2.1 Structural Analysis of Metal /Graphene Structure

To fully understand the reaction kinetics on metal monolayer/graphene ( ) surfaces and to effectively tune CO₂RR electrocatalytic activity and stability, it is crucial to have a clear understanding of the structure and composition of the structure. In particular, the covalent bonding between the metal and graphene is a critical factor that can significantly impact the surface reactivity of 2D hybrid electrocatalysts. The electronic mixing between the metal and graphene can modify the electronic structure and activity of the surface, making it essential to scrutinize the electronic structure of the surface.

Figure 1a reveals that the bridge site yields the strongest covalent bonding between carbon and and transition metal atoms such as Ru, Rh, Pd, Ir, and Pt. In contrast, the ferromagnetic elements such as Fe, Co, and Ni prefer to adsorb in the on-top position of carbon as shown in Figure 1b. Group 11 elements such as Cu, Ag, and Au show strong van der Waals (vdW) interactions, with distances to graphene of 3.84 Å, 3.18 Å, and 3.59 Å, respectively (Figure S-4). To understand the various adsorption characteristics of these metals, we analyzed the local density of states (LDOS) to scrutinize the electronic structure of valence orbitals of metal monolayer (denoted as . As illustrated in Figure S-5, there is a distinct difference in the density of orbitals below the Fermi level, especially in the energy range, , among the physisorbed metals and the chemisorbed metals at the bridge-site and on-top position of graphene. For the bridge site-binding metals such as , , , , and , both spin-up and spin-down electron states exhibit a high density at . In contrast, for the top site-adsorbed metals such as , , and , the spin-down state is dominant in comparison to the spin-up state due to the spin asymmetry originating from magnetic properties. Physisorbed metals, such as , , and , exhibit distinct electronic characteristics. Please note that the energy levels near the Fermi level are practically unoccupied for both spin-up and spin-down states, indicating that the high and low density of states near the Fermi level play an essential role in the formation of strong and weak covalent bonds between metal and graphene, respectively.

Although the metal LDOS provides general insight into strong/weak bond formation, it remains challenging to define a more descriptive bond formation mechanism with LDOS because the five orbitals do not contribute equally to interatomic orbital hybridization. To unravel the role of specific orbitals in interplanar metal–carbon interactions, we further analyzed the orbital resolved density of states (ORDOS).

First, we attribute the distribution of several small peaks in of , , and to the intraplanar orbitals and , which are mostly associated with metallic bonding. Considering the ligand positions in the geometry where and orbitals lie in the x–y plane (as shown in Figure S-6), , , and orbitals are utilized for the interplanar bonding. However, , , and orbitals are completely unoccupied in the same energy range, making difficult to identify covalency in , , and systems.

Second, for and metals such as , , , , and that bind at the bridge site of graphene, both spin up and down states in , , and orbitals exhibit higher electronic density than and , in general, indicating these interplanar orbitals are more responsible than the intraplanar orbitals for the covalent bonding (as shown in Figures S-7 and S-8).

Third, for ferromagnetic metals such as , , and , spin-down states are solely present in for , , and orbitals while the spin-up states in the same energy range are found instead in the intraplanar orbitals and (as shown in Figure S-9). Here, we discovered that the orbital has a much higher peak density than and orbitals, indicating that the contribution of the spin-down state in orbital is the most influential to the formation of bond at the top site of graphene.

The specific orbitals involved in covalent bonding formation are summarized in Figure 2. Typically, a single state at the -band center, , is used to approximate the band of d-states involved in the interaction and its correlation with the adsorption energy of the metal on graphene. In the case of metals ( , , , , and ) that adsorb at the bridge site of graphene, the upshift of of , , and orbitals in toward the Fermi level results in a stronger covalent bond. The strongest covalent bond is observed for , followed by , , , and . For example, of is the closest to the Fermi level, which lies at , followed by ( ), ( )_, ( ), and ( ), and the binding energy on graphene is the strongest for ( ), followed by ( ), ( )_, ( ), and ( ). However, the ferromagnetic elements , , and are weakly adsorbed on graphene compared to the and metals due to the downshift of of orbitals in away from the Fermi level, with values of , , and , respectively. To summarize, not all d orbitals equally participate in the bond formation, but rather the orbitals in the Z-directions within play a decisive role in determining the strength of the covalency.

