p‐d Orbital Hybridization Engineered Single‐Atom Catalyst for Electrocatalytic Ammonia Synthesis

The rational design of metal single‐atom catalysts (SACs) for electrochemical nitrogen reduction reaction (NRR) is challenging. Two‐dimensional metal–organic frameworks (2DMOFs) is a unique class of promising SACs. Up to now, the roles of individual metals, coordination atoms, and their synergy effect on the electroanalytic performance remain unclear. Therefore, in this work, a series of 2DMOFs with different metals and coordinating atoms are systematically investigated as electrocatalysts for ammonia synthesis using density functional theory calculations. For a specific metal, a proper metal‐intermediate atoms p‐d orbital hybridization interaction strength is found to be a key indicator for their NRR catalytic activities. The hybridization interaction strength can be quantitatively described with the p−/d‐ band center energy difference (∆d‐p), which is found to be a sufficient descriptor for both the p‐d hybridization strength and the NRR performance. The maximum free energy change (ΔGmax) and ∆d‐p have a volcanic relationship with OsC4(Se)4 located at the apex of the volcanic curve, showing the best NRR performance. The asymmetrical coordination environment could regulate the band structure subtly in terms of band overlap and positions. This work may shed new light on the application of orbital engineering in electrocatalytic NRR activity and especially promotes the rational design for SACs.


Introduction
Ammonia, an important chemical raw material, plays an important role in the fields of industry, agriculture production, energy storage, and conversion. [1,2]At present, ammonia mainly comes from the traditional Haber-Bosch ammonia synthesis process, which operates under harsh conditions, i.e., high temperature (300-500 °C) and high pressure (150-300 atm). [3,4]This process requires a lot of energy input, but the conversion rates and yields are quite low and results in serious environmental pollution problems.[7] Electrochemical techniques can activate the adsorbed N 2 molecules on the catalyst by donating electrons, while thermodynamic equilibrium has almost no limit on the conversion rate.
Due to the extremely high stability of the nonpolar N≡N (941 kJ mol −1 ) triple bond in N 2 , an efficient and inexpensive catalyst with high selectivity is required to reduce energy consumption.10][11] Metal atoms can be distributed in the substrate independently and regularly, which can not only reduce the metal loading and improve the utilization efficiency of metal atoms but also change the adsorption and desorption selectivity of the active components on the catalyst to different molecules, thereby affecting the kinetics of the reaction.In addition, the simplified SACs system is more conducive to exploring the path of the reaction mechanisms and provides excellent guidance for the design of better catalysts.
Two-dimensional metal-organic frameworks (2DMOFs) with metals and organic ligands form a unique class of SACs.18][19][20] Kambe et al. synthesized a two-dimensional planar MOFs (π-conjugated metal bis[dithiolene] complex [MC 4 S 4 ]) material for the first time and demonstrated its high electrical conductivity. [21]Afterward, researchers conducted extensive research on it.For example, NiC 4 S 4 nanosheet has high electrical conductivity and catalytic activity in detecting toxic CO, and it can bind and release ethylene molecules under neutral and reducing