## 2 Materials and Methods
### Catalytic Activity Experiments  
The catalytic tests were carried out in a tubular quartz reactor, coupled with different analyzers in parallel: a mass spectrometer, a micro-gas chromatograph, and a UV-NO\({}_{\mathrm{x}}\) analyzer. A total of 60 mg of catalyst was used for each experiment and the total inlet gas flow was kept at 100 mL/min during the experiment (GHSV = 100,000 h\({}^{-1}\)). The NO\({}_{\mathrm{x}}\) adsorption/reduction cycles were performed at a constant temperature in the range 150-350 \({}^{\circ}\)C (with the exception of Ba6/CZ that was only investigated under 250-350 \({}^{\circ}\)C). In a typical experiment, the catalyst was pre-treated in inert atmosphere at 500 \({}^{\circ}\)C for 30 min; then, it was cooled down to the adsorption/reduction temperature. The adsorption phase was carried out by feeding to the reactor 1000 ppm of NO + 3% \(v/v\) of O\({}_{2}\) in He (as balance), up to catalyst saturation. After ca. 1 h, NO and O\({}_{2}\) concentrations were decreased stepwise to zero, followed by He purge at the same temperature. The subsequent reduction step was performed by feeding to the reactor 2000 ppm H\({}_{2}\) in He (as balance) during a variable time, but around 1 h in most of the cases. The reason for this variability is the different rates of decay of MS signals and/or the different reactivities of the catalysts at the two temperatures of interest. Nevertheless, the time was kept until all the N-reduction product emissions decayed in all the cases. Finally, to ensure a complete release/decomposition of the previously adsorbed NO\({}_{\mathrm{x}}\) species (in case they were not reduced during the reduction step), Temperature Programmed Desorption (TPD) was performed by increasing the temperature progressively up to 500 \({}^{\circ}\)C under He (10 \({}^{\circ}\)C/min). An additional experiment consisting of consecutive pulses of NO + O\({}_{2}\) (for 20 min each) and subsequent pulses of H\({}_{2}\) (for 15 min each) was performed for the Ba6/Cu2 CZ sample at a constant temperature of 300 \({}^{\circ}\)C and using the same gas concentrations. After finishing these cycles, a TPD was carried out, heating up to 500 \({}^{\circ}\)C (10 \({}^{\circ}\)C/min) under He, in order to release/decompose the remaining N-species (previously adsorbed); since N-species balance during each NOx adsorption cycle pointed out a certain NOx adsorbed amount remaining at the end of the cycle. The selectivity towards the different reduction products detected was estimated according to the following Equations (1)-(4). Even though very minor N\({}_{2}\)O and NH\({}_{3}\) productions were monitored in some of the experiments, these compounds were also taken into account for calculation purposes:  
\[\mathrm{S_{N_{2}}(\%)=100\cdot\frac{2n_{N_{2}}}{2n_{N_{2}}+n_{NO}+\ n_{NH_{3}}+2n_{N _{2}O}}} \tag{1}\]  
\[\mathrm{S_{NO}(\%)=100\cdot\frac{n_{NO}}{2n_{N_{2}}+n_{NO}+\ n_{NH_{3}}+2n_{N _{2}O}}} \tag{2}\]  
\[\mathrm{S_{NH_{3}}(\%)=100\cdot\frac{n_{NH_{3}}}{2n_{N_{2}}+n_{NO}+\ n_{NH_{3}}+2n_{N _{2}O}}} \tag{3}\]  
\[\mathrm{S_{N_{2}O}(\%)=100\cdot\frac{2n_{N_{2}O}}{2n_{N_{2}}+n_{NO}+\ n_{NH_{3}}+2n_{N _{2}O}}} \tag{4}\]  
where \(n_{N2}\), \(n_{NO}\), \(n_{N2}\)O, and \(n_{NH3}\) are the total molar amounts of N\({}_{2}\), NO, N\({}_{2}\)O, and NH\({}_{3}\), respectively, evolved during the reduction phase and calculated by the integrals of the corresponding concentration curves vs. time. Complementary in situ DRIFTS experiments were performed using a FT/IR-4000 Series spectrometer (JASCO Corporation, Tokyo, Japan), with a high-temperature reaction chamber, 4 cm\({}^{-1}\) of resolution, and 16 scans per spectrum, in the 4000-500 cm\({}^{-1}\) spectral range. The experiments were carried out in the interval of 150-350 \({}^{\circ}\)C, with approximately 60-70 mg of sample to fill the crucible, which was placed inside the reaction chamber; the flow was kept constant during the entire experiment, at 100 mL/min.