doi.org/10.26434/chemrxiv.14377016.v2

Cooperative Single-Atom Active Centers for Attenuating Linear ScalingEffect in Nitrogen Reduction ReactionKe Ye, Min Hu, Qin-Kun Li, Yi Luo, Jun Jiang, Guozhen Zhang

Submitted date: 07/04/2021 • Posted date: 08/04/2021Licence: CC BY-NC-ND 4.0Citation information: Ye, Ke; Hu, Min; Li, Qin-Kun; Luo, Yi; Jiang, Jun; Zhang, Guozhen (2021): CooperativeSingle-Atom Active Centers for Attenuating Linear Scaling Effect in Nitrogen Reduction Reaction. ChemRxiv.Preprint. https://doi.org/10.26434/chemrxiv.14377016.v2

We elucidate how the cooperation of two active centers can attenuate the linear scaling effect in NRR, throughthe first-principle study on 39 SACs comprised of two adjacent (~4 Å apart) four N-coordinated metal centers(MN4 duo) embedded in graphene.

File list (2)

download fileview on ChemRxivNRR_manuscript_new.pdf (1.28 MiB)

download fileview on ChemRxivNRR SI_new_v2.docx (1.97 MiB)

1

Cooperative single-atom active centers for attenuating linear scaling

effect in nitrogen reduction reaction

Ke Yea†, Min Hua†, Qin-Kun Lib, Yi Luoa, Jun Jianga, Guozhen Zhanga*

a Hefei National Laboratory for Physical Sciences at the Microscale, Chinese Academy of Sciences Center for Excellence in

Nanoscience, School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui

230026, China.

b Department of Materials Science and NanoEngineering, Rice University, Houston, Texas, 77005, United States.

KEYWORDS: density-functional calculation; single-atom catalysis; scaling relations; nitrogen reduction reaction.

ABSTRACT: Cooperative effects of adjacent active centers are critical for single-atom catalysts (SACs) as active site density

matters. Yet how it affects scaling relationships in many important reactions like nitrogen reduction reaction (NRR) is underexplored.

Herein we elucidate how the cooperation of two active centers can attenuate the linear scaling effect in NRR, through the first-

principle study on 39 SACs comprised of two adjacent (~4 Å apart) four N-coordinated metal centers (MN4 duo) embedded in

graphene. Bridge-on adsorption of dinitrogen-containing species appreciably tilts the balance of adsorption of N2H and NH2 towards

N2H and thus substantially loosens the restraint of scaling relations in NRR, achieving low onset potential (V) and direct N≡N

cleavage (Mo, Re) at room temperature, respectively. The potential of MN4 duo in NRR casts new insight into circumventing

limitations of scaling relations in heterogeneous catalysis.

Heterogeneous catalysis lies at the heart of the chemical

industry.1 The ideal scenario for heterogeneous catalysis, as

illustrated by the Sabatier principle, seeks a delicate balance

between the activation of reactants and the desorption of

products.2 Yet for most reactions involving multiple

intermediates, scaling relationships between adsorption

strengths of different intermediates make such a balance

difficult to achieve, limiting optimization of catalysts.3

Breaking scaling relations is crucial for heterogeneous catalyst

design. Nørskov and co-workers have suggested using multiple

active centers to achieve it based on the first-principle

calculations4, which is supported by two recent experimental

studies.5-6 However, the ambiguity, and complexity of

structures of active centers in heterogeneous catalysis make it

difficult to gain a straightforward and precise understanding on

how catalysts could work around the restraint of scaling

relations posed to reactions. A simpler catalyst model with a

well-defined structure of the active center would be helpful to

decipher it.

The emerging single-atom catalysts (SACs) combining the

merits of both homogeneous and heterogeneous catalysts have

demonstrated excellent performances in a number of different

reactions.7-11 Because SACs possess simple and unified active

centers with well-defined composition and coordination

environments, they are deemed an ideal type of catalysts model

to provide mechanistic insight into heterogeneous catalysis.

Particularly, the advent of high-density SACs due to the rapid

advance of synthetic technologies12-18 and precise control of

inter-site distance19-21 would facilitate the study of cooperative

effects of multiple active centers. The synergetic effects

between adjacent active sites on heterogeneous catalysis have

drawn increasing attention in experimental work.5, 22-26 In

parallel, the computational approach plays an indispensable role

in dissecting mechanisms and structure-property relationships

associated with SACs.27 Previously, we have conducted a first-

principle study on cooperative communications between two

neighboring active centers, and impacts of active site density on

oxygen reduction reaction (ORR) and nitrogen reduction

reaction (NRR) respectively.28-30, which has prompted ourself

to continue the exploration of cooperative single-atom active

centers.

In the present work, we employed high-density SACs as

model systems to systematically investigate impacts of multiple

active centers on scaling relationships between adsorption

strengths of different reaction intermediates in electrocatalytic

nitrogen reduction reaction (eNRR).4, 31 eNRR has been inspired

by enzymatic catalysis of nitrogenase at mild conditions and

regarded as a promising solution of energy-saving nitrogen

2

fixation.31 Unfortunately, it is hampered by the challenge of

realizing optimal activation energy (Ea) of N2 and adsorption

energy (ΔEads) of nitrogen-containing intermediate species

simultaneously due to the scaling relations that couple favorable

(unfavorable) Ea and unfavorable (favorable) ΔEads together.

For eNRR, based on the Bell-Evans-Polanyi principle, the

strong coupling between adsorption strength of *NH2 and *N2H

(* denotes adsorbed species) is in the center of scaling relations

that undermine catalytic activities.4 To surpass this limitation,

it requires a decoupling mechanism to allow them to be

optimized independently.

Scheme 1. Various adsorption configurations of N2 on (a)

MN4/G and (b) MN4 duo/G.

Well-established eNRR mechanisms, however, resolve

around associative pathways (Figure S1)32 assuming single

active center, which adsorbs dinitrogen via either end-on or

side-on manners (Scheme 1). Meanwhile, alternative adsorption

mode of N2 via ensemble active centers33 has largely been

underexplored. Previously, we found an alternative reaction

path based on cooperative bridge-on adsorption of N2 (Scheme

1) by two closely arranged (~6 Å) Mo-N-C sites.29 This

discovery naturally raised the question that whether the bridge-

on manner might initiate a game-changing strategy of NRR.34 It

then motivated us to explore in this work how the scaling

relations evolve from single active center to two cooperative

active centers as the bridge-on adsorption pattern of N2 and

other nitrogen species are adopted.

Figure 1. Top view of MN4/G and MN4 duo/G models used in

this work, with the annotation of the philosophy of building

them.

A single metal center coordinated with four nitrogen atoms

(shorted as MN4) constitutes the essential moiety of many

excellent molecular catalysts derived from metal porphyrins

and metal phthalocyanines.35-37 The marriage of MN4 active

center and two-dimensional carbon support (shorted as MN4/C)

benefits from the ease of synthesis13-18, which has generated

quite a few promising SACs, including NRR catalysts38-43. As

shown in Figure 1, we placed two adjacent MN4 within

graphene (shorted as MN4 duo/G) as a prototype model of high-

density MN4 SACs to investigate how the cooperation of single-

atom centers will impact scaling relations in NRR. Note that our

MN4 duo model is different from other dual-atom M-N-C

models44-48 (Figure S2) in two aspects: (1) our model consists

of two well-separated MN4 centers while others either have a

metal-metal bond (essentially dimer) or share coordinating

atoms; (2) our model focuses on cooperation between two

individual active centers while others emphasize one active

center with two interconnecting metal atoms.

The results and discussion are organized into two parts. In the

first part, we surveyed the scaling relationship between

adsorption strength of *NH2 and *N2H in NRR occurring on 39

different MN4/G and MN4 duo/G (Figure S3), represented by

their respective Gibbs adsorption free energies (∆G*NH2 and

∆G*N2H), and showed how it appreciably shifts as the

adsorption mode of *N2 and *N2H varies from end-on to side-

on to bridge-on. Equivalently, the significant changes of scaling

relations for bridge-on mode were demonstrated in the form of

a favorable shift of the volcano plot. In the second part, under

the guidance of altered scaling relations, we investigated

several potential NRR catalysts, and achieved low onset

potential (V) and direct N≡N cleavage (Mo, Re) at room

temperature (energy barrier < 0.85 eV), respectively. Our

results demonstrate the importance of cooperation of

monodispersed active centers, which casts new insight into the

rational design of SACs for NRR at mild conditions.

RESULTS AND DISCUSSION

After building two different sets of MN4-type SACs: MN4/G

and MN4 duo/G (M=transition metals and main group IIIA-VA

metals), we first examined their stabilities in terms of

thermodynamic stability represented by formation energy (Ef)

and electrochemical stability represented by dissolution

potential (Udiss). The majority of them are found to be

thermodynamically stable (See Figure S4, Table S1, and

associated text in Supporting Information). Since we used the

atomic energy in bulk metal as the reference state of the metal,

the assignment of “unstable” in the sense of formation energy

does not mean it would decompose or undergo aggregation. We

expected a large energy barrier for metal migration from one

site to another will prevent them from clustering.29 Further, as

we explore the scaling relationship of adsorption of different

intermediates of NRR, these seemly “unstable” MN4 duo

models are all valuable data points that can help sketch the

whole picture we need.