conditions; [22] IrC 4 S 4 shows high catalytic activity for oxygen reduction and methanol resistance; [23] while CoC 4 S 4 has been proven to be an efficient electrocatalyst for hydrogen evolution from water. [24]Recently, Liu et al. proved that different metal active centers have different adsorption energy for N 2 , and metal Os has moderate adsorption energy for N 2 , leading to the minimum reaction overpotential. [25]However, the role of individual metals, coordination atoms, and their synergy effect on the electroanalytic performance are not clear, which further hinders the systematic engineering of efficient NRR SACs.Therefore, a comprehensive theoretical study of this issue will facilitate the further development of novel NRR catalysts and provide useful guidance for promoting sustainable NH 3 production.
The rational design of metal single-atom catalysts (SACs) for electrochemical nitrogen reduction reaction (NRR) is challenging.Two-dimensional metalorganic frameworks (2DMOFs) is a unique class of promising SACs.Up to now, the roles of individual metals, coordination atoms, and their synergy effect on the electroanalytic performance remain unclear.Therefore, in this work, a series of 2DMOFs with different metals and coordinating atoms are systematically investigated as electrocatalysts for ammonia synthesis using density functional theory calculations.For a specific metal, a proper metalintermediate atoms p-d orbital hybridization interaction strength is found to be a key indicator for their NRR catalytic activities.The hybridization interaction strength can be quantitatively described with the p−/d-band center energy difference (Δd-p), which is found to be a sufficient descriptor for both the p-d hybridization strength and the NRR performance.The maximum free energy change (ΔG max ) and Δd-p have a volcanic relationship with OsC 4 (Se) 4 located at the apex of the volcanic curve, showing the best NRR performance.The asymmetrical coordination environment could regulate the band structure subtly in terms of band overlap and positions.This work may shed new light on the application of orbital engineering in electrocatalytic NRR activity and especially promotes the rational design for SACs.
To this end, we systematically investigated a series of 2DMOFs including MC 4 X 4 (M=Os, Ru, Ir; X=O, S, Se, NH, Figure 1a) as electrocatalysts for NRR based on density functional theory (DFT) calculations.The results show that for good NRR catalytic activities, the p-d hybridization interactions between the metals and adsorbate atoms should be neither too strong nor too weak, which further affects the adsorption performance of reaction intermediates.For a specific type of metal, both the p-d hybridization strength and the NRR performance are found to be determined by the p-/d-band center energy difference (Δd-p).The maximum free energy change (ΔG max ) of the NRR and Δd-p have a volcanic relationship, OsC 4 (Se) 4 , IrC 4 O 4 , and RuC 4 (Se) 4 are located at the apex of the volcano diagrams.Furthermore, OsC 4 (Se) 4 , IrC 4 O 4 , and RuC 4 (Se) 4 are nitrogen-free, which can effectively prevent the catalyst from decomposing to form NH 3 . [26]They all have a great degree of inhibitory effect on the competing reaction of hydrogen evolution (HER), making them with high NRR selectivity.Our results systematically proved the application of orbital engineering in electrocatalytic NRR activity, paving the way for the design of a new type of SACs for NRR.

