Study of the Glycerol Hydrogenolysis Reaction on Cu, Cu–Zn, and Cu–ZnO Clusters

Quantum chemistry calculations have been performed to access the efficacy of Cu-based catalysts in various mechanistic steps of the glycerol hydrogenolysis reaction. Calculations are first performed for reactants in the gas phase (noncatalyzed system) and reactants in the gas phase with a 3-atom Cu cluster (catalyzed system). We demonstrate that the glycerol to ethylene glycol conversion is preferred in the noncatalyzed system but glycerol conversion to 1,2-propanediol via the 2-acetol intermediate is preferred in the catalyzed system. We next analyze the adsorption energies of the reactant and product species involved in the glycerol to 1,2-PDO reaction on an 8-atom Cu cluster and Cu cluster doped with a Zn atom or a ZnO molecule. Finally, we study the effects of Zn or ZnO doping on the activation barriers of the two steps of the glycerol to 1,2-PDO reaction.


INTRODUCTION
Glycerol conversion to value-added products has received significant scientific attention in recent years. One of the main motivating forces for this trend is the fact that glycerol (propane-1,2,3-triol) is produced in large quantities during biodiesel production, 1,2 that is, roughly 10% by weight of the produced biodiesel. Two of the most useful value-added products of glycerol are 1,2-propanediol (1,2-PDO) and 1,3propanediol (1,3-PDO), 3 which are formed by the hydrogenolysis of glycerol. From a mechanistic perspective, PDO formation requires the use of catalysts that facilitate the formation of a C�O bond, which is otherwise less favored than the formation of a C�C bond. Several transition metal and noble metal catalysts 4−7 have been tried over the years for the hydrogenolysis reaction, which exhibit various degrees of selectivity to the formation of 1,2-PDO and 1,3-PDO. In general, while 1,3-PDO is considered more valuable than 1,2-PDO, the latter is generally the dominant product of the hydrogenolysis reaction. 8 1,2-PDO finds use in the manufacturing of unsaturated polyester resins, paints, and cosmetics and as starting materials in printing, pharmaceuticals, etc. 3,9,10 The actual mechanism of the glycerol hydrogenolysis reaction is debated, and several possible reaction schemes have been proposed. 9 Figure 1 shows probably the most accepted scheme showing the common products of the hydrogenolysis reaction. The formation of PDO from glycerol (I) proceeds via an acetol intermediate, which involves the cleavage of the C−OH bond to form a C�O bond. Depending on which C−OH bond is attacked, 2-acetol (II) or 1-acetol (III) can be formed, which may then be hydrogenated to form 1,2-PDO (IV) or 1,3-PDO (V), respectively. In principle, IV and V may further hydrogenolyze to form the over-hydrogenolysis products, 2-propanol (VI) and 1-propanol (VII), respectively. As an alternative to the formation of the acetol intermediate, the hydrogenolysis reaction may also result in the formation of ethylene glycol (VIII) by cleavage of the C−C bond, followed by its subsequent hydrogenolysis to ethanol (IX). IX and methanol (X) may also be formed by the hydrogenation of PDO. Taking into consideration all the above-mentioned possible reactions, one should use catalysts that facilitate the cleavage of the C− OH bond without attacking the C−C bond of the glycerol molecule, to have higher selectivity toward PDO. Moreover, the formation of IX and X needs to be suppressed by selection of appropriate reaction conditions. As an alternate to the mechanism proposed in Figure 1, the formation of 1,2-PDO by hydrogenolysis may also occur by glycerol dehydrogenation to glyceraldehyde followed by its dehydration and hydrogenation to 1,2-PDO or a "direct" glycerol hydrogenolysis. 9 In this paper, we are interested in Cu-based catalysts, in which the formation of PDO via an acetol intermediate has been established in several experimental studies. [4][5][6]11,12 Recently, Pandey et al. 14 have investigated the use of different acid-and base-supported Cu−Zn bimetallic catalysts for glycerol hydrogenolysis in the vapor phase, in which Cu− Zn/MgO was found to be most selective to 1,2-PDO and resulted in almost 100% conversion. Mondal et al. 13 have also reported nearly 100% conversion with 94% selectivity to 1,2-PDO with the Cu−Zn(4:1)/MgO catalyst in the liquid phase. They attributed the increased performance to a "hydrogen spillover" effect, which is the migration of the hydrogen atoms from the metal catalyst onto the nonmetal supports. Hydrogen spillover may increase the reducibility of the Cu catalyst, thus increasing the reaction selectivity toward 1,2-PDO. A similar finding was also reported in a study by Xia et al., 15  Although experimental studies have provided many insights into the reaction pathways, theoretical analysis using complementary tools may provide better interpretation at the molecular level. Hirunsit et al. 18 have performed theoretical and experimental studies on glycerol hydrogenolysis over Cu/ Al 2 O 3 that showed selectivity for 1,2-PDO. Using density functional theory (DFT) calculations, they have demonstrated that the improved catalytic activity on Cu/Al 2 O 3 compared to that of pure Cu results from the presence of acidic Al sites. The mechanisms of glycerol dehydration have been studied by Nimlos et al. 19 using quantum chemistry calculations (using CBS-QB3). They determined the activation barriers to 1,2dehydration and for pericyclic 1,3-dehydration. Geng et al. 20 described four possible routes of glycerol pyrolysis using quantum chemistry calculations and investigated the energy barriers and reaction rate constants to analyze the possible pyrolysis mechanisms. Laino et al. 21 investigated the dehydration mechanism of glycerol in the gas phase and showed that the glycidol barrier is 66.8 kcal/mol, which is the rate-limiting step of glycerol decomposition. More recently, Karim et al. 22 described the water dissociation and dehydrogenation of glycerol over Au(111) and PdAu alloy catalyst surfaces to produce hydrogen. Guan et al. 23 have performed thermodynamic analysis of glycerol hydrogenolysis to propanediols over supported Cu clusters using periodic density functional theory. They reported that Cu/MgO exhibits better activity than that of Cu/ZrO 2 and also shows selectivity to 1,2-PDO in comparison to 1,3-PDO. Chen et  indicates a Cu atom with x bonded neighbors, i.e., coordination number x. For clusters containing Zn atoms, "_Near" or "_Away" is suffixed to indicate Cu atoms bonded to or away from Zn atom, respectively. al. 24 showed an efficient reaction pathway for glycerol to synthesis gas using C−C bond scission.
This study is the extension of our previous study, 25 wherein we performed DFT calculations to study the structure and stability of Cu, Cu−Zn, and Cu−ZnO clusters and adsorption of glycerol and hydrogen on each and every possible coordination of these clusters. In this study, we shift our focus to the hydrogenolysis reaction and first establish that the hydrogenolysis to PDO indeed follows the formation of an acetol intermediate when using a Cu 3 cluster, unlike a noncatalyzed system where ethylene glycol formation is preferred. Next, we study the adsorption energies of reactants and products, activation barriers, rate constants, and reaction energies on each possible coordination site of Cu and Zn atoms in Cu 8 , Cu 7 Zn, and Cu 7 ZnO for the glycerol to 1,2-PDO reaction via the 2-acetol intermediate. The current study together with our previous study 25 thus provides useful molecular insights into the use of Cu−Zn and Cu−ZnO catalysts for the glycerol hydrogenolysis reaction.

COMPUTATIONAL DETAILS
DFT calculations are carried out using Gaussian 09 software 26 with the Gauss View 5 user interface. Optimized geometries are obtained by DFT calculations performed using the B3LYP 27 functional combined with the double-ζ-type LanL2DZ 28−30 basis set, which has been validated and used successfully in our previous study. 25 Minimum energy geometries of catalyst clusters (Figure 2), reactants and products, reactants and products adsorbed on catalyst clusters, and transition states of reactions are obtained using optimization calculations. Doublet spin multiplicity is chosen for Cu 3 , Cu 7 Zn, and Cu 7 ZnO clusters having one unpaired electron, and singlet spin multiplicity is chosen for the Cu 8 cluster having no unpaired electrons. The initial assumptions for these calculations are computed by optimization performed using Hartree-Fock(HF)/LanL2DZ theory, which are then reoptimized using B3LYP/LanL2DZ. Energies and vibrational frequencies are then computed for these optimized geometries. No imaginary vibration frequencies are obtained for the minimum energy configurations except for the transition states. Transition states are characterized as having only one imaginary vibrational frequency. Separately, intrinsic reaction coordinate (IRC) 31 calculations are also performed to confirm the obtained transition states. The activation barriers for reactions shown in Figure 3 are computed as the difference between the energies of the transition state and the reactants. The adsorption energy of a species ("adsorbate") on a catalyst cluster is computed by the following equation, as used in our previous study. 25 where E cl·ad is the energy of the cluster with the adsorbate (reactant, transition states, products) and E cl and E ad are the individual energies of the cluster and adsorbate, respectively. The reaction rate constants (k) are calculated using transition state theory 32,33 as i k j j j j j y where k B is the Boltzmann constant, h is the Planck constant, R is the gas constant, and ΔG ≠ is the Gibbs free energy of activation at temperature T = 298.15 K. ΔG ≠ is calculated as the difference between the Gibbs free energy of the transition state and the reactant(s). The reaction energy is calculated as the difference of electronic energy (with zero-point correction) between products and reactants. Note that the energies of clusters on which the reactant(s)/product(s) are adsorbed are also included for the purpose of calculation of reaction energy and free energy differences.

