Supporting Information

A systematic investigation the catalytic performances of monolayer carbon nitride nanosheet C1-xNx

Yuwen Cheng,a,b Yan Song,a,* Yumin Zhangb,*

aSchool of Materials Science and Engineering, Harbin Institute of Technology at Weihai, 2 West

Wenhua Road, Weihai, 264209, PR China

bNational Key Laboratory of Science and Technology for National Defence on Advanced

Composites in Special Environments, Harbin Institute of Technology, Harbin, 150001, PR China

*Corresponding Author

E-mail: sy@hitwh.edu.cn; zhym@hit.edu.cn

Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2020

1. Computational details

1.1 Calculation methods of evaluating HER and OER activity

The mechanisms of HER and OER on C1-xNx surface are shown in Figure S1. The HER and OER

activity of C1-xNx can be evaluated by calculating the reaction Gibbs free energy of each step

based on following thermodynamic approximations.1-3 Hydrogen electrode is assumed to be in

equilibrium

(S1)H + (aq) + e - ⇌

12H2(g)

Thus,

(S2)μ 0

H + + μ 0

e - =12μ 0

H2(g)

The experimental standard Gibbs free energy for following reaction is 2.46 eV:

(S3)H2O⇌

12O2(g) + H2(g)

By defining, G=H-TS, where G is Gibbs free energy, which can also be represented by chemical

potential μ. H is the enthalpy of a system, which equals to EDFT corrected by the zero-point energy

(ZPE). S is the entropy of the system. The ZPE and entropy at 298 K (T) were retrieved from Ref.

6. As a results

G=EDFT ZPE TS (S4)+ ‒

At the standard condition (T=298.15K, P=0.035bar), the approximation chemical potential of H2

molecule and H2O molecule can be defined as:

(S5)

12μ 0

H2(g) =12(E

H2DFT + ZPEH2(g) ‒ TS 0

H2(g))

1.1.1 Reaction Gibbs free energy of hydrogen adsorption

The HER catalytic activity of materials can be evaluated by the change of the reaction Gibbs free

energy of hydrogen adsorption (∆GH*) under the standard conditions (Figure S1a), ∆GH* can be

evaluated via eq (S6),

(S6)∆GH * = ∆EH + ∆EZPE ‒ T∆SH

where ∆EH, ∆EZPE and ∆SH are the difference of hydrogen adsorption energy, zero-point energy

and the entropy between adsorbed hydrogen and hydrogen in gas phase, respectively. The ∆SH can

be approximated as eq (S7)

(S7)∆SH≅ -

12S 0

H2

due to the fact that the vibrational entropy in the adsorbed state is small according to previous

study,4 and is the entropy of H2 gas under the standard condition.5 Here, the values of EZPE and S 0

H2

S are referred from Ref 5. Therefore, eq (S6) can be written as eq (8)

(S8)∆GH * = μH * ‒ μ

H + ‒ μe - ‒ μ * ‒

12μH2

‒ μ *

=(EH * + EZPE(H * ) ‒ TS * H) ‒

12(EH2

+ EZPE(H2) ‒ TSH2) ‒ (E * + EZPE( * ) ‒ TS * )

=∆E(H ∗ ) + ∆EZPE(H * ) ‒ T∆SH *

1.1.2 Calculation of standard free energy diagram for oxygen evolution reaction

According to previous literatures,1,2,7 the OER consists of four intermediate steps under the

standard conditions at electrode potential U, each step on the active sites releases of a proton and

an electron (Figure S1b):

∆G1 (S9)H2O(l) + * →HO * + (H + + e - )

∆G2 (S10)HO * →O * + (H + + e - )

∆G3 (S11)O * + H2O(l)→HOO * + (H + + e - )

∆G4 (S12)HOO * → * + O2(g) + (H + + e - )

where O*, OH*, and OOH* are the adsorbed intermediates, the symbol * represents active sites on

the catalyst surface, (l) and (g) refer to liquid and gas phases, respectively. ∆G1, ∆G2, ∆G3, and

∆G4 are the reaction Gibbs free energy of (S9)-(S12), respectivelt. The overpotential of OER

processes can be determined by calculating the reaction free energies of the four elementary steps.

