Photochemical CO2 conversion on pristine and Mg-doped gallium nitride (GaN): a comprehensive DFT study based on a cluster model approach

This journal is © The Royal Society of Chemistry and the Chinese Chemical Society 2021 Mater. Chem. Front. Cite this: DOI: 10.1039/d1qm01118a Photochemical CO 2 conversion on pristine and Mg-doped gallium nitride (GaN): a comprehensive DFT study based on a cluster model approach† Valeria Butera * a and Hermann Detz ab The photochemical reduction of carbon dioxide (CO 2 ) into methanol is very appealing since it requires sunlight as the only energy input. However, the development of highly selective and efficient photocatalysts is still very challenging. It has been reported that CO 2 can be spontaneously activated on gallium nitride (GaN). Moreover, the photocatalytic activity for CO 2 conversion into methanol can be drastically enhanced by incorporating a small amount of Mg dopant. In this work, density functional theory (DFT) based on a cluster model approach has been applied to further explore the photocatalytic activity of bare GaN towards CO 2 adsorption and conversion. We extended the investigation of Mg-doping replacing one Ga atom with Mg on three different sites and evaluated the consequent effects on the band gaps and CO 2 adsorption energies. Finally, we explore different routes leading to the production of methanol and evaluate the catalytic activity of bare GaN by applying the energetic span model (ESM) in order to identify the rate-determining states which are fundamental for suggesting modifications that can improve the photocatalytic activity of this promising material. Introduction The chemical transformation of carbon dioxide (CO 2 ) into chemicals and fuel has been receiving growing attention since it can potentially mitigate the negative environmental impact of increasing greenhouse gas emissions in the atmosphere and furnish a new renewable carbon source. 1–7 In previous studies, we focused on homogeneous catalytic CO 2 conversion to cyclic carbonates 8,9 and methanol 10 using sustainable alkali halide– glycol complexes and Ru-complexes, respectively. Recently, our focus has been on photochemical CO 2 reduction since it requires sunlight as the only energy input. Significant attention has been paid to this subject in recent years, and substantial advances in the hydrogenation of CO 2 to hydrocarbons and oxygenates have been achieved. Among these products, methanol is one of the most desired since it can be used as a liquid fuel-like renewable energy source and a chemical feedstock for other useful chemicals. Due to the high thermodynamic stability of the CO 2 molecule, the first step of its reduction involves the adsorption and its consequent activation on the photocatalyst surface. Various semiconductor photocatalysts, including oxides, oxynitrides, sulfides, and phosphides, have been investigated over the last few decades. 11–18 It has been observed that the presence of oxygen vacancies in metal oxide surfaces dominates the CO 2 adsorption. 19,20 However, this adsorption is hindered by the adsorption of O 2 , which occupies the vacancies leading to an inactive surface. Moreover, metal oxide semiconductors generally exhibit a large band gap, which limits the absorption of the visible and infrared solar spectrum. Therefore, it is of both fundamental and practical interest to explore alternative photocatalysts that can harvest a large part of the solar spectrum and can lead to spontaneous activation of the CO 2 molecule. In this regard, the thermodynamically stable wurtzitestructure gallium nitride (GaN) has been proposed as a promising material for the reduction of highly stable CO 2 molecules due to its unique electronic and optical properties. GaN has a wide band gap of 3.4 eV which can be tuned to absorb nearly the entire solar spectrum by alloying it with In and Al. Mi and collaborators 21 have demonstrated the photochemical reduction of CO 2 to CH 3 OH, CO, and CH 4 with sunlight by a joint experimental and computational study based on periodic boundary condition (PBC) calculations. The authors also discovered that, with the incorporation of Mg dopant, the rate of CO 2 reduction to CH 3 OH, CH 4 , and CO is enhanced nearly 50-fold due to the reduced surface potential barrier and the enhanced adsorption of CO 2 molecules on the surface of the nanowire. In a very recent study, Liu and co-workers 22 demonstrated that bulk GaN a CEITEC – Central European Institute of Technology, Brno University of Technology, Purkyn ˇova 123, Brno 612 00, Czech Republic. E-mail: [email protected] b Center for Microand Nanostructures & Institute of Solid State Electronics, TU Wien, 1040 Vienna, Austria †Electronic supplementary information (ESI) available. See DOI: 10.1039/ d1qm01118a Received 5th August 2021, Accepted 1st October 2021 DOI: 10.1039/d1qm01118a rsc.li/frontiers-materials MATERIALS CHEMISTRY FRONTIERS RESEARCH ARTICLE Open Access Article. Published on 06 October 2021. Downloaded on 11/8/2021 8:17:47 AM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. View Article Online View Journal Mater. Chem. Front. This journal is © The Royal Society of Chemistry and the Chinese Chemical Society 2021 is an efficient catalyst for the selective direct hydrogenation of CO 2 to DME, and DME was rigorously revealed as the primary product. The authors have performed DFT calculations using PBC methods in order to investigate the details of the reaction conversion mechanism. According to the authors, the reaction proceeds