Figure 5 . PESs for the formation of crotonaldehyde from two acetaldehyde molecules catalyzed by MgO or ZnO.
Acetaldehyde molecules formed in the previous step adsorbed on the metal oxide whose energetics are shown in Fig. 5 along with the PESs of the reaction. Similar to the adsorption of ethanol, the adsorption energy of acetaldehyde was larger for ZnO than for MgO (see energetics ofInt6_Mg and Int6_Zn ). This result also reflects the strong Lewis acidic nature of the Zn atom in ZnO. The next step of aldol condensation is carbanion formation, which results from proton transfer from the methyl group of acetaldehyde to the metal oxide cluster, where the relevant TS is schematically described in Fig. 5 (TS6-7_Mg, TS6-7_Zn ). The barrier heights of the proton transfer were computed to be 9.8 kcal/mol and 4.3 kcal/mol for MgO and ZnO, respectively. The smaller barrier height of ZnO implies the strong Lewis basic nature of the O atom in ZnO. The resulting carbanion can now attack the C atom of the carbonyl group of the neighboring acetaldehyde to formInt8_M (M =Mg or Zn) via TS7-8_M . The associated barrier heights for this step were computed to be 6.0 and 11.8 kcal/mol for MgO and ZnO, respectively. The calculated atomistic charge of the carbanion was -0.79 e for MgO and -0.74 e for ZnO, which indicated the carbanion on MgO was more anionic. The lower barrier height of the C-C bond formation step due to MgO catalyst thus was contributed from the larger anionic nature of carbanion on MgO. The C-C bond formation reaction in aldol condensation forms Int8_M(Fig. 5) and the resulting intermediate now had four C atoms, which constitutes the basic skeleton of butadiene. After the formation ofInt8_M , the proton on the metal oxide is transferred back to the O atom via TS8-9_M to form 3-hydroxybutanal (Int9_M ). The barrier for this step was very low (Fig. 5). We note that the energetics of Int6_M and Int9_M , which is the final product of aldol condensation, are virtually identical, i.e., less than 2 kcal/mol, regardless of the catalysts. This result implies that the thermodynamic driving force that leads to the formation of Int6_M from Int9_M is not sufficient.
To form crotonaldehyde, dehydration of 3-hydroxybutanal should occur as the next step. TS9-10_M in Fig. 5 corresponds to C-H bond cleavage occurring at the α-C of 3-hydroxybutanal. The resulting intermediate is Int10_M . In the case of MgO, we could locateInt10’_Mg where the hydroxy group is not bonded to the catalyst, followed by the formation of Int10_Mg . The barrier height of TS9-10_M differs by the involved catalysts as shown in Fig. 5. In the case of MgO, the barrier height was computed to be 20.9 kcal/mol, whereas that of ZnO is 8.9. Thus, ZnO is a more effective catalyst for this step. After the formation of Int10_M , a reaction proceeds to form crotonaldehyde via TS10-11_M , which corresponds to the TS of the OH group transfer to the catalyst, followed by the formation of Int11_M . The barrier height of this elementary reaction by MgO was computed to be 8.4 kcal/mol and that of ZnO, 8.4 kcal/mol. Int11_M is an intermediate where crotonaldehyde, proton and the OH group are adsorbed on the catalyst where the latter two groups are chemically adsorbed. Desorption of crotonaldehyde leads to the formation of Int12_M as described in Fig. 5. After desorption, water-molecule formation on the catalyst and water desorption where the processes finally regenerate the catalysts. The PESs in Fig. 5 show that the energetics ofInt12_Zn is lower than that of Int13_Zn implying that H2O is easily dissociated into H and OH on ZnO. The aldol condensation followed by the dehydration is endothermic by 3.6 kcal/mol.