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The Role of Cobalt Clusters (Con, n = 1–5) Supported on Defective γ–Graphyne for Efficient Hydrogen Adsorption: A First Principles Study

The Role of Cobalt Clusters (Con, n = 1–5) Supported on Defective γ–Graphyne for Efficient... IntroductionThe increasing demand for fossil fuels implies a rapid growing of air pollution and subsequent effects to be associated with human health issues, such as respiratory diseases.[1,2] Therefore, in the scientific community it is a top priority to find new alternatives to replace such fossil fuels. Hydrogen has been considered as a potential fuel to support sustainable and clean energy development,[3,4] due to the high energy density of 33.3 kW h kg−1.[5] Even though hydrogen storage represents a safe and efficient methodology, it also represents a challenge for the development of novel materials.[6] An important feature to be considered is that the adsorption energy required to obtain a reversible hydrogen storage should be in the range from 0.2 to 0.7 eV per H2.[7–10] One of the best candidate materials to be used as a hydrogen storage material is the carbon‐based nanostructures, such as fullerenes,[11] carbon nanotubes,[7,12] graphene,[13] and graphynes.[9,14]One the most attractive 2D carbon‐based material, which has been widely assessed and scrutinized as a potential hydrogen storage media is the γ‐graphyne (γ‐GY) structure. The γ‐GY was proposed by Baughman et al.,[15] and exhibits a geometry formed of a single atomic layer with an arrangement of carbon atoms with sp1${\text{sp}}^{1}$‐ and sp2${\text{sp}}^{2}$‐hybridizations. A peculiar characteristic rises upon the hybridization of sp2${\text{sp}}^{2}$+sp1${\text{sp}}^{1}$+sp1${\text{sp}}^{1}$+sp2${\text{sp}}^{2}$ bonding, resulting in the formation of acetylene linkages (–C≡ C–). Such bonding is connected by six‐membered rings.[15–18] In recent years, the γ‐GY synthesis has been achieved via a mechanochemical reaction using CaC2 and PhBr6 as precursors.[19–23] The intrinsic cavity of γ‐GY structure is very attractive to metal adatoms which prefer to interact in the plane of metal‐decorated γ‐GY. Therefore, metal atoms, including alkaline metals (AM), alkaline‐earth metals (AEM), and transition metal (TM) atoms, have been explored by experimental and theoretical works.[8,9,24–42]Currently, the γ‐GY structure has been used as an ideal support to reduce the amount of TM atoms. Chen et al.[43,44] reported that pristine γ‐GY structure is sufficiently stable to be used as a support of small Au and Ag clusters. They found that the TM clusters prefer to be adsorbed on the hollow site over the acetylenic ring, in which an exothermic process is involved. Meanwhile, some 2D carbon‐based materials have been widely documented by theoretical calculations through vacancy defects to highlight the adsorption improvement of 3d$3\text{d}$‐TM clusters for hydrogen storage applications.[45–59] Moreover, the vacancy defects play an important role in the adsorption stability of 3d$3\text{d}$‐TM clusters. Recently, the small Co clusters have been explored for hydrogen storage, both free‐standing clusters and supported on graphene.[56,60–63] The combination of different sizes of Co clusters on the graphene surface favors the hydrogen storage capacity.[56,60] Several theoretical works have explored the capacity of the small free Co clusters to adsorb H2 molecules.[61–64] Nevertheless, the interaction of small TM clusters (Con) on the γ‐GY structure with vacancy defects has not been fully understood. Motivated by the recent experimental evidence reported by Cui et al.,[22,23] the novel synthesis of the 2D carbon monolayer structures derived from the pristine γ‐GY, such as –C≡ C– vacancy (GY‐def) and the nitrogen‐doped (GYN‐def) systems have already been performed. However, the ability to adsorb TM atoms or small TM clusters on these monolayers has not yet been explored.In this work, DFT calculations were perform to understand the role of the local defects at the 2D carbon monolayers on the adsorption of small cobalt clusters (Con, n= 1–5). A systematic study of the hydrogen storage is also performed. The adsorption energy values, charge difference density (Δρ$\Delta\rho$), and density of states (DOS) were analyzed. The capacity to retain hydrogen was also evaluated by Born–Oppenheimer molecular dynamics simulations. The theoretical results may aid to tailor novel materials with specific properties and intended to be applied as hydrogen storage systems.Results and DiscussionElectronic Structure of GYN MonolayersThe atomic structure of γ‐GY monolayer can be described by two unit cells (hexagonal cells). The molecular representation of the two optimized structures are depicted in Figure S1, Supporting Information. Both hexagonal structures are equivalent. Figure S1a, Supporting Information represents a six‐membered ring geometry, while Figure S1b, Supporting Information shows a twelve‐membered ring structure. Note that both contain 12 carbon atoms. The representation of the total density of states (DOS), partial DOS (PDOS), and electronic band structure along the Γ – K – M – Γ path in the hexagonal cell are depicted in Figure S1, Supporting Information. They maintain the same electronic behavior (band gap close to 0.47 eV at the Γ point). The Fermi level (EF${}_{\text{F}}$) is located at the half between the valence band maximum (VBM) and conduction band minimum (CBM). It is worth noting that the structural parameters did not show significant changes as shown in Table S1, Supporting Information. These results are consistent with previous theoretical works.[14–16,65] Therefore, the Perdew–Becke–Ernzerhof (PBE)‐D2/DZP level of theory adequately describes the electronic and structural properties of the pristine γ‐GY monolayer.The description of the electronic structure of the pristine γ‐GY monolayer from the fully optimized 2 × 2 × 1 supercell is depicted in Figure 1a. The characteristic structural parameters of pristine γ‐GY are presented in Figure 1a. These values are similar to those obtained in previous works.[14–16,65] Then, we designed the γ‐GY system with a vacancy defect by removing the central –C≡ C– bonding atoms (GY‐def), as it is shown in Figure 1b. Finally, we obtained an additional structure by doping with nitrogen in the benzene‐rings (in the GY‐def model) to obtain two pyridine‐rings (GYN‐def), as it is depicted in Figure 1c. The characteristic structural parameters are inserted in the molecular representation in Figure 1a–c. The vacancy generated in the GY‐def and GYN‐def structures (GYNs‐def) slightly varies by 1.0 Å. The vacancy defects generated in these structures (GY‐def and GYN‐def) allow the retention of Co atoms in the center of geometry, as occurs in graphene‐like monolayers.