through the formation of adsorbed H 2 COH* species which can be hydrogenated to methanol or dissociate to CH 2 * and OH*. The energy barrier involved in the former process is calculated to be B1 eV, which is higher than the latter. Their DFT results well explain why DME rather than methanol is formed as the primary product on GaN surfaces, i.e. the difficult hydrogenation of CH 2 OH* to CH 3 OH* and the unfavourable formation of CH 3 O*. The CO 2 photoreduction to hydrocarbons requires the presence of H + species which can be formed by water oxidation on GaN surfaces or via the dissociation of hydrogen molecules (H 2 ). In this regard, the hydrogen evolution reaction 23–26 represents a competing reaction. Calculations based on a cluster model approach have some advantages over PBC methods, such as the use of hybrid functionals at a lower computational cost, that allows for a highly accurate description of electronic properties; the ability to add/subtract a charge carrier without suffering from interactions with similar charge carriers due to periodic boundary conditions, 27,28 which makes cluster approaches suitable for the study of charged systems. Thanks to the reduced size, a cluster approach can be used to intercept all the stationary points, including the more complex transition states, involved in the catalytic cycle and to determine the rate determining states. 29–31 On the other hand, a PBC approach allows for the investigation of extended surfaces and provides an accurate description of the structural properties of the surface and molecular adsorbates. The complementarity of the two computational methods can therefore lead to an in-depth understanding of the structure– property relationship. 32 In this work, we have used DFT calculations based on a cluster model approach in order to further explore the photocatalytic activity of bare GaN towards CO 2 conversion. Based on the findings reported by Mi and collaborators, 21 we have extended the investigation of Mg-doping replacing one Ga atom with Mg on three different sites and evaluated the consequent effects on the band gaps and CO 2 adsorption energies. This provides a more realistic picture of the stochastic distribution of dopant atoms within the crystal and on its surface. Based on the results published by Liu and co-workers, 22 we have explored different routes leading to the production of methanol that could potentially involve lower energy barriers. The catalytic activity of bare GaN has been evaluated by applying the energetic span model (ESM) 33,34 in order to identity the ratedetermining states and to suggest modifications that can improve the photocatalytic activity of this promising material. Eventually, the influence of Mg-doping at different sites on the catalytic CO 2 conversion into methanol has been investigated. As will be discussed in more detail in the next sections, the reliability of the selected cluster models has been confirmed by the good agreement of the geometric parameters, that include calculated bond distances and angles, compared to the ones reported in ref. 21. Moreover, similar trends of the adsorption energies using the two different computational approaches have been computed, which further support the potential use of the selected cluster models to determine adsorption energies as a valid alternative to the more extended surfaces used in PBC calculations. The stability of the pure and Mg-doped GaN clusters has also been evaluated and the details are discussed in the ESI.†Therefore, these models can be used for further investigations allowing a better understanding of the photocatalytic activity of GaN-based materials at a notably reduced computational cost. Results and discussion GaN cluster selection and CO 2 adsorption Two different cluster models have been selected in this study: A_GaN built up of three Ga–N moiety rows and 2 layers for a total number of 58 atoms; B_GaN, including four Ga–N moiety rows and three layers (112 atoms). Both the optimized structures are shown in Fig. 1. For the sake of simplicity, throughout the text, all the structures labeled with ‘‘A’’ and ‘‘B’’ will refer to the smaller and bigger size cluster models, respectively, while ‘‘GaN’’ and ‘‘Mg’’ will be used to indicate the pristine and Mg-doped models, respectively. To identify the three different studied doping sites, the superscripts ‘‘surf’’, ‘‘FL’’ and ‘‘bulk’’ will be adopted to refer to the surface, first layer and bulk, respectively. As the first step of our investigation, we have focused on the adsorption of CO 2 on the surface of both the cluster models. The relative adsorption energies, E(CO 2 ) ads , are calculated as: E(CO 2 ) ads =E cluster+CO 2 E cluster E CO 2 (1) where E cluster is the energy of the optimized cluster, E CO 2 is the energy of the CO 2 molecule, and E cluster+CO 2 is the energy of the cluster when the CO 2 molecule is coordinated to the surface. The linear CO 2 has therefore been added to both A_GaN and B_GaN at an initial distance of about 3 Å from the surface. In both the systems, during the relaxation, the CO 2 is spontaneously coordinated to the GaN surface via a single C–N bond and the consequent deformation of the O–C–O from the original angle of 1801to a bent conformation (see Fig. 1 and Table 1). The C coordination is also confirmed by NBO analysis which underlines the formation of a single bond between C and N2, with a higher contribution of the N hybrid orbitals (63%) with respect to the C hybrid orbitals (37%), as well as a higher polarization