All possible adsorption patterns of N2 as illustrated in

Scheme 1 were investigated for all MN4 and MN4 duo models.

The main group metals of interest could not effectively activate

3

adsorbed N2, because they invoke physisorption or very weak

chemisorption. Transition metals develop five different

scenarios for the adsorption of N2 (Table S2). In the rest of

presentation, only MN4 and MN4 duo enabling substantial

chemisorption of N2 will be examined in the study of scaling

relations of NRR intermediates.

For associative NRR pathways, the first (*N2 + H+ + e- →

*N2H) and sixth (*NH2 + H+ + e- → *NH3) reductive

hydrogenation steps are the most likely potential-limiting

steps.34 Their respective free energy changes (∆G1 and ∆G6) are

coupled through an inversely proportional relationship. Since

∆G1 and ∆G6 scale well with ∆G*N2H for better ∆G*NH2

respectively (Figure S5), the key scaling relations in NRR

eventually fall onto ∆G*N2H and ∆G*NH2.

Figure 2. (a) The scaling relationship between ∆G*NH2 and

∆G*NH2 for end-on adsorption mode on MN4/G. (b) The

differential charge density profiles of end-on *N2H and

*NH2 by VN4/G and YN4/G with an isosurface value of

5×10−3 e Å−3. Yellow and blue bubbles represent charge

accumulation and depletion, respectively. (c) Projected

crystal orbital Hamilton population (pCOHP) between the

metal centers (V and Y) and the nitrogen adatom. The values

of integrated COHP (ICOHP) are shown in red bold italics.

On MN4/G, as expected, the adsorption of NH2 scales well

with N2H in end-on mode (Figure 2a), in line with their scaling

relationship established on pure metals surfaces.4 The transition

metals can be divided into two groups based on two respective

fitting lines. Group 1 (labels in blue) includes the elements in

groups IB-IVB, while group 2 (labels in red) contains those in

groups VB-VIIIB. (Figure S6) Note that the balance between

adsorption of N2H and NH2 shifts towards N2H from group 1 to

group 2, which can be interpreted by the amount of charge

transfer from metal to nitrogen species (Figure 2b) based on

Bader charge profile and the bonding strength between them

(Figure 2c) using the integrated crystal orbital Hamilton

population (ICOHP)49-52 values (more negative value indicates

stronger bonding). Take V and Y for example, more negative

charges transfer from V to N2H than to NH2, while less from Y

to N2H than NH2; the M-N bonding interaction is appreciably

stronger in MN4-N2H than in MN4-NH2 for V, while it’s weaker

in the former than the latter for Y. The same distinction between

group 1 and 2 can be found on all types of adsorption mode on

both MN4/G and MN4 duo/G (Figure S7). Since preferable

enhancing the adsorption of N2H over NH2 is favorable to

mitigate the uphill energetics of activating the adsorbed N2 and

producing NH3 from NH2, we then focus on the study of

transition metals in group 2 in the rest of work.

From MN4/G to MN4 duo/G, the scaling relationships

between ∆G*N2H and ∆G*NH2 in end-on and side-on adsorption

modes do not change significantly (Figure 3), as only one metal

center bonds with adsorbates. However, bridge-on adsorption

of N2H on MN4 duo/G appreciably alters the landscape of

scaling relations (Figure 3a). As Figure 3a shows, bridge-on

mode appreciably reduces the slope and shifts up the intercept

of scaling line relative to end-on mode while side-on mode

reduces slope at the cost of shifting down the intercept. Note

that smaller slope and higher intercept values enable

strengthening adsorption of N2H much more than NH2, which

facilitates dinitrogen activation without impeding the final

reductive hydrogenation producing ammonia. Again, the

strengthening of N2H in bridge-on mode relative to end-on and

side-on is demonstrated using Bader charge and ICOHP profiles

(Figure 3b). Compared to end-on and side-on modes where only

one metal center bond with N2H, bridge-on mode has two

collaborative metal centers binding to N2H, which increases

electrons transferred to anti-bonding orbitals of N2H and overall

metal-nitrogen bonding strength.

In addition, ∆G1 barely scales with ∆G*N2H (Figure 3c) for

bridge-on mode, which is in sharp contrast to the well scaling

between the two in end-on and side-on modes. Here the internal

energy part plays a dominant role while the entropy factor has

negligible contribution (Table S3). The change of dependence

of ∆G1 on ∆G*N2H can be explained by the change of binding

strength from *N2 to *N2H. The integral of partial density of

states (pDOS) of nitrogen atoms from -3 eV to 0 eV (Fermi

level is reset to 0) is an indicator of effective number of

electrons involved in the bonding interaction between nitrogen

and metal atoms. Thus, the difference of this integral between

*N2 and *N2H roughly reflects the difference of their binding

strength to metal centers. Clearly, bridge-on mode has the

smallest difference while end-on and side-on bear comparable

changes (Figure 3d). As two cooperative metal centers

accommodate dinitrogen-containing species together, they not

only bind them stronger but also mitigate the uphill energetics

of first dinitrogen hydrogenation. Consequently, in bridge-on

associated NRR pathways, ∆G1 and ∆G6 are decoupled (Figure

S8), creating room for substantial improvement of overall

catalytic activity, as seen in the volcano plots of NRR occurring

on MN4 duo (Figure 4).

Based on the volcano plot associated with bridge-on

adsorption mode (Figure 4c), we have identified four selected

MN4 duo/G models (M = Mo, Re, V, Os) as potential NRR

catalysts. Although Tc appears to be the closest element to the

4

vertex of volcano curve, it has to be excluded because it is

radioactive. Then, for OsN4 duo/G, initial N2 adsorption adopts

an end-on rather than bridge-on mode (Table S4). Thus, we

skipped Os as well. In the rest of presentation, we mainly

discussed Mo, Re, and V. Intriguingly, V, Mo, and Re are in

one diagonal line in the periodic table, which may account for

their similar catalytic activities in NRR. In addition to

homonuclear MN4 duo/G models, we have also considered

heteronuclear MN4 duo/G models in the form of hybrid MN4

duo. Therefore, we have a total of six MN4 duo/G models,

including VN4 duo, MoN4 duo, ReN4 duo, VN4-MoN4, MoN4-

ReV4, and ReV4-VN4.

Figure 3. (a) The scaling relationships between ∆G*NH2 and ∆G*N2H as N2H is adsorbed on MN4 duo/G via end-on, side-on,

and bridge-on modes, respectively. (b) The differential charge densities of *N2H in bridge-on, side-on, and end-on (from left

to right) adsorption modes by VN4 duo/G with an isosurface value of 5×10−3 e Å−3, and their respective pCOHP between two

V atoms and the nitrogen adatoms. Yellow and blue bubbles represent charge accumulation and depletion, respectively. The

values of ICOHP are shown in red bold italics. (c) The scaling relationships between ∆G*N2H and ∆G1 as both N2 and N2H are

adsorbed on VN4 duo/G via, respectively. (d) Electronic densities of states of *N2 (up) and *N2H (down) adsorbed via end-on,

side-on, and bridge-on modes on VN4 duo/G, respectively.

Figure 4. The scaling relationships between ∆G1 and ∆G*N2H (red line) and between ∆G6 and ∆G*N2H (black line) for end-on,

side-on, and bridge-on (from left to right) adsorption modes of *N2 and *N2H. The blue dash line in each panel indicates the

theoretical lower bound of energetics of presumable potential-limiting steps of NRR in respective adsorption mode.

5

Using these models, we calculated the full NRR pathways

starting from bridge-on adsorption and obtained the onset

potential of NRR that signifies the activity of the catalyst of

interest. We first examined the adsorption energies of bridge-

on adsorbed N2, associated charge redistribution, and geometric

changes of reactant-active center complexes. As shown in Table

S5, the computed binding energies are between -1.46 and -1.82

eV for bridge-on adsorption, accompanied by substantial charge

transfer (0.59 ~ 0.93 |e| by Bader charge analysis) from both two

MN4 sites to N2. The corresponding charge distribution is also

demonstrated by the differential charge densities of N2-MN4

duo binding complexes (Figure S9), which illustrates electron

gain in the antibonding orbital of N2. As a result, the adsorbed

N2 is activated, with an appreciable stretching of N-N bond

from 1.11 Å (free N2 in the gas phase) to 1.18 ~ 1.23 Å.

Figure 5. The reaction profile of the bridge-on adsorption initiated0020030NRR pathway on VN4 duo/G model. Roman

numbers denote all reaction species along the pathway.