Stabilities of MC 4 X 4
The optimized structures of MC 4 X 4 are all planar (Figure S1, Supporting Information).Their stabilities were evaluated by the formation energies (E form ) which were calculated by the following formula: where E M3 C6X6 ð Þ 2 , E C6X6H6 , and E MÀbulk were the total energies of M 3 (C 6 X 6 ) 2 , C 6 X 6 H 6 , and metal bulk, respectively, N represented the number of metal atoms in the bulk. [27]A more negative E form corresponds to higher stability of the catalyst.A stable M 3 (C 6 X 6 ) 2 structure should satisfy the criterion E form < 0. Tables S1-S3, Supporting Information, show the formation energies of M 3 (C 6 X 6 ) 2 , and the E form values are in the range from −3.56 to −10.59 eV.Such negative values of E form strongly attest that the good structural stability of the established M 3 (C 6 X 6 ) 2 model.We then calculated their phonon spectra to explore the dynamic stability of metal Os as a representative.The phonon spectrum results of OsC 4 X 4 are shown in Figure S2, Supporting Information.All systems have no imaginary frequency, which further confirms their stability.

N 2 Adsorption on MC 4 X 4
The first step of NRR is the chemisorption and activation of the N 2 molecule by the catalytic active center, which activate the N≡N bond. [28,29]Therefore, we first calculated the N 2 adsorption energy on MC 4 X 4 based on: where E N2 , E MC4X4 , and E MC4X4ÀN2 are the total energies of an isolated N 2 molecule, MC 4 X 4 nanosheet, and the adsorbed system, respectively.According to these definitions, a negative E ads value indicates an exothermic adsorption process.
The adsorption of N 2 can be both dissociative and associative (Figure 3a).However, dissociative absorption requires very high energy barriers (from 4.93 to 5.74 eV for OsC 4 X 4 ) (Figure S3, Supporting Information) as compared with associative absorption (see below for details).This is because the scission of N≡N requires a high kinetic barrier which makes the dissociative adsorption of N 2 under milder conditions unfavorable. [30]Consequently, only the associative path is considered as the main mechanism of the reaction.
For associative absorption, the N 2 molecule can be adsorbed on MC 4 X 4 in two modes: side-on and end-on (Figure 1b,c).In the sideon mode, N 2 is absorbed parallelly to the MC 4 X 4 nanosheet forming two chemical bonds with the transition metal atom.While in the endon mode, N 2 is vertically absorbed on the transition metal atom.For the end-on adsorption configuration, OsC 4 X 4 has negative N 2 adsorption energies (E ads : from −0.02 to −1.62 eV) (Table S4, Supporting Information); for the side-on adsorption configuration, the N 2 adsorption energies on OsC 4 X 4 are relatively weaker than in the end-on adsorption configuration (Figure 2a).For IrC 4 X 4 and RuC 4 X 4 , end-on adsorption configurations also have more negative adsorption energies (Tables S5 and S6, Supporting Information).The comparison results reveal that N 2 molecules prefer to be absorbed as the end-on configuration.
According to the Sabatier principle, the ideal NRR catalysts should have moderate adsorption energy for different intermediates (N 2 , NNH, NH, NH 2 , and NH 3 , etc.), which should not be too strong or too weak.This indicates that the excessive adsorption energy of N 2 on OsC 4 (NH) 4 may have a negative impact on the entire NRR process.The N≡N triple bond lengths of the absorbed N 2 on OsC 4 O 4 (1.13 Å), OsC 4 S 4 (1.14 Å), OsC 4 (Se) 4 (1.14 Å), and OsC 4 (NH) 4 (1.14 Å) become larger than that (1.10 Å) of an isolated N 2 molecule; for the asymmetrical structures, the N≡N triple bond lengths are all approximately 1.14 Å (Figure S4, Supporting Information).These results indicate that the triple bond of the N 2 molecule is activated.The distances between Os and adsorbed N atoms are also related to different coordinating atoms: OsC 4 (NH) 4 has the shortest Os=N bond (1.82 Å), while the others have longer Os=N bond length (from 1.84 to 1.89 Å), which corresponds to the strength of the adsorption energy.
In order to have a deeper understanding of the effect of different coordination atoms on the absorption N 2 adsorption on nanosheet, we calculated the charge density difference and Bader charge of

Electrochemical Catalytic Activity of OsC 4 X 4 for the NRR
We then used the side-on absorption configuration for intermediates involved in the six protons and electrons transfer process in NRR (N 2 + 6H + + 6 e − = 2NH 3 ).The potential determination steps (PDS) are determined as the most energetic step.The overpotential (η) of the whole NRR is computed based on: where U e is the equilibrium potential (U e = −0.18V for NRR) and U L is the limiting potential, defined as the minimum applied potential to make the PDS occur spontaneously: We considered both distal and alternating reaction pathways for the hydrogenation process of NRR (Figure 3a). [31]In the distal path, the first distal N atom reacts with three consecutive (H  Compared with the distal hydrogenation path, the alternate hydrogenation pathway is not preferred because a much higher barrier (0.51, 0.  4 is comparable with that of previously reported Feembedded metal-organic frameworks (0.35 V). [32] Therefore, OsC 4 (Se) 4 could serve as a promising NRR electrocatalyst.

