Hydrogen Adsorption on the Vertical Heterostructures of Graphene and Two-Dimensional Electrides: A First-Principles Study.

Synergetic effects in two-dimensional heterostructures have attracted considerable attention in the field of catalysis. Herein, we present a first-principles study of hydrogen adsorption on the vertical heterostructures of graphene and electride (Ca2N or Y2C) monolayers. Density functional theory calculations revealed that a substantial charge transfer from the electride layers to the graphene facilitated hydrogen adsorption onto the graphene. The graphene/Ca2N and graphene/Y2C heterostructures possess adsorption free energies of 0.73 and 0.51 eV, respectively, much lower than that of the pristine graphene (1.9 eV). Moreover, doping graphene with N can further reduce the adsorption free energy of the heterostructures down to 0.29 eV, close to the optimal zero value. These results suggest that heterostructure formation activates graphene for hydrogen-evolution reactions, providing an innovative and promising strategy for hydrogen production.

Introduction

To mitigate the global energy crisis and protect the global environment, researchers are committed to discovering clean and renewable energy sources. Molecular hydrogen (H2) is an attractive fuel. Hydrogen has the highest gravitational energy density, and its only combustion byproduct is pollution-free water. Hydrogen-evolution reaction (HER) is crucial for the production of hydrogen from water as a green energy source. Currently, the best catalyst material for the HER is platinum. In view of the limited economic efficiency and storage capacity of current materials, researchers need to discover new materials or modify existing materials to improve the HER performance. Generally, the performance can be improved by (1) increasing the intrinsic activity of the catalyst (such as by using defects, doping, and coupling between substrates and monolayers) and (2) exposing additional active sites (such as by using heterostructures and nanoparticles).[1−3] In vertical heterostructures, layers are stacked by van der Waals (vdW) interactions, allowing many combinations of 2D materials without the lattice mismatch issues. Various combinations of remarkably different two-dimensional (2D) materials make 2D vertical heterostructures one of the most promising materials for improving the HER performance, as demonstrated theoretically and experimentally in previous studies.[4,5]

Electrides are unique ionic compounds, wherein electrons are localized in the lattice gap and act as anions to balance the entire chemical formula. Dye et al. synthesized the first organic electride crystal composed of alkali metals and organic components: Cs+(18C6)2e–.[6] However, organic electrides possess several disadvantages, such as poor thermal stability (they decompose easily above 230 K) and sensitivity to water and air. Matsuishi and Honoso et al. successfully synthesized the first inorganic electride that was stable at room temperature: [Ca24Al28O64]4+ (also known as C12A7:e–).[7] The decomposition temperature of C12A7:e– is 1600 °C, and it can be stabilized at 300 °C. In addition, it is used in synthetic ammonia-catalyzed organics,[8,9] light-emitting diodes, and other materials.[10,11] Lee et al. successfully verified the first 2D electride, Ca2N,[12] which consists of positively charged ionic and negatively charged electron layers. Zhang et al. discovered a new 2D electride, Y2C, containing early transition group elements.[13] The electron anion between the positively charged Y2C layers possesses more electrons than that in Ca2N. Kim et al. combined 2D electrides with the layered material MoTe2.[14] The 2D electride [Ca2N]+·e– diffuses electrons into MoTe2, producing an electron doping density in excess of 1.6 × 1014 cm–2 and introducing changes in the lattice symmetry. Dhakal et al. reported the 2H to 1T′ phase transition and intermediates in bulk MoS2 by using MoS2/[Ca2N]+·e– heterostructures.[15] Therefore, 2D electrides may enable substantial electron doping to other 2D materials, resulting in a dramatic change in the electronic properties. Accordingly, we have constructed vertically stacked heterostructures of graphene and 2D electrides, utilizing the strong charge transferability to improve the HER performance of the material. Here, we choose representative 2D electrides that have been achieved in experiments, Ca2N and Y2C.

In this study, we used first-principles density functional theory (DFT) calculations to investigate hydrogen (H) adsorption on vertical heterostructures of graphene and electride (Ca2N and Y2C) monolayers. The DFT calculations revealed a substantial charge transfer from the electride layers to the graphene, facilitating H adsorption. This work proposes a novel strategy for improving the catalytic performance of 2D materials, which would presumably be applicable to other 2D heterostructures.