Then we investigated the N≡N bond dissociation following

the bridge-on adsorption. The transition state structures are

showing in Figure S10. Remarkably, 3 out of 6 selected models,

including MoN4 duo, ReN4 duo, and MoN4-ReN4, enable direct

N≡N bond breaking with a reaction barrier below 0.91 eV

(Table S6), a well-documented threshold for chemical reactions

available at room temperature.53 This unusual phenomenon

suggests a dissociative NRR mechanism, in sharp contrast to

common N≡N bond dissociation aided by reductive

hydrogenation seen in associative NRR pathways. Intriguingly,

this pathway will avoid the formation of *N2H, one of two key

intermediate species in NRR, suggesting the possibility of

circumventing the well-established scaling relationship for

NRR by direct N≡N bond dissociation through the joint effort

of two adjacent active centers.

To understand it, we adopted the N-N distance as the reaction

coordinate to understand the trend of energy barriers of N-N

dissociation. Intriguingly, the barriers are positively correlated

with the distances (Figure S11-a), because a smaller difference

of N-N distance between the transition state (TS) and initial

state will result in a smaller barrier for N-N bond dissociation.

This is typical for an early TS, whose structure is close to the

corresponding initial state. Then we examined the relationship

between the stabilities of all six models and the corresponding

energy barrier of TS and found that the lower stability of the

catalyst results in a smaller energy barrier (Figure S11-b). Since

the ReN4 duo is the least stable one among these six models, it

has the lowest direct N2 dissociation barrier. Similarly, MoN4

duo and MoN4-ReN4 enables direct N2 dissociation at room

temperature for their relative lability. The direct N≡N breaking

aided by bridge-on adsorption may open a new possibility of

breaking scaling relationships applied on NRR, which will be

investigated in the future. In contrast, as the stabilities increase,

which are the cases of VN4 duo, VN4-MoN4, and VN4-ReN4,

the dissociative pathway is unfavorable at room temperature;

thus, NRR will proceed via associative mechanisms in which

N≡N breaking takes place after one or two steps of reductive

hydrogenation. Their bridge-on adsorption initiated NRR

pathways is similar to the one occurring on MoN3 duo

6

embedded in graphene.29 The balance between stability and

lability of these catalysts may be a key factor for determining

the preferred reaction pathways of NRR occurring on them.

The full reaction coordinates of NRR with all six of these

models are collected in Figure S12 through Figure S17. Based

on the Gibbs free energy data therein, we found that VN4 duo/G

possesses the lowest limiting potential (0.18 V) and thus bears

the highest theoretical activity. The reaction coordinates are

shown in Figure 5. For the strong adsorption, the ΔG*N2→*N2H

for bridge-on *N2 is 0.11eV and the N−N distance is stretched

to 1.31Å. The second reductive hydrogenation (*NNH →

*HNNH) is endothermic (ΔG*N2H→*HNNH = 0.16 eV), with the

N−N distance of 1.37 Å. Intriguingly, this bridge-on *HNNH

resembles the bridging “diazene” species found in

nitrogenase.54-55 Then *HNNH dissociates and produces two

*NH, each of which is attached to one V atom. The energy

barrier (0.78 eV) for this N≡N bond breaking can be easily

overcome at room temperature. Then the two *NH alternately

undergo reductive hydrogenation steps, producing two *NH2.

Both reductive hydrogenation of *NH2 and desorption of NH3

from *NH3 are thermodynamically uphill. The electrochemical

step can be promoted only by applying an external potential. At

U= −0.17 V, ΔG*NH2→*NH3 becomes zero, and the uphill

energetics is substantially mitigated (Figure 5). This remarkably

low limiting potential benefits from the cooperation of two

adjacent VN4 sites that help breaking the scaling relationship of

NRR by properly balancing the adsorption energies of *N2H

and *NH2. For the endergonic (∼0.7 eV) desorption of

ammonia, we expect that the solvation of ammonia can mitigate

the unfavorable energetics because it will stabilize the desorbed

ammonia.4, 39, 43, 56-57 Thus, NH3 desorption may not be a main

obstacle in NRR and, hence, is not considered in detail here.

CONCLUSION

In this work, we have conducted a systematic first-principle

study on impacts of bridge-on N2 adsorption by two adjacent

MN4 sites on scaling relationships within electrocatalytic NRR

and found the key to attenuate the scaling relations is to create

inhomogeneous adsorption between dinitrogen-containing

species and nitrogen-containing species.

We confirmed that the scaling relationship between

adsorption of N2H and NH2 hold for NRR occurring on single

active center, regardless of MN4 or MN4 duo. Since the room of

improvement of NRR activity associated with one active center

is limited, we have to go beyond conventional end-on and side-

on adsorption modes. Intriguingly, the side-on fashion benefits

from different metal-nitrogen bonding patterns for *N2H and

*NH2, hinting a path for the evolution of NRR catalysts.43-44, 58

The bridge-on adsorption mode can be viewed as a two-center

version of “side-on”. It further widens the gap of metal-nitrogen

bonding strengths between *N2H and *NH2, enabling us to

decouple the optimization of (*N2 + e- + H+ → *N2H) and

(*NH2 + e- + H+ → *NH3). Thus, it shows the potential of

making substantial progress towards breaking scaling relations

in NRR. Importantly, the bridge-on pattern relies on the

proximity of two metal active sites, which could well explain

other reported promising NRR catalytic systems invoking

bridge-on like activation of N2 by multiple active centers.59-61

Based on the survey, we then identified VN4 duo and ReN4

duo as promising NRR catalysts through associative

mechanisms and dissociative mechanisms, respectively. For

VN4 duo, the remarkably low onset potential (0.18 eV) indicates

the level of excellent activity of NRR that can be achieved by

high-density SACs. For ReN4 duo, the most appealing feature

is the low energy barrier (0.52 eV) of direct N≡N bond

dissociation enabling a dissociative mechanism for NRR at

room temperature, which for sure will inspire more mechanistic

study on dissociative pathways with multiple concerted active

centers. We also expect it motivates more exploration on how

the delicate balance between stability and lability of active

centers would affect the dynamics of N2 activation process.

In summary, through a comprehensive understanding of

scaling relationships for NRR in MN4-type single-atom

catalysts, we found cooperation of two adjacent single-atom

active centers can attenuate scaling relation effect and facilitate

nitrogen fixation. Although our computational models are based

on ideal reaction conditions, we expect our work casting new

light on NRR mechanisms with collective active centers will be

helpful for the rational design of high-density SACs and

prompting mechanistic study on breaking scaling relationships

existing in other reactions (e.g. CO2 reduction62 and oxygen

reduction reaction) aided by cooperative multiple active

centers. We will also continue the investigation of cooperative

single-atom active centers under more realistic reaction

conditions in the future work.

COMPUTATIONAL DETAILS

All spin-polarized density functional theory (DFT)

calculations were performed using the Perdew-Burke-

Ernzerhof (PBE)63 functional in conjunction with plane-wave

projected augmented wave (PAW)64 method as implemented in

Vienna ab initio simulation program (VASP)65-66. The kinetic

cutoff energy for the plane-wave basis set was set to be 480 eV.

The Gaussian smearing method was adopted with a width of 0.1

eV to describe partial occupancies of each orbital. The first

Brillouin zone was sampled by a Monkhorst–Pack scheme with

a 3 × 3 × 1 k-point grid. To avoid the interaction between two

periodic units, a vacuum space exceeds 15 Å was employed.

Structures were fully relaxed until the forces were converged to

less than 0.02 eV Å-1. The Grimme’s D3 dispersion correction

scheme was used to describe the van der Waals interaction. The

solvent effect on scaling relations are not taken into account as

a previous study showed that no significant change that can alter

the scaling relations has been found as solvent effect was

incorporated.67 More details regarding adopted computational

models, calculation of various energy values and selection of

energetic descriptors are given in the Supporting Information.

ASSOCIATED CONTENT

Supporting Information

7

Computational detail, geometrical structures and stability

validation of MN4 and MN4 duo models, the adsorption energies of

N2, differential charge densities, various scaling relationships and

Gibbs free energy diagrams for NRR occurring on selected MN4

duo models.

AUTHOR INFORMATION

Corresponding Author

*Guozhen Zhang, Email: guozhen@ustc.edu.cn

ORCID

Guozhen Zhang: 0000-0003-0125-9666

Jun Jiang: 0000-0002-6116-5605

Author Contributions

†K.Y. and M.H. contributed equally to this work.

Note

The authors declare no competing financial support.

ACKNOWLEDGMENTS

This work was financially supported by the Ministry of Science and

Technology of the People’s Republi0063 of China (No.

2018YFA0208702, 2018YFA0208603, and 2017YFA0303500)

and the National Natural Science Foundation of China (21703221,

21790351, and 21633006). The Supercomputing Center of

University of Science and Technology of China is acknowledged

for the computing resource.