The thermo-chemistry of these electrochemical reactions was obtained by using DFT calculations

combined with SHE model developed by Nørskov and co-work.1 The thermodynamic approach

establishes a minimum set of requirements for the reactions based on the binding interactions of

the intermediates and the assumption that there are no extra barriers from adsorption or

dissociation of O2 or proton/electron transfer reactions. Considering the ZPE and entropy

corrections, the free energies of adsorption, ∆Gads, can obtained by following equation:

(S13)ΔGads = ΔE + ΔZPE ‒ TΔS

For each step, the ∆G is defined as the difference between free energies of the initial and final

states, and is given by the expression:

(S14)ΔG = ΔE + ΔZPE ‒ TΔS ‒ eU ‒ kBTln𝐻 +

Where ∆E is the change of the energy after adsorbed intermediate species, U is the potential at the

electrode. The reactions Gibbs free energy of (S9)-(S12) can be calculated using eq (S14). The

values of ∆EZPE and T∆S of intermediates adsorbates (O*, HO*, HOO*) are referred from Ref. 2.

The theoretical onset overpotential η, which is determined by the potential limiting steps (PLS),

can be obtained from the following equation.7

(S15)η = max (ΔG1, ΔG2, ΔG3, ΔG4)/e ‒ 1.23[V]

The value of is independent of pH. η

1.1.3 Volcano curve

For HER, to get exchange current, we adopted Nørskov’s assumption.4 When the proton

transfer is exothermic ( ), the expression for the exchange current at pH=0 is:∆G

H * < 0

(S16)i0 =- ek0

11 + exp( - ∆G

H * /kBT)

For another case, if the proton transfer is endothermic ( ), under the same condition as ∆G

H * > 0

above, the exchange current is

(S17)i0 =- ek0

11 + exp(∆G

H * /kBT)

where the k0 is the rate constant and kB is the Boltzmann constant, and k0 is the rate constant,

which is set as 1 owing to the lack of available experimental data.8 The overpotential for HER is

defined as the negative of absolute value of the . The theoretical calculation overptotential is ∆G

H *

defined as ηHER=-|∆GH*|/e×103 in unit of mV. The optimum ∆GH* for HER is 0 eV, and the

corresponding overpotantial is 0 mV.9

1.2 Calculation methods of evaluating nitrogen reduction into ammonia

1.2.1. Reaction mechanisms of nitrogen reduction into ammonia

The mechanism of NRR on C2N (x=1/3) surface is shown in Figure S2. Four possible reduction

reactions mechanisms (enzymatic, consecutive, alternating, and distal) of N2 are taken into

account.

1.2.2. Reaction Gibbs free energy (ΔG) of each elemental step of NRR

The calculations of the reaction Gibbs free energy (ΔG) of each elemental step was based on the

computational hydrogen electrode model proposed by Nørskov and coauthors.10,11 which can be

calculated by:

(S18)∆G = ∆EDFT + ∆EZPE ‒ TΔS + eU + ∆GpH

where is the adsorption energy of a specific step. and are the difference of zero ∆EDFT ∆EZPE ΔS

point energy and the difference of entropy between the adsorbed state and the free-standing state,

respectively, which are referenced the latest works about NRR.12-14 The calculated values of zero

point energy and the entropy are derived from the previous work.12 T is the room temperature,

which is equal to 298K. eU is the contributions from the electrode potential. is the ∆GpH

contributions of pH, which can be defined as . The pH will not ∆GpH =- kBTln[H + ] = pH × kBln10

change the overpotential and thus only the pH = 0 is considered in this work. The adsorption

energy ( ) of different intermediates is calculated by∆EDFT

(S19)∆EDFT = Etotal ‒ (Ecatal + Eadsorp)

where and are the total energies of the slab with and without intermediates. is the Etotal Ecatal Eadsorp

total energy of an isolate intermediate, such as N2 and *NH. The ƞonset is determined by the

potential limiting steps (PLS), corresponding to the most positive reaction Gibbs free energy

(∆Gmax), and can be calculated by: Uonset = -ΔGmax/e. Therefore, the ƞNRR is determined by the

potential limiting steps (PLS), corresponding to the most positive reaction Gibbs free energy

(∆Gmax) and defined as eq (20)

(S20)ηNRR = Uequ ‒ Ulim

where is the equilibrium potential of NRR (~-0.16 V), and is the limiting potential, Uequ Ulim

which is evaluated as =-∆Gmax/e.12 The pH is set to 0 and only the electrode potential effect is Ulim

taken into account in the NRR process.

