experimental error) with the DFT calculated values of 32-35 and 29 kJ mol\({}^{-1}\), respectively [92]. Figure 4: Van’t Hoff plots corresponding to the IR absorption bands at 2175 and 2158 cm\({}^{-1}\) in Figure 3 (adapted from [92]). Figure 3: VITR spectra of carbon monoxide adsorbed on Na-FER [(Si:Al) = (8:1)]. From top to bottom, temperature goes from 207 to 274 K; and equilibrium pressure from 0.19 to 1.35 mbar (adapted from [92]). According to those theoretical DFT calculations [92], the IR absorption band peaking at 2175 cm\({}^{-1}\) corresponds to the C-O stretching mode of carbon monoxide C-bonded to Na\({}^{+}\) ions which constitute _single_ (i.e., isolated) cation sites, as shown in Figure 5a (calculated \(\
u_{\text{CO}}\) values in the range of 2174-2178 cm\({}^{-1}\)), while the band at 2158 cm\({}^{-1}\) comes from adsorption complexes in which the CO molecule bridges two nearby Na\({}^{+}\) cations, which constitute a _dual_ cation site, as shown in Figure 5b. It is worth of note that (in general terms) the bridged adsorption complex is usually more stable than the C-bonded complex at a single site. Nevertheless, the corresponding \(\
u_{\text{CO}}\) value is smaller for the bridged complex, because polarization of the CO molecule through the O atom partially counteracts polarization through the C atom. It should also be noted that the stabilization energy of the bridged Na\({}^{+}\cdots\)CO\(\cdots\)Na\({}^{+}\) complex on a dual site is sharply dependent on the distance apart between the two cations. Calculated values [92] for both, Na\({}^{+}\) and K\({}^{+}\) are shown in Figure 6. The optimum inter-cation distance is of about 6.6 and 7.9 A for Na\({}^{+}\) and K\({}^{+}\), respectively.