[42,66,67] The charge density contours in the xy$\textit{xy}$ plane were calculated for the γ‐GY, GY‐def, and GYN‐def systems, as shown in Figure 1d–f, respectively. The vacancy defect does not cause structural distortion or local rearrangement in the carbon bonds. As a consequence, the 2D hierarchy is kept for the GY‐def, and GYNs‐def structures (GYNs), which could be optimal to be implemented as a support. The electronic structure properties of the GYN systems were compared to the pristine γ‐GY structure. Figure S2, Supporting Information shows the PDOS and electronic band structure for all monolayers under study. The pristine γ‐GY maintained the semiconductor character with a direct band gap of 0.40 eV at the Γ point. The same behavior is maintained in the GYN‐def system, where the N orbitals contribution is located in deep states (close to −1.9 eV). However, the GY‐def system showed the absence of a band gap, which suggests the rising of a metallic character (see Figure S2b,c, Supporting Information). Electron localized function (ELF) analysis was also used to construct map slices, and to identify the high density locations in the carbon bonding (see Figure 1g–i). Figure 1g–i show the cases of the GYN‐def structures where the presence of an electronic density in the vacancy of the GY‐def structure is weaker as compared to the GYN‐def system. Therefore, the local electronic environment in all the proposed monolayers are completely different.1FigureRelaxed geometries: a) pristine γ‐GY, b) GY‐def, c) GYN‐def. Charge density contour plot of the d) pristine γ‐GY, e) GY‐def, f) GYN‐def monolayers. Contour plots of the electron localization function (ELF) map sliced (xy$\textit{xy}$ plane) for the systems under study: g) γ‐GY, h) GY‐def, and i) GYN‐def monolayers, respectively. The local maxima of ELF defines localization domains corresponding to regions of chemical interest. The values of ELF are in the range (0.0 to 1.0) with 1 (red) meaning complete localization and 0.6 (pink) corresponding to a delocalized electron distribution.Adsorption of Con Clusters on γ‐GY, GY‐def, and GYN‐def MonolayersThe geometry of the Con clusters generated by Da Silva et al.[68] were considered throughout this work. Figure 2a shows the energy stability of the Con clusters, which is reported with the values of the cohesion energies (Ecoh${}_{\text{coh}}$). The trend of the cohesion energy shows that as the size of the Con clusters increases, the energy stability is favored. Therefore, the nature of the Con clusters to agglomerate into larger nanostructures could be expected. The Co–Co bond length increases as the size of the Con clusters increase (see Figure 2a). All relaxed Con systems maintain the initial structural geometry according to Da Silva et al.[68] The lowest‐energy configurations in the adsorption of Con (n = 1–5) clusters onto the pristine γ‐GY, GY‐def, and GYN‐def surfaces were studied by considering four different sites; namely, in the center of the 12‐membered ring (H1), in the six‐membered ring (H2), in the bridge of the –C≡ C– bonds (B1), and at the bridge of the –C=C– bonds (B2). Such locations were evaluated at the top initial position, at 2.5 Å with respect to the carbon monolayers (see Figure 2b). Additionally, the Con clusters present two possible adsorption configurations. That is, horizontal and vertical positions. Therefore, these configurations were also considered in the geometry relaxation procedure.2Figurea) Geometric structures of small (Con) clusters (n = 2–5) with cohesive energy, and b) molecular scheme of pristine γ‐GY with four different adsorption sites: Hole‐1,2 (H1,H2), and Bridge‐1,2 (B1,B2), respectively.The proposed configurations, Con@γ‐GY and Con@GYNs‐def were fully optimized. The results are presented in Figures S3– S7, Supporting Information, which correspond to the Con clusters (n = 1–5) supported on the monolayers under study. The relative energy values are shown for each case to identify the lowest‐energy configurations.Figure 3 and 4 show the adsorption energy (Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$) values and charge density difference (ΔρCon/GYN${\Delta}{\rho}_{{\text{Co}}_{n}\text{/GYN}}$) for all configurations of lowest‐energy. According to Figure 3, the cobalt clusters are adsorbed through an exothermic process. For the cluster adsorption onto GYN monolayers, Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$ increases linearly as the size of the Con cluster increases. This behavior is absent in the pristine γ‐GY system. Therefore, vacancy defects induce the adsorption of Con clusters. Experimentally, a high Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$ value would suggest that the Con clusters lack of diffusion on the carbon monolayers. Figure 4, depicts the isosurfaces of electronic density difference, which were obtained in accordance to Equation 5. For the lowest‐energy system of the form Con@γ‐GY, the Co atoms are preferably adsorbed on the hollow site of the 12‐membered ring. The Con@GY‐def and Con@GYN‐def systems revealed a similar trend, excluding the interaction with the Co3 cluster. In this case, one of the Co atoms is selective to migrate to a 12‐membered ring (Co3@GYN‐def). The region around the Con atoms is subjected to electron depletion for most of the cases, except the Co4@γ‐GY and Co4@GYN systems, due to the presence of the Co atoms (see Figure 4). Additionally, the Hirshfeld charge (Q) total values on the Con clusters were also reported. Charge transfer increases when the size of the Con clusters increase. The largest amount of charge transferred (Q = 0.73 e) is observed for the Co5@GY‐def system. It could be attributed to the strong adsorption energy of 19.68 eV. In the lowest‐energy configurations, the Co atoms prefer to interact in the red regions, where the electronic density is high (red color) and located in accordance to the sliced ELF map (see Figure 1g–i). As a consequence, the vacancy defect plays an important role in the adsorption of the Con clusters.3FigureAdsorption energy (Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$) values for lowest‐energy configurations.4FigureIsosurface of the charge density difference for the lowest‐energy systems: a–c) Co1@GYNs, d–f) Co2@GYNs, g–i) Co3@GYNs, j–l) Co4@GYNs, m–o) and Co5@GYNs. The values under each cobalt structure stand for the Hirshfeld charges (Q). The yellow and blue isosurfaces represent the accumulation and depletion of electron density, respectively. The isosurface level is set to be 0.0025 e Å−3.The influence of the Con clusters on the carbon‐monolayer was assessed with the PDOS in Figure S8, Supporting Information. The presence of Co atoms contributes with electronic states above at the Fermi level (EF${}_{\text{F}}$). This indicates that one to five Co atoms are the responsible to tune the systems into a metallic electronic behavior. The high contributions of the Co‐PDOS are located from −1.0 eV up to the Fermi level for the Co1 − 4 systems. While for the Co5 interactions, the Co‐PDOS high contributions are located from 2.0 eV to the Fermi level. In these energy ranges, C‐PDOS are present, which may indicate an overlap of these electronic states, associated with probable chemical interactions among the Co atoms and the carbon monolayers (see Figure S8, Supporting Information). This behavior can be confirmed with the ΔρCon/GYN${\Delta}{\rho}_{{\text{Co}}_{n}\text{/GYN}}$ isosurfaces (see Figure 4).H2 Adsorption on Isolated Con ClustersThe capacity of hydrogen storage by the Con clusters was evaluated with the adsorption of xH2 molecules (x = 1–6) on free Con clusters. That is, one to six H2 molecules were added to interact with each of the Con clusters. It is worth to denote that these configurations were fully optimized. The local minima are presented in Figures S9– S13, Supporting Information. The initial position of the H2 molecules was located at a distance about 2.50 Å from each of the free Con clusters. For all Con clusters, adsorption and dissociation of the H2 molecules are evident. As depicted in Figure 5, the number of adsorbed H2 molecules is directly proportional to the adsorption energy per molecule. As a consequence, the free Con clusters have the capacity to chemisorb xH2 molecules. This behavior is in agreement with DFT calculations previously performed, in which the ability of Con clusters to adsorb and dissociate H2 has been predicted.