Reaction Mechanism with and without Catalyst
Clusters. The reaction mechanisms of glycerol hydrogenolysis are first studied for the system without and with a Cu 3 cluster. Figure 3 shows the activation barriers for each of the reactions defined as the difference in the energy of the transition state and the reactant(s). The minimum energy geometries of the reactant(s), transition state (TS), and product(s) of the reactions are shown in Table 1, along with their first harmonic frequency. The activation barrier is lowered for all reactions with the use of a Cu 3 cluster except reactions I (glycerol) to III (1-acetol) and I to VIII (ethylene glycol) and X (methanol). Although the activation barrier for the reaction I to II (2acetol) undergoes a minor reduction (≈2.2 kcal/mol) with the use of the Cu 3 cluster, the activation barrier of the subsequent reaction II to IV (1,2-PDO) undergoes a drastic reduction (activation barrier difference of ≈69.9 kcal/mol) with the use of the Cu 3 cluster. In contrast, the activation barrier for the conversion of I to VIII and X undergoes an increase with the use of the Cu 3 cluster, and its magnitude (76.435 kcal/mol) is much larger than that of I to II (60.151 kcal/mol) and I to III (67.517 kcal/mol). It is therefore obvious that the a Cu catalyst is highly selective to 1,2-PDO via 2-acetol as established in experimental studies. 13,18 Also, Cu plays a dominant role in the second conversion step, i.e., 2-acetol (II) to 1,2-PDO (IV). While the conversion of I to II has a lower activation barrier than that of II to IV without a Cu 3 cluster, the latter reaction has a much lower activation barrier when a Cu 3 cluster is used.
Our results for the noncatalyzed system are in reasonable agreement with those of a previous study of Nimlos et al. 19 who have obtained the activation barriers of neutral glycerol dehydration as 70.9 kcal/mol for 1,2-dehydration and 65.2 kcal/mol for 1,3-dehydration. Unlike their case, we have  With regard to the over-hydrogenolysis products of IV in the presence of the Cu 3 cluster, the conversion of IV to VII has a lower activation barrier (52.784 kcal/mol) compared to the conversion of IV to IX+X (60.295 kcal/mol). This is also observed without a Cu 3 cluster, where the latter reaction has an activation barrier (83.870 kcal/mol) higher than that of the former reaction (76.856 kcal/mol). Note that the activation barrier for the formation of 2-propanol (VI) from 1,2-PDO (IV) is 76.974 kcal/mol with a cluster and 83.461 kcal/mol without a cluster, both of which is higher than that of the 1propanol (VII) case reported in Figure 3. Thus, it can be concluded that VII is the most preferred over-hydrogenolysis product of glycerol.
In the following, we study the conversion of I to IV via II in more detail. Minimum energy 8-atom clusters, Cu 8 , Cu 7 Zn, and Cu 7 ZnO, are taken from our previous study. 25 This cluster size is selected because of the existence of a three-dimensional (3D) structure and availability of several types of coordination sites. In Section 3.2, we discuss the study of the adsorption of the reactants and products of these reactions. This is followed by a discussion of the activation barriers, reaction energy, and rate constants in Section 3.3.

Adsorption of Species.
The adsorption energies of the reactants and products (Table 2) are calculated using eq 1 at every possible coordination site of 8-atom clusters as shown in Figure 2. The adsorbed structures of the reactants, products, and transition states are given in Table 3. It can be inferred from Table 3 that the hydrogen molecule does not get adsorbed or weakly adsorbed on the cluster site during the reaction as also found in our previous study, 25 but it stays near the cluster. Similarly, the water molecule is also not adsorbed or weakly adsorbed on the cluster surface but stays near the cluster. These are reflected in the less negative values of adsorption energy for hydrogen and water molecules in Table  2. It may therefore be concluded that the hydrogen and water molecules are in the gas phase during the hydrogenolysis reaction, and the species having more negative adsorption energy values, i.e., glycerol (I), 2-acetol (II), and 1,2-PDO (IV), are adsorbed on the cluster. In particular, the average adsorption energies of hydrogen and water molecules over all Cu and Zn atoms are the least negative for the Cu 7 ZnO cluster.