Origin of NRR Catalytic Activity
The adsorption strength of the reaction intermediates was determined by the electronic state of the catalyst surface.In order to explore the difference in absorption strength on different nanosheets, we further studied the electronic structures of OsC 4 X 4 .Since the formation of *N 2 H is the PDS, we also analyzed the projected density of states (PDOS) of *N 2 H (Figure 4a, Figure S6, Supporting Information).Obviously, the results show that both the d orbital of the metal atom and the p orbital of -N 2 H contribute to the total density of states around the Fermi level for all the systems.The metal and the intermediate (N 2 H) form covalent bonds through p-d hybridization interaction.And thus, the p and d peaks in the PDOS overlap with each other near the Fermi level, while there are differences in the position of the d band center and p band center.We define the difference between d band center (E d ) and p band center (E p ) as Δd-p: *N 2 H was scaled well with E d which meets the well-known d-band center theory in electrocatalyst. [33]nd thus, ΔG max decreases almost linearly with the increase of E d levels toward E f (Figure 4b).For the 4-coordinated Os (4f 14 5 d6 6 s2 ), it is the dz 2 that dominates the d band position.The dz 2 orbital can maximize the head-on orbital overlapping to form a sigma bond when interacting with N 2 and N-containing intermediates as it is perpendicular to the basal plane. [34,35]This can also explain why Os metal gives better performance.Interestingly, ΔG max is found to have an obvious volcanic relationship with the Δd-p, OsC 4 (Se) 4 is located near the apex of the volcanic curve and has the best NRR performance (Figure 4c).The Δd-p can quantitively describe the bonding strength between the metal and the intermediates.A too large or too small difference is detrimental to the NRR process.On one hand, a larger Δd-p would suggest weak orbital resonance/overlaps that result in weaker bonding but stronger adsorption of the intermediate.For example, OsC 4 O 4 has a large Δd-p of 2.51 eV but a strong absorption of *N.On the other hand, a smaller Δd-p will result in weak adsorption of the intermediate by the catalyst, which will eventually lead to the deactivation of the catalyst surface.For example, OsC 4 (NH) 4 has a Δd-p of 1.64 eV and a weak absorption of *N.Therefore, for a highly active NRR catalyst, an appropriate energylevel difference is required to balance the adsorption and desorption of intermediates.This also opens a way of engineering the metal-coordination atom bonding interaction in SACs for better the NRR electrocatalytic activity.
To characterize the metal-coordination atom interaction strength, we further computed the crystal orbital Hamilton population (COHP) (  Energy Environ.Mater.2024, 7, e12587 increases with the decrease of Δd-p.This linear correlation gives a quantitative explanation for the role of different metal centers and coordination atoms in determining the bonding/antibonding orbital populations, which is the origin of the observed trends for the adsorption energies of intermediates.This also suggests that our Δd-p can be used as an indicator for the metal-coordination atom bonding strength.A smaller Δd-p would suggest a stronger metal-coordination atom bond, but weaker absorption of the NRR intermediates (Figure S10, Supporting Information).Furthermore, both COHP and ΔE (*N) have a linear relationship with Δd-p (Figure 4d), revealing the reliability of the Δd-p descriptor in revealing the catalytic activity of OsC 4 X 4 catalysts.
In order to explore the universality of the conclusions, we further calculated the E d of M (M = Ir, Ru (that are next to Os element)), E p of N 2 H, and the corresponding ΔG max values of NRR (Tables S8 and  S9, Supporting Information).The changing trend between the E d and ΔG max still has a good linear relationship (Figures S12 and S13, Supporting Information).Then we calculate the Δd-p against the corresponding ΔG max , similarly, there are obvious volcanic relationships between the Δd-p and ΔG max .IrC 4 O 4 and RuC 4 (Se) 4 are located at the apex of the volcanic curve and have the best NRR activity.Therefore, we can conclude that for a specific metal, a proper metalintermediate atoms p-d orbital hybridization interaction strength is a key indicator for their NRR catalytic activities (Figures S14, Supporting Information).

