2.1. Structure Optimisation of the Reactants
In
Figure 1 are reported the results of the optimisation calculations performed on all reactants and catalysts. The “undoped” B
12N
12 fullerene is characterised by a Th-symmetrical structure with both B and N atoms. The value of Mulliken charge for the B atom is 0.57 and for the N atom is −0.57. As can be evinced from
Figure 1a and
Table S1, the B
12N
12 cluster consists of four- and six-membered rings. Two kinds of B-N bonds are present: the length of the B-N bond within the four-membered ring is 1.487 Å, whereas that within the six-membered ring is 1.439 Å. Following the introduction of a Ni atom in the B
12N
12 cluster, two different configurations are obtained, depending on which element is replaced by Ni: the B
11N
12Ni cluster (
Figure 1b) and the B
12N
11Ni cluster (
Figure 1c).
In the B
11N
12Ni cluster, the lengths of the bonds linking the metal centre to the two adjacent nitrogen atoms N(1) and N(2) are 1.893 Å and 1.927 Å, respectively, with the relevant bond angle measuring 108.7°. By comparison with the undoped B
12N
12 cluster, Ni doping results in bond length increases and bond angle decreases; furthermore, following the doping process, the Ni atom is convex significantly outward as shown in
Figure 1b and
Table S2. In the B
11N
12Ni cluster, the value of the Mulliken charge is −0.43 for N(1) and −0.34 for N(2) as a result of a charge transfer from the N atoms to the Ni centre.
In the B
12N
11Ni cluster, the lengths of the bonds linking the metal centre to the two adjacent boron atoms B(1) and B(2) are 1.960 Å and 1.977 Å, respectively; these bonds are thus longer than the Ni-N bonds in B
11N
12Ni, and the relevant bond angle measures 92.01°. The Ni atom is more convex outward as shown in
Figure 1c and
Table S3. In the B
12N
11Ni cluster, the value of the Mulliken charge is 1.26 for B(1) and 1.12 for B(2), as a result of a charge transfer from the B atoms to the Ni atom.
To render more intuitive the charge distribution in the BN fullerene before and after its doping with Ni, we analysed the molecular electrostatic potential of the B
12N
12, B
11N
12Ni and B
12N
11Ni clusters on the molecular van der Waals surface (electron density: 0.001). In the structures reported in
Figure 2, the more intense the blue colour, the more positive the charge, and the more intense the red colour, the more negative the charge. As can be evinced from the mentioned
Figure 2a, in undoped BN fullerene, the B atoms are positively charged and the N atoms are negatively charged. In
Figure 2b, the electrostatic potential minimum is −0.95 eV above N(2) and the maximum is 2.23 eV above the Ni atom. In
Figure 2c, the electrostatic potential minimum is −0.79 eV above N(1) and the maximum is 2.08 eV above the Ni atom. In the B
11N
12Ni and B
12N
11Ni clusters, the Ni atom is highest electropositive, so it has the potential to act as a nucleophilic reaction site, and the N atoms around the metal centre exhibit stronger electronegativity than their counterparts in undoped BN fullerene, which may in turn favour electrophilic reactions.
To deepen understanding of the characteristic of the BN fullerene before and after its doping with Ni, we performed the frontier molecular orbital analysis on the B
12N
12, B
11N
12Ni and B
12N
11Ni cluster. The energies of the frontier orbitals are listed in
Table 1. The value of the LUMO − HOMO energy gap of the B
12N
12 cluster is 6.72 eV, which is consistent with that reported in the literature [
29]. Furthermore, the energy of the HOMO of each of the two BN clusters doped with the nickel atom is higher than that of the HOMO of the undoped cluster and the energy of the LUMO of each of the two BN clusters doped with the nickel atom is lower than that of the LUMO of the undoped cluster. The lower the energy of LUMO, the more conducive to the filling of electrons, and the higher the energy level of HOMO, the more conducive to the loss of electrons. Therefore, the energy gap between HOMO and LUMO is reduced as a result of the doping process, the change that favours in the next adsorption of the reactants, thus promoting the catalytic reaction activity.
