Supporting Information. DFT Study of Methane Synthesis from Syngas on Ce Doped Ni(111) Surface

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1 Supporting Information DFT Study of Methane Synthesis from Syngas on Ce Doped Ni(111) Surface Kai Li, 1 Cong Yin, 2 Yi Zheng, 3 Feng He, 1 Ying Wang, 1 Menggai Jiao, 1 Hao Tang, 2,* Zhijian Wu 1,* 1 State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun ,P. R. China 2 Energy Conversion R&D Center, Central Academy of Dongfang Electric Corporation, Chengdu , P. R. China 3 Network Center, Changchun Normal University, Changchun, , P. R. China Brief description of the Microkinetic Model The microkinetic model is often used to describe the heterogeneous catalytic reaction. 1 Though the microkinetic analysis based on DFT calculations, a more detailed analysis will be available for comparison with experiments, which will eventually advance the microscopic understanding of catalysis. In the microkinetic model, the reactor was modeled as a flow reactor. Since the reaction is a dynamic process, the reaction rate and the coverage/concentration of the intermediates vary, while they remain constant when the reaction reaches steady state. Thus, the micorkinetic model based on the steady state is employed to quantify the coverage/concentration of each intermediate (CO, CH x O, CH x, OH and O) in the reactions with different temperature and H 2 /CH 4 ratios. Expressions for relative coverage (θ ) of the intermediates and products are developed from the total catalytic site balance and the steady state approximation. The total amount of metal catalytic sites in the reaction is considered as a constant. The sum of the occupied ( θ x ) and the free metal ( θ * ) sites are defined as 1. S1

2 The reaction network included in the microkinetic model is summarized in Table 3 of the manuscript. The adsorption process of H 2 (R1) and CO (R2) is assumed in equilibrium. The equilibrium constant 2 is estimated according to K = exp [-(ds -T S)/k B T], where ds is the calculated adsorption energy of H 2 and CO, and S is the entropy change of gas phase H 2 and CO obtained from NIST Chemistry WebBook. 3 Since the adsorption of CH 4 and H 2 O on Ce-Ni(111) is weaker physisorption compared with other intermediates in Table 1 of the manuscript, the desorption of CH 4 and H 2 O is considered as a spontaneous process with no barrier at temperature of 300 ~550 C. Thus the coverage of CH 4 and H 2 O is set as 0 in the microkinetic model. The site balance of surface species included in the reaction mechanism and free sites (*) can be written as follows: θ + θ + θ + θ + θ + θ + θ + θ + θ =, (1) CO CHO CH3 CH2 CH O H OH * 1 The coverage of surface H and CO are obtained by θ H H K 2 1 θ* = P and θ CO = P Kθ. For the surface species including CO, CH x O, CH x, OH and O, the CO 2 * coverage of them are obtained from steady state approximation. 4 For P1: CO CHO CH 4 on the Ce-Ni(111) surface, the steady-state approximation formula is as follows: dθcho 1 1 CHO : k2θ COθ H k = 2 θchoθ* k5 θchoθ* + k5 θchθo = 0 (2) dt dθch 1 1 CH : = k5 θchoθ* k5 θchθo k18θ CHθ H + k18 θchθ 2 * = 0 (3) dt dθch CH 2 : = k18θ CHθ H k18 θchθ 2 * k19θ CHθ 2 H + k19 θchθ 3 * = 0 (4) dt dθch3 1 1 CH 3 : k19θ CHθ 2 H k = 19 θchθ 3 * k20θ CHθ 3 H + k20 θchθ 4 * = 0(5) dt dθo 1 1 O : k5 θchoθ* k = 5 θchθo k21θ Oθ H + k21 θohθ* = 0 (6) dt S2

3 dθoh 1 1 OH : k21θ Oθ H k = 21 θohθ* k22θohθ H + k22 θh2oθ* = 0 (7) dt The rate constants of all elementary reactions are calculated using the harmonic transition state theory 5-7 based on the following equation: k = where vi exp( E act RT ), (8) vi is the pre-exponential factor. According to the harmonic transition state theory, the pre-exponential factor (ν i ) of each reaction pathway is estimated using the following definition: ν i = 3N IS f 1 i 3N 1 TS f 1 i, (9) where IS f i and TS fi are the vibrational frequencies at the initial state and the transition state. It is noted that for TS the imaginary frequency is excluded. Since the reaction is occurred at high temperature, the activation energy (E act ) including the entropy ( ST) and enthalpy ( CPd ) corrections, is calculated as follows: T E act = ST + CPd. T where is the effective barriers including the zero point energy, S is the entropy and C p is the heat capacity. The entropy correction is calculated as follows 8 : hf i K 1 BT TS = K T ln(1 e ) hv ( ) K T B i i i hfi B KBT e 1 The enthalpic temperature correction is calculated as follows 8 : 1 C d = hf + K T P T i i hfi B KBT ( e 1) where f is vibrational frequency and i represent the different modes of vibration for the intermediates. The evaluated values for P1 and P2 on Ce-Ni(111) are shown in Table S3-S8. S3