[60–63] The adsorption energy (Eads-H2/Con${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}}$) values are relatively similar (with an average of 1.94 eV per H2) when the Co2--5${}_{2\text{--}5}$ clusters interact with up to 6H2 molecules. The adsorption and dissociation of the H2 molecules are present around the free Con clusters (see Figures S9– S13, Supporting Information). This behavior may predict the tendency to use a smaller number of Co atoms to obtain comparable adsorption energies.5FigureAdsorption energies (Eads-H2/Con${}_{\text{ads-H}{}_{2}{\text{/Co}}_{n}}$) per H2 molecules (eV per H2) for the different Con (n = 1–5) clusters.Interaction of xH2 Molecules (x = 1–5) with Con@γ‐GY, Con@GY‐def, and Con@GYN‐def SystemsThe effect of the carbon monolayers (γ‐GY, GY‐def, and GYN‐def systems) on the ability to adsorb hydrogen molecules was studied by evaluating the interaction of the H2 molecules (x = 1–5) with Con@γ‐GY, Con@GY‐def, and Con@GYN‐def systems. The hydrogen saturation was considered as hydrogen storage. Several configurations were proposed. The initial configuration corresponds to a H2 molecule located at a distance about 2.50 Å from each of the Co atoms exposed on the surface. All model systems were fully optimized for a number of xH2 molecules (x = 1–5) at the DFT/PBE‐D2/DZP level of theory.The adsorption energies (given in eV per H2) for each number of H2 molecules are depicted in Figure 6. The adsorption energies (Eads-H2/Con@GYN${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}}$) of the xH2 molecules on the Con@‐γ‐GY systems showed an increasing behavior when H2, 2H2, and 4H2 molecules were adsorbed, excluding the Co4@γ‐GY system (see Figure 6a). The magnitude of the interaction with the 3H2 molecules increases as the size of the Co3@γ‐GY systems increase. Particularly, the xH2‐Con@GY‐def systems exhibited adsorption energy values smaller than 0.8 eV per H2. This behavior in adsorption energy can be attributed to the position of the Co atoms exposed on a smaller surface area. In Figure 6b, a repulsive behavior was evidenced when the 3H2, and 4H2 molecules interacted on the Co2@GY‐def and Co3@GY‐def systems. This could be due to a decrease in Eads-H2/Con@GYN${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}}$ values. Small adsorption energy values ranging from 0.30 to 0.65 eV per H2 for the Co4@GY‐def and Co5@GY‐def systems were evaluated. Figure 6c shows the adsorption energy behavior of the xH2 molecules adsorbed on the Con@GYN‐def systems. A smaller range from 0.30 to 0.60 eV per H2 was obtained when 3H2, 4H2, and 5H2 molecules interact with the Co4@GYN‐def and Co5@GYN‐def systems. Based on the adsorption energy reported in Figure 6, the carbon monolayers act as ideal supports that effectively improve the hydrogen storage capacity of the Con clusters. The molecular structure in each inset corresponds to the systems that effectively retained the H2 molecules. Figure 7 shows the 5H2‐Co5@γ‐GY, 5H2‐Co5@GY‐def, and 5H2‐Co5@GYN‐def systems from top and side views. The adsorption energy values are within the ideal range to obtain a reversible hydrogen storage (0.2 to 0.70 eV per H2).[10,42,69,70] For all cases, dissociation and adsorption of the H2 molecule are present on the deposited Co5 cluster. Particularly, the 5H2‐Co5@GY‐def system shows two H2 molecules interacting close to the Co5 cluster. To corroborate the interaction of the two H2 molecules, the electronic density is shown in Figure S14, Supporting Information. According the computed isosurface of the 5H2‐Co5@GY‐def system, the electronic density of the H2 molecules slightly interacts with the supported Co5 cluster. As a consequence, the resulting interaction distance (H–Co ≈ 2.77 Å) could be associated with an electrostatic type interaction. The difference of adsorption energy between the PBE‐D2 method and VDW functional corroborated this assumption (the difference amounts to 0.07 eV).6FigureAdsorption energies (Eads-H2/Con@GYN${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}}$) of xH2 molecules (x = 1–5) for systems: a) Con@γ‐GY, b) Con@GY‐def, c) Con@GYN‐def. The molecular structure inset in each plot corresponds to the interaction enclosed in a black circle. All numerical values are reported in Tables S2– S4, Supporting Information.7FigureMolecular representation of the lowest energy geometries of systems: a) 5H2‐Co5@γ‐GY, b) 5H2‐Co5@GY‐def, and c) 5H2‐Co5@GYN‐def. Adsorption energy (Eads-H2/Con@GYN${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}}$) is reported under each structure.Molecular Dynamics StudyThe structural and thermal stability of the systems under study were also investigated by using Born–Oppenheimer molecular dynamics (BOMD) calculations with the same periodic boundary conditions. The selected systems were those that showed largest adsorption energies, such as 5H2‐Co5@γ‐GY, 5H2‐Co5@GY‐def, and 5H2‐Co5@GYN‐def systems at a temperature of 1000 K with a simulation time >1000 fs (1 ps). Figure 8 shows the evolution of these systems with the profile of the molecular dynamics simulation over time (BOMD simulations starting from the relaxed geometries). The 5H2‐Co5@γ‐GY system exhibit variations of the potential energy in an interval of ≈3 eV. After 1 ps, the hydrogen atoms remain in the Co5 cluster. The 5H2‐Co5@GY‐def system presents a potential energy variation of ≈8 eV, where an instability in the Co–H bonds is observed. Consequently, at the time step of 1 ps, the desorption of six‐H2 molecules could be identified. The 5H2‐Co5@GYN‐def system exhibits variations at an energy interval of ≈6 eV, and a bond elongation in the GYN‐def monolayer. After 1 ps of time step, the Co5 cluster maintained the adsorption with eight hydrogen atoms. Therefore, after completing the BOMD simulations, the behavior of the systems under study shows 100%, 60%, and 80% of hydrogen retention for Co5@γ‐GY, Co5@GY‐def, and Co5@GYN‐def systems, respectively. Multimedia material (video.mov) was also included in the Supporting Information, corresponding to the BOMD simulations. Therefore, the high retention capacity of H2 molecules of the Co5@γ‐GY system after the BOMD simulation may be associated with the adsorption energy (0.74 eV per H2). While the difference in retention capacity for Co5@GY‐def (60%) and Co5@GYN‐def (80%) systems may be associated to the geometrical disposition in which the Co atoms are exposed on the surface area (see Figure 7b,c). Likewise, a structural stability of the Co5 cluster on the surfaces is observed. This is strongly correlated with the high adsorption energy values according to Figure 3. This feature may aid to reduce the instability issue in small Con clusters[71,72] by depositing Co atoms in modified carbon monolayers.8FigureMolecular dynamics profile at a temperature of 1000 K for systems: a) 5H2‐Co5@γ‐GY, b) 5H2‐Co5@ GY‐def, and c) 5H2‐Co5@GYN‐def.ConclusionsBy using DFT‐D2 calculations, the capacity to adsorb Con clusters (n = 1–5) on pristine γ‐GY, GY‐def, and GYN‐def surfaces was studied. Electronic structure properties and charge transfer in the systems were analyzed. According to the Eads${}_{\text{ads}}$ values, the Con clusters are selective to the adsorption on surfaces with vacancy defects. Large Eads${}_{\text{ads}}$ values may be associated to the large charge transfer by the Co atoms toward the carbon surfaces, according to the isosurface of charge density difference and Hirshfeld charge values. The structural stability of the supported Co5 clusters is evident by keeping its trigonal bipyramidal geometry. The behavior of isolated and supported Con clusters was evaluated by adsorption of xH2 molecules (x = 1–6). The analysis of adsorption energies per H2 molecule showed that the Con@γ‐GY, Con@GY‐def, and Con@GYN‐def systems exhibited an improvement in the ideal energy range for efficient reversible hydrogen storage. Additionally, BOMD calculations were performed on the structurally stable systems 5H2‐Co5@γ‐GY, 5H2‐Co5@GY‐def, and 5H2‐Co5@GYN‐def. The temperature effect plays an important role to reduce the amount of interacting H2 molecules in our systems. These systems are capable to store hydrogen with 60% of efficiency. Furthermore, we contributed to understand the molecular interaction among H2 and Con@GYN‐def systems. These results could be implemented as a tool to guide the design of novel nanomaterials for hydrogen storage systems.Experimental SectionAll calculations in this work were performed by using DFT as implemented in the SIESTA computational code.