coefficient of N (0.80) than C (0.60). NBO analysis also shows the formation of a double bond between C and O1 and a single bond between C and O2. In 1B_GaN, two O–Ga interactions are established between the negatively charged oxygen atoms O1 (0.718) and O2 (0.790) and the positive Ga1 (+1.740) and Ga3 (+2.123) atoms, respectively. As for 1A_GaN, the interaction between O1 and Ga1 becomes stronger as underlined by the O1–Ga1 bond whose distance is 0.342 Å shorter than in 1B_GaN.However,theO2– Ga3bonddistanceis0.712Ålonger.Overall,increasingthesizeof the cluster has little influence on the CO 2 adsorption mode as also shown by the selected geometric parameters reported in Table 1. Research Article Materials Chemistry Frontiers Open Access Article. Published on 06 October 2021. Downloaded on 11/8/2021 8:17:47 AM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. View Article Online This journal is © The Royal Society of Chemistry and the Chinese Chemical Society 2021 Mater. Chem. Front. Moreover, very similar adsorption energies of 2.11 and 2.05 eV have been calculated for the adsorption of CO 2 on A_GaN and B_GaN, respectively, whose optimized structures 1A_GaN and 1B_GaN are shown in Fig. 1c. Mi et al. 21 calculated an adsorption energy of 1.76 eV of one CO 2 molecule on GaN(100) using PBC calculations. As shown in Table 1, the geometric parameters computed by the authors are ingoodagreementwiththose obtained using our selected cluster models. The effect of Mg-doping on the CO 2 adsorption energies has been evaluated on both the A_GaN and B_GaN models. Three different doping positions have been considered as shown in Fig. 2, while the corresponding adsorption energies are reported in Table 2. Mi et al. 21 computed an adsorption energy of 2.48 eV for CO 2 on the Mg-doped GaN surface. The doping site considered by the authors can be compared to our A_Mg surf and B_Mg surf systems, whose calculated adsorption energies are 3.23 and 3.12 eV for 1A_Mg surf and 1B_Mg surf , respectively. According to those results, our cluster models tend to overestimate the adsorption energies giving more negative values. However, both the methods show a much stronger CO 2 adsorption energy in the presence of the Mg dopant which corresponds to 0.7 eV for the PBC calculations in ref. 21, and 1.1 eV for our cluster model calculations. As shown in Table 2, the stronger adsorption of the CO 2 molecule in the presence of the Mg dopant is particularly enhanced when Mg replaces a gallium atom of the surface as in A_Mg surf and B_Mg surf in Fig. 2. On the other hand, when Mg occupies a ‘‘bulk-like’’ position (A_Mg bulk and B_Mg bulk in Fig. 2), the calculated adsorption energy is much more similar to the undoped case. For a better understanding of the influence of Mg doping on the adsorption energy, the total adsorption energy, E ads ,ofCO 2 on the B_Mg Table 1 Adsorption energies (Ads energy) of CO 2 on A_GaN and B_GaN clusters, along with the main calculated geometric parameters. Values from ref. 21 are also shown for direct comparison A_GaN B_GaN Ref. 21 B3LYP/6-31+G** B3LYP/6-31+G** PBC Ads energy (eV) 2.11 2.05 1.76 C–N2 (Å) 1.475 1.418 1.41 O1–Ga1 (Å) 1.918 2.323 2.24 O2–Ga3 (Å) 2.793 2.081 2.10 Ga1–N2–Ga3 (1) 170.4 167.0 O1–C–O2 (1) 123.8 129.4 128.3 Fig. 2 Top: side view of the A_Mg cluster models doped by replacing one Ga atom of the surface (A_Mg surf ), first layer (A_Mg FL ) and bulk (A_Mg bulk )withMg. Bottom: side view of the B_Mg cluster models doped by replacing one Ga atom of the surface (B_Mg surf ), first layer (B_Mg FL ) and bulk (B_Mg bulk )withMg. Fig. 1 Top: (a) side and (b) top view of the A_GaN cluster model and (c) 1A_GaN intermediate; bottom: (a) side and (b) top view of the B_GaN cluster model and (c) 1B_GaN intermediate. Table 2 Adsorption energies (eV) of CO 2 on A_Mg and B_Mg clusters, for the three studied doping sites 1A_Mg surf 1B_Mg surf 1A_Mg FL 1B_Mg FL 1A_Mg bulk 1B_Mg bulk 3.23 3.12 2.95 2.54 2.65 2.29 Materials Chemistry Frontiers Research Article Open Access Article. Published on 06 October 2021. Downloaded on 11/8/2021 8:17:47 AM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. View Article Online Mater. Chem. Front. This journal is © The Royal Society of Chemistry and the Chinese Chemical Society 2021 clusters has been decomposed into two main contributions, i.e., interaction and distortion energies: E ads =E int +E dist (2) The interaction energy, E int , is given by the difference between the energy of the whole system and that of the single components taken at the final geometry of the adsorbed state, thus accounting for the bare electronic effects occurring at the adsorbate–surface interface: Eint ¼Esystem E adsorbate þE surface  (3) The distortion energy, E dist , is given by eqn (4): Edist ¼E adsorbate þE surface Eadsorbate Esurface (4) where the terms with and without the * are taken, respectively, at the geometry of the final adsorbed state and the unperturbed equilibrium structures of each single component. This contribution accounts for the structural arrangements of both molecule and surface occurring upon adsorption. As seen in Table 3, a positive contribution of about 4 eV, due to the distortion of the bare and Mg-doped GaN as a consequence of the CO 2 adsorption, has been calculated. Moreover, the positive deformation energy confirms also that the CO 2 molecule is activated upon coordination, changing from a linear structure to a bent one. On the other hand, the very negative terms of the interaction energy indicate a strong