To better understand the molecular orbital energy changes associated with the doping of the B
12N
12 cluster with a Ni atom and the contribution of each component to the total density of states, we plotted the total density of states and the density of partial states of the undoped B
12N
12, B
11N
12Ni and B
12N
11Ni clusters. These plots are reported in
Figure 3, where each cluster’s frontier orbitals are also indicated. As can be evinced from
Figure 3a, the value of LUMO − HOMO gap is large, thus the B
12N
12 cluster displays the features of an insulator. The p orbitals of the N atoms are the main contributors of the HOMO and of the lower energy occupied molecular orbitals; on the other hand, the p orbitals of the B atoms are the main contributors of the LUMO and of the higher energy unoccupied molecular orbitals. The features of the plot reported in
Figure 3b suggest that, after replacing a B atom with a Ni atom, a new unoccupied molecular orbital is added in the original forbidden band, and this new orbital becomes the LUMO of the B
11N
12Ni cluster. Notably, the original HOMO increases in energy and shifts to the right. Therefore, upon doping the B
12N
12 cluster with a nickel atom to form the B
11N
12Ni cluster, the LUMO − HOMO energy gap decreases. In the B
11N
12Ni cluster; moreover, the p orbitals of the N atoms are the main contributors to the HOMO, LUMO and the lower energy occupied molecular orbitals, with the contribution to these orbitals of the Ni atom being negligible. The HOMO and LUMO population maps of the B
11N
12Ni cluster are also reported in
Figure 3b; in this case, the electrons are concentrated from N atoms to around the Ni atom compared to the undoped B
12N
12 cluster (see
Figure 3a). As can be evinced from
Figure 3c, after replacing an N atom with a Ni atom, a new occupied molecular orbital is added to the original forbidden band, and this new orbital becomes the HOMO of the B
12N
11Ni cluster. Notably, the energy of the original LUMO decreases and moves to the left. As a result of these changes, the LUMO − HOMO energy gap of the B
12N
11Ni cluster is smaller than that of the B
12N
12 cluster. Additionally, in the B
12N
11Ni cluster, the p orbitals of the B atoms are the main contributors of the HOMO and of the higher energy unoccupied molecular orbitals; on the other hand, the p orbitals of the N atoms are the main contributors of the lower energy occupied molecular orbitals. The s and p orbitals of the B atoms are major contributors of the LUMO, and the orbitals of the Ni atom make some contribution to the HOMO and LUMO. Based on the HOMO and LUMO population maps of the B
12N
11Ni cluster, we can infer that electrons accumulate near the Ni atom and the B atoms in the metal centre’s immediate vicinity. We speculate that Ni and its surrounding B atoms have strong activity.
2.2. Adsorption of C2H2 and H2 onto BN Fullerene or the BN-Ni Cluster
Implementing our computational approach, we obtained the stable adsorption configuration and the value for the adsorption energy of acetylene and hydrogen onto BN fullerene and nickel-doped BN clusters. The stable adsorption configurations are reported in
Figure 4, whereas the values for the adsorption energies are reported in
Table 2.
In
Figure 4a and
Table S4 are depicted the optimised configuration of acetylene adsorbed on the B
12N
12 cluster. According to our data, almost no differences exist between the structures of acetylene and the B
12N
12 clusters before and after adsorption. Acetylene and the cluster are quite far from each other, and the adsorption of acetylene on the cluster is physical in nature, with the value of the adsorption energy calculated to be −2.83 kcal/mol.