[73] In order to describe the exchange‐correlation term, the generalized gradient approximation was applied with the exchange‐correlation functional proposed by PBE.[74,75] The long‐range van der Waals forces were described by the semiempirical correction in the Grimme's scheme (D2).[76] The Troullier–Martins[77] norm‐conserving pseudopotentials were used and a double‐ζ plus basis set was considered, including a polarization function (DZP) with an energy shift of 0.2 eV for all calculations. The real‐space mesh cut‐off energy was set to 250 Ry (3400 eV). The convergence threshold of the density matrix, the total energy and Hellmann‐Feynman forces were set to 10−4 eV, 10−5 eV, and 0.04 eV Å−1, respectively. A Monkhorst–Pack grid[78] of 3 × 3 × 1 k‐points was used for the Brillouin zone sampling. The DOS were calculated with 6 × 6 × 1 k‐points. The optimized structures were modeled using the 2 × 2 × 1 supercell (48 carbon atoms) of the pristine γ–GY. A 20 Å of vacuum was left in the z‐direction to separate the neighboring slabs, and avoid spurious interactions. The cohesive energy (Ecoh${}_{\text{coh}}$) of isolated Con clusters were obtained according to the following equation1Ecoh=ECon−nEisolated-Con\begin{equation} {E}_{\text{coh}}=\frac{{E}_{{\text{Co}}_{n}}-n{E}_{\text{isolated-Co}}}{n} \end{equation}where ECon${E}_{{\text{Co}}_{n}}$ corresponds to the total energy of the free cobalt cluster. The term Eisolated-Co${E}_{\text{isolated-Co}}$ is the free energy of a single Co‐atom, and n is the total number of atoms at the cluster. To evaluate the stability of the adsorbed Con clusters (n = 1–5) onto the γ‐GY, GY‐def, and GYN‐def monolayers (GYNs), several possible configurations with different relative positions of the M atoms were proposed. For the search of the lowest‐energy configuration, the adsorption energy (Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$) was calculated as2Eads-Co/GYN=−[Et(Con@GYNmonolayer)−Et(GYNsmonolayer)−Et(Con)]\begin{eqnarray} {E}_{\text{ads-Co/GYN}}=-[{E}_{t}(C{o}_{n}@\textit{GY}{N}_{\text{monolayer}})-{E}_{t}(\textit{GYN}{s}_{\text{monolayer}})-{E}_{t}({\text{Co}}_{n})] \nonumber\\ \end{eqnarray}in which Et(Con@GYNmonolayer${}_{\text{monolayer}}$) is the total energy of the proposed GYN monolayers, interacting with the Co atoms. Et(GYNmonolayer)${}_{t}({\text{GYN}}_{\text{monolayer}})$, and Et(Con)${}_{t}({\text{Co}}_{n})$ stand for the energy of the given GYN monolayers, and the isolated Co cluster adsorbates, respectively. In Equation (2), positive Eads-Co/GYN${}_{\text{ads-Co/GYN}}$ values indicate a stable exothermic adsorption.The interaction of the H2 molecules with the bare Con clusters was also assessed (Eads-H2/Con${E}_{\text{ads-H}{}_{2}{\text{/Co}}_{n}}$), in accordance to the following adsorption energy relationship3Eads-H2/Con=−[Et(Con+xH2)−Et(Con)−Et(xH2)]x\begin{equation} {E}_{\text{ads-H}{}_{2}{\text{/Co}}_{n}}=-\displaystyle \frac{[{E}_{t}({\text{Co}}_{n}+x{\text{H}}_{2})-{E}_{t}({\text{Co}}_{n})-{E}_{t}(x{\text{H}}_{2})]}{x} \end{equation}In Equation (3), the term Et(Con+xH2)${E}_{t}({\text{Co}}_{n}+x{\text{H}}_{2})$ represents the total energy of the H2 molecules that were grafted on the bare Con clusters. Additionally, the terms Et(Con)${E}_{t}({\text{Co}}_{n})$ and Et(H2)${E}_{t}({\text{H}}_{2})$ are the total energy of the bare Con clusters and the isolated H2 molecule. The x indicates the number of H2 molecules that were grafted to the Con clusters.Moreover, the adsorption energy of H2 molecules deposited on the composite system Con$C{o}_{n}$@GYN‐monolayer was obtained in accordance to4Eads-H2/Con@GYN=−[Et(Con@GYNmonolayer+xH2)−Et(Con@GYNmonolayer)−Et(x∫H2)]x\begin{eqnarray} &&\hspace*{-7pt}{E}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}} \nonumber\\ &&\hspace*{-7pt}=-\!\frac{[{E}_{t}({\text{Co}}_{n}@{\text{GYN}}_{\text{monolayer}}+x{\text{H}}_{2})-{E}_{t}({\text{Co}}_{n}@{\text{GYN}}_{\text{monolayer}})-{E}_{t}(x\int {H}_{2})]}{x} \hspace*{-6pt}\nonumber\\ \end{eqnarray}in which x is the number of hydrogen molecules, Et$E_{t}$(Con@GYNmonolayer${}_{\text{monolayer}}$ + xH2), is the optimized total energy, Et(Con@GYNmonolayer${}_{\text{monolayer}}$) and Et(x${}_{t}(x$H2), corresponded to the Con@GYN configuration energy, and the hydrogen molecule energy with no interaction, respectively. Since it is expected that the adsorption of the Con${\text{Co}}_{n}$ clusters on the GYN monolayers, and the adsorption of the H2 molecules on the composite Con${\text{Co}}_{n}$@GYN‐monolayers, represent an exothermic reaction, a minus sign was imposed for Equations (2–4). This is considered throughout the discussion of the present work.The charge density difference (ΔρCon/GYN${\Delta}{\rho}_{{\text{Co}}_{n}/\text{GYN}}$) corresponding to the electron redistribution caused by the presence of the Con clusters on the GYN monolayers, is given by the following equation5ΔρCon/GYN=ρCon@GYNmonolayer−ρGYNmonolayer−ρCon\begin{equation} {\Delta}{\rho}_{{\text{Co}}_{n}/\text{GYN}}={\rho}_{{\text{Co}}_{n}@{\text{GYN}}_{\text{monolayer}}}-{\rho}_{{\text{GYN}}_{\text{monolayer}}}-{\rho}_{{\text{Co}}_{n}} \end{equation}In Equation (5), ρCon@GYNmonolayer${\rho}_{{\text{Co}}_{n}@{\text{GYN}}_{\text{monolayer}}}$, ρGYmonolayer${\rho}_{{\text{GY}}_{\text{monolayer}}}$, and ρCon${\rho}_{{\text{Co}}_{n}}$ corresponded to the electronic density of the given carbon‐monolayers interacting with the Con clusters, the isolated carbon‐monolayer, and the isolated Con clusters, respectively.The temperature effect was also assessed, since it represents a relevant factor in hydrogen storage devices.[79] BOMD simulations were performed using the Quantum ESPRESSO (QE) code.[80] BOMD calculations were carried out from the relaxed structures, with an equilibrium time‐step of 1.69 fs. Moreover, 600 steps were considered, and a constant temperature of 1000 K (NVT Nosé–Hoover thermostat) during 1000 fs (1 ps). This temperature was chosen to understand the structural stability of the supported Co clusters.AcknowledgementsThe authors would like to acknowledge the financial support given by DGAPA‐UNAM (Dirección General de Asuntos del Personal Académico) under Project No. PAPIIT‐(IN111420, IG100720, IN106122). J.M. would like to acknowledge the Supercomputing Department of Universidad Nacional Autónoma de México for the computing resources under Project No. LANCAD‐UNAM‐DGTIC‐370 and LANCAD‐UNAM‐DGTIC‐310, and the support given by Fondo Sectorial de Investigación para la Educación‐CONACYT under Project No. A1‐S‐13294; and Fronteras de la Ciencia‐CONACYT under Project No. 21077. Project No. 270810 (Laboratorio Nacional de Conversión y Almacenamiento de Energía‐CONACYT) is also acknowledged. C.A.C. wants to acknowledge DGAPA‐UNAM for the postdoctoral fellowship.Conflict of InterestThe authors declare no conflict of interest.Author ContributionsC.A.C. contributed to the investigation, methodology, conceptualization, software, and writing the original draft. R.S. contributed to the conceptualization, methodology, and visualization. J.M. contributed to the project administration, writing the review and editing, investigation, and resources. L.E.S. contributed to the supervision, project administration, funding acquisition, writing the review and editing, and formal analysis.Data Availability StatementThe data that support the findings of this study are available in the supplementary material of this article.H. Gu, Y. Cao, E. Elahi, S. K. Jha, Environ. Sci. Pollut. Res. 2019, 26, 13115.Ümit Ağbulut, S. Sarıdemir, Int. J. Ambient Energy 2021, 42, 1569.A. Züttel, L. Schlapbach, Nature 2001, 411, 353.N. Z. Muradov, T. N. Veziroğlu, Int. J. Hydrogen Energy 2008, 33, 6804.S. S. 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The Role of Cobalt Clusters (Con, n = 1–5) Supported on Defective γ–Graphyne for Efficient Hydrogen Adsorption: A First Principles Study