REFERENCES

(1) Nørskov, J. K.; Studt, F.; Abild-Pedersen, F.; Bligaard, T.

Fundamental Concepts in Heterogeneous Catalysis; John Wiley & Sons,

Inc., 2014.

(2) Medford, A. J.; Vojvodic, A.; Hummelshøj, J. S.; Voss, J.; Abild-

Pedersen, F.; Studt, F.; Bligaard, T.; Nilsson, A.; Nørskov, J. K. From the

Sabatier Principle to a Predictive Theory of Transition-Metal

Heterogeneous Catalysis. J. Catal. 2015, 328, 36-42.

(3) Zhao, Z.-J.; Liu, S.; Zha, S.; Cheng, D.; Studt, F.; Henkelman, G.; Gong,

J. Theory-Guided Design of Catalytic Materials Using Scaling

Relationships and Reactivity Descriptors. Nat. Rev. Mater. 2019, 4, 792-804.

(4) Montoya, J. H.; Tsai, C.; Vojvodic, A.; Norskov, J. K. The Challenge

of Electrochemical Ammonia Synthesis: A New Perspective on the Role of

Nitrogen Scaling Relations. Chemsuschem 2015, 8, 2180-6.

(5) Wang, P.; Chang, F.; Gao, W.; Guo, J.; Wu, G.; He, T.; Chen, P.

Breaking Scaling Relations to Achieve Low-Temperature Ammonia

Synthesis through Lih-Mediated Nitrogen Transfer and Hydrogenation. Nat.

Chem. 2017, 9, 64-70.

(6) Mao, C.; Wang, J.; Zou, Y.; Qi, G.; Yang Loh, J. Y.; Zhang, T.; Xia, M.;

Xu, J.; Deng, F.; Ghoussoub, M.; Kherani, N. P.; Wang, L.; Shang, H.; Li,

M.; Li, J.; Liu, X.; Ai, Z.; Ozin, G. A.; Zhao, J.; Zhang, L. Hydrogen

Spillover to Oxygen Vacancy of TiO2-XHy/Fe: Breaking the Scaling

Relationship of Ammonia Synthesis. J. Am. Chem. Soc. 2020, 142, 17403-

17412.

(7) Qiao, B.; Wang, A.; Yang, X.; Allard, L. F.; Jiang, Z.; Cui, Y.; Liu, J.;

Li, J.; Zhang, T. Single-Atom Catalysis of Co Oxidation Using Pt1/FeOx.

Nat. Chem. 2011, 3, 634-41.

(8) Cui, X.; Li, W.; Ryabchuk, P.; Junge, K.; Beller, M. Bridging

Homogeneous and Heterogeneous Catalysis by Heterogeneous Single-

Metal-Site Catalysts. Nat. Catal. 2018, 1, 385-397.

(9) Wang, A.; Li, J.; Zhang, T. Heterogeneous Single-Atom Catalysis. Nat.

Rev. Chem. 2018, 2, 65-81.

(10) Mitchell, S.; Perez-Ramirez, J. Single Atom Catalysis: A Decade of

Stunning Progress and the Promise for a Bright Future. Nat. Commun. 2020,

11, 4302.

(11) Zhuo, H. Y.; Zhang, X.; Liang, J. X.; Yu, Q.; Xiao, H.; Li, J.

Theoretical Understandings of Graphene-Based Metal Single-Atom

Catalysts: Stability and Catalytic Performance. Chem. Rev. 2020, 120,

12315-12341.

(12) Wan, X.; Liu, X.; Li, Y.; Yu, R.; Zheng, L.; Yan, W.; Wang, H.; Xu,

M.; Shui, J. Fe–N–C Electrocatalyst with Dense Active Sites and Efficient

Mass Transport for High-Performance Proton Exchange Membrane Fuel

Cells. Nat. Catal. 2019, 2, 259-268.

(13) Yin, P.; Yao, T.; Wu, Y.; Zheng, L.; Lin, Y.; Liu, W.; Ju, H.; Zhu, J.;

Hong, X.; Deng, Z.; Zhou, G.; Wei, S.; Li, Y. Single Cobalt Atoms with

Precise N-Coordination as Superior Oxygen Reduction Reaction Catalysts.

Angew. Chem. Int. Ed. 2016, 55, 10800-5.

(14) Chen, Y.; Ji, S.; Wang, Y.; Dong, J.; Chen, W.; Li, Z.; Shen, R.; Zheng,

L.; Zhuang, Z.; Wang, D.; Li, Y. Isolated Single Iron Atoms Anchored on

N-Doped Porous Carbon as an Efficient Electrocatalyst for the Oxygen

Reduction Reaction. Angew. Chem. Int. Ed. 2017, 56, 6937-6941.

(15) Wu, J.; Zhou, H.; Li, Q.; Chen, M.; Wan, J.; Zhang, N.; Xiong, L.; Li,

S.; Xia, B. Y.; Feng, G. Densely Populated Isolated Single Co-N Site for

Efficient Oxygen Electrocatalysis. Adv. Energy Mater. 2019, 9, 1900149.

(16) Bauer, G.; Ongari, D.; Tiana, D.; Gaumann, P.; Rohrbach, T.; Pareras,

G.; Tarik, M.; Smit, B.; Ranocchiari, M. Metal-Organic Frameworks as

Kinetic Modulators for Branched Selectivity in Hydroformylation. Nat.

Commun. 2020, 11, 1059.

(17) Liu, K.; Zhao, X.; Ren, G.; Yang, T.; Ren, Y.; Lee, A. F.; Su, Y.; Pan,

X.; Zhang, J.; Chen, Z.; Yang, J.; Liu, X.; Zhou, T.; Xi, W.; Luo, J.; Zeng,

C.; Matsumoto, H.; Liu, W.; Jiang, Q.; Wilson, K.; Wang, A.; Qiao, B.; Li,

W.; Zhang, T. Strong Metal-Support Interaction Promoted Scalable

Production of Thermally Stable Single-Atom Catalysts. Nat. Commun.

2020, 11, 1263.

(18) Xiong, Y.; Sun, W.; Xin, P.; Chen, W.; Zheng, X.; Yan, W.; Zheng, L.;

8

Dong, J.; Zhang, J.; Wang, D.; Li, Y. Gram-Scale Synthesis of High-

Loading Single-Atomic-Site Fe Catalysts for Effective Epoxidation of

Styrene. Adv. Mater. 2020, e2000896.

(19) Wu, J.; Xiong, L.; Zhao, B.; Liu, M.; Huang, L. Densely Populated

Single Atom Catalysts. Small Methods 2019, 4, 1900540.

(20) He, Z.; He, K.; Robertson, A. W.; Kirkland, A. I.; Kim, D.; Ihm, J.;

Yoon, E.; Lee, G. D.; Warner, J. H. Atomic Structure and Dynamics of

Metal Dopant Pairs in Graphene. Nano Lett. 2014, 14, 3766-72.

(21) Lin, Y. C.; Teng, P. Y.; Yeh, C. H.; Koshino, M.; Chiu, P. W.; Suenaga,

K. Structural and Chemical Dynamics of Pyridinic-Nitrogen Defects in

Graphene. Nano Lett. 2015, 15, 7408-13.

(22) Li, H.; Wang, L.; Dai, Y.; Pu, Z.; Lao, Z.; Chen, Y.; Wang, M.; Zheng,

X.; Zhu, J.; Zhang, W.; Si, R.; Ma, C.; Zeng, J. Synergetic Interaction

between Neighbouring Platinum Monomers in CO2 Hydrogenation. Nat.

Nanotechnol. 2018, 13, 411-417.

(23) Zou, N.; Zhou, X.; Chen, G.; Andoy, N. M.; Jung, W.; Liu, G.; Chen,

P. Cooperative Communication within and between Single Nanocatalysts.

Nat. Chem. 2018, 10, 607-614.

(24) Jiao, J.; Lin, R.; Liu, S.; Cheong, W. C.; Zhang, C.; Chen, Z.; Pan, Y.;

Tang, J.; Wu, K.; Hung, S. F.; Chen, H. M.; Zheng, L.; Lu, Q.; Yang, X.; Xu,

B.; Xiao, H.; Li, J.; Wang, D.; Peng, Q.; Chen, C.; Li, Y. Copper Atom-Pair

Catalyst Anchored on Alloy Nanowires for Selective and Efficient

Electrochemical Reduction of CO2. Nat. Chem. 2019, 11, 222-228.

(25) Fu, J.; Dong, J.; Si, R.; Sun, K.; Zhang, J.; Li, M.; Yu, N.; Zhang, B.;

Humphrey, M. G.; Fu, Q.; Huang, J. Synergistic Effects for Enhanced

Catalysis in a Dual Single-Atom Catalyst. ACS Catal. 2021, 11, 1952-1961.