In
Figure 4b and
Table S5 are depicted the stable configuration of acetylene adsorbed on the B
11N
12Ni cluster. In this case, some changes in the configuration of acetylene and the B
11N
12Ni cluster are observed as a result of the adsorption process. Acetylene is close to the B
11N
12Ni cluster and is 2.146 Å apart. The C(2) of acetylene and the Ni atom of the cluster are close to each other, and the C≡C bond is slightly elongated with respect to ‘free’ acetylene (to a value of 1.215 Å). Following acetylene adsorption, the Ni atom is relatively more convex, with the length of the Ni–N(2) bond increasing to a value 1.942 Å and that of the Ni–N(3) bond increasing to 1.952 Å. The value of the N(2) –Ni–N(3) bond angle is reduced to 101.8°. Acetylene is physically adsorbed onto the B
11N
12Ni cluster, with the value for the adsorption energy calculated to be −11.92 kcal/mol. The Mulliken charge for C(1) has a value of −0.094 and for C(2) is −0.160; in this case, the Mulliken charge for Ni has a value of −0.163; consequently, the charge transfer from acetylene to the Ni centre.
In
Figure 4c and
Table S6 a stable configuration of acetylene adsorbed onto the B
12N
11Ni cluster is depicted. As can be evinced from this figure, the configurations of acetylene and of the B
12N
11Ni cluster are significantly different from their “free” counterparts, with acetylene undergoing an obvious deformation as a result of the adsorption process. Acetylene’s C(1) is adsorbed onto the Ni atom of the cluster, with a value for the length of the Ni–C(1) bond of 1.894 Å. Acetylene’s C(2) is adsorbed onto the B(1) atom of the cluster, and the C(2)–B(1) bond length has a value of 1.857 Å. The C–C bond is elongated to a value of 1.344 Å, and the Ni atom in the B
12N
11Ni cluster is convex to C(1). Following acetylene adsorption, the length of Ni–B(1) bond increases to 2.399Å and that of the Ni-B(2) bond increases to 2.035Å. Furthermore, the value for the B(1)–Ni–B(2) bond angle decreases to 88.19°. Acetylene is chemisorbed on the B
12N
11Ni cluster, and the adsorption energy is calculated to have a value of −40.40 kcal/mol. The Mulliken charge for C(2) has a value of −0.061 and that for B(1) is 0.584, as a result of the charge transfer from C(2) to B(1). The Mulliken charge for C(1) has a value of −0.497 and that for the Ni atom is −0.515, with the charge being transferred from the Ni atom to C(1); in this case, the Mulliken charge for B(2) has a value of 0.922, and charge is transferred from B(2) to the Ni atom.
In
Figure 4d and
Table S7 are depicted the optimised configuration of hydrogen adsorbed on the B
12N
12 cluster. Following this adsorption process, the configurations of hydrogen and cluster remain almost unchanged. Hydrogen and the B
12N
12 cluster are quite far from each other. Hydrogen adsorption on the B
12N
12 cluster is physical in nature, and the adsorption energy is calculated to have a value of −0.05 kcal/mol.
In
Figure 4e and
Table S8, the stable configuration of hydrogen adsorbed on the B
11N
12Ni cluster is depicted. As can be evinced from this figure, the configurations of hydrogen and the cluster change significantly following adsorption. Hydrogen is completely dissociated on the B
11N
12Ni cluster, and the adsorption energy is −1.90 kcal/mol. The distance between the two hydrogen atoms is 2.793 Å. H1 is adsorbed on the N(2) atom, and the length of the H–N bond is 1.019 Å. H(2) is adsorbed on the Ni atom, and the length of the H–Ni bond is 1.409 Å. The Ni atom protrudes away from the N(1) atom, and the value for the N(2)–Ni–N(3) bond angle is reduced to 98.28°. The Mulliken charge for H(2) has a value of 0.137, as a result of the charge transfer from H(2) to the Ni centre. The Mulliken charge for N(1) has a value of −0.834 and that for H(1) is 0.459, with the charge being transferred from H(1) to N(1).