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10.1002/adts.202200354
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Abstract

IntroductionThe increasing demand for fossil fuels implies a rapid growing of air pollution and subsequent effects to be associated with human health issues, such as respiratory diseases.[1,2] Therefore, in the scientific community it is a top priority to find new alternatives to replace such fossil fuels. Hydrogen has been considered as a potential fuel to support sustainable and clean energy development,[3,4] due to the high energy density of 33.3 kW h kg−1.[5] Even though hydrogen storage represents a safe and efficient methodology, it also represents a challenge for the development of novel materials.[6] An important feature to be considered is that the adsorption energy required to obtain a reversible hydrogen storage should be in the range from 0.2 to 0.7 eV per H2.[7–10] One of the best candidate materials to be used as a hydrogen storage material is the carbon‐based nanostructures, such as fullerenes,[11] carbon nanotubes,[7,12] graphene,[13] and graphynes.[9,14]One the most attractive 2D carbon‐based material, which has been widely assessed and scrutinized as a potential hydrogen storage media is the γ‐graphyne (γ‐GY) structure. The γ‐GY was proposed by Baughman et al.,[15] and exhibits a geometry formed of a single atomic layer with an arrangement of carbon atoms with sp1${\text{sp}}^{1}$‐ and sp2${\text{sp}}^{2}$‐hybridizations. A peculiar characteristic rises upon the hybridization of sp2${\text{sp}}^{2}$+sp1${\text{sp}}^{1}$+sp1${\text{sp}}^{1}$+sp2${\text{sp}}^{2}$ bonding, resulting in the formation of acetylene linkages (–C≡ C–). Such bonding is connected by six‐membered rings.[15–18] In recent years, the γ‐GY synthesis has been achieved via a mechanochemical reaction using CaC2 and PhBr6 as precursors.[19–23] The intrinsic cavity of γ‐GY structure is very attractive to metal adatoms which prefer to interact in the plane of metal‐decorated γ‐GY. Therefore, metal atoms, including alkaline metals (AM), alkaline‐earth metals (AEM), and transition metal (TM) atoms, have been explored by experimental and theoretical works.[8,9,24–42]Currently, the γ‐GY structure has been used as an ideal support to reduce the amount of TM atoms. Chen et al.[43,44] reported that pristine γ‐GY structure is sufficiently stable to be used as a support of small Au and Ag clusters. They found that the TM clusters prefer to be adsorbed on the hollow site over the acetylenic ring, in which an exothermic process is involved. Meanwhile, some 2D carbon‐based materials have been widely documented by theoretical calculations through vacancy defects to highlight the adsorption improvement of 3d$3\text{d}$‐TM clusters for hydrogen storage applications.[45–59] Moreover, the vacancy defects play an important role in the adsorption stability of 3d$3\text{d}$‐TM clusters. Recently, the small Co clusters have been explored for hydrogen storage, both free‐standing clusters and supported on graphene.[56,60–63] The combination of different sizes of Co clusters on the graphene surface favors the hydrogen storage capacity.[56,60] Several theoretical works have explored the capacity of the small free Co clusters to adsorb H2 molecules.[61–64] Nevertheless, the interaction of small TM clusters (Con) on the γ‐GY structure with vacancy defects has not been fully understood. Motivated by the recent experimental evidence reported by Cui et al.,[22,23] the novel synthesis of the 2D carbon monolayer structures derived from the pristine γ‐GY, such as –C≡ C– vacancy (GY‐def) and the nitrogen‐doped (GYN‐def) systems have already been performed. However, the ability to adsorb TM atoms or small TM clusters on these monolayers has not yet been explored.In this work, DFT calculations were perform to understand the role of the local defects at the 2D carbon monolayers on the adsorption of small cobalt clusters (Con, n= 1–5). A systematic study of the hydrogen storage is also performed. The adsorption energy values, charge difference density (Δρ$\Delta\rho$), and density of states (DOS) were analyzed. The capacity to retain hydrogen was also evaluated by Born–Oppenheimer molecular dynamics simulations. The theoretical results may aid to tailor novel materials with specific properties and intended to be applied as hydrogen storage systems.Results and DiscussionElectronic Structure of GYN MonolayersThe atomic structure of γ‐GY monolayer can be described by two unit cells (hexagonal cells). The molecular representation of the two optimized structures are depicted in Figure S1, Supporting Information. Both hexagonal structures are equivalent. Figure S1a, Supporting Information represents a six‐membered ring geometry, while Figure S1b, Supporting Information shows a twelve‐membered ring structure. Note that both contain 12 carbon atoms. The representation of the total density of states (DOS), partial DOS (PDOS), and electronic band structure along the Γ – K – M – Γ path in the hexagonal cell are depicted in Figure S1, Supporting Information. They maintain the same electronic behavior (band gap close to 0.47 eV at the Γ point). The Fermi level (EF${}_{\text{F}}$) is located at the half between the valence band maximum (VBM) and conduction band minimum (CBM). It is worth noting that the structural parameters did not show significant changes as shown in Table S1, Supporting Information. These results are consistent with previous theoretical works.[14–16,65] Therefore, the Perdew–Becke–Ernzerhof (PBE)‐D2/DZP level of theory adequately describes the electronic and structural properties of the pristine γ‐GY monolayer.The description of the electronic structure of the pristine γ‐GY monolayer from the fully optimized 2 × 2 × 1 supercell is depicted in Figure 1a. The characteristic structural parameters of pristine γ‐GY are presented in Figure 1a. These values are similar to those obtained in previous works.[14–16,65] Then, we designed the γ‐GY system with a vacancy defect by removing the central –C≡ C– bonding atoms (GY‐def), as it is shown in Figure 1b. Finally, we obtained an additional structure by doping with nitrogen in the benzene‐rings (in the GY‐def model) to obtain two pyridine‐rings (GYN‐def), as it is depicted in Figure 1c. The characteristic structural parameters are inserted in the molecular representation in Figure 1a–c. The vacancy generated in the GY‐def and GYN‐def structures (GYNs‐def) slightly varies by 1.0 Å. The vacancy defects generated in these structures (GY‐def and GYN‐def) allow the retention of Co atoms in the center of geometry, as occurs in graphene‐like monolayers.