interaction between the CO 2 molecule and the surface favoring the overall adsorption process. Particularly, following the same trend of the adsorption energy, the interaction energy becomes stronger when the cluster models are doped with Mg, and a more negative interaction energy is calculated when Mg replaces a surface Ga atom as in 1B_Mg surf , while a more positive value is obtained for the ‘‘bulk-like’’ replacement. Therefore, the replacement of Mg on the surface will lead to a stronger interaction energy and an overall stronger adsorption energy. Methanol production: The adsorption energies of one methanol molecule on the selected cluster models have been calculated and the corresponding values are reported in Table 4. Thanks to the agreement between the small and big cluster models on the computed CO 2 adsorption energies, only the small clusters have been considered. These values show that the adsorption of the methanol molecule is less strong (more positive) than that of CO 2 for the bare and Mg-doped clusters. However, the methanol adsorption energy on A_GaN is slightly higher than the Mg-doped cases. The adsorption mode of the methanol molecule on the GaN is not particularly influenced by the Mg doping. Moreover, very similar adsorption energies have been calculated for the Mg-doping at the three different sites (see Table 4). Our calculations show that the adsorption of CO 2 on pristine A_GaN is 0.42 eV stronger than that of methanol (see Tables 1 and 4). This difference increases when the Mg-doped clusters are taken into account and it becomes 1.71, 1.42 and 1.11 eV (see Tables 2 and 4) for A_Mg surf ,A_Mg FL and A_Mg bulk , respectively. In other words, replacing one Ga atom with Mg favors the CO 2 adsorption (particularly when a surface Ga atom is replaced) but has no influence on the methanol adsorption facilitating its release. Band gaps and HOMO/LUMO orbitals For all six Mg-doped and two bare GaN clusters, the band gaps have been calculated as the energy difference between the Lowest Unoccupied Molecular Orbital (LUMO) and Highest Occupied Molecular Orbital (HOMO). The computed band gap of the pristine B_GaN is 3.5 eV which is very similar to the experimental one (3.4 eV). According to our results, reported in Table 5, the presence of Mg lowers the band gap. This effect is much enhanced when Mg replaces a surface Ga as in B_Mg surf . Even though the smaller A_GaN and A_Mg models dramatically underestimate the band gaps, the obtained trend confirms that calculated with the bigger cluster model. The band gaps can also be derived from the gap between the photoemission (PES) and inverse-photoemission (IPES) energy levels. 27,35 It is indeed possible to compute the electron affinity/ ionization potential of pristine and Mg-doped GaN by the addition/removal of an electron from the neutral system. This would be analogous to the measurement of the fundamental gap arising from the PES/IPES process, as explained in more detail in the ESI.†By applying this method to the smaller cluster models, A_GaN and A_Mg surf , we obtain band gap values of 2.86 and 2.27 eV, respectively. Even though these values still underestimate the band gaps, they give more realistic values showing that the smaller clusters can be used for qualitative analysis at a very reduced computational cost. Table 3 Calculated E int and E dist contributions to the CO 2 adsorption energy on the pristine B_GaN and B_Mg cluster models. Energies are given in eV 1B_GaN 1B_Mgsurf 1B_MgFL 1B_Mgbulk E int E dist E int E dist E int E dist E int E dist 5.94 3.89 6.95 3.83 6.63 4.10 6.22 3.93 Table 4 Methanol adsorption energies, E, (eV) on the pristine A_GaN and A_Mg cluster models along with the calculated Ga–O distance (Å) A MeOH _GaN A MeOH _Mg surf A MeOH _Mg FL A MeOH _Mg bulk E1.69 1.52 1.53 1.54 Ga–O 2.009 2.006 2.012 2.013 Table 5 Band gaps of all the selected clusters calculated as the difference between the HOMO and LUMO orbitals. Energies are given in eV A_GaN B_GaN A_Mg surf B_Mg surf A_Mg FL B_Mg FL A_Mg bulk B_Mg bulk 1.24 3.52 0.59 2.49 1.13 3.29 1.15 3.27 Research Article Materials Chemistry Frontiers Open Access Article. Published on 06 October 2021. Downloaded on 11/8/2021 8:17:47 AM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. View Article Online This journal is © The Royal Society of Chemistry and the Chinese Chemical Society 2021 Mater. Chem. Front. Fig. 3 shows the HOMO orbitals of the B_GaN and B_Mg clusters. The HOMO orbital of the pristine GaN is localized on the bottom-left part of the cluster. On the other hand, when the surface Ga atom is replaced with Mg, as in B_Mg surf , the HOMO orbital involves mostly the atoms of the surface layer. A more extended character of the HOMO orbital is calculated in the case of Mg-doping as in B_Mg FL and B_Mg bulk . The analysis of the LUMO orbitals, instead, shows a very similar character of the LUMO for all the studied clusters. For this reason, in Fig. 4 only the undoped case is shown. Therefore, both the ‘‘A’’ and ‘‘B’’ cluster models have underlined the spontaneous coordination of the CO 2 molecule on the pristine and Mg-doped surfaces and its consequent activation is thanks to the formation of a strong C–N single bond. Moreover, both the ‘‘A’’ and ‘‘B’’ clusters confirm that replacing a surface Ga atom with Mg leads to stronger (more negative) adsorption and interaction energies, along with notably reducing the band gap. Absorption spectra TD-DFT, which is a popular tool for computing the electronic excitation energies