Results and Discussion

We first investigated the interface structures and stabilities of the graphene/electride vertical heterostructures. The optimized lattice constants for the monolayer graphene, Ca2N, and Y2C were 2.47, 3.61, and 3.62 Å, respectively, consistent with those reported in previous experimental and theoretical reports. The lattice parameter of graphene, Ca2N, and Y2C are 2.458, 3.6, and 3.6164 Å in previous studies.[12,13,16] To minimize the lattice mismatch, we constructed the heterostructures by stacking 3 × 3 graphene, 2 × 2 Ca2N and 3 × 3 graphene, and 2 × 2 Y2C layers in the given order. The lattice mismatch for graphene and Ca2N (Figures a) and graphene and Y2C (Figures b) were 2.6% and 2.3%. The graphene/Ca2N and graphene/Y2C interlayer distances were 2.56 and 2.48 Å, respectively; there is no specific bonds between the layers. Because graphene, monolayer Ca2N, and monolayer Y2C had already been successfully fabricated, we used the formation energies to evaluate the structural stability of the heterostructures. The formation energy of the graphene/Ca2N and graphene/Y2C heterostructures was −4.95 and −4.12 eV, respectively. The interlayer binding energies of the graphene/Ca2N and graphene/Y2C heterostructures were −107.93 and −89.83 meV/Å2, respectively, indicating that heterostructure formation is energetically favorable. In addition, ab initio molecular dynamics (AIMD) simulations were performed using a Nosé–Hoover heat-bath scheme to evaluate the thermal stability of the heterostructures. With consideration of the lattice translational constraints, a 2 × 2 × 1 supercell for the graphene/Ca2N and graphene/Y2C heterostructures containing 120 atoms was employed in the AIMD simulation. The graphene/Ca2N and graphene/Y2C heterostructures remained intact at 300 K after the simulation of 5 ps. Figure shows the final structures together with the energy profiles during MD simulations, and the layer structures are only slightly deformed, demonstrating their robust thermal stability at room temperature. The structure snapshots in the simulations are displayed in Figure S1.

Figure 1

Side (left panel) and top (right panel) views of (a) graphene/Ca2N and (b) graphene/Y2C heterostructures. Brown, ocean blue, green, and white spheres represent C, Ca, Y, and N atoms, respectively.

Figure 2

Final structures after molecular dynamics simulation for 5 ps (left panel) and the corresponding energy profiles (right panel): (a) graphene/Ca2N and (b) graphene/Y2C heterostructures.

To evaluate the catalytic activity of the HER, we further investigated the H adsorption energies of the graphene/Ca2N and graphene/Y2C heterostructures by considering different adsorption sites on the graphene surface. The H atom was found to be most stable on top of a C atom. Figure shows the optimized adsorption configurations of an H atom on the graphene surface. Because of the hydrogen adsorption, the two heterojunction graphene layers were slightly deformed. However, this did not affect the stability of the entire structure. Table lists the calculated adsorption energies for the most stable sites (ΔEH*). The HER is a multistep chemical reaction that includes two adsorption processes and a desorption process on the electrode surface. The first step is electrochemical adsorption, which is also called the Volmer reaction (H+ + e– → H*). In this process, hydrogen atoms are adsorbed onto the active sites of the catalyst. The second step is desorption, in which adsorbed H* atoms are reduced by Heyrovsky (H+ + e– + H* → H2) or Tafel reactions (H* + H* → H2) to form H2 molecules. A suitable ΔEH* value is desirable in the HER to promote desorption. In this regard, the graphene/Ca2N and graphene/Y2C heterostructures demonstrated balanced ΔEH* values (0.36 and 0.13 eV, respectively) for both the adsorption and desorption processes relative to those of graphene (1.56 eV), Ca2N (−2.89 eV), and Y2C (−2.88 eV).

Figure 3

Atomic structures of the H-adsorbed heterostructures: (a) graphene/Ca2N and (b) graphene/Y2C heterostructures. The red circles indicate H atoms.

Table 1

Calculated Adsorption Energies and Free Energies for Hydrogen

	ΔEH* (eV)	ΔGH* (eV)
graphene	1.56	1.90
Ca2N	–2.89	– 2.67
Y2C	– 2.88	– 2.65
Ca2N-G	0.36	0.73
Y2C-G	0.13	0.51