[42,66,67] The charge density contours in the xy$\textit{xy}$ plane were calculated for the γ‐GY, GY‐def, and GYN‐def systems, as shown in Figure 1d–f, respectively. The vacancy defect does not cause structural distortion or local rearrangement in the carbon bonds. As a consequence, the 2D hierarchy is kept for the GY‐def, and GYNs‐def structures (GYNs), which could be optimal to be implemented as a support. The electronic structure properties of the GYN systems were compared to the pristine γ‐GY structure. Figure S2, Supporting Information shows the PDOS and electronic band structure for all monolayers under study. The pristine γ‐GY maintained the semiconductor character with a direct band gap of 0.40 eV at the Γ point. The same behavior is maintained in the GYN‐def system, where the N orbitals contribution is located in deep states (close to −1.9 eV). However, the GY‐def system showed the absence of a band gap, which suggests the rising of a metallic character (see Figure S2b,c, Supporting Information). Electron localized function (ELF) analysis was also used to construct map slices, and to identify the high density locations in the carbon bonding (see Figure 1g–i). Figure 1g–i show the cases of the GYN‐def structures where the presence of an electronic density in the vacancy of the GY‐def structure is weaker as compared to the GYN‐def system. Therefore, the local electronic environment in all the proposed monolayers are completely different.1FigureRelaxed geometries: a) pristine γ‐GY, b) GY‐def, c) GYN‐def. Charge density contour plot of the d) pristine γ‐GY, e) GY‐def, f) GYN‐def monolayers. Contour plots of the electron localization function (ELF) map sliced (xy$\textit{xy}$ plane) for the systems under study: g) γ‐GY, h) GY‐def, and i) GYN‐def monolayers, respectively. The local maxima of ELF defines localization domains corresponding to regions of chemical interest. The values of ELF are in the range (0.0 to 1.0) with 1 (red) meaning complete localization and 0.6 (pink) corresponding to a delocalized electron distribution.Adsorption of Con Clusters on γ‐GY, GY‐def, and GYN‐def MonolayersThe geometry of the Con clusters generated by Da Silva et al.[68] were considered throughout this work. Figure 2a shows the energy stability of the Con clusters, which is reported with the values of the cohesion energies (Ecoh${}_{\text{coh}}$). The trend of the cohesion energy shows that as the size of the Con clusters increases, the energy stability is favored. Therefore, the nature of the Con clusters to agglomerate into larger nanostructures could be expected. The Co–Co bond length increases as the size of the Con clusters increase (see Figure 2a). All relaxed Con systems maintain the initial structural geometry according to Da Silva et al.[68] The lowest‐energy configurations in the adsorption of Con (n = 1–5) clusters onto the pristine γ‐GY, GY‐def, and GYN‐def surfaces were studied by considering four different sites; namely, in the center of the 12‐membered ring (H1), in the six‐membered ring (H2), in the bridge of the –C≡ C– bonds (B1), and at the bridge of the –C=C– bonds (B2). Such locations were evaluated at the top initial position, at 2.5 Å with respect to the carbon monolayers (see Figure 2b). Additionally, the Con clusters present two possible adsorption configurations. That is, horizontal and vertical positions. Therefore, these configurations were also considered in the geometry relaxation procedure.2Figurea) Geometric structures of small (Con) clusters (n = 2–5) with cohesive energy, and b) molecular scheme of pristine γ‐GY with four different adsorption sites: Hole‐1,2 (H1,H2), and Bridge‐1,2 (B1,B2), respectively.The proposed configurations, Con@γ‐GY and Con@GYNs‐def were fully optimized. The results are presented in Figures S3– S7, Supporting Information, which correspond to the Con clusters (n = 1–5) supported on the monolayers under study. The relative energy values are shown for each case to identify the lowest‐energy configurations.Figure 3 and 4 show the adsorption energy (Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$) values and charge density difference (ΔρCon/GYN${\Delta}{\rho}_{{\text{Co}}_{n}\text{/GYN}}$) for all configurations of lowest‐energy. According to Figure 3, the cobalt clusters are adsorbed through an exothermic process. For the cluster adsorption onto GYN monolayers, Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$ increases linearly as the size of the Con cluster increases. This behavior is absent in the pristine γ‐GY system. Therefore, vacancy defects induce the adsorption of Con clusters. Experimentally, a high Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$ value would suggest that the Con clusters lack of diffusion on the carbon monolayers. Figure 4, depicts the isosurfaces of electronic density difference, which were obtained in accordance to Equation 5. For the lowest‐energy system of the form Con@γ‐GY, the Co atoms are preferably adsorbed on the hollow site of the 12‐membered ring. The Con@GY‐def and Con@GYN‐def systems revealed a similar trend, excluding the interaction with the Co3 cluster. In this case, one of the Co atoms is selective to migrate to a 12‐membered ring (Co3@GYN‐def). The region around the Con atoms is subjected to electron depletion for most of the cases, except the Co4@γ‐GY and Co4@GYN systems, due to the presence of the Co atoms (see Figure 4). Additionally, the Hirshfeld charge (Q) total values on the Con clusters were also reported. Charge transfer increases when the size of the Con clusters increase. The largest amount of charge transferred (Q = 0.73 e) is observed for the Co5@GY‐def system. It could be attributed to the strong adsorption energy of 19.68 eV. In the lowest‐energy configurations, the Co atoms prefer to interact in the red regions, where the electronic density is high (red color) and located in accordance to the sliced ELF map (see Figure 1g–i). As a consequence, the vacancy defect plays an important role in the adsorption of the Con clusters.3FigureAdsorption energy (Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$) values for lowest‐energy configurations.4FigureIsosurface of the charge density difference for the lowest‐energy systems: a–c) Co1@GYNs, d–f) Co2@GYNs, g–i) Co3@GYNs, j–l) Co4@GYNs, m–o) and Co5@GYNs. The values under each cobalt structure stand for the Hirshfeld charges (Q). The yellow and blue isosurfaces represent the accumulation and depletion of electron density, respectively. The isosurface level is set to be 0.0025 e Å−3.The influence of the Con clusters on the carbon‐monolayer was assessed with the PDOS in Figure S8, Supporting Information. The presence of Co atoms contributes with electronic states above at the Fermi level (EF${}_{\text{F}}$). This indicates that one to five Co atoms are the responsible to tune the systems into a metallic electronic behavior. The high contributions of the Co‐PDOS are located from −1.0 eV up to the Fermi level for the Co1 − 4 systems. While for the Co5 interactions, the Co‐PDOS high contributions are located from 2.0 eV to the Fermi level. In these energy ranges, C‐PDOS are present, which may indicate an overlap of these electronic states, associated with probable chemical interactions among the Co atoms and the carbon monolayers (see Figure S8, Supporting Information). This behavior can be confirmed with the ΔρCon/GYN${\Delta}{\rho}_{{\text{Co}}_{n}\text{/GYN}}$ isosurfaces (see Figure 4).H2 Adsorption on Isolated Con ClustersThe capacity of hydrogen storage by the Con clusters was evaluated with the adsorption of xH2 molecules (x = 1–6) on free Con clusters. That is, one to six H2 molecules were added to interact with each of the Con clusters. It is worth to denote that these configurations were fully optimized. The local minima are presented in Figures S9– S13, Supporting Information. The initial position of the H2 molecules was located at a distance about 2.50 Å from each of the free Con clusters. For all Con clusters, adsorption and dissociation of the H2 molecules are evident. As depicted in Figure 5, the number of adsorbed H2 molecules is directly proportional to the adsorption energy per molecule. As a consequence, the free Con clusters have the capacity to chemisorb xH2 molecules. This behavior is in agreement with DFT calculations previously performed, in which the ability of Con clusters to adsorb and dissociate H2 has been predicted.