and the properties related to the optical spectra, 36–38 has been used to investigate the light absorption of pure and Mg-doped GaN materials determining their vertical electronic absorption energies of optical transitions. The corresponding simulated spectra are shown in the ESI,†while the main excitation energies and the related oscillator strengths are listed in Table 6. We report all excitations falling in the energy interval in terms of wavelengths between B700–350 nm (corresponding to B1.8–3.5 eV). This energy interval includes the visible spectrum (400–700 nm). The main difference between pristine and Mgdoped clusters is that the inclusion of Mg leads to absorption features at lower energies and this effect is particularly evident for the B_Mg surf cluster which includes a Mg surface atom: pure GaN shows peaks that are located at about 3 eV, which means B400 nm in the visible region of violet light, and some further peaks are present out of the visible window (less than 400 nm); on the other hand, the presence of Mg shifts the absorption up to 666.32 nm, extending the range of the absorption of visible light and, consequently, improving the photocatalytic performance of gallium nitride. The analysis of the TD-DFT calculations underlines that in the first excited state for both B_Mg surf and B_Mg bulk the HOMO–LUMO transition dominates with a transition coefficient of about 0.70. In the case of B_Mg FL , two transitions are involved: the HOMO1-LUMO and HOMO -LUMO, with transition coefficients of 0.6 and 0.4, respectively (see Fig. 4d). Eventually, in the B_GaN cluster, several transitions contribute to the first excited state with very similar coefficients (see Fig. 4b). In these two latter cases, examining the relevant canonical orbitals is not Fig. 3 Top and side view of the HOMO orbitals of B_GaN (a), B_Mg surf (b), B_Mg FL (c) and B_Mg bulk (d); top and side view of the LUMO orbital of the pristine B_GaN (e). Fig. 4 Top and side view of the HOTO of B_GaN (a) and B_Mg FL (c) cluster models; canonical orbitals involved in the transition to the first excited state of B_GaN (b) and B_Mg FL (d). Table 6 Main excitation energies (eV and nm) and related oscillator strengths (f) for the first five excited states of the B_GaN and B_Mg cluster models calculated with the TD-DFT method B_GaN B_Mg surf B_Mg FL B_Mg bulk eV nm feV nm feV nm feV nm f ES1 2.98 416.2 0.0143 1.86 666.3 0.0033 2.61 474.9 0.0135 2.63 471.6 0.0237 ES2 3.06 405.7 0.0114 2.36 525.6 0.0446 2.67 463.5 0.0167 2.71 456.8 0.0018 ES3 3.08 402.1 0.0020 2.65 467.2 0.0102 2.85 434.7 0.0118 2.88 429.7 0.0036 ES4 3.25 381.8 0.0038 2.68 461.8 0.0050 2.92 425.1 0.0061 2.95 420.1 0.0115 ES5 3.28 377.6 0.0006 2.70 458.9 0.0217 2.95 419.9 0.0040 3.00 412.7 0.0188 Materials Chemistry Frontiers Research Article Open Access Article. Published on 06 October 2021. Downloaded on 11/8/2021 8:17:47 AM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. View Article Online Mater. Chem. Front. This journal is © The Royal Society of Chemistry and the Chinese Chemical Society 2021 particularly helpful and therefore the analysis of the Natural Frontier Orbitals (NTOs) has been performed and the corresponding Highest Occupied Transition Orbitals (HOTOs) are shown in Fig. 4a and c for B_GaN and B_Mg FL , respectively. CO 2 conversion on A_GaN As the first step of our investigation of the CO 2 conversion into methanol, we have considered the coordination of: (a) a CO 2 molecule followed by the coordination of a hydrogen molecule (mechanism 1, Fig. 5) and (b) a hydrogen molecule followed by CO 2 (mechanism 2, Fig. 6). For a direct comparison with the adsorption energy given in the previous section, the electronic energies calculated at B3LYP/6-31+G** will be discussed while comparing the reaction mechanisms. However, free energies are also reported in the Potential Energy Surfaces (PESs) and they will be discussed in more detail in the next section where the energetic span model will be applied in order to identify both the rate-determining intermediate, TDI, and the rate-determining transition state, TDTS. Mechanism 1. As mentioned in the previous section, the addition of a CO 2 molecule to A_GaN leads to its spontaneous coordination to the surface through the C–N1 bond as in 1A_GaN, which lies at 2.11 eV below the reaction coordinate. When a hydrogen molecule is added to 1A_GaN to form 2A_GaN, no spontaneous adsorption is observed and the calculated H 2 -Ga bond distance is 2.573 Å. The reaction can proceed via TS2A_GaN in which the calculated imaginary frequency of 1032.54i cm 1 is associated with the breaking of the H–H bond and the consequent formation of the O–H and Ga–H bonds, as shown in 3A_GaN. The energy barrier is 0.4 eV with respect to the previous intermediate. The second transition state, TS2A_GaN, involves a hydride nucleophilic attack at the carbon atom and breaking of the C–OH bond. The calculated energy barrier with respect to 3A_GaN is 2.9 eV. The IRC calculations show that in the subsequent intermediate, 4A_GaN, the HCO group is rotated in order to form an O–Ga bond, while the OH group is transferred to the adjacent Ga surface atom. This intermediate is calculated to be B1eVmore stable than the previous one. A second uncoordinated molecule of H 2 is added to the system as in 5A_GaN and it is heterolytically broken as shown by the imaginary frequency of 1094.62i cm 1 Fig. 5 (a) Schematic representations of all the intercepted stationary points along with the (b) calculated B3LYP energy profile for the