(26) Tang, Y.; Wei, Y.; Wang, Z.; Zhang, S.; Li, Y.; Nguyen, L.; Li, Y.;

Zhou, Y.; Shen, W.; Tao, F. F.; Hu, P. Synergy of Single-Atom Ni1 and Ru1

Sites on Ceo2 for Dry Reforming of Ch4. J. Am. Chem. Soc. 2019, 141,

7283-7293.

(27) Zhang, X.; Chen, A.; Chen, L.; Zhou, Z. 2d Materials Bridging

Experiments and Computations for Electro/Photocatalysis. Adv. Energy

Mater. 2021.

(28) Li, Q.-K.; Li, X.-F.; Zhang, G.; Jiang, J. Cooperative Spin Transition

of Monodispersed FeN3 Sites within Graphene Induced by CO Adsorption.

J. Am. Chem. Soc. 2018, 140, 15149-15152.

(29) Ye, K.; Hu, M.; Li, Q. K.; Han, Y.; Luo, Y.; Jiang, J.; Zhang, G.

Cooperative Nitrogen Activation and Ammonia Synthesis on Densely

Monodispersed Mo-N-C Sites. J. Phys. Chem. Lett. 2020, 11, 3962-3968.

(30) Han, Y.; Li, Q. K.; Ye, K.; Luo, Y.; Jiang, J.; Zhang, G. Impact of

Active Site Density on Oxygen Reduction Reactions Using Monodispersed

Fe-N-C Single-Atom Catalysts. ACS Appl. Mater. Interfaces 2020, 12,

15271-15278.

(31) Chen, J. G.; Crooks, R. M.; Seefeldt, L. C.; Bren, K. L.; Bullock, R.

M.; Darensbourg, M. Y.; Holland, P. L.; Hoffman, B.; Janik, M. J.; Jones,

A. K.; Kanatzidis, M. G.; King, P.; Lancaster, K. M.; Lymar, S. V.; Pfromm,

P.; Schneider, W. F.; Schrock, R. R. Beyond Fossil Fuel-Driven Nitrogen

Transformations. Science 2018, 360.

(32) Honkala, K.; Hellman, A.; Remediakis, I.; Logadottir, A.; Carlsson,

A.; Dahl, S.; Christensen, C. H.; Nørskov, J. K. Ammonia Synthesis from

First-Principles Calculations. Science 2005, 307, 555-558.

(33) Jeong, H.; Lee, G.; Kim, B. S.; Bae, J.; Han, J. W.; Lee, H. Fully

Dispersed Rh Ensemble Catalyst to Enhance Low-Temperature Activity. J.

Am. Chem. Soc. 2018, 140, 9558-9565.

(34) Qing, G.; Ghazfar, R.; Jackowski, S. T.; Habibzadeh, F.; Ashtiani, M.

M.; Chen, C. P.; Smith, M. R., 3rd; Hamann, T. W. Recent Advances and

Challenges of Electrocatalytic N2 Reduction to Ammonia. Chem. Rev. 2020,

120, 5437-5516.

(35) Wang, Y.; Yuan, H.; Li, Y.; Chen, Z. Two-Dimensional Iron-

Phthalocyanine (Fe-Pc) Monolayer as a Promising Single-Atom-Catalyst

for Oxygen Reduction Reaction: A Computational Study. Nanoscale 2015,

7, 11633-41.

(36) Melville, O. A.; Lessard, B. H.; Bender, T. P. Phthalocyanine-Based

Organic Thin-Film Transistors: A Review of Recent Advances. ACS Appl.

Mater. Interfaces 2015, 7, 13105-18.

(37) Maitarad, P.; Namuangruk, S.; Zhang, D.; Shi, L.; Li, H.; Huang, L.;

Boekfa, B.; Ehara, M. Metal-Porphyrin: A Potential Catalyst for Direct

Decomposition of N2O by Theoretical Reaction Mechanism Investigation.

Environ. Sci. Technol. 2014, 48, 7101-10.

(38) Li, X. F.; Li, Q. K.; Cheng, J.; Liu, L.; Yan, Q.; Wu, Y.; Zhang, X. H.;

Wang, Z. Y.; Qiu, Q.; Luo, Y. Conversion of Dinitrogen to Ammonia by

Fen3-Embedded Graphene. J. Am. Chem. Soc. 2016, 138, 8706-9.

(39) Zhao, J.; Chen, Z. Single Mo Atom Supported on Defective Boron

Nitride Monolayer as an Efficient Electrocatalyst for Nitrogen Fixation: A

Computational Study. J. Am. Chem. Soc. 2017, 139, 12480-12487.

(40) Han, L.; Liu, X.; Chen, J.; Lin, R.; Liu, H.; Lu, F.; Bak, S.; Liang, Z.;

Zhao, S.; Stavitski, E.; Luo, J.; Adzic, R. R.; Xin, H. L. Atomically

Dispersed Molybdenum Catalysts for Efficient Ambient Nitrogen Fixation.

Angew. Chem. Int. Ed. 2019, 58, 2321-2325.

(41) Tao, H.; Choi, C.; Ding, L.-X.; Jiang, Z.; Han, Z.; Jia, M.; Fan, Q.;

Gao, Y.; Wang, H.; Robertson, A. W.; Hong, S.; Jung, Y.; Liu, S.; Sun, Z.

Nitrogen Fixation by Ru Single-Atom Electrocatalytic Reduction. Chem

2019, 5, 204-214.

(42) Zhao, W.; Zhang, L.; Luo, Q.; Hu, Z.; Zhang, W.; Smith, S.; Yang, J.

Single Mo1(Cr1) Atom on Nitrogen-Doped Graphene Enables Highly

Selective Electroreduction of Nitrogen into Ammonia. ACS Catal. 2019, 9,

3419-3425.

(43) Choi, C.; Back, S.; Kim, N.-Y.; Lim, J.; Kim, Y.-H.; Jung, Y.

Suppression of Hydrogen Evolution Reaction in Electrochemical N2

Reduction Using Single-Atom Catalysts: A Computational Guideline. ACS

Catal. 2018, 8, 7517-7525.

(44) Guo, X.; Gu, J.; Lin, S.; Zhang, S.; Chen, Z.; Huang, S. Tackling the

Activity and Selectivity Challenges of Electrocatalysts toward the Nitrogen

Reduction Reaction Via Atomically Dispersed Biatom Catalysts. J. Am.

9

Chem. Soc. 2020, 142, 5709-5721.

(45) Wang, X.; Qiu, S.; Feng, J.; Tong, Y.; Zhou, F.; Li, Q.; Song, L.; Chen,

S.; Wu, K. H.; Su, P.; Ye, S.; Hou, F.; Dou, S. X.; Liu, H. K.; Max Lu, G.

Q.; Sun, C.; Liu, J.; Liang, J. Confined Fe-Cu Clusters as Sub-Nanometer

Reactors for Efficiently Regulating the Electrochemical Nitrogen

Reduction Reaction. Adv. Mater. 2020, 32, e2004382.

(46) He, T.; Puente Santiago, A. R.; Du, A. Atomically Embedded

Asymmetrical Dual-Metal Dimers on N-Doped Graphene for Ultra-

Efficient Nitrogen Reduction Reaction. J. Catal. 2020, 388, 77-83.

(47) Deng, T.; Cen, C.; Shen, H.; Wang, S.; Guo, J.; Cai, S.; Deng, M.

Atom-Pair Catalysts Supported by N-Doped Graphene for the Nitrogen

Reduction Reaction: D-Band Center-Based Descriptor. J. Phys. Chem. Lett.

2020, 11, 6320-6329.

(48) Lv, X.; Wei, W.; Huang, B.; Dai, Y.; Frauenheim, T. High-Throughput

Screening of Synergistic Transition Metal Dual-Atom Catalysts for

Efficient Nitrogen Fixation. Nano Lett. 2021, 21, 1871-1878.

(49) Deringer, V. L.; Tchougreeff, A. L.; Dronskowski, R. Crystal Orbital

Hamilton Population (COHP) Analysis as Projected from Plane-Wave

Basis Sets. J. Phys. Chem. A 2011, 115, 5461-6.

(50) Maintz, S.; Deringer, V. L.; Tchougreeff, A. L.; Dronskowski, R.

Analytic Projection from Plane-Wave and Paw Wavefunctions and

Application to Chemical-Bonding Analysis in Solids. J. Comput. Chem.

2013, 34, 2557-67.

(51) Maintz, S.; Deringer, V. L.; Tchougreeff, A. L.; Dronskowski, R.

Lobster: A Tool to Extract Chemical Bonding from Plane-Wave Based Dft.

J. Comput. Chem. 2016, 37, 1030-5.

(52) Nelson, R.; Ertural, C.; George, J.; Deringer, V. L.; Hautier, G.;

Dronskowski, R. Lobster: Local Orbital Projections, Atomic Charges, and

Chemical-Bonding Analysis from Projector-Augmented-Wave-Based

Density-Functional Theory. J. Comput. Chem. 2020, 41, 1931-1940.