Suppression of Hydrogen Evolution Reaction (HER)
Hydrogen evolution reaction (HER) is a competitive reaction of NRR, so we further study the selectivity of NRR and HER on OsC 4 X 4 .The HER free energies (ΔG(*H)) are shown in Table S10, Supporting Information, and Figure 5a.The |ΔG(*H)| of OsC 4 (Se) 4 is 0.79 eV, which is much higher than the NRR energy barrier (0.53 eV), indicating that it not only has the highest NRR activity but also can inhibit the occurrence of HER.More importantly, a general inverse relationship between the NRR energy barrier (ΔG max ) and HER energy barrier (|ΔG(*H)|) is found for OsC 4 X 4 (Figure S15a, Supporting Information).For example, as the NRR energy barrier became larger from OsC 4 Se  S11 and S12; Figure S16, Supporting Information).There is also a general inverse relationship between the NRR energy barrier and HER energy barrier (Figure S15b,c, Supporting Information).The NRR is more selective over the OsC 4 (Se) 4 , RuC 4 (Se) 4 , and IrC 4 O 4 , which are located at the apex of the volcano curve between ΔG max and Δd-p.These data fully proved the inhibitory effect of MC 4 X 4 on HER.

Conclusions
In this work, the role of individual metal, symmetrical and asymmetrical coordination environment, and the p-d synthetic effect on the electrochemical catalytic performance of NRR on 2DMOFs MC 4 X 4 (M = Os, Ru, Ir; X = O, S, Se, NH) nanosheets have been studied based on DFT calculations.The results show that metal atoms are active centers in the NRR process and play a crucial role in the capture and activation of N 2 , while the distal mechanism is energetically more favorable for the conversion of N 2 to NH 3 .It is also found that the catalytic activity of MC 4 X 4 is related to the type of coordinating atoms: for a specific type of metal, a proper metal-intermediate atoms p-d hybridization interaction strength is the key indicator for NRR catalytic activities.The ΔG max and Δd-p have a volcanic relationship with OsC 4 (Se) 4 , IrC 4 O 4 , RuC 4 (Se) 4 located at the apex of the volcanic curve and have better NRR performances.The OsC 4 (Se) 4 shows the best NRR catalytic activity with the lowest overpotential (0.35 V).At the same time, MC 4 X 4 can inhibit competing HER and have good selectivity for NRR.Our results systematically proved the application of orbital engineering in electrocatalytic NRR activity, opening an exciting road to the rational design of SACs for advancing sustainable NRR.

Experimental Section
[38] The Perdew-Burke-Ernzerhof (PBE) function of the Generalized Gradient Approximation (GGA) is used to describe the exchange-correlation energy. [39]To describe the expansion of the electronic eigenfunctions, the projector-augmented wave (PAW) method was applied with a kinetic energy cutoff of 500 eV. [40,41]The total energy and force convergence threshold were set to 10 −5 eV and 0.02 eV Å−1 , respectively.The Brillouin zone was sampled with a 4 × 4 × 1 k-point grid of the Monkhorst-Pack scheme. [42] 15 Å vacuum was set above the nanosheets to avoid interaction between the two periodic images.The van der Waals interactions were considered using the empirical correction via the DFT + D3 scheme. [43,44]Charge density difference and Bader charge analysis were used to describe the charge transfer, the atomic configuration, and charge density difference diagram were shown in the VESTA code. [45,46]Projected crystal orbital Hamilton population (pCOHP) was Energy Environ.Mater.2024, 7, e12587 calculated using LOBSTER to analyze the interaction between TM atoms and intermediates. [47]he calculated hydrogen electrode model is used to simulate the electrochemical reaction. [48]The Gibbs free energy change (ΔG) of each elementary step is calculated by the following formula: where ΔE is the reaction energy that can be directly obtained by the total energies of DFT.ΔE ZPE and ΔS are the difference in zero-point energy and entropy between the products and the reactants at room temperature (T = 298.15K), respectively.The difference in zero-point energy could be calculated from the vibration frequency.The entropy and vibrational frequencies of free molecules (such as H 2 , N 2 , and NH 3 ) were taken from the NIST database.The effect of the applied electrode potential and pH are contained by the correction of ΔG U and ΔG pH , respectively.

Figure 1 .
Figure 1.a) Structures of MC 4 X 4 (M = Ru, Os, Ir; X = O, S, Se, NH) and two represent adsorption modes of *N 2 on metal site of MC 4 X 4 : b) side-on; c) end-on.