CO 2 conversion to methanol on the A_GaN cluster model according to mechanism 1. Energies are in eV and relative to the asymptote of the reactant. Free energies (eV) are shown in parentheses. Research Article Materials Chemistry Frontiers Open Access Article. Published on 06 October 2021. Downloaded on 11/8/2021 8:17:47 AM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. View Article Online This journal is © The Royal Society of Chemistry and the Chinese Chemical Society 2021 Mater. Chem. Front. calculated in TS5_GaN. The overcoming of an energy barrier of 1.3 eV leads to the formation of the 6A_GaN intermediate in which a N–H bond and a C–H bond are formed. In this intermediate, the carbon atom of the H 2 C–O* species coordinates to a surface nitrogen atom via asp 3 carbon with a calculated bond distance of 1.572 Å, while the oxygen atom binds to a surface Ga atom via a Ga–O bond of 1.868 Å. The C–O bond is 1.409 Å which is longer than a CQO double bond. Therefore, these results show that this mechanism does not lead to the formation of acetaldehyde. Eventually the third molecule of hydrogen is added to the system which remains uncoordinated as in 7A_GaN. The last transition state, TS7_GaN, of the proposed mechanism involves the hydrogenation of the coordinated H 2 CO thanks to the breakingoftheH–HbondandtheformationofbothCHandOH. The calculated imaginary frequency is 1307.49i cm 1 and the involved activation barrier with respect to 7A_GaN is 3.44 eV. Eventually, the 8A_GaN intermediate is formed in which the methanol molecule is coordinated via aGa–OHbondwhose calculated distance is 1.951 Å, while a hydrogen bond is also formed between the hydrogen of the methanol and the oxygen of the adsorbed OH, whose distance is 1.423 Å. This intermediate lies at 4.4 eV below the reaction asymptote. Mechanism 2. As seen before, when a H 2 molecule is added to 1A_GaN, neither spontaneous molecular nor dissociative adsorption is observed. Moreover, no transition state associates to the coordination of H 2 or its dissociation and further coordination has been intercepted. On the other hand, our calculations show that when the H 2 molecule is added to the A_GaN in the absence of the coordinated CO 2 , it spontaneously gives dissociative adsorption leading to the formation of N–H and Ga–H bonds as in 9A_GaN, which lies at 2.08 eV below the reactants’ asymptote. Liu and co-workers 22 have performed PBC calculations showing that H 2 molecules dissociate at Ga–N pairs in a heterolytic pathway with low activation barriers of Fig. 6 (a) Schematic representations of all the intercepted stationary points along with the (b) calculated B3LYP energy profile for the CO 2 conversion to methanol on the A_GaN cluster model according to mechanism 2. Energies are in eV and relative to the asymptote of the reactant. Free energies (eV) are shown in parentheses. Materials Chemistry Frontiers Research Article Open Access Article. Published on 06 October 2021. Downloaded on 11/8/2021 8:17:47 AM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. View Article Online Mater. Chem. Front. This journal is © The Royal Society of Chemistry and the Chinese Chemical Society 2021 0.09 eV on GaN(100). The different result can be associated to the higher reactivity of cluster models in comparison with PBC calculations. However, both the approaches underline the ease of the hydrogen adsorption process. Our calculations show that 9A_GaN is almost isoenergetic with 1A_GaN and therefore there is no preference in the adsorption of one molecule over the other as the first step of the reaction mechanism. This result was also confirmed by Liu and collaborators, 22 who underlined that the comparable adsorption of H 2 and CO 2 paves the way for the facile hydrogenation of CO 2 on the catalyst surface. The presence of the adsorbed hydrogen atoms on the GaN cluster does not prevent the further coordination, and consequent activation, of the approaching CO 2 molecule. Indeed, our calculation shows that when the linear inactivated molecule of CO 2 is added to 9A_GaN at an initial C–N1 distance of 2.710 Å, during the optimization it coordinates as described in 1A_GaN, leading to the formation of the intermediate 10A_GaN which is found to be 1.68 eV more stable than the previous intermediate. From 10A_GaN, the reaction can proceed via two different routes: (a) proton transfer from the surface nitrogen to the oxygen of the activated CO 2 (TS10_GaN); (b) nucleophilic attack at the activated carbon of CO 2 by the hydride bound to the surface Ga atom (TS100_GaN). The former transition state is found to be 1.47 eV more stable than the latter, with a calculated activation energy of 1.62 eV with respect to 10A_GaN. This result is also in agreement with those reported by Liu and co-workers 22 who report that the hydrogenation of CO 2 to COOH* is more favorable than that to HCOO. The formed intermediate 11A_GaN is 2.66 eV more stable than the separated reactants. The reaction proceeds via TS11_GaN in which the hydride attacks the electrophilic carbon coordinated to the surface nitrogen as underlined by the imaginary frequency of 1235.38i cm 1 .Inthe formed intermediate, 12A_GaN, the carbon atom shows sp 3 hybridization which involves a single bond with the previously formed OH group, a second single bond with the transferred hydrogen, a third single bond with the second oxygen of the original CO 2 molecule, and eventually a fourth single bond with the surface nitrogen atom. Once the intermediate 12A_GaN is formed, two different