## 2 Experimental Section
### Catalysts Characterization  
Ten mg of either Ce(NO\({}_{3}\))\({}_{3}\cdot\)6H\({}_{2}\)O or rhodium nitrate impregnated on Ce25 (Rh(NO\({}_{3}\))\({}_{3}\)/Ce25) were decomposed in a thermobalance TG-DTA (METTLER TOLEDO model TGA/SDTA851e/LF/1600, L'Hospitalet de Llobregat, Barcelona, Spain) coupled to a mass spectrometer (PFEIFFER VACUUM model THERMOSTAR GSD301T, Alcobendas, Madrid, Spain) under 100 mL/min flow of synthetic air, with a heating rate of 50 \({}^{\circ}\)C/min.  
A Bruker D8-advance device (Rivas Vaciamadrid, Madrid, Spain) was used to obtain diffractograms between 10\({}^{\circ}\) and 80\({}^{\circ}\) (20), with steps of 0.02\({}^{\circ}\) and a step time of 3 s. CuK\(\alpha\) radiation (\(\lambda\) = 1.540598 A) was used. The average crystal size (D) was determined using the Scherrer and Williamson-Hall equations [20].  
Raman spectra were recorded in a Jobin Yvon Horiba Raman dispersive spectrometer with a variable-power He-Ne laser source (632.8 nm) and using a confocal microscope with a 50\(\times\) objective of long focal length (Horiba Scientific, Tres Cantos, Madrid, Spain). The spectrum of each sample was obtained as the average signal of 12 individual spectra of different areas of the sample. The acquisition time for each individual spectrum was 10 s.  
Physical adsorption and desorption isotherms of N\({}_{2}\) were obtained at -196 \({}^{\circ}\)C in an automatic volumetric system (Autosorb-6, Quantachrome GmbH & Co. KG, Odelzhausen, Upper Bavaria, Germany). Samples were outgassed at 150 \({}^{\circ}\)C for 4 h under vacuum before the N\({}_{2}\) adsorption measurements. The BET surface areas were determined from the N\({}_{2}\) adsorption isotherms.  
Experiments of temperature programmed reduction with H\({}_{2}\) (H\({}_{2}\)-TPR) were carried out in a Micromeritics Pulse ChemiSorb 2705 device, (Micromeritics Germany GmbH, Aachen, North Rhine-Westphalia Germany), consisting of a tubular quartz reactor (inner diameter 5 mm) coupled to a TCD analyzer. A cold trap consisting of a mixture of isopropyl alcohol and liquid nitrogen at \(-89\)\({}^{\circ}\)C was placed before the TCD. 20 mg of fresh catalyst were pre-treated _in situ_ at 500 \({}^{\circ}\)C for 1 h in a 50 mL/min flow of 5% O\({}_{2}\) in He. After cooling to room temperature, the flow gas was switched to 40 mL/min of 5 vol% H\({}_{2}\) in Ar and the temperature was increased at 10 \({}^{\circ}\)C/min up to 1050 \({}^{\circ}\)C.  
TEM characterization was performed using a JEOL (JEM-2010) microscope, equipped with an EDS analyzer (OXFORD, model INCA Energy TEM100, Wiesbaden, Hesse, Germany). The samples were dispersed on ethanol and placed on a cupper grid with lacey carbon film. The Rh particle size distribution was estimated on a selected catalyst from the TEM pictures. For this estimation, the size of around 100 rhodium particles was measured with the software analiSYS.  
XPS characterization of selected catalysts was carried out in a VG-Microtech Multilab electron spectrometer using a MgK\(\alpha\) (1253.6 eV) radiation source. To obtain the XPS spectra, the pressure of the analysis chamber was maintained at 5 \(\times\) 10\({}^{-10}\) mbar. The binding energy (BE) and the kinetic energy (KE) scales were adjusted by setting the C1s transition at 284.6 eV, and BE and KE values were determined with the Peak-fit software of the spectrometer. XPS spectra were recorded with selected fresh catalysts and with the same catalysts pre-treated _in situ_ under N\(\alpha\) at 225 \({}^{\circ}\)C for different periods of time. The _in situ_ pre-treatments were carried out in an auxiliary reaction chamber, where the sample was heated to 225 \({}^{\circ}\)C and the gas mixture (1000 ppm N\({}_{2}\)O/He, 1 atm total pressure) was fed. After the pre-treatment, the sample was introduced into the XPS chamber, avoiding exposure to air. The oxidation states of rhodium and cerium have been determined with similar assignations to those reported elsewhere [21, 22].