For the Cu 8 cluster, more negative adsorption energy is obtained for I on the 5Co site (−15.962 kcal/mol). In contrast, more negative adsorption energies for II and IV are obtained for the 4Co site, which are −13.695 and −15.472 kcal/mol, respectively. After Zn doping, i.e., for the Cu 7 Zn cluster, the most negative adsorption energies are obtained for I and IV on the 4Co_Away site and for II on the 4Co_Near site. This implies that the presence of Zn on the neighboring site favors adsorption of II on the Cu atom but not the adsorption of I and IV. In the case of the Cu 7 ZnO cluster, the adsorption energies of I, II, and IV are most negative on the Zn atom, which implies that ZnO doping facilitates stronger adsorption of species. The same can be inferred by looking at the average adsorption energy over Cu and Zn atoms for all clusters, which is most negative for the Cu 7 ZnO cluster. Also, if the adsorption energy is averaged only over Cu atoms in the cluster, adsorption energies are still most negative for the Cu 7 ZnO cluster, implying that ZnO doping facilitates increased adsorption on Cu sites as well. In our earlier study, 25 we have already established an increase in the physical stability of Cu clusters with ZnO doping. Table 4 shows the activation barriers, rate constants, and reaction energies of I to II + water (via TS1) and II + hydrogen to IV (via TS2) without a catalyst and with Cu 8 , Cu 7 Zn, and Cu 7 ZnO clusters at every possible coordination sites. Some of the values (indicated by *) in Table 4 could not be computed using B3LYP/LanL2DZ theory despite repeated trials, and therefore, values computed using HF/LanL2DZ theory are shown for these cases. Activation barriers (E a ) are calculated as the differences of the transition state energy (TS1, TS2) and the respective reactant(s) energy with zero-point energy corrections. Reaction rate constants are calculated using eq 2. Reaction energies are calculated as the differences of the energy of product(s) and reactant(s) of the reactions. Very low rate constants (∼10 −33 s −1 ) for I to II + water and ∼10 −47 s −1 for II + hydrogen to IV and much higher activation barriers were found for the reaction without the catalyst clusters compared with the reaction with the catalyst clusters, which establishes that the reactions are not feasible without a catalyst. All the reactions are found to be exothermic as implied by the negative  Table 4 was found to be Cu 7 ZnO < Cu 7 Zn < Cu 8 < (Without a Catalyst). Note that the variation of reaction energies with the choice of the catalyst cluster should not be interpreted as a change in the equilibrium constant, as apart from the reactant(s) and product(s), the energy of the clusters is also included in their calculation. In this case, one of the reasons for more negative reaction energies for Cu 7 Zn and Cu 7 ZnO clusters compared to the Cu 8 cluster is the highly negative reaction energies for Zn sites. The average rate constants k 1 and k 2 in Table 4 follow the order Cu 8 < Cu 7 ZnO < Cu 7 Zn. E a depends strongly on the coordination for Cu sites. For the Cu 8 cluster, E a values for both the reactions are much lower for the 5Co site compared to the 4Co site. The same trend is observed when comparing 5Co_Near and 4Co_Near or 5Co_Away and 4Co_Away sites for the Cu 7 ZnO cluster. Similarly, E a values for both the reactions on the 5Co_Away site of the Cu 7 Zn cluster are lower than those of the 4Co_Away site. However, this general trend is not followed for the 5Co_Near site of the Cu 7 Zn cluster, which has a higher activation barrier compared to the 4Co_Near site. The lowest E a values (among all coordination sites of all clusters studied) were found for the 4Co_Near site of the Cu 7 Zn cluster for the first reaction and the 5Co_Away site of the Cu 7 Zn cluster for the second reaction. Also considering the previous conclusion regarding the average rate constants, we may therefore conclude that Cu 7 Zn has the highest catalytic activity among the clusters studied.

CONCLUSIONS
In summary, we have performed detailed DFT calculations to analyze the glycerol hydrogenolysis reactions with Cu, Cu−Zn, and Cu−ZnO clusters. The main findings of this study may be summarized as follows: were found for the glycerol to 1,2-PDO reaction without the catalyst clusters, which establishes that the reactions are not feasible without a catalyst. (f) Activation barriers depend strongly on the coordination for Cu sites. When averaged over all possible coordination sites, Cu 7 Zn has the highest catalytic activity among the clusters studied. Although the findings of this study appear to be quite conclusive, some of the drawbacks of the computational method adopted here require further deliberation. First, the catalyst clusters containing three and eight atoms used here for computational convenience are not the true representation of the bulk catalysts used in experimental studies on glycerol hydrogenolysis. Second, the effects of variations in Zn/ZnO doping are not considered. Third, experimental studies typically have catalysts supported on a surface (e.g., MgO), which is not considered in the model. Despite these obvious shortcomings, the fact that such simple cluster models are able to confirm some of the experimental findings and that these calculations are relatively easier to perform provides confidence in the possible use of these models in the computational screening of catalysts.