(53) Young, D. C., A Practical Guide for Applying Techniques to Real

World Problems, John Wiley & Sons, Inc., New York, 1st edn, 2001.

(54) Saouma, C. T.; Kinney, R. A.; Hoffman, B. M.; Peters, J. C.,

Transformation of an [Fe(η2-N2H3)]+ Species to Pi-Delocalized [Fe2(μ-

N2H2)]2+/+ complexes. Angew. Chem. Int. Ed. 2011, 50, 3446-9.

(55) Hoffman, B. M.; Lukoyanov, D.; Yang, Z. Y.; Dean, D. R.; Seefeldt,

L. C. Mechanism of Nitrogen Fixation by Nitrogenase: The Next Stage.

Chem. Rev. 2014, 114, 4041-62.

(56) Peterson, A. A.; Abild-Pedersen, F.; Studt, F.; Rossmeisl, J.; Nørskov,

J. K. How Copper Catalyzes the Electroreduction of Carbon Dioxide into

Hydrocarbon Fuels. Energy Environ. Sci. 2010, 3, 1311-1315.

(57) Skulason, E.; Bligaard, T.; Gudmundsdóttir, S.; Studt, F.; Rossmeisl,

J.; Abild-Pedersen, F.; Vegge, T.; Jonsson, H.; Nørskov, J. K. A Theoretical

Evaluation of Possible Transition Metal Electro-Catalysts for N2 Reduction.

Phys. Chem. Chem. Phys. 2012, 14, 1235-1245.

(58) Ling, C.; Ouyang, Y.; Li, Q.; Bai, X.; Mao, X.; Du, A.; Wang, J. A

General Two‐Step Strategy–Based High‐Throughput Screening of Single

Atom Catalysts for Nitrogen Fixation. Small Methods 2018, 3, 1800376.

(59) Wang, S.; Shi, L.; Bai, X.; Li, Q.; Ling, C.; Wang, J. Highly Efficient

Photo-/Electrocatalytic Reduction of Nitrogen into Ammonia by Dual-

Metal Sites. ACS Cent. Sci. 2020, 6, 1762-1771.

(60) Qiu, W.; Xie, X. Y.; Qiu, J.; Fang, W. H.; Liang, R.; Ren, X.; Ji, X.;

Cui, G.; Asiri, A. M.; Cui, G.; Tang, B.; Sun, X. High-Performance

Artificial Nitrogen Fixation at Ambient Conditions Using a Metal-Free

Electrocatalyst. Nat. Commun. 2018, 9, 3485.

(61) Ma, X. L.; Liu, J. C.; Xiao, H.; Li, J. Surface Single-Cluster Catalyst

for N2-to-NH3 Thermal Conversion. J. Am. Chem. Soc. 2018, 140, 46-49.

(62) Ouyang, Y.; Shi, L.; Bai, X.; Li, Q.; Wang, J. Breaking Scaling

Relations for Efficient CO2 Electrochemical Reduction through Dual-Atom

Catalysts. Chem. Sci. 2020, 11, 1807-1813.

(63) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient

Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865.

(64) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994,

50, 17953.

(65) Furthmüller, G. K. J., Efficient Iterative Schemes for Ab Initio Total-

Energy Calculations Using a Plane-Wave Basis Set. Phy. Rev. B 1996, 54,

11169-11186.

(66) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the

Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758-1775.

(67) Park, J.; Roling, L. T. Elucidating Energy Scaling between Atomic

and Molecular Adsorbates in the Presence of Solvent. AIChE Journal 2020,

66:e17036.

TOC graphics

10

download fileview on ChemRxivNRR_manuscript_new.pdf (1.28 MiB)

Supporting Information

Cooperative single-atom active centers for attenuating linear

scaling effect in nitrogen reduction reaction

Ke Ye[a]†, Min Hu[a]†, Qin-Kun Li[b], Yi Luo[a], Jun Jiang[a], Guozhen Zhang[a]*

a. Hefei National Laboratory for Physical Sciences at the Microscale, Chinese Academy of Sciences Center for Excellence in

Nanoscience, School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui 230026,

China

b.Department of Materials Science and NanoEngineering, Rice University, Houston, Texas, 77005, United States

Email: guozhen@ustc.edu.cn

S1

CONTENT

1. Computation detail.........................................................................................4

2. The descriptors used for NRR.........................................................................4

Figure S1. Three main pathways for associative mechanisms of NRR.........4

3. The definition and stability test of MN4/G and MN4 duo/G models.................5

Figure S2. Representation of various dual-atom M-N-C models...................5

Figure S3. Representation of (a) MN4/G and (b) MN4 duo/G models and (c)

the scope of metals investigated in this work.............................................6

Table S1. Atomic radius(R) of 39 metal elements, computed formation

energy(Ef), computed dissolution potential(Udiss), and the distance from

metal atom to graphene layer(d) of metal atoms in all 39 different MN4/G

models and MN4 duo/G models....................................................................8

Figure S4. Computed formation energy(Ef) and dissolution potential(Udiss)

of metal atoms in all 39 different (a) MN4/G models and (b) MN4 duo/G

models, respectively....................................................................................9

Table S2. The adsorption energies of dinitrogen in various patterns on 39

different MN4/G and MN4 duo/G models. The × symbol represents

physisorption.............................................................................................10

4. The linear scaling relationships in NRR........................................................11

Figure S5. The scaling relationships between ∆G1 and ∆G*N2H for end-on

(a) and side-on (b) adsorption modes, and between ∆G6 and ∆G*NH2 for

both two modes (c)....................................................................................11

Figure S6. Two subgroups of transition metals based on scaling relations

between ∆G*N2H and ∆G*NH2. Group 1 include elments (in blue) in groups

IB-IVB; group 2 include elements (in red) in groups VB-VIIIB.....................11

Figure S7. The scaling relationships between ∆G*N2H and ∆G*NH2 for (a)

end-on adsorption mode on MN4/G; (b) side-on adsorption mode on MN4/G;

(c) end-on adsorption mode on MN4 duo/G; (d) side-on adsorption mode

on MN4 duo/G; (e) bridge-on adsorption mode on MN4 duo/G. Blue and red

dots represent metal atoms from subgroup 1 and subgroup 2,

respectively................................................................................................12

Table S3. The entropy factor (TS) of *N2 and *N2H on MN4 duo/G via bridge-

on mode.....................................................................................................12

Figure S8. The relationship between ∆G1 and ∆G6 for bridge-on adsorption

initiated NRR occurring on MN4 duo/G.......................................................13

5. The catalytic activity related to the bridge-on adsorption model................13

Table S4. The adsorption energies of dinitrogen adsorbed on six selected

MN4 duo/G via end-on, side-on, and bridge-on manners...........................13

Table S5. The computed binding energies(ΔE*N2) of bridge-on manner on

six selected MN4 duo/G, the bond length of adsorbed dinitrogen, and the

amount of Bader charge transferred from MN4 duo/G to adsorbed

S2

dinitrogen...................................................................................................14

Figure S9. Differential charge densities of chemisorbed N2 on the selected

MN4 duo/G models. The charge depletion and accumulation were depicted

in blue and yellow, respectively. The iso-surface value is 0.005 e/Å3........14

Figure S10. The transition state (TS) for the N-N bond dissociation of

bridge-on *N2. The N-N distance and imaginary frequency in each of TS

are given in Å and cm-1, respectively.........................................................15

Table S6. The energy barriers and N-N distances of transition states for N-

N bond breaking for bridge-on adsorbed N2 on selected MN4 duo/G models.

...................................................................................................................15

Figure S11. Calculated energy barriers for direct N-N bond breaking as a

function of the formation energy of MN4 duo and a function of the N-N

distance in transition states, respectively..................................................16

Figure S12. Gibbs free energy diagram for NRR on VN4 duo/G models.....16

Figure S13. Gibbs free energy diagram for NRR on MoN4 duo/G models.. .16

Figure S14. Gibbs free energy diagram for NRR on ReN4 duo/G models....17

Figure S15. Gibbs free energy diagram for NRR on MoN4-ReN4 duo/G

models.......................................................................................................17

Figure S16. Gibbs free energy diagram for NRR on MoN4-VN4 duo/G

models.......................................................................................................18

Figure S17. Gibbs free energy diagram for NRR on ReN4-VN4 duo/G models.

...................................................................................................................18

6. Reference.....................................................................................................19

S3

1. Computation detail

The Gibbs free energy change (ΔG) of every elemental step was calculated by using the

computational hydrogen electrode (CHE) model proposed by Nørskov and co-workers1-3, which uses

one-half of the chemical potential of hydrogen as the chemical potential of the proton-electron pair.