1.3. Calculation methods of evaluating CO2RR activity

The possible mechanism of CO2RR on C2N surface is shown in Figure S3. The CO2RR is

complicated. There are at least six potential reaction pathways (P1, P2, P3, P4, P5, and P6) for

CO2RR (as shown in Figure S3). However, previous works show that for most catalysts the most

possible pathway for CO2RR is it along the P1 way (light orange arrows in Figure S3),15-18 and the

proposed reaction mechanism on C2N is:

*+CO2→*CO2 ∆G1 (S21)

*+CO2+H++e-→*COOH ∆G2 (S22)

*COOH+H++e-→*HCOOH ∆G3 (S23)

*HCOOH+H++e-→*CHO+H2O ∆G4 (S24)

*CHO+H++e-→*H2CO ∆G5 (S25)

*H2CO+H++e-→*CH2OH ∆G6 (S26)

*CH2OH+H++e-→*HOCH3 ∆G7 (S27)

*CH2OH+H++e-→*CH3+H2O ∆G8 (S28)

*CH3+H++e-→*CH4 ∆G9 (S29)

In addition, CO is the one of potential side reactions product in above P1 way. The reaction of

forming CO (P2) is as below:

*+CO2→*CO2 ∆G1 (S30)

*+CO2+H++e-→*COOH ∆G2 (S31)

*COOH+H++e-→*CO+H2O ∆G10 (S32)

*CO+H++e-→*COH ∆G11 (S33)

If the reaction free energy of eqs (32) and (33) is lower than that of eqs (23) and (24),

respectively, the product of CO will be hydrogenated into COH (may along P3, P4 or P5). The

free energy of each reaction is calculated by using “Computational Hydrogen Electrode (CHE)”

model proposed by Norskov et al.,17 where the reaction H+ + e- → 1/2H2 (g) is defined to be in

equilibrium at zero voltage with H2 at pressure of atmospheric pressure and room temperature.

The chemical potential of proton and electron pair can be assumed to be half of that of gaseous

hydrogen (μ(H+) + μ(e-) = 1/2μ(H2)) at a potential of 0 V in the CHE. To obtain chemical

potential of proton and electron pair, we can be simply calculated chemical potential of gaseous

H2 based on this relation. The free energy change (∆G) of each elementary reaction is calculated

as ∆G = ∆E + ∆EZPE − T∆S (S34)

where ∆E is the electronic energy difference directly obtained from DFT calculations, ∆EZPE is the change in zero-point energies, T is the temperature, and ∆S is the entropy change. The ZPE and S of each species can be obtained from previous literatures. 17,18

The limiting potential UL is obtained byUL = -∆GMax/e (S35)

where the ∆GMax is the maximum free energy change of the whole process.1.4. Calculation method of binding energy

The binding energy ( ) of TM on the C1-xNx surface was calculated through eq (S36)Eb

(S36)Eb = Etotal - (EC1 - xNx

+ ETM)

where and are the total energies of the C1-xNx slab with and without metal binding. EtotalEC1 - x𝑁𝑥

is the energy of the isolate metal.19ETM

1.5 Formation energy of B doped C1-xNx

The formation energy of B doped C1-xNx can be obtained through:

Ef=E(B-total)+E(N)-E(total)-E(B) (S37)

where E(B-total) and E(total) are the total energy of with and without B doped C1-xNx. E(N) and E(B) are

the total energies of isolate N and B, respectively, which are evaluated referring to its bulk ground

states (N2 molecule and B bulk).20

1.6 Cohesive energy of C1-xNx

The cohesive energy of C1-xNx is defined as:

(S38)Ecoh = (EC1 - xNx

‒ n1EC - n2EN)/(n1 + n2)

where EC, EN, and are the energies of a single C atom, single N atom, and the total energy EC1 - xNx

of the monolayer, respectively. E(C) is evaluated referring to graphene. The n1 and n2 are EC1 - xNx

the numbers of the total carbon and nitrogen atoms, respectively.21

2. Figures and Tables

Figure S1. Schematic of the C2N surface as bi-functional catalyst for overall water splitting. Elementary reaction structures of (a) HER and b) OER. The adsorbed states for reactions include *H, *O, *OH, and *OOH species. The gray, blue, red, and white balls represent the C, N, O, and H atoms, respectively.

Figure S2. Schematic of NRR mechanisms for NRR on C2N surface. The * represents active sites for NRR.

Figure S3. Schematic of CO2RR mechanisms for CO2 reduction on C2N surface. The * represents active sites for CO2RR.

Figure S4. Atomic configurations of C1-xN after AIMD simulations under 500K, (a) C3N, (b)

C3N side view, (c) C2N, (d) C2N side view, (e) g-C3N4, and (f) g-C3N4 side view. The

simulation is run for 3 ps with a time step of 2 fs.

Figure S5. Schematic structures of C1-xNx for HER, OER, NRR, and CO2RR, (a) C3N for HER, (b) C2N for HER, (c) g-C3N4 for HER, (d) C3N for OER, (e) C2N for OER, (f) g-C3N4 for OER, (g) C3N for NRR, (h) C2N for NRR, (i) g-C3N4 for NRR, (j) C3N for CO2RR, (k) C2N for CO2RR, and (l) g-C3N4 for CO2RR.

Figure S6. Volcano curve of exchange current (i0) as a function of ∆GH* of C1-xNx.

Figure S7. Standard free energy diagrams for OER under electrode potentials U=0 V for (a) C3N-C1, (b) C3N-C3, (c) C3N-N, (d) C2N-N, (e) g-C3N4-N1, and (f) g-C3N4-N2.

Figure S8. Reaction Gibbs free energy diagrams of CO2RR into CH4 as well as into CO of C1-xNx, (b) C3N-N, (c) C2N-N, and (d) g-C3N4-N.

Figure S9. Schematic structures of (a) pure C2N, (b) BC-C2N, (c) ) BN-C2N, and (c) ) B-C2N.

Figure S10. Reaction Gibbs free energy diagrams of NRR on (a) BC-C2N and (b) BN-C3N4.

Figure S11. Band structure and density of states of (a, b) pure C2N and (c, d) BN-C2N.

Figure S12. Limiting potential (UL) for CO2RR of TM-C1-xNx (TM=Cu and Pd).

Figure S13. Atomic configurations of BN-C2N and Pd-C3N after AIMD simulations under 500K, (a) BN-C2N, (b) BN-C2N side view, (c) Pd-C3N, and (d) Pd-C3N side view. The simulation is run for 3 ps with a time step of 2 fs.

Table S1. The reactions Gibbs free energies (∆G1-4) of four elementary steps of C2N, C3N, and g-C3N4 for OER at different sites.

System ∆G1 (eV) ∆G2 (eV) ∆G3 (eV) ∆G4 (eV)C2N-C 2.38 0.05 3.17 -0.68C2N-N 3.58 0.35 1.16 -0.17C3N-C1 0.73 -0.37 3.41 1.15C3N-C2 1.02 0.31 2.05 1.54C3N-C3 2.21 0.24 1.27 1.20C3N-N 2.13 1.54 1.21 0.04

g-C2N4-C 2.07 1.62 1.92 -0.69g-C2N4-N1 3.36 -0.02 2.22 -0.64g-C2N4-N2 2.11 1.43 1.76 -0.38

Table S4. The reactions Gibbs free energies (∆G1-11) (eV) of elementary steps of C1-xNx and TM-C1-xNx systems (TM=Cu and Pd) for CO2RR.

