FULL PAPER WWW.C-CHEM.ORG SurfKin: An Ab Initio Kinetic Code for Modeling Surface Reactions Thong Nguyen-Minh Le,[a] Bin Liu,[b] and Lam K Huynh*[a,c] In this article, we describe a C/C11 program called SurfKin (Surface Kinetics) to construct microkinetic mechanisms for modeling gas–surface reactions Thermodynamic properties of reaction species are estimated based on density functional theory calculations and statistical mechanics Rate constants for elementary steps (including adsorption, desorption, and chemical reactions on surfaces) are calculated using the classical collision theory and transition state theory Methane decomposition and water–gas shift reaction on Ni(111) surface were chosen as test cases to validate the code implementations The good agreement with literature data suggests this is a powerful tool to facilitate the analysis of complex reactions on surfaces, and thus it helps to effectively construct detailed microkinetic mechanisms for such surface reactions SurfKin also opens a possibility for designing nanoscale model cataC 2014 Wiley Periodicals, Inc lysts V Introduction mental techniques have validated the microkinetic models derived from the first-principles methods, which have become a bridge between microscopic properties and macroscopic performances.[12–18] Many microkinetic models have been developed for a variety of important surface processes using common DFT-based computational tools, including SIESTA,[18] DACAPO,[12–16] and Vienna ab initio simulation package (VASP),[17] in combination with HREELS experiments.[12–14,16] The information derived from these calculations or experiments is the basis to create sequences of elementary reaction steps and estimate rate parameters for each step using statistical thermodynamics,[12,14–16] collision theory,[14,15] and transition state theory (TST).[14,16,17] The developed microkinetic models are essential for simulation of model reactors It can be seen that the development of microkinetic models from the firstprinciples calculations has become a powerful method for studying catalytic surface processes In this article, we presented a C/C11 program called SurfKin (Surface Kinetics) for modeling gas–surface reactions from first-principles methods The code uses detailed kinetic mechanisms from DFT-based calculations Alternatively, it can be combined with the data obtained either from experiments or Microscopic understanding of gas–surface reactions has always been an interest and also a challenge in surface chemistry, specifically in determination of detailed reaction mechanisms The molecular-level information of a reaction network is essentially the starting point of developing a microkinetic model for the understanding of the chemistry/physics occurring on catalyst surfaces under realistic reaction conditions Characterization of elusive surface intermediates is a very challenging task, which cannot be easily done by performing experiments only It is widely known that semiempirical kinetic models, or power law kinetic models can provide a well-described picture at the macroscopic scale, but the lack of detailed information of reacting species at the molecular-level limits their applicability to develop reliable kinetic models to capture a wide range of reaction conditions For example, kinetic models for ammonia decomposition over various transition metals were developed based on experimental data.[1–3] In these studies, assumptions are usually made on the rate-determining steps and dominant surface coverages, which depend on actual conditions,[4] as fitting parameters The unity bond index-quadratic exponential potential (UBI-QEP) method is another semiempirical approach that provides whole surface reaction energetics for constructing microkinetic models.[5–11] In this approach, heats of adsorption, reaction enthalpies, and activation energies were calculated within 1–3 kcal/mol to the experimental thermodynamic parameters.[5,6] Due to its empirical nature, this practical method is simple and effective to predict the energetics of surface intermediates.[6] However, the UBI-QEP method cannot describe accurately the nonenergetic contributions to rate coefficients, and results from quantum mechanical methods are essential in this aspect Additionally, compared to UBI-QEP, density functional theory (DFT) calculations provide a more solid framework to obtain reliable rate parameters; thus it can be effectively extended to a wide range of reaction conditions Recent advances in DFT-based electronic structure calculations and experi1890 Journal of Computational Chemistry 2014, 35, 1890–1899 DOI: 10.1002/jcc.23704 [a] T N.-M Le , L K Huynh Molecular Science and Nano-Materials Laboratory, Institute for Computational Science and Technology, Quang Trung Software Park, Dist 12, Ho Chi Minh City, Vietnam E-mail: lamhuynh.us@gmail.com [b] B Liu Department of Chemical Engineering, Kansas State University, 1005 Durland Hall, Manhattan, Kansas, 66506 [c] L K Huynh Applied Chemistry Department, School of Biotechnology, International University, Vietnam National University, Ho Chi Minh City, Vietnam Contract grant sponsor: Department of Science and Technology, Ho Chi Minh City (L.K.H.); Contract grant sponsor: Kansas State University (B.L.) C 2014 Wiley Periodicals, Inc V WWW.CHEMISTRYVIEWS.COM FULL PAPER WWW.C-CHEM.ORG simulations (if available) to model complex chemical processes in real conditions Statistical mechanics is used to estimate thermodynamic properties, such as entropies and enthalpies for both gas-phase and adsorbed species Kinetic analyses are performed based on kinetic theories, such as the collision theory and the canonical TST The analyses of methane decomposition and water–gas shift reaction on a model Ni(111) surface were performed to illustrate the applications of SurfKin as an effective tool that integrates quantum mechanical calculations and statistical mechanics to study surface chemistry Rotational partition function (qrotation ) For adsorbed species, there is only the rotation about the z-axis of the center of mass, thus the rotational partition function takes the form q2D rotation À Á1=2 p1=2 ðIZZ Þ1=2 8p2 kB T ; rh (3) where r is the symmetry number and IZZ is moment of inertia about the z-axis that passing through the center of mass of the species Vibrational partition function (qvibration ) For species with Nvib Theoretical Methods normal modes, the vibrational partition function is given by Statistical thermodynamic analysis Thermodynamic properties (e.g., entropy and enthalpy) of the reaction species were calculated using a well-established statistical mechanical approach Details on thermodynamic property calculations for gas-phase molecules can be found elsewhere.[19] In this section, we only briefly describe the implementation for adsorbed molecules in SurfKin The thermodynamic properties of adsorbed species can be effectively derived from the total partition function, which can be factored out into four corresponding components as follows qtotal 5qelectronic 3qtranslation 3qrotation 3qvibration (1) Nvib Nvib Y Y ; qvibration ðqvib Þi 12e2bhcmi i51 i51 where b5 kB1T , c is the speed of light and mi (cm21) denotes the ith vibrational frequency Thermodynamic property calculations From the above partition functions, standard molar entropy (S0 ), standard molar enthalpy (H0 ) can be calculated using the following equations ! 2pmkB T A 11 h2 1=2 ! À Á1=2 p 1 ðIZZ Þ1=2 8p2 kB T S02D2rotation ðTÞ5R ln rh ! X hcmi =kB T À Á S0vibration ðTÞ5R 2ln 12e2bhcmi bhcm i e 21 i S02D2translation ðTÞ5R ln Electronic partition function (qelectronic ) The contribution of the electronic partition function depends on how high the temperature and energy difference between ground state and the first excited state Usually, the difference is too high compared to kBT in the common temperature range of interest (i.e., T < 2000 K) As a result, the electronic partition function is restricted to the ground state Therefore, the focus is on the contributions of translational, rotational and vibrational partition functions to the total partition function of a species of interest If a molecule strongly binds to the surface, translation and rotation are considered as frustrated motions and thus effectively treated as harmonic vibrations In the case of weakly bound or indirect adsorption, the molecules create a precursor state on the surface that translation on two dimensions and rotation about direction perpendicular to the surface (defined as z-axis) must be explicitly considered.[16] Translational partition function (qtranslation ) Translational