The Gibbs free energy of H adsorption (ΔGH*) is widely used to describe the catalytic activity of the HER. The ΔGH* value onto a catalyst should be close to zero to ensure optimal catalytic activity.[17,18] As depicted in Figure , the adsorption energies of Ca2N (−2.67 eV) and Y2C (−2.65 eV) are far from zero and are both negative. As electronic materials exhibit similar properties, Ca2N can be transformed into Ca2NH ([Ca2N]+·H–) by the reaction between an anionic electron and hydrogen, similar to C12A7:e–.[19] This implies that hydrogen atoms can be easily adsorbed onto the surface but are extremely difficult to desorb. Additionally, the catalyst is subject to hydrogen poisoning, which is unfavorable for the HER. However, it was discovered that hydrogen atoms adsorb less easily onto the surface of graphene but are easily desorbed. The experiment demonstrated that graphene was not suitable for HER. Our DFT calculations confirmed graphene’s poor HER catalytic activity, as reflected by the corresponding ΔGH* value (1.90 eV), which is consistent with the experimental results.[20] With the construction of the graphene/Ca2N and graphene/Y2C heterostructures, the ΔGH* value of graphene was found to be significantly lowered, and the resulting values for the graphene/Ca2N and graphene/Y2C heterostructures were 0.73 and 0.51 eV, respectively. The corresponding ΔGH* for the 2 × 2 × 1 supercells of the heterostructures were 0.76 and 0.50 eV, indicating that ΔGH* were well converged with respect to the cell sizes. Overall, these indicate that the heterostructures exhibit a significantly improved HER catalytic activity.

Figure 4

Calculated free energy (ΔGH*) diagram for the HER at the equilibrium potential (URHE = 0 V) for the two vertical heterostructures. For comparison, the values for pristine graphene are also provided.

To determine the reason for this improved HER performance, we explored the electronic structures of the heterostructures. Figure illustrates the charge density difference between the heterostructures without H adsorption. These plots were obtained by subtracting the charge densities of graphene and Ca2N from those of the heterostructures, which demonstrated charge distribution changes on graphene. The presence of 2D Ca2N or Y2C altered the charge distribution of graphene. The C atoms in the graphene exhibited various degrees of charge accumulation. To examine this, a charge density analysis was performed. Table indicates that the number of charges on the graphene in the graphene/Ca2N and graphene/Y2C heterostructures increased by 1.66 and 2.08, respectively, in comparison with pure graphene, and the number of C atoms was 18. Thus, Ca2N and Y2C can be regarded as providing 0.09 |e| and 0.12 |e| for each C atom, respectively. This indicates that the probability of hydrogen atoms receiving electrons from graphene significantly increased, which is conducive to hydrogen adsorption.

Figure 5

Charge density difference plots before H adsorption: (a) graphene/Ca2N heterostructure and (b) graphene/Y2C heterostructure. Here, the charge density difference (Δρ) is defined as Δρ = ρ(graphene/electride) – ρ(graphene) – ρ(electride). Yellow represents the accumulation of charge. Blue represents the loss of charge.

Table 2

Number of Electrons (ne) for Graphene (18 C atoms) in Different Systems

system	ne
graphene	72
graphene/Ca2N	73.66
graphene/Y2C	74.08

To further illustrate the electronic structures of the heterostructure, the atom-decomposed density of states (DOS) for clean heterostructures without H was calculated. Figure shows these atom-decomposed DOS. The DOS for C atoms exhibited changes near the Fermi level (EF) because of heterostructure formation. Compared with the semimetallic DOS of pure graphene, the C atom DOS of graphene in the graphene/Ca2N and graphene/Y2C heterostructures demonstrated a prominent peak at EF, which primarily results from C p orbitals. The graphene/Y2C heterostructure exhibited particularly higher peaks at EF. The abundance of the DOS at EF indicates that the conductivity of the material may have improved, which is also crucial for the catalytic performance of HER.[21] In contrast, it also implies that the heterostructures possess additionally available electrons for hybridization with the s orbital of H.

Figure 6

Atom-decomposed density of states (DOS) without H in graphene: (a) Graphene/Ca2N heterostructure and (b) graphene/Y2C heterostructure. For comparison, the corresponding DOS of pristine graphene is also displayed in (c). Zero-energy references represent the Fermi level of each system.

Furthermore, we considered the local DOS of the heterostructure after H adsorption (Figure ). For this description, we chose the site on graphene, where the H atom was adsorbed. The peaks at EF disappeared for the sites of the graphene/Ca2N and graphene/Y2C heterostructures after adsorption, which demonstrates strong hybridization of the C p orbitals with the H s orbital, similar to the case of the lateral heterostructure of graphene and h-BN.[22] In comparison with the results for pure graphene, the peak of the H s orbital appears at the EF of the DOS (Figure c). This result explains the enhanced H adsorption of C atoms onto graphene in the heterostructures.

Figure 7

Local density of states (LDOS) of the adsorption sites with H: (a) adsorption site on Graphene/Ca2N heterostructure and (b) adsorption site on Graphene/Y2C heterostructure. For comparison, LDOS of the adsorbed H and adsorption site of graphene are also displayed in (c).