2.2 Change in Electronic Structure of Metal/Graphene Structure

The establishment of strong covalency via orbital hybridization results in a significant modification of the electronic structure of the metal surface. Specifically, we observe a remarkable reduction of the orbital LDOS near the Fermi level, particularly in for the strongly chemisorbed metals such as , , , , and , compared to pure (Figure S-10). This reduction in electron density is driven by charge transfer from metal to graphene, as indicated by the Bader charge analysis in Table S-2. In contrast, due to weaker covalency, the interatomic electronic mixing between ferromagnetic metals and graphene leads to relatively minor modification in the orbital LDOS. For instance, in , there is no significant downshift or upshift of orbitals for spin-up and -down states, and only a slight decrease of LDOS within . Similarly, for the reduction of the spin-down state is greater in the same range, which may be attributed to the greater amount of charge transferred ( ) to graphene for ( ) than for ( ). These changes in the orbitals will be further discussed in relation to the binding energy of HCOO in Section 3.4.

2.3 Structural Analysis of Metal/Graphene/Metal Structure

The electronic structure of metal surfaces in can be further modified by depositing an additional metal film on the graphene side, creating structures, as shown in Figure 1C. In a previous study, Choi et al. discovered that electron density accumulation at the bond could facilitate the formation of additional covalent bonding.¹¹

In this study, we deposited , , , and , identified as either physisorbed or weakly adsorbed to graphene, on the graphene side of , , , , , , , and structures. Surprisingly, , once physisorbed on pristine graphene, was found to be chemisorbed on hybridized graphene in , , , and structures. The binding energy of became as strong as per atom on , followed by per atom on , per atom on , and on structures. Similarly, , , and formed stronger chemical bonding on the hybridized graphene in structures than on the pristine graphene.

To validate our computational models, we attempted electrochemical deposition of under the same conditions directly onto graphene and onto graphene supported by . As shown in Figure 3, we found impossible to synthesize , but we could synthesize with the help of on the reverse side of graphene.

To gain a deeper understanding of the atomic-level formation of structures, we analyze the electronic structure of graphene in structures, where the graphene serves as an active site in this context. Due to orbital hybridization, the orbitals of graphene in structures undergo significant changes in comparison to pristine graphene, as depicted in Figure 4. The most notable difference is the appearance of a sharp electron density peak near the Fermi level, especially between , which results from charge transfer from metal to graphene. We have confirmed that the newly generated peaks are exclusively attributed to this additional charge in the graphene, rather than strain imposed by the metal. The electronic structure of the hybridized graphene is modified not only by the mismatch of lattice parameters between metal and graphene (known as the strain effect), but also by the charge polarization induced by the heteronuclear interactions between metal and carbon atoms (known as the ligand effect). To isolate the contributions of the strain and ligand effects from the change in electronic structure, we obtained the strain contribution by manipulating the lattice parameter of pure graphene corresponding to structures and calculating their electronic structures, as shown in Figure S-11. Regardless of the level of strain, the shape of the band for strained graphene remains very similar to that of pristine graphene, with only an upshift of the average position of the orbital (denoted as ) towards the Fermi level.

Since not all three orbitals of the graphene in equally contribute to the formation of structures, we performed ORDOS analysis to decompose the orbitals of graphene in the structures, as shown in Figure S-12. This analysis revealed that the electron density peaks generated near the Fermi level primarily arise from the intraplanar orbital, while no significant electron density was found in the and orbitals in this energy range. Therefore, we determined that the intraplanar orbital in the valence region at plays a crucial role in the adsorption of additional metal monolayers on graphene side of structures.

We then quantified the area under the spin up and down ( ) of the band at and correlated it with the binding energy of , , , and as shown in Figure 5. Our results showed that as increases, the binding energy of additional metal on graphene tends to increase as well. Specifically, had the highest value of , exhibiting the strongest binding energies, followed by ( ), ( ), ( ), ( ), and ( ). Although for is slightly higher than , the reason shows the stronger binding energy is that the average position of the band is farther from the Fermi level for ( ) than for ( ), which is analogous to the -band center theory.

Therefore, we can conclude that the role of of the band at is critical in the formation of structures. Additionally, the average position of the orbital in the same energy range should also be considered if values are similar.

2.4 Electrochemical CO₂RR to HCOOH on and structures

We investigated the electrocatalytic reduction of CO₂ (CO₂RR) to HCOOH, considering the competitive hydrogen evolution reaction (HER). We established the following elementary steps for CO₂RR:

(1)

(2)

(3)

In this pathway, CO₂ and a proton-electron pair are adsorbed as a formate; the addition of a second proton-electron pair to this adsorbate results in the production of HCOOH where the overall CO₂RR to HCOOH occurs at vs reversible hydrogen electrode (RHE).¹⁴ In aqueous electrolytes, the HER inevitably takes place via the following sequential steps¹⁵ which competes with the CO₂RR:

(4)

(5)

(6)

To promote selectivity toward HCOOH, the unwanted side reactions should be suppressed. Because HER is a very fast reaction with essentially no overpotential, it is quite challenging to find a catalyst that performs CO₂RR preferentially at a reasonable overvoltage.