4 References: (1) Reuter, K.; Frenkel, D.; Scheffler, M. The Steady State of Heterogeneous Catalysis, Studied by First-Principles Statistical Mechanics. Phys. Rev. Lett. 2004, 93, (2) Liu, P.; Rodriguez, J. A.; Water-Gas-Shift Reaction on Metal Nanoparticles and Surfaces. J. Chem. Phys. 2007, 126, (3) (Accessed Feb 9, 2015). (4) Bukoski, A.; Abbott, H. L.; Harrisona, I. Microcanonical Unimolecular Rate Theory at Surfaces. III. Thermal Dissociative Chemisorption of Methane on Pt(111) and Detailed Balance. J. Chem. Phys. 2005, 123, (5) Vineyard, G. H. Frequency Factors and Isotope Effects in Solid State Rate Processes. J. Phys. Chem. Solids 1957, 3, (6) Wert, C.; Zener, C. Interstitial Atomic Diffusion Coefficients. Phys. Rev. 1949, 76, (7) Mei, D. H.; Xu, L. J.; Henkelman, G. Potential Energy Surface of Methanol Decomposition on Cu(110). J. Phys. Chem. C 2009, 113, (8) Bendavid, L. I.; Carter, E. A. CO 2 Adsorption on Cu 2 O (111): A DFT+ U and DFT-D study. J. Phys. Chem. C 2013, 117, S4

5 Table S1. The energy barriers ( E DFT, ev), reaction energies ( DFT, ev) and interaction ( E int, ev) in the initial state for the studied elementary reactions. Elementary reaction E DFT DFT E int in IS R1 H 2 2H R2 CO C+O R3 CO+H COH R4 CO+H CHO R5 CHO CH+O R6 CHO+H CHOH R7 CHO+H CH 2 O R8 CH 2 O CH 2 +O R9 CH 2 O+H CH 2 OH R10 CH 2 O+H CH 3 O R11 CH 3 O CH 3 +O R12 CH 3 O+H CH 3 OH R13 COH C+OH R14 CHOH CH+OH R15 CH 2 OH CH 2 +OH R16 CH 3 OH CH 3 +OH R17 C+H CH R18 CH+H CH R19 CH 2 +H CH R20 CH 3 +H CH R21 O+H OH R22 OH+H H 2 O Table S2. The energy barriers (, ev) and reaction energies (,ev) involved in P1 for the pure Ni(111). CO+H CHO CHO CH+O CH+H CH CH 2 +H CH CH 3 +H CH O+H OH OH+H H 2 O S5

6 Table S3. The entropy and enthalpy corrections for energy barrier and reaction energy at 300 C. ST CPdT ST C d P T R4 CO+H CHO R5 CHO CH+O R18 CH+H CH R19 CH 2 +H CH R20 CH 3 +H CH R21 O+H OH R22 OH+H H 2 O Table S4. The entropy and enthalpy corrections for energy barrier and reaction energy at 350 C. ST CPdT ST C d P T R4 CO+H CHO R5 CHO CH+O R18 CH+H CH R19 CH 2 +H CH R20 CH 3 +H CH R21 O+H OH R22 OH+H H 2 O Table S5. The entropy and enthalpy corrections for energy barrier and reaction energy at 400 C. ST CPdT ST C d P T R4 CO+H CHO R5 CHO CH+O R18 CH+H CH R19 CH 2 +H CH R20 CH 3 +H CH R21 O+H OH R22 OH+H H 2 O S6

7 Table S6. The entropy and enthalpy corrections for energy barrier and reaction energy at 450 C. ST CPdT ST C d P T R4 CO+H CHO R5 CHO CH+O R18 CH+H CH R19 CH 2 +H CH R20 CH 3 +H CH R21 O+H OH R22 OH+H H 2 O Table S7. The entropy and enthalpy corrections for energy barrier and reaction energy at 500 C. ST CPdT ST C d P T R4 CO+H CHO R5 CHO CH+O R18 CH+H CH R19 CH 2 +H CH R20 CH 3 +H CH R21 O+H OH R22 OH+H H 2 O Table S8. The entropy and enthalpy corrections for energy barrier and reaction energy at 550 C. ST CPdT ST C d P T R4 CO+H CHO R5 CHO CH+O R18 CH+H CH R19 CH 2 +H CH R20 CH 3 +H CH R21 O+H OH R22 OH+H H 2 O S7

8 Table S9. The calculated rate constants (s -1 ) in the pathway P1 at different temperatures on the Ce-Ni(111) surface. 350 ºC 400 ºC 450 ºC 500 ºC 550 ºC k/ k -1 k/ k -1 k/ k -1 k/ k -1 k/ k -1 R1 R2 R / / / / / R / / / / / R / / / / / R / / / / / R / / / / / R / / / / / R / / / / / Table S10. The coverage (molecule/cm 2 ) of CHO and CH x in the pathway P1 on the Ce-Ni(111) surface at 350 ºC H 2 /CO CHO CH CH 2 CH Table S11. The coverage (molecule/cm 2 ) of CHO and CH x in the pathway P1 on the Ce-Ni(111) surface at 400 ºC H 2 /CO CHO CH CH 2 CH S8

9 Table S12. The coverage (molecule/cm 2 ) of CHO and CH x in the pathway P1 on the Ce-Ni(111) surface at 450 ºC H 2 /CO CHO CH CH 2 CH Table S13. The coverage (molecule/cm 2 ) of CHO and CH x in the pathway P1 on the Ce-Ni(111) surface at 500 ºC H 2 /CO CHO CH CH 2 CH S9

10 Figure S1. The differential charge densities of O, OH, H 2 O, CH x O, COH and CH x OH (x=1-3). The isosurface levels for (c) H 2 O and (j) CH 3 OH are e/bohr 3, e/bohr 3 for the remaining. The yellow and blue regions denote the gain and loss of electrons. The blue, red, white, pink and gray balls denote Ni, O, Ce, H and C, respectively. S10

11 Figure S2. The barriers and structures of CH x O CH x-1 OH (x=1-3) reactions S11

12 Figure S3. The rate constants of CH C + H as a function of the temperatures on the Ce-Ni(111) and pure Ni(111) surfaces. S12