Figure 2 .
Figure 2. a) The computed adsorption energies of N 2 molecule on OsC 4 X 4 nanosheet; the charge density difference, as well as Bader charge analysis at of *N 2 on b) OsC 4 O 4 , c) OsC 4 S 4 , d) OsC 4 (Se) 4 , and e) OsC 4 (NH) 4 .Charge accumulation and depletion are illustrated by yellow and blue regions with the isosurface of 0.002 e Å−3 .

Figure 3 .
Figure 3. a) Schematic diagram for the electrochemical reduction of N 2 into NH 3 through dissociative and associative pathways; and the reaction free energy diagrams and the absorbed intermediates configurations of NRR on b) OsC 4 O 4 ; c) OsC 4 S 4 ; d) OsC 4 (Se) 4 ; e) OsC 4 (NH) 4 .For the system studied, the N 2 was mainly associatively absorbed on the slab, then hydrogenation of N 2 → NH 3 mainly underwent through distal pathway.

Figure 5 .
Figure 5. a) The max energy barriers of NRR and HER on OsC 4 X 4 ; b) the selectivity of NRR and HER on OsC 4 X 4 .
The reaction free energy diagrams of the NRR process on OsC 4 O 4 , OsC 4 S 4 , OsC 4 (Se) 4 , and OsC 4 (NH) 4 nanosheets are displayed in Figure3b-e.In the first (H + + e − ) transferring step, the adsorbed N 2 is hydrogenated to *N 2 H, where H binds to the N at the far end.After the formation of *N 2 H species, the N-N bond is further elongated to 1.22, 1.21, 1.22, and 1.18 Å on OsC 4 O 4 , OsC 4 S 4 , OsC 4 (Se) 4 , and OsC 4 (NH) 4 , respectively.The N orbital hybridization has changed from sp to sp 2 which requires a reaction barrier of 0.70 eV for OsC 4 O 4 , 0.55 eV for OsC 4 S 4 , 0.53 eV for OsC 4 (Se) 4 , and 1.77 eV for OsC 4 (NH) 4 , respectively.For the asymmetrical structures, the N-N bond is elongated to 1.22, 1.21, 1.23, 1.21, 1.22, and 1.22 Å for OsC 4 O 2 S 2 , OsC 4 O 2 Se 2 , OsC 4 O 2 (NH) 2 , OsC 4 S 2 Se 2 , OsC 4 S 2 (NH) 2 , and OsC 4 Se 2 (NH) 2 .The energy barriers of *N 2 + H + + e − → *N 2 H step are 0.59, 0.61, 0.79, 0.58, 0.65, and 0.62 eV respectively (Figure S5, Supporting Information).This indicates that the formation of *N 2 H is a nonspontaneous process.This step is thus also identified as the rate-determined step with the highest reaction barrier for all the NRR reactions on OsC 4 O 4 , OsC 4 S 4 , OsC 4 (Se) 4 , OsC 4 O 2 S 2 , OsC 4 O 2 Se 2 , OsC 4 O 2 (NH) 2 , OsC 4 S 2 Se 2 , OsC 4 S 2 (NH) 2 , and OsC 4 Se 2 (NH) 2 catalysts.The *N 2 H intermediate is further hydrogenated with the second pair of H + /e − forming two different *N 2 H 2 species: *NNH 2 (distal hydrogenation pathway) and *NHNH (alternate hydrogenation pathway).In the distal hydrogenation reaction pathway, the formation of *NNH 2 from *N 2 H on OsC 4 O 4 , OsC 4 S 4 , OsC 4 (Se) 4 , OsC 4 O 2 S 2 , OsC 4 O 2 Se 2 , OsC 4 S 2 Se 2 and OsC 4 S 2 (NH) 2 are all barrierless and downhill in the free energy diagram.A barrier of 0.18, 0.08, and 0.22 eV is required to + + e − ) pairs to generate one ammonia molecule and leave the catalyst surface.The remaining N atom then continues to be hydrogenated to produce another NH 3 molecule.In the alternating path, the two N atoms of absorbed N 2 on the catalyst surface are alternately hydrogenated, and the second NH 3 molecule is released immediately following the release of the first NH 3 molecule.