routes have been explored: (a) the former consists of the addition of a further molecule of hydrogen whose H–H bond breaks forming Ga–H and O–H bonds. As will be discussedinmoredetailintheESI,†following this route which involves TS120_GaN, we did not succeed in intercepting the final transition state leading to the formation of methanol; (b) the latter involves the breaking of the C–OH bond which is broken via TS12_GaN by overcoming an energy barrier of 0.72 eV with respect to 12A_GaN, and leads to the formation of 13A_GaN in which the OH group is transferred to the next Ga surface atom, while the carbon atom gets back to sp 2 hybridization. As seen for 1A_GaN, when a second molecule of hydrogen is added to 13A_GaN, it does not spontaneously coordinate to the surface. Three different mechanisms have been considered. We will describe the details of the selected one in this section while the details of the other two routes can be found in the ESI.† The H–H bond of the uncoordinated H 2 molecule is broken via TS13_GaN: one hydrogen atom adsorbs on the GaN surface while the second binds the carbon atom forming the intermediate 14A_GaN,inwhichtheH 2 C–O species coordinates to a surface nitrogen atom in a similar way as seen for the 6A_GaN intermediate and no acetaldehyde is formed. These results support the experimental findings based on which no acetaldehyde was observed. The calculated imaginary frequency is 520.83i cm 1 , while the activation barrier is 0.8 eV with respect to 14A_GaN. Also in this case, the addition of a further hydrogen molecule to the reaction system does not lead to its spontaneous adsorption and the molecule is kept at a distance of B2.600 Å from the surface as in intermediate 15A_GaN.Fromthisintermediate, two different mechanisms can occur which can be defined as (a) concerted and (b) step-wise mechanisms. The concerted mechanism consists of the direct hydrogenation of the adsorbed H 2 C–O species via the final TS15_GaN whose imaginary frequency is 1284.50i cm 1 and which involves the highest activation energy of 3.63 eV. The last intermediate 16A_GaN lies at 5.70 eV below the reactants’ asymptote and shows that the methanol molecule coordinates to a surface Ga atom whose calculated bond distance is 2.000 Å, along with a hydrogen atom adsorbed on a second surface Ga with a computed distance of 1.593 Å and eventually a Ga–OH bond of 1.793 Å. In the step-wise mechanism the added uncoordinated hydrogen molecule first breaks forming O–H and Ga–H bonds via TS150_GaN with a very low activation energy of 0.17 eV and forming the intermediate 17A_GaN that lies at 2.44 eV below the separated reactants. In the last step, a C–H bond is formed through TS16_GaN which involves an energy barrier of 3.70 eV. It is important to note that the stabilization energies of the last intermediates (8A_GaN and 16A_GaN) of the proposed catalytic cycles are much more negative than the ones discussed in the previous section (A MeOH_ GaN and A MeOH_ Mg). Since the adsorption mode of the methanol molecule is the same, the more negative stabilization energies are due to the presence of more adsorbed species in the former case. Therefore, in order to get a more realistic view, the coverage effect should be investigated on a more extended surface, which will be the focus of our further investigation. Energetic span model and rate determining states: According to the energetic span model (ESM), the turnover frequency (TOF) can be derived from electronic-structure calculations by identifying the energetic span of the cycle, dE, which is defined as the energy difference between the points of highest and lowest energy along the reaction profile corresponding to the complete catalytic cycle. Kozuch and Shaik 33 extended this model including the DG r of the reaction and defining dE ij as: dEij ¼GTSðÞjGIðÞij4i dEij ¼GTSðÞjGIðÞiDGr jj ji ( Therefore, if the j-th transition state lies after the i-th intermediate, then dE ij is just the energy difference between them; if the j-th transition state precedes the i-th intermediate, then dE ij is their energy difference minus the DG r . The highest dE ij corresponds to the energy span of the cycle connecting the Research Article Materials Chemistry Frontiers Open Access Article. Published on 06 October 2021. Downloaded on 11/8/2021 8:17:47 AM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. View Article Online This journal is © The Royal Society of Chemistry and the Chinese Chemical Society 2021 Mater. Chem. Front. TOF-determining intermediate (TDI) and the TOF-determining transition state (TDTS). By applying this method to the potential energy surface of Fig. 5 and considering the free energies given in parentheses, we can identify 6A_GaN as the TDI and TS5A_GaN as the TDTS with a corresponding dEof 3.7 eV. Therefore, the rate determining state involves the last hydrogenation for the production of methanol. The same dE, involving very similar structures of TDI and TDTS, is calculated when the (c) route of the potential energy surface in Fig. 6 is considered. Along the (b) route, the application of the ESM leads to the identification of the rate-determining states, which involve the formation of the third C–H bond and the consequent production of methanol. Therefore, our calculations show that the last step leading to the methanol formation is the most challenging. Interestingly, no difference in terms of energy barrier has been found between the hydrogenation of the adsorbed H 2 CO species with an approaching inactivated hydrogen