In
Figure 4f and
Table S9, the stable configuration of hydrogen adsorbed on the B
12N
11Ni cluster is depicted. As can be evinced from this figure, the configurations of hydrogen and the B
12N
11Ni cluster change very significantly following adsorption. Hydrogen is completely dissociated on the B
12N
11Ni cluster, and the adsorption energy is calculated to have a value of −4.28 kcal/mol. The distance between the two H
2-derived hydrogen atoms is 2.379 Å. H(1) is adsorbed on B(1), and the length of the H(1)–B(1) bond is 1.217 Å. H(2) is adsorbed on the Ni atom, and the length of the H(2)–Ni bond is 1.557 Å. The Ni atom protrudes away from B(1), and the value for the N(2)–Ni–N(3) bond angle is reduced to 80.62°. The value of the Mulliken charge for H(2) is −0.089, as a result of the charge transfer from H(2) to the Ni atom. The Mulliken charge for H(1) is 0.079 and that for B(1) is 1.633; in this case, charge is transferred from H(1) to B(1).
2.3. Acetylene Selective Hydrogenation Reaction Mechanism
The addition reaction between acetylene and hydrogen taking place on the catalyst’s surface starts with the stable co-adsorption (CO) of the two reactants on the said surface; it then passes through several transition states (TS) and intermediates (IM), to finally yield the reaction product (P).
2.3.1. Effect of Co-Adsorption Structure on Hydrogenation of Acetylene to Ethylene
To study the effect that different co-adsorbed structures have on acetylene hydrogenation, we investigated the mechanism of acetylene hydrogenation under two different co-adsorptions on the surface of the B
12N
11Ni cluster. In
Figure 5a and
Tables S10–S16, the configuration changes associated with each step of reaction pathway for the hydrogenation of acetylene to ethylene taking place on the surface of the B
12N
11Ni cluster are depicted. In
Figure 5b, the energy changes associated with each step of the pathway is reported.
The reaction pathway starts with co-adsorption configuration CO involving the B12N11Ni cluster; initially, the two carbon atoms of acetylene are adsorbed on the Ni centre and boron atom B(2); on the other hand, dihydrogen is adsorbed around the Ni centre, with the two H atoms partially dissociating from each other. The distance between the two H2-derived hydrogen atoms is slightly larger than the isolation state. The adsorption energy of the co-adsorbed structure is −42.41 kcal/mol. H(2) vibrates in the C(1) direction, and H(1) vibrates in the B(3) direction to produce the transition state TS1 (characterised by a single imaginary frequency of −1248.70 cm−1), then reaction intermediate IM1 is produced. In it, H(1) has been adsorbed on B(3), H(2) has been added to C(1) and the distance between C(1) and Ni has increased with respect to the case of the co-adsorbed structure CO. Notably, the value for the energy barrier separating TS1 from CO is 6.54 kcal/mol. Next, H(1) attacks C(1) to produce transition state TS2, the species characterised by a single imaginary frequency (−356.31 cm−1); notably, the value for the energy barrier separating IM1 from TS2 is 26.07 kcal/mol. Intermediate IM2 is subsequently produced, whereby the CH3CH group has been adsorbed on the B12N11Ni cluster. Finally, H(3) migrates from C(1) to C(2), and ethylene is produced by way of transition state TS3 (characterised by a single imaginary frequency of −1028.14 cm−1). The process whereby IM2 turns into TS3 is the rate controlling step of the reaction pathway, and the overall pathway’s activation energy is calculated as 41.79 kcal/mol.