According to this method, ΔG can be determined as follows:

ΔG = ΔE + ΔZPE - TΔS + ΔGU + ΔGpH

where ΔE is the electronic energy difference directly obtained from DFT calculations, ΔZPE is the

change in zero-point energies, T is the temperature (T = 300 K), and ΔS is the entropy change. ΔG U is

the free energy contribution related to the applied electrode potential U, ΔG pH is the pH-dependent

correction of free energy of solvated protons. ΔGpH is computed as 2.303 × kBT × pH (or equivalently,

0.059 × pH), in which kB is the Boltzmann constant and the value of pH is set to be zero. The ZPE of

adsorbed species was extracted from the harmonic vibrational frequency calculations. For simplicity,

only the adsorbate vibrational modes were calculated explicitly, while the catalyst sheet was fixed

based on the assumption that vibrations of the sheets are negligible, as adopted in previous theoretical

studies.4 The entropies of adsorbed species were neglected. The entropies and vibrational frequencies

of molecules in the gas phase were taken from the NIST database.5 The onset potential (UOnset) is

determined by the potential-limiting step which has the most positive ∆G (∆Gmax) as computed by UOnset

= − ∆Gmax/e. The solvent effect on scaling relations are not taken into account as a previous study

showed that no significant change that can alter the scaling relations has been found as the solvent

effect was incorporated.6

2. The descriptors used for NRR

Figure S1. Three main pathways for associative mechanisms of NRR.

The associative mechanisms of NRR has three different types of forms —— distal, alternating,

and enzymatic, all of which consist of six consecutive reductive hydrogenation steps (Figure S1). These

S4

three pathways have an NH3 moiety formed before the complete breaking of the N-N bond. The

complexity of these series of reactions makes it tedious to identify the effectiveness of a potential NRR

catalyst based on the exploration of full reaction pathways. To accelerate the evaluation of catalysts’

activities, we employed the energetic descriptors proposed by Ling et al.7 They chose the Gibbs free

energy changes (∆G) of the first and last reduction steps in NRR as descriptors, i.e. ∆G*N2→*N2H for

*N2 + H+ + e- → *N2H, and ∆G*NH2→*NH3 for *NH2 + H+ + e- → *NH3, for these two uphill steps are

the most likely potential-limiting steps of associative mechanisms of NRR.

3. The definition and stability test of MN4/G and MN4 duo/G models

Figure S2. Representation of various dual-atom M-N-C models.

S5

Figure S3. Representation of (a) MN4/G and (b) MN4 duo/G models and (c) the scope of metals

investigated in this work.

Single MN4/G consists of one metal atom coordinated with four pyridinic nitrogen atoms in the

graphene matrix. MN4 duo/G consists of two adjacent metal atoms coordinated respectively with four

pyridinic nitrogen atoms in the graphene matrix. We first built the single MN4/G model by anchoring

one metal atom onto a nitrogen-doped double vacancy (DV) of graphene (Figure S3a), which has been

a well-established molecular scaffold to stabilize single active site under electrochemical conditions.8-10

Then we built MN4 duo/G by placing two MN4 moieties adjacent to each other, in which two metal

atoms are separated by ~ 4 Å (Figure S3b). We examined a total of 39 metal elements, as collected in

Figure S2c, to get a comprehensive overview of the scale relationships in NRR.

The stabilities of all 39 different MN4/G models and 39 MN4 duo/G models have been evaluated

from two dimensions: formation energy (Ef) for thermodynamic stability and dissolution potential

(Udiss) for electrochemical stability, which are defined as:

Ef = EMN4/G – EN4/G –E(metal, bulk) (1)

Udiss = U diss。 (metal, bulk) – Ef/ne (2)

Where E(M, bulk) is the average energy of one metal atom in its most stable bulk structure, EMN4/G and

EN4/G are the total energies of MN4/G and MN4 duo/G models and graphene substrate, U diss。 (metal,

bulk) and n are the standard dissolution potential of bulk metal and the number of electrons involved in

the dissolution, respectively. Based on the above definition, systems with Ef < 0 eV are considered to

be thermodynamically stable, while materials with Udiss > 0 V vs SHE are regarded as

electrochemically stable. The exact values of Ef and Udiss are listed in Table S1. We note that most of

the experimentally synthesized SACs11 are thermodynamically and electrochemically stable according

S6

to the above evaluation criteria. As Figure S4a shows, these models are unevenly distributed into four

different zones: 18 out of 39 metals are stable from both thermodynamic and electrochemical points of

view, 12 are thermodynamically stable yet electrochemically unstable, 4 are electrochemically stable

yet thermodynamically unstable, and 5 are unstable in either dimension. Likewise, their corresponding

MN4 duo models are also divided into four different categories (Figure S4b).

The geometries of various MN4/G models also drew our attention. As Table S1 shows, FeN4,

CoN4, and NiN4 bear almost co-planar configurations, all other MN4/G contain a metal center sitting

above the N4/G plane ranging from 0.05 Å (MnN4 and AlN4) to 2.77 Å (HgN4). And for most of the

metals, the deviation from the plane of nitrogen-doped graphene is no less in MN4 duo@G than

MN4/G. Since the DV of N-doped graphene has a fixed cavity, the out-of-plane distance for the metal

center may be determined by its radii and the metal-nitrogen bonding strength (Table S1).

S7

MetalR /Å

MN4/G MN4 duo/G

Ef /eV Udiss /V d /Å (Ef) /eV (Udiss) /Vd /Å

Sc 1.70 -3.98 -0.75 1.23 -3.63 -0.87 1.48

Ti 1.60 -2.59 -0.33 0.91 -2.53 -0.37 0.34

V 1.53 -1.91 -0.22 0.97 -1.65 -0.36 1.14

Cr 1.39 -2.36 0.27 0.45 -2.04 0.11 0.79

Mn 1.39 -2.71 0.17 0.05 -2.18 -0.10 0.40

Fe 1.32 -2.18 0.64 0.03 -1.65 0.37 0.26

Co 1.26 -2.26 0.85 0.01 -1.78 0.61 0.05

Ni 1.24 -2.58 1.03 0.03 -1.71 0.59 0.02

Cu 1.32 -1.27 0.98 0.25 -0.90 0.79 0.24

Zn 1.22 -2.08 0.28 0.51 -1.63 0.06 0.92

Y 1.90 -3.76 -1.12 1.57 -3.39 -1.24 1.90

Zr 1.75 -2.11 -0.92 1.23 -2.22 -0.90 0.73

Nb 1.64 -0.48 -0.94 1.31 -0.47 -0.94 1.64

Mo 1.54 0.43 -0.34 1.22 0.28 -0.29 1.49

Tc 1.47 0.40 0.20 0.87 0.31 0.24 1.24

Ru 1.46 0.09 0.41 0.83 -0.05 0.49 1.07

Rh 1.42 -1.00 1.10 0.41 -1.13 1.16 0.77

Pd 1.39 -1.49 1.70 0.34 -0.94 1.42 0.68

Ag 1.44 0.89 -0.09 0.64 0.44 0.36 2.13

Cd 1.44 -0.51 -0.14 1.65 -0.43 -0.18 1.99

La 2.07 -3.96 -1.06 1.75 -3.51 -1.21 2.03

Hf 1.75 -2.34 -0.96 1.27 -2.28 -0.98 0.60

Ta 1.70 -0.24 -0.52 1.01 -0.16 -0.55 1.63

W 1.62 1.20 -0.30 1.23 1.09 -0.26 1.45

Re 1.51 1.32 -0.14 0.91 1.26 -0.12 1.30

Os 1.44 0.91 -0.95 0.78 0.69 -0.93 0.94

Ir 1.41 -0.51 1.33 0.43 -0.62 1.37 0.73

Pt 1.36 -1.63 1.99 0.34 -1.08 1.72 0.68

Au 1.36 0.62 1.29 0.42 1.07 1.14 0.77

Hg 1.32 0.21 0.74 2.77 0.05 0.82 2.63

Al 1.21 -4.11 -0.29 0.05 -3.50 -0.49 0.30

Ga 1.22 -2.10 0.15 0.27 -1.58 -0.02 0.38

Ge 1.22 -1.70 1.09 1.35 -1.15 0.81 1.55

In 1.42 -1.30 1.16 1.84 -1.38 1.24 2.21

Sn 1.39 -1.82 0.77 1.70 -1.42 0.57 1.94

Sb 1.39 -0.71 -0.01 1.49 -0.12 -0.21 1.84

Tl 1.45 -1.12 0.78 2.21 -1.33 0.99 2.58

Pb 1.46 -1.46 0.60 1.89 -1.14 0.44 2.25

Bi 1.48 -0.22 0.72 1.71 0.24 0.26 2.20

Table S1. Atomic radius(R) of 39 metal elements, computed formation energy(Ef), computed

dissolution potential(Udiss), and the distance from metal atom to graphene layer(d) of metal atoms in all

39 different MN4/G models and MN4 duo/G models.

S8

Figure S4. Computed formation energy(Ef) and dissolution potential(Udiss) of metal atoms in all 39

different (a) MN4/G models and (b) MN4 duo/G models, respectively.