molecule, and the transfer of an adsorbed hydrogen atom. This is due to the very strong bonds that the adsorbed species establish with the GaN surface atoms that prevent easy bond breaking/formation. The application of the ESM to the mechanism proposed by Liu and collaborators 22 leads to a dEof 3.3 eV. In their investigation, the TDI is the intermediate in which the CO 2 molecule is activated on GaN as the bent COO* species while H 2 is adsorbed dissociatively on Ga–N Lewis pairs (an intermediate that can be compared to our 10A_GaN). The TDTS of the catalytic cycle proposed by Liu and collaborators 22 is the transition state associated to the C–H bond formation via an adsorbed hydrogen transfer to the H 2 COH* (comparable to TS17_GaN). Therefore, their study also identifies the last step of the methanol production as the rate-determining state. The authors indeed suggest that the dissociation of CH 2 OH* into CH 2 * (which is further hydrogenated to CH 3 *) and OH* is significantly more favorable than the formation of methanol, explaining why their experimental findings show that methanol is not the primary product of the CO 2 hydrogenation. Even though we were not able to identify an alternative mechanism for the methanol production involving lower energy barriers, our investigation furnishes a wider picture of the possible conversion route which contributes to a deeper understanding of the complex reaction mechanism. Moreover, the application of the ESM allows us to identify the rate determining states which is key information for the development of catalysts with improved performances. Experimental All the calculations have been performed using a cluster model approach. Two cluster models of 58, A_GaN, and 112, B_GaN, atoms have been carved out from the crystallographic structure of wurzite GaN, cutting along the (100) plane. We retained the cluster’s overall zero spin and neutral charge by passivating with capping H atoms only those dangling bonds of our cluster that would have formed covalent bonds to Ga or N atoms in a bulk surface structure. The capping H atoms along with the outermost N and Ga atoms, underlined in green in Fig. 1, have been kept fixed while the rest of the atoms were allowed to relax. These optimizations were performed at the B3LYP 39 level of theory as implemented in the Gaussian 16 quantum chemistry package 13,40 and using the LANL2DZ 14,41 pseudo potential for Ga atoms and the fully electron basis sets 6-31G for N and H. To check the accuracy of the selected computational protocol, preliminary tests were performed using the more accurate double hybrid PBE0DH 15,42 functional that combines exact HF exchange with an MP2-like correlation to a DFT calculation. Moreover, the Counterpoise error as implemented in Gaussian 16 software has been evaluated. These results, whose details can be found in the ESI,†have confirmed the reliability of the B3LYP functional, which was therefore selected in our study. Frequency calculations have been done to check the nature of the stationary points (minimum and transition state). In order to obtain more accurate adsorption energy values, single-point calculations using the more extended 6-31+G** basis sets, except for Ga, on the fully optimized geometry, have also been performed and the obtained energies will be discussed throughout the text (unless differently specified). To evaluate the influence of Mg on CO 2 adsorption, we replaced the three-coordinated Ga(+3) atom on the surface of the pristine A_GaN and B_GaN cluster models by Mg(+2), leading to the formation of A_Mg and B_Mg clusters, whose net charge is 1. Conclusions In this work, DFT calculations based on a cluster model approach have been used to explore the photocatalytic activity of bare GaN towards CO 2 conversion. Two different cluster models have been selected: A_GaN built up of three Ga–N moiety rows and 2 layers for a total number of 58 atoms and B_GaN, including four Ga–N moiety rows and three layers (112 atoms). We extended the investigation of the Mg-doping effect considering three different doping sites. Our calculations have shown that the CO 2 molecule spontaneously coordinates on the pristine and Mg-doped surfaces for both the selected cluster models. This coordination implies the consequent activation of CO 2 thanks to the formation of a strong C–N single bond and the change from the CO 2 linear structure to a bent one. The activation of the CO 2 molecule upon coordination is also confirmed by a similar positive contribution of about 4 eV for all the investigated cases related to its deformation along with the distortion of the bare and Mg-doped GaNclustersasaconsequenceoftheCO 2 adsorption. On the other hand, both the clusters confirm that replacing a surface Ga atom with Mg leads to stronger (more negative) adsorption and interaction energies. The most negative interaction energy is calculated when Mg replaces a surface Ga atom as in 1B_Mg surf , whilethemorepositivevaluesareobtainedforthe‘‘bulk-like’’ replacement. Therefore, the replacement of Mg on the surface leads to a stronger interaction energy and an overall stronger adsorption energy. Small pristine A_GaN and Mg-doped A_Mg clusters have been used to calculate the adsorption energies of one molecule of methanol which is the final product of the catalytic cycle. Materials Chemistry Frontiers Research Article Open Access Article. Published on 06 October 2021. Downloaded on 11/8/2021 8:17:47 AM. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. View Article Online