System ∆G1 ∆G2 ∆G3 ∆G4 ∆G5 ∆G6 ∆G7 ∆G8 ∆G9 ∆G10 ∆G11

C2N-C 0.21 2.31 -1.30 2.45 -1.28 0.91 -1.33 0.84 -1.95 -1.10 3.37C2N-N 0.17 0.86 -1.10 0.73 0.49 -0.35 -0.75 --0.39 0.26 -1.69 1.71C3N-C 0.39 1.00 -0.39 0.34 0.08 -0.34 -0.75 -0.51 -0.49 0.25 1.88C2N-N 0.63 -0.03 -1.02 0.96 0.09 -0.36 -0.77 -0.04 -0.97 0.19 2.18

g-C3N4C 0.22 2.47 -2.71 -0.53 -1.58 1.01 -0.18 0.94 -0.93 -1.29 2.41g-C3N4-N 0.25 2.37 -2.21 1.86 -0.27 0.85 -2.65 1.26 -2.31 -0.10 2.52Cu-C2N -0.23 -1.39 0.28 -0.24 0.68 -1.31 -0.69 -0.43 -0.08 -0.29 1.22Pd-C2N Cu-C3N

-0.550.23

0.320.87

-0.120.40

-0.140.11

0.810.03

0.19-2.07

-0.240.47

-0.62-0.93

-0.29-0.70

0.17-1.23

2.331.12

Pd-C3N -0.45 -0.02 0.63 -0.62 -0.39 -0.43 0.40 -1.62 -1.17 1.10 0.20Cu-g-C3N4 -0.27 -0.05 0.14 -0.05 -0.64 0.77 -0.19 -1.12 -0.82 -0.98 3.09

Pd-g-C3N4 -0.87 0.12 0.02 0.43 0.88 -0.16 -0.29 -1.13 -0.54 -0.84 1.52

Table S3. The Gibbs reaction free energies (eV) of intermediates (∆G1-12) through enzymatic and consecutive mechanisms in B doped C2N, C3N, and g-C3N4 for NRR.Systems ∆G1 ∆G2 ∆G3 ∆G4 ∆G5 ∆G6 ∆G7 ∆G8 ∆G9 ∆G10 ∆G11 ∆G12 ∆G13

BC-C2N 0.21 1.35 -0.37 -1.25 -0.07 -1.24 0.11 0.02 -0.34 -0.40 -1.29 -0.35 -0.55BN-C2N -1.00 0.94 1.21 -0.11 -0.93 -0.08 -1.19 -0.16 0.32 -0.72 -0.12 -0.36 -0.22BC-C3N 0.22 1.47 0.05 0.78 0.37 -0.12 -1.07 -0.82 0.44 -0.41 -1.07 -1.24 0.89BN-C3N 0.23 1.58 0.53 0.26 -0.26 0.45 -1.35 -0.44 0.24 0.20 -0.56 -0.55 -1.70BN-g-C3N4 0.29 0.69 1.58 0.46 -0.91 -0.29 -2.23 -0.50 0.87 0.28 -1.50 -0.68 -0.56B-C2N -0.53 0.98 -0.31 -0.71 -0.32 -0.35 -1.39 0.87 -0.88 1.70 -1.58 -2.44 0.08

Table S4. The Gibbs reaction free energies (eV) of intermediates (∆G14-21) through alternating and distal mechanisms in B doped C2N, C3N, and g-C3N4 for NRR.

Systems ∆G14 ∆G15 ∆G16 ∆G17 ∆G18 ∆G19 ∆G20 ∆G21

BC-C2N 0.31 1.51 -0.06 -0.61 -0.03 -1.83 -0.62 -0.27BN-C2N -1.04 0.73 -0.26 -0.54 -0.76 -0.59 -0.36 0.21BC-C3N 0.30 1.37 0.57 -1.12 0.37 -2.42 0.54 0.29BN-C3N 0.21 0.88 0.18 0.57 -1.43 0.73 0.96 0.20BN-g-C3N4 0.36 1.16 -0.37 -0.59 0.47 -1.38 -0.31 0.62B- C2N -0.45 0.90 -0.22 -0.59 -0.54 -1.81 -0.78 1.64

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