To evaluate the global activity and selectivity of CO₂RR to HCOOH on all studied and catalysts, we calculated the free energy changes in the two-step CO₂RR, and the limiting potential at which all the elementary reaction steps become exergonic was obtained with respect to the free energy of HCOO binding energy ( ), since HCOO is the only intermediate specie in CO₂RR to HCOOH, formed as a result of CO₂ protonation. Since HCOO* governs both Equations (1) and (2), it is reasonable to set as a descriptor.¹⁶ Properly tailoring the electronic structure of the active site to acquire moderate HCOO binding energy is necessary, as too strong or too weak binding energy of HCOO results in high overpotential.

In general, the deposition of extra metal on the hybridized graphene in structures induces weaker interactions with the HCOO species in comparison to structures. Unlike the traditional -band center theory, where the upward shift of the -band center relative to the Fermi level presents more binding affinity to adsorbate, the -band center of structures exhibits the opposite trend (as shown in Figure S-13). The -band center theory is limited to the orbital hybridization, and the simple -band center correlation does not hold for the adsorption of HCOO on the hybridized metal surface.¹⁷ Instead, it is the specific orbital in the specific energy range that determines the binding affinity to HCOO. In a previous study, it was revealed that and orbitals govern the chemisorption to bidentate HCOO specie, and as the density of these orbitals near the Fermi level decreases, the binding energy of HCOO tends to show an ascending trend.¹⁸ Similarly, the density of and combined of and structures between 1.0  and 0.0 is correlated with the binding strength to HCOO.

For example, Figure 6 shows the scaling relation between the adsorption energy of HCOO* and the density of and on various and structures. Although there is a general consensus that the higher density of and leads to a stronger interaction with HCOO*, cases tend to deviate from the scaling relation due to the coupling interaction between the metal orbital and carbon orbital, broadening of -bandwidth of , and an upsurge in density. Thus, the increased and density in , which are contradictory to the studied structures. Consequently, the density of and may not be the only indicator to the binding energies of HCOO*, and a more precise approach is perhaps required for future studies.

Figure 7 shows that has the highest limiting potential of vs. RHE, which is closest to the calculated equilibrium potential at vs. RHE. This indicates that the overpotential is the smallest for this catalyst, followed by , , , , and . Among structures, and are active toward HCOOH production. However, exhibits high HCOOH productivity, but the adsorption of HCOO destabilizes the surface due to poor covalency between and graphene. Similar structural deformation is observed for and . Such deformation is not found in , , and structures, where the binding energy of HCOO is generally stronger than in their respective counterparts. Consequently, the limiting potentials for shift up, while for , and they shift down.

It is crucial to evaluate the competing HER for selectivity since the equilibrium potential for HER is more positive than that for CO₂RR to HCOOH. As a result, , , and electrocatalysts have limiting potentials (U_L) that are more positive than that of HER, as shown in Figure S-14. This is surprising, as pure monometallic nanoparticles are known to be excellent catalysts for HER. In addition, we considered CO₂RR to CO formation via COOH*. According to the free energy profile in Figure S-15, for at −0.29 V, the U_L for CO formation, CO₂RR to HCOOH pathway remains endergonic while the CO pathway becomes exergonic, indicating a preference for CO production. On the other hand, we found that and are more selective toward HCOOH formation over CO.

As a validation of the theoretical predictions, we experimentally assessed the electrochemical onset potential for HCOOH formation, as illustrated in Figure S-16. Although the onset potential for could not be obtained, presumably due to a more positive U_L for CO than HCOOH, and exhibit the highest onset potentials followed by , , and . Despite a marginal computational prediction favoring HER over CO₂RR to HCOOH in by 0.021 V, the experimental data showed a higher selectivity toward HCOOH, possibly due to the intrinsic error in DFT calculations. The and cases were chosen to verify the computational prediction that these structural inverses should have similar reaction potential, while was chosen because it is predicted to have a significantly lower potential than the first two. The computational model predictions align well with the experimental data, confirming the order and similarity in onset potentials for and with and exhibiting a higher and lower potential, respectively.

This 2D hybrid catalyst design methodology is not limited to CO₂RR but can also be applied to other electrochemical reactions, such as nitrogen reduction reaction, which is still challenging with conventional metallic electrocatalysts.