To further tune the ΔGH value toward zero, we explored the doping of graphene with simple atoms. With consideration of its similar atomic radius, a single N atom was selected to replace the C atom. There have been several studies on the doping of graphene with N atoms.[23−25] The doping of N atoms on the graphene surface potentially reduces the adsorption energy of H, which is consistent with our results. Thus, doping or building a heterojunction can reduce the ΔGH value. Considering the five doping sites on graphene, as depicted in Figure a,e, we compared their energies and structures to obtain the most stable site (Figure b,f). Figure c,g shows the optimized adsorption configurations of an H atom on the graphene surface. On the basis of this, we calculated the corresponding hydrogen adsorption energy of graphene. As presented in Table , the ΔGH value of N-doped graphene is 0.69 eV, which is significantly lower than that of pristine graphene. In the heterostructures, the ΔGH value of N-doped graphene/Ca2N was reduced to 0.30 eV. In the N-doped graphene/Y2C heterostructure, the ΔGH value was 0.29 eV. Thus, in general, the presence of doping and heterostructures reduces the hydrogen adsorption energy on the graphene surface from 1.9 to 0.29 eV.

Figure 8

Atomic geometries of (a,e) pristine and (b,f) N-doped graphene/Ca2N and graphene/Y2C heterostructures. In (b,f), the N dopant is indicated by an arrow. The corresponding H-adsorbed structures were also displayed in (c,g). Red and white spheres represent H and N atoms, respectively.

Table 3

Calculated Adsorption Energies and Free Energies of Hydrogen

	graphene		graphene/Ca2N		graphene/Y2C
	ΔEH* (eV)	ΔGH* (eV)	ΔEH* (eV)	ΔGH* (eV)	ΔEH* (eV)	ΔGH* (eV)
N doping	0.31	0.69	–0.08	0.30	–0.10	0.29

Conclusions

In this work, we discussed the adsorption properties of atomic H on the graphene surface of graphene/electride heterostructures. The formation of heterostructures allowed the remaining electrons of the electride to transfer to the surface of the graphene. We found substantial charge transfer from the 2D electrides to graphene layers. As a result, the electronic configuration of graphene was substantially modified, making it active for HER. The catalytic performance could be significantly improved relative to that of pristine graphene and electrides. The results also indicate that more charge transfer occurs in the graphene/Y2C heterostructure, which shows that it has a superior HER catalytic performance. We constructed heterostructures after single-atom doping of graphene and discovered that N atom doping could produce better results and significantly reduce the Gibbs free energy of hydrogen adsorption. These findings have important implications for hydrogen production based on 2D materials and provide additional possibilities for further research on metal-free 2D catalytic materials.

Computational Methods

First-principles DFT calculations were conducted by using the plane-wave basis set and pseudopotentials as implemented in the Vienna ab initio simulation package.[26−28] The projector-augmented wave method and the Perdew–Burke–Ernzerhof exchange-correlation functional were employed in the calculations.[29,30] A semiclassical dispersion correction scheme (DFT-D3) was employed to include the effects of long-range interactions. All of the atoms were allowed to completely relax until the forces exerted on each atom were less than 0.01 eV/Å during the structural optimization and the energy difference was less than 10−6 eV. The plane-wave cutoff energy was set to 550 eV. The Brillouin zone was sampled using 9 × 9 × 1 k-meshes for the optimization of atomic structures and using 18 × 18 × 1 k-meshes electronic structure calculations. For ab initio molecular dynamics (AIMD) simulations, all of the atoms were allowed to completely relax until the forces exerted on each atom were less than 0.02 eV/Å and the energy difference was less than 10–4 eV. The plane-wave cutoff energy was set to 400 eV. The Brillouin zone was sampled using 2 × 2 × 1 k-meshes. The formation energy (Eform) of the vertical heterostructure is defined as Eform = Etot (graphene/electride) – Etot (graphene) – Etot (electride), The interlayer binding energy per area was calculated by using a formula,[25], where Etot (graphene/electride), Etot (graphene), and Etot (electride) are the total energies of the vertical heterostructures, graphene, and electride, A is the surface area, respectively. The Gibbs free energy of H adsorption was calculated as ΔGH*= ΔEH*+ ΔEZPE – TΔS, where ΔEH*, ΔEZPE, and ΔS represent the adsorption energy of H, vibrational zero-point energy, and entropy difference, respectively. ΔS was calculated by using the formula ΔS = S(H*) – 1/2·S(H2), where S(H*) and S(H2) represent the entropy of the adsorbed H atom and H2 in the gas phase under standard conditions, respectively, and the former is approximately zero.[17,31,32]