[60–63] The adsorption energy (Eads-H2/Con${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}}$) values are relatively similar (with an average of 1.94 eV per H2) when the Co2--5${}_{2\text{--}5}$ clusters interact with up to 6H2 molecules. The adsorption and dissociation of the H2 molecules are present around the free Con clusters (see Figures S9– S13, Supporting Information). This behavior may predict the tendency to use a smaller number of Co atoms to obtain comparable adsorption energies.5FigureAdsorption energies (Eads-H2/Con${}_{\text{ads-H}{}_{2}{\text{/Co}}_{n}}$) per H2 molecules (eV per H2) for the different Con (n = 1–5) clusters.Interaction of xH2 Molecules (x = 1–5) with Con@γ‐GY, Con@GY‐def, and Con@GYN‐def SystemsThe effect of the carbon monolayers (γ‐GY, GY‐def, and GYN‐def systems) on the ability to adsorb hydrogen molecules was studied by evaluating the interaction of the H2 molecules (x = 1–5) with Con@γ‐GY, Con@GY‐def, and Con@GYN‐def systems. The hydrogen saturation was considered as hydrogen storage. Several configurations were proposed. The initial configuration corresponds to a H2 molecule located at a distance about 2.50 Å from each of the Co atoms exposed on the surface. All model systems were fully optimized for a number of xH2 molecules (x = 1–5) at the DFT/PBE‐D2/DZP level of theory.The adsorption energies (given in eV per H2) for each number of H2 molecules are depicted in Figure 6. The adsorption energies (Eads-H2/Con@GYN${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}}$) of the xH2 molecules on the Con@‐γ‐GY systems showed an increasing behavior when H2, 2H2, and 4H2 molecules were adsorbed, excluding the Co4@γ‐GY system (see Figure 6a). The magnitude of the interaction with the 3H2 molecules increases as the size of the Co3@γ‐GY systems increase. Particularly, the xH2‐Con@GY‐def systems exhibited adsorption energy values smaller than 0.8 eV per H2. This behavior in adsorption energy can be attributed to the position of the Co atoms exposed on a smaller surface area. In Figure 6b, a repulsive behavior was evidenced when the 3H2, and 4H2 molecules interacted on the Co2@GY‐def and Co3@GY‐def systems. This could be due to a decrease in Eads-H2/Con@GYN${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}}$ values. Small adsorption energy values ranging from 0.30 to 0.65 eV per H2 for the Co4@GY‐def and Co5@GY‐def systems were evaluated. Figure 6c shows the adsorption energy behavior of the xH2 molecules adsorbed on the Con@GYN‐def systems. A smaller range from 0.30 to 0.60 eV per H2 was obtained when 3H2, 4H2, and 5H2 molecules interact with the Co4@GYN‐def and Co5@GYN‐def systems. Based on the adsorption energy reported in Figure 6, the carbon monolayers act as ideal supports that effectively improve the hydrogen storage capacity of the Con clusters. The molecular structure in each inset corresponds to the systems that effectively retained the H2 molecules. Figure 7 shows the 5H2‐Co5@γ‐GY, 5H2‐Co5@GY‐def, and 5H2‐Co5@GYN‐def systems from top and side views. The adsorption energy values are within the ideal range to obtain a reversible hydrogen storage (0.2 to 0.70 eV per H2).[10,42,69,70] For all cases, dissociation and adsorption of the H2 molecule are present on the deposited Co5 cluster. Particularly, the 5H2‐Co5@GY‐def system shows two H2 molecules interacting close to the Co5 cluster. To corroborate the interaction of the two H2 molecules, the electronic density is shown in Figure S14, Supporting Information. According the computed isosurface of the 5H2‐Co5@GY‐def system, the electronic density of the H2 molecules slightly interacts with the supported Co5 cluster. As a consequence, the resulting interaction distance (H–Co ≈ 2.77 Å) could be associated with an electrostatic type interaction. The difference of adsorption energy between the PBE‐D2 method and VDW functional corroborated this assumption (the difference amounts to 0.07 eV).6FigureAdsorption energies (Eads-H2/Con@GYN${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}}$) of xH2 molecules (x = 1–5) for systems: a) Con@γ‐GY, b) Con@GY‐def, c) Con@GYN‐def. The molecular structure inset in each plot corresponds to the interaction enclosed in a black circle. All numerical values are reported in Tables S2– S4, Supporting Information.7FigureMolecular representation of the lowest energy geometries of systems: a) 5H2‐Co5@γ‐GY, b) 5H2‐Co5@GY‐def, and c) 5H2‐Co5@GYN‐def. Adsorption energy (Eads-H2/Con@GYN${}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}}$) is reported under each structure.Molecular Dynamics StudyThe structural and thermal stability of the systems under study were also investigated by using Born–Oppenheimer molecular dynamics (BOMD) calculations with the same periodic boundary conditions. The selected systems were those that showed largest adsorption energies, such as 5H2‐Co5@γ‐GY, 5H2‐Co5@GY‐def, and 5H2‐Co5@GYN‐def systems at a temperature of 1000 K with a simulation time >1000 fs (1 ps). Figure 8 shows the evolution of these systems with the profile of the molecular dynamics simulation over time (BOMD simulations starting from the relaxed geometries). The 5H2‐Co5@γ‐GY system exhibit variations of the potential energy in an interval of ≈3 eV. After 1 ps, the hydrogen atoms remain in the Co5 cluster. The 5H2‐Co5@GY‐def system presents a potential energy variation of ≈8 eV, where an instability in the Co–H bonds is observed. Consequently, at the time step of 1 ps, the desorption of six‐H2 molecules could be identified. The 5H2‐Co5@GYN‐def system exhibits variations at an energy interval of ≈6 eV, and a bond elongation in the GYN‐def monolayer. After 1 ps of time step, the Co5 cluster maintained the adsorption with eight hydrogen atoms. Therefore, after completing the BOMD simulations, the behavior of the systems under study shows 100%, 60%, and 80% of hydrogen retention for Co5@γ‐GY, Co5@GY‐def, and Co5@GYN‐def systems, respectively. Multimedia material (video.mov) was also included in the Supporting Information, corresponding to the BOMD simulations. Therefore, the high retention capacity of H2 molecules of the Co5@γ‐GY system after the BOMD simulation may be associated with the adsorption energy (0.74 eV per H2). While the difference in retention capacity for Co5@GY‐def (60%) and Co5@GYN‐def (80%) systems may be associated to the geometrical disposition in which the Co atoms are exposed on the surface area (see Figure 7b,c). Likewise, a structural stability of the Co5 cluster on the surfaces is observed. This is strongly correlated with the high adsorption energy values according to Figure 3. This feature may aid to reduce the instability issue in small Con clusters[71,72] by depositing Co atoms in modified carbon monolayers.8FigureMolecular dynamics profile at a temperature of 1000 K for systems: a) 5H2‐Co5@γ‐GY, b) 5H2‐Co5@ GY‐def, and c) 5H2‐Co5@GYN‐def.ConclusionsBy using DFT‐D2 calculations, the capacity to adsorb Con clusters (n = 1–5) on pristine γ‐GY, GY‐def, and GYN‐def surfaces was studied. Electronic structure properties and charge transfer in the systems were analyzed. According to the Eads${}_{\text{ads}}$ values, the Con clusters are selective to the adsorption on surfaces with vacancy defects. Large Eads${}_{\text{ads}}$ values may be associated to the large charge transfer by the Co atoms toward the carbon surfaces, according to the isosurface of charge density difference and Hirshfeld charge values. The structural stability of the supported Co5 clusters is evident by keeping its trigonal bipyramidal geometry. The behavior of isolated and supported Con clusters was evaluated by adsorption of xH2 molecules (x = 1–6). The analysis of adsorption energies per H2 molecule showed that the Con@γ‐GY, Con@GY‐def, and Con@GYN‐def systems exhibited an improvement in the ideal energy range for efficient reversible hydrogen storage. Additionally, BOMD calculations were performed on the structurally stable systems 5H2‐Co5@γ‐GY, 5H2‐Co5@GY‐def, and 5H2‐Co5@GYN‐def. The temperature effect plays an important role to reduce the amount of interacting H2 molecules in our systems. These systems are capable to store hydrogen with 60% of efficiency. Furthermore, we contributed to understand the molecular interaction among H2 and Con@GYN‐def systems. These results could be implemented as a tool to guide the design of novel nanomaterials for hydrogen storage systems.Experimental SectionAll calculations in this work were performed by using DFT as implemented in the SIESTA computational code.[73] In order to describe the exchange‐correlation term, the generalized gradient approximation was applied with the exchange‐correlation functional proposed by PBE.[74,75] The long‐range van der Waals forces were described by the semiempirical correction in the Grimme's scheme (D2).[76] The Troullier–Martins[77] norm‐conserving pseudopotentials were used and a double‐ζ plus basis set was considered, including a polarization function (DZP) with an energy shift of 0.2 eV for all calculations. The real‐space mesh cut‐off energy was set to 250 Ry (3400 eV). The convergence threshold of the density matrix, the total energy and Hellmann‐Feynman forces were set to 10−4 eV, 10−5 eV, and 0.04 eV Å−1, respectively. A Monkhorst–Pack grid[78] of 3 × 3 × 1 k‐points was used for the Brillouin zone sampling. The DOS were calculated with 6 × 6 × 1 k‐points. The optimized structures were modeled using the 2 × 2 × 1 supercell (48 carbon atoms) of the pristine γ–GY. A 20 Å of vacuum was left in the z‐direction to separate the neighboring slabs, and avoid spurious interactions. The cohesive energy (Ecoh${}_{\text{coh}}$) of isolated Con clusters were obtained according to the following equation1Ecoh=ECon−nEisolated-Con\begin{equation} {E}_{\text{coh}}=\frac{{E}_{{\text{Co}}_{n}}-n{E}_{\text{isolated-Co}}}{n} \end{equation}where ECon${E}_{{\text{Co}}_{n}}$ corresponds to the total energy of the free cobalt cluster. The term Eisolated-Co${E}_{\text{isolated-Co}}$ is the free energy of a single Co‐atom, and n is the total number of atoms at the cluster. To evaluate the stability of the adsorbed Con clusters (n = 1–5) onto the γ‐GY, GY‐def, and GYN‐def monolayers (GYNs), several possible configurations with different relative positions of the M atoms were proposed. For the search of the lowest‐energy configuration, the adsorption energy (Eads-Co/GYN${E}_{\text{ads-Co/GYN}}$) was calculated as2Eads-Co/GYN=−[Et(Con@GYNmonolayer)−Et(GYNsmonolayer)−Et(Con)]\begin{eqnarray} {E}_{\text{ads-Co/GYN}}=-[{E}_{t}(C{o}_{n}@\textit{GY}{N}_{\text{monolayer}})-{E}_{t}(\textit{GYN}{s}_{\text{monolayer}})-{E}_{t}({\text{Co}}_{n})] \nonumber\\ \end{eqnarray}in which Et(Con@GYNmonolayer${}_{\text{monolayer}}$) is the total energy of the proposed GYN monolayers, interacting with the Co atoms. Et(GYNmonolayer)${}_{t}({\text{GYN}}_{\text{monolayer}})$, and Et(Con)${}_{t}({\text{Co}}_{n})$ stand for the energy of the given GYN monolayers, and the isolated Co cluster adsorbates, respectively. In Equation (2), positive Eads-Co/GYN${}_{\text{ads-Co/GYN}}$ values indicate a stable exothermic adsorption.The interaction of the H2 molecules with the bare Con clusters was also assessed (Eads-H2/Con${E}_{\text{ads-H}{}_{2}{\text{/Co}}_{n}}$), in accordance to the following adsorption energy relationship3Eads-H2/Con=−[Et(Con+xH2)−Et(Con)−Et(xH2)]x\begin{equation} {E}_{\text{ads-H}{}_{2}{\text{/Co}}_{n}}=-\displaystyle \frac{[{E}_{t}({\text{Co}}_{n}+x{\text{H}}_{2})-{E}_{t}({\text{Co}}_{n})-{E}_{t}(x{\text{H}}_{2})]}{x} \end{equation}In Equation (3), the term Et(Con+xH2)${E}_{t}({\text{Co}}_{n}+x{\text{H}}_{2})$ represents the total energy of the H2 molecules that were grafted on the bare Con clusters. Additionally, the terms Et(Con)${E}_{t}({\text{Co}}_{n})$ and Et(H2)${E}_{t}({\text{H}}_{2})$ are the total energy of the bare Con clusters and the isolated H2 molecule. The x indicates the number of H2 molecules that were grafted to the Con clusters.Moreover, the adsorption energy of H2 molecules deposited on the composite system Con$C{o}_{n}$@GYN‐monolayer was obtained in accordance to4Eads-H2/Con@GYN=−[Et(Con@GYNmonolayer+xH2)−Et(Con@GYNmonolayer)−Et(x∫H2)]x\begin{eqnarray} &&\hspace*{-7pt}{E}_{\text{ads-H}{}_{2}/{\text{Co}}_{n}@\text{GYN}} \nonumber\\ &&\hspace*{-7pt}=-\!\frac{[{E}_{t}({\text{Co}}_{n}@{\text{GYN}}_{\text{monolayer}}+x{\text{H}}_{2})-{E}_{t}({\text{Co}}_{n}@{\text{GYN}}_{\text{monolayer}})-{E}_{t}(x\int {H}_{2})]}{x} \hspace*{-6pt}\nonumber\\ \end{eqnarray}in which x is the number of hydrogen molecules, Et$E_{t}$(Con@GYNmonolayer${}_{\text{monolayer}}$ + xH2), is the optimized total energy, Et(Con@GYNmonolayer${}_{\text{monolayer}}$) and Et(x${}_{t}(x$H2), corresponded to the Con@GYN configuration energy, and the hydrogen molecule energy with no interaction, respectively. Since it is expected that the adsorption of the Con${\text{Co}}_{n}$ clusters on the GYN monolayers, and the adsorption of the H2 molecules on the composite Con${\text{Co}}_{n}$@GYN‐monolayers, represent an exothermic reaction, a minus sign was imposed for Equations (2–4). This is considered throughout the discussion of the present work.The charge density difference (ΔρCon/GYN${\Delta}{\rho}_{{\text{Co}}_{n}/\text{GYN}}$) corresponding to the electron redistribution caused by the presence of the Con clusters on the GYN monolayers, is given by the following equation5ΔρCon/GYN=ρCon@GYNmonolayer−ρGYNmonolayer−ρCon\begin{equation} {\Delta}{\rho}_{{\text{Co}}_{n}/\text{GYN}}={\rho}_{{\text{Co}}_{n}@{\text{GYN}}_{\text{monolayer}}}-{\rho}_{{\text{GYN}}_{\text{monolayer}}}-{\rho}_{{\text{Co}}_{n}} \end{equation}In Equation (5), ρCon@GYNmonolayer${\rho}_{{\text{Co}}_{n}@{\text{GYN}}_{\text{monolayer}}}$, ρGYmonolayer${\rho}_{{\text{GY}}_{\text{monolayer}}}$, and ρCon${\rho}_{{\text{Co}}_{n}}$ corresponded to the electronic density of the given carbon‐monolayers interacting with the Con clusters, the isolated carbon‐monolayer, and the isolated Con clusters, respectively.The temperature effect was also assessed, since it represents a relevant factor in hydrogen storage devices.[79] BOMD simulations were performed using the Quantum ESPRESSO (QE) code.[80] BOMD calculations were carried out from the relaxed structures, with an equilibrium time‐step of 1.69 fs. Moreover, 600 steps were considered, and a constant temperature of 1000 K (NVT Nosé–Hoover thermostat) during 1000 fs (1 ps). This temperature was chosen to understand the structural stability of the supported Co clusters.AcknowledgementsThe authors would like to acknowledge the financial support given by DGAPA‐UNAM (Dirección General de Asuntos del Personal Académico) under Project No. PAPIIT‐(IN111420, IG100720, IN106122). J.M. would like to acknowledge the Supercomputing Department of Universidad Nacional Autónoma de México for the computing resources under Project No. LANCAD‐UNAM‐DGTIC‐370 and LANCAD‐UNAM‐DGTIC‐310, and the support given by Fondo Sectorial de Investigación para la Educación‐CONACYT under Project No. A1‐S‐13294; and Fronteras de la Ciencia‐CONACYT under Project No. 21077. Project No. 270810 (Laboratorio Nacional de Conversión y Almacenamiento de Energía‐CONACYT) is also acknowledged. 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Journal

Advanced Theory and Simulations – Wiley

Published: Nov 1, 2022

Keywords: Co cluster; density functional theory; graphyne; hydrogen adsorption; molecular dynamics

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