S9

MetalMN4 MN4 duo

End-on Side-on End-on Side-on Bridge-on

Sc -0.78 -0.70 -0.86 × -1.52

Ti -1.10 -1.15 -0.81 × -1.91

V -1.14 -0.78 -1.15 -0.75 -1.46

Cr -0.44 × -0.50 × ×

Mn -0.16 × -0.36 × ×

Fe -0.59 × -0.67 × ×

Co -0.22 × -0.26 × ×

Ni × × × × ×

Cu × × × × ×

Zn -0.12 × × × ×

Y -0.62 -0.54 -0.72 × -1.30

Zr -1.01 -1.13 -0.94 × -1.73

Nb -1.14 -1.26 × × -2.55

Mo -1.21 -1.29 -1.17 -0.86 -1.76

Tc -1.07 -0.66 -1.21 -0.56 -1.12

Ru -1.22 × -0.91 -0.08 ×

Rh × × × × ×

Pd × × × × ×

Ag × × -0.35 × -0.46

Cd -0.14 × -0.18 × -0.40

La -0.30 -0.19 × × -0.95

Hf -1.07 -1.19 -0.78 × -2.03

Ta -1.26 -1.52 -1.33 × -2.81

W -1.46 -1.63 -1.41 -1.31 -2.27

Re -1.38 -1.13 -1.43 -0.93 -1.61

Os -1.28 × -0.97 -0.03 -0.46

Ir × × × × ×

Pt × × × × ×

Au × × × × ×

Hg × × × × ×

Al × × × × ×

Ga × × × × ×

Ge × × × × ×

In × × × × ×

Sn × × × × ×

Sb × × × × ×

Tl × × × × ×

Pb × × × × ×

Bi × × × × ×

Table S2. The adsorption energies of dinitrogen in various patterns on 39 different MN 4/G and MN4

duo/G models. The × symbol represents physisorption

S10

4. The linear scaling relationships in NRR

Figure S5. The scaling relationships between ∆G1 and ∆G*N2H for end-on (a) and side-on (b)

adsorption modes, and between ∆G6 and ∆G*NH2 for both two modes (c).

Figure S6. Two subgroups of transition metals based on scaling relations between ∆G*N2H and ∆G*NH2.

Group 1 include elments (in blue) in groups IB-IVB; group 2 include elements (in red) in groups VB-

VIIIB.

S11

Figure S7. The scaling relationships between ∆G*N2H and ∆G*NH2 for (a) end-on adsorption mode on

MN4/G; (b) side-on adsorption mode on MN4/G; (c) end-on adsorption mode on MN4 duo/G; (d) side-

on adsorption mode on MN4 duo/G; (e) bridge-on adsorption mode on MN4 duo/G. Blue and red dots

represent metal atoms from subgroup 1 and subgroup 2, respectively.

MN4 duo/GTS(eV)

*N2 *N2H

V 0.07 0.08Nb 0.09 0.09

Mo 0.07 0.08

Tc 0.08 0.08

Ta 0.07 0.10

W 0.07 0.09

Re 0.06 0.08

Os 0.08 0.08

Table S3. The entropy factor (TS) of *N2 and *N2H on MN4 duo/G via bridge-on mode.

S12

Figure S8. The relationship between ∆G1 and ∆G6 for bridge-on adsorption initiated NRR occurring on

MN4 duo/G.

5. The catalytic activity related to the bridge-on adsorption model

MN4 duo@G End-on Side-on Bridge-on

V -1.15 -0.75 -1.46

Mo -1.17 -0.86 -1.76

Re -1.43 -0.93 -1.61

Os -0.97 -0.03 -0.46

Tc -1.21 -0.56 -1.12

Table S4. The adsorption energies of dinitrogen adsorbed on six selected MN4 duo/G via end-on, side-

on, and bridge-on manners.

Metal ΔE(*NN) Bond length (*N2)/Å transferred charge* (*N2)/|e-|

Mo-Mo -1.76 1.20 0.80

Re-Re -1.61 1.19 0.59

V-V -1.46 1.23 0.93

Mo-Re -1.64 1.21 0.73

Mo-V -1.82 1.21 0.82

Re-V -1.64 1.18 0.64

S13

Table S5. The computed binding energies(ΔE*N2) of bridge-on manner on six selected MN4 duo/G, the

bond length of adsorbed dinitrogen, and the amount of Bader charge transferred from MN 4 duo/G to

adsorbed dinitrogen.

Figure S9. Differential charge densities of chemisorbed N2 on the selected MN4 duo/G models. The

charge depletion and accumulation were depicted in blue and yellow, respectively. The iso-surface

value is 0.005 e/Å3.

S14

Figure S10. The transition state (TS) for the N-N bond dissociation of bridge-on *N2. The N-N distance

and imaginary frequency in each of TS are given in Å and cm-1, respectively.

VN4 duo MoN4 duo ReN4 duo VN4-MoN4 VN4-ReN4 MoN4-ReN4

Ea/eV 1.91 0.85 0.52 1.51 1.23 0.65

Ef -1.65 0.28 1.26 -0.70 -0.22 0.75

D(N-N)/Å 2.04 1.75 1.61 1.93 1.84 1.69

Table S6. The energy barriers and N-N distances of transition states for N-N bond breaking for bridge-

on adsorbed N2 on selected MN4 duo/G models.

S15

Figure S11. Calculated energy barriers for direct N-N bond breaking as a function of the formation

energy of MN4 duo and a function of the N-N distance in transition states, respectively.

Figure S12. Gibbs free energy diagram for NRR on VN4 duo/G models.

Figure S13. Gibbs free energy diagram for NRR on MoN4 duo/G models.

S16

Figure S14. Gibbs free energy diagram for NRR on ReN4 duo/G models.

Figure S15. Gibbs free energy diagram for NRR on MoN4-ReN4 duo/G models.

S17

Figure S16. Gibbs free energy diagram for NRR on MoN4-VN4 duo/G models.

Figure S17. Gibbs free energy diagram for NRR on ReN4-VN4 duo/G models.

S18

6. Reference

(1) Nørskov, J. K.; Rossmeisl, J.; Logadottir, A.; Lindqvist, L.; Kitchin, J. R.; Bligaard, T.; Jonsson, H.

Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode. J. Phys. Chem. B 2004, 108,

17886-17892.

(2) Rossmeisl, J.; Logadottir, A.; Nørskov, J. K. Electrolysis of Water on (Oxidized) Metal Surfaces.

Chem. Phys. 2005, 319, 178-184.

(3) Peterson, A. A.; Abild-Pedersen, F.; Studt, F.; Rossmeisl, J.; Nørskov, J. K. How Copper Catalyzes

the Electroreduction of Carbon Dioxide into Hydrocarbon Fuels. Energy Environ. Sci. 2010, 3, 1311-

1315.

(4) Zhao, J.; Chen, Z. Single Mo Atom Supported on Defective Boron Nitride Monolayer as an

Efficient Electrocatalyst for Nitrogen Fixation: A Computational Study. J. Am. Chem. Soc. 2017, 139,

12480-12487.

(5) Computational Chemistry Comparison and Benchmark Database. http://cccbdb.nist.gov/.

(6) Park, J.; Roling, L. T. Elucidating Energy Scaling between Atomic and Molecular Adsorbates in the

Presence of Solvent. AIChE Journal 2020, 66: e17036.

(7) Ling, C.; Ouyang, Y.; Li, Q.; Bai, X.; Mao, X.; Du, A.; Wang, J. A General Two‐Step Strategy–

Based High‐Throughput Screening of Single Atom Catalysts for Nitrogen Fixation. Small Methods

2018, 3, 1800376.

(8) Liu, X.; Jiao, Y.; Zheng, Y.; Jaroniec, M.; Qiao, S. Z. Building up a Picture of the Electrocatalytic

Nitrogen Reduction Activity of Transition Metal Single-Atom Catalysts. J. Am. Chem. Soc. 2019, 141,

9664-9672.

(9) Guo, X.; Gu, J.; Lin, S.; Zhang, S.; Chen, Z.; Huang, S. Tackling the Activity and Selectivity

Challenges of Electrocatalysts toward the Nitrogen Reduction Reaction Via Atomically Dispersed

Biatom Catalysts. J. Am. Chem. Soc. 2020, 142, 5709-5721.

(10) Wang, Y.; Tang, Y. J.; Zhou, K. Self-Adjusting Activity Induced by Intrinsic Reaction

Intermediate in Fe-N-C Single-Atom Catalysts. J. Am. Chem. Soc. 2019, 141, 14115-14119.

(11) Xiong, Y.; Sun, W.; Xin, P.; Chen, W.; Zheng, X.; Yan, W.; Zheng, L.; Dong, J.; Zhang, J.; Wang,

D.; Li, Y. Gram-Scale Synthesis of High-Loading Single-Atomic-Site Fe Catalysts for Effective

Epoxidation of Styrene. Adv. Mater. 2020, e2000896.

S19

download fileview on ChemRxivNRR SI_new_v2.docx (1.97 MiB)