In another reaction route, the reaction pathway starts with co-adsorption configuration CO2. In
Figure 6a and
Tables S17–S30 are depicted the configuration changes associated with the various steps of the pathway and the energy changes are reported in
Figure 6b. The adsorption energy of CO2 is calculated as −51.87kcal/mol. The two acetylene carbon atoms get adsorbed on the Ni atom, and the two H
2-derived hydrogen atoms completely dissociate and get individually adsorbed onto the two B atoms bound to the nickel centre. Subsequently, the transition state TS1 is produced, which corresponds to the structure characterised by only one imaginary frequency (−1193.64 cm
−1). In this structure, the B–H bond is elongated to a value of 1.736 Å, and H(2) attacks C(2) to produce the reaction intermediate IM1, which is characterised by an energy barrier of 19.51 kcal/mol. The H(1) atom, which is bound to B(1), then approaches C(1), and, after passing through the transition state TS2, which is the structure characterised by only one imaginary frequency (−1182.85 cm
−1), the intermediate IM2 is produced. The process just described, whereby TS2 turns into IM2, is the rate-determining step in acetylene hydrogenation to ethylene. The energy barrier of the entire reaction is calculated to be 28.17 kcal/mol, whereas the desorption energy of ethylene is 17.15 kcal/mol.
Our data indicate that the activation energy of the second reaction pathway is lower than the first reaction pathway, so the second is the optimal pathway for acetylene hydrogenation to ethylene via catalysis by the B12N11Ni cluster. The starting points of these reaction pathways consist in different co-adsorbed structures. By comparing the data we collected on the two reaction pathways, we determined that the co-adsorbed structures would greatly affect the reaction.
In CO2, hydrogen is completely dissociated, and the H2-derived H atoms are adsorbed on the B atoms where the B atoms are nearby both sides of the two acetylenic carbons. The adsorption positions of the hydrogen atoms render favourable these atoms’ attack on different carbon atoms. In CO, as acetylene occupies the adsorption site on the catalyst, the two H2-derived hydrogen atoms can only be adsorbed around the Ni atom. After H(1) is added to C(1), the vinyl group rotates away from the Ni centre, as a result of an increase in steric hindrance, and H(2) can only be added to the C(1) atom, which is the closest to it, to produce the CH3CH moiety. For the migration of H atoms between two carbon atoms to take place, an extremely high energy barrier needs to be overcome, which accounts for the higher activation energy of the first pathway. What is why a suitable co-adsorbing structure can facilitate the reaction, and an unsuited co-adsorbing structure can be adverse.
2.3.2. Effect of Different Ni-Doped Catalysts on the Acetylene Hydrogenation Activity
To compare the effect that different Ni doping sites on the B
12N
12 clusters have on the acetylene hydrogenation activity, we also explored the mechanism of acetylene hydrogenation to ethylene on the B
11N
12Ni cluster. In
Figure 7a and
Tables S31–S42 are depicted the configuration changes associated with the various steps of the optimal pathway on the B
11N
12Ni cluster and the energy changes are reported in
Figure 7b. Herein, acetylene is adsorbed around the Ni atom, and the two H
2-derived hydrogen atoms are completely dissociated, with each of them adsorbed on either the Ni atom or one of the nitrogen atoms bound to the metal centre. The value for the co-adsorption energy is calculated to be −17.60 kcal/mol. The only imaginary frequency of the first transition state TS1 is −237.87 cm
−1. In this state, H(1) attacks C(1) to produce the intermediate IM1, whose formation is characterised by an energy barrier of 2.13 kcal/mol. H(2), which is attached to N(1), then attacks C(2), and, after passing through transition state TS2 characterised by a single imaginary frequency of −1890.66 cm
−1, the intermediate IM2 is produced. The process whereby TS2 is transformed into IM2 is the rate determining step in the hydrogenation of acetylene to ethylene; the energy barrier of reaction pathway is calculated to be 26.54 kcal/mol, whereas the desorption energy of ethylene is 9.75 kcal/mol.
Our data indicate that the activation energy on the B11N12Ni cluster is lower than the B12N11Ni cluster, so the hydrogenation of acetylene to ethylene on B11N12Ni clusters has better reaction activity. This shows that compared with the structure in which nickel is coordinated with three boron atoms, nickel is more active in coordination with three nitrogen atoms. Similarly, the desorption energy of ethylene on the B11N12Ni cluster is lower than the B12N11Ni cluster. It demonstrates that ethylene is more easily desorbed from the B11N12Ni cluster, thereby reducing the possibility of deep hydrogenation. We surmise that the B11N12Ni cluster is more ethylene-selective than the B12N11Ni cluster.
2.3.3. Selectivity of Acetylene Hydrogenation to Ethylene
For the purpose of determining whether the B11N12Ni and B12N11Ni clusters have ethylene selectivity, deep hydrogenation was continued to produce ethane after getting ethylene and compared its activation energy with that of ethylene.
In
Figure 7, we hydrogenated intermediate IM2 further, so as to produce intermediate IM3, which is characterised by ethylene and hydrogen co-adsorbed on the B
11N
12Ni cluster. In this intermediate, hydrogen is completely dissociated: H(5) is adsorbed on Ni and H(6) is adsorbed on N(3); the distance between Ni and N(3) has increased from 1.952 Å to 3.099 Å with respect to IM2. After transition state TS3, which is characterised by having only one imaginary frequency of −185.86 cm
−1, is produced, H(5) is added to C(1) to produce intermediate IM4. At this time, the distance between H(6) and C(2) is large. Following the ensuing formation of transition state TS4 (characterised a single imaginary frequency of −428.73 cm
−1), H(6) rotates in the C(2) direction so that intermediate IM5 forms, wherein Ni and N(3) are close in space to each other. After the ensuing formation of transition state TS5, which is characterised by a single imaginary frequency of −1535.98 cm
−1, H(6) is added to C(2) to form ethane. The energy required for the described process to take place is calculated to be 34.04 kcal/mol, and this process is the rate-controlling step in the generation of ethane. As the activation energy required to form ethane is greater than that required for ethylene production (26.54 kcal/mol), the hydrogenation of acetylene occurring on the B
11N
12Ni cluster is a selective process, with ethylene being the favoured product, with a calculated value for the selectivity of 24.29.
To compare the effect that different Ni doping sites on the B
12N
12 clusters have on the ethylene selectivity of the acetylene hydrogenation, we also explored the mechanism of acetylene hydrogenation to ethane after the formation of ethylene on the B
12N
11Ni cluster. As can be inferred from the data reported in
Figure 6, intermediate IM2 is further hydrogenated to form intermediate IM3. In this intermediate, dihydrogen has dissociated completely, and the two resulting hydrogen atoms are adsorbed on different boron atoms located in the vicinity of the nickel centre. Ethylene, at this stage, is not obviously deformed and adsorbed on the top of the Ni atom. The distance between Ni and B(2) increases with respect to the IM2 case to 2.026 Å. After the transition state TS3, which is characterised by a single imaginary frequency of −154.31 cm
−1, is produced, the C–C bond of ethylene increases in length, and C(1) approaches B(2), leading to the formation of intermediate IM4. The ensuing formation of intermediate IM5 is achieved by the preliminary formation of transition state TS4 (characterised by a single imaginary frequency of −1151.81 cm
−1), whereby H(5) is added to ethylic carbon C(2). Notably, in IM5 C(2) rotates away from the N atom. This rotation may be due to the increase in steric hindrance associated with the attachment of three hydrogen atoms to C(2). After transition state TS5, characterised by a single imaginary frequency of −302.29 cm
−1, has been produced, H(6) migrates from B(1) to the vicinity of B(2), the atom to which the ethyl group is attached, and the intermediate IM6 is produced. The energy required for this process to occur is calculated to be 34.65 kcal/mol, and this process is the rate-limiting step in ethane formation. Then transition state TS6 (characterised by a single imaginary frequency of −1063.04 cm
−1) is produced, and finally H(6) is added to C(1) to form ethane. As the activation energy required for ethane formation is greater than that required for ethylene formation (28.17 kcal/mol), the acetylene hydrogenation reaction taking place on the B
12N
11Ni cluster is selective for ethylene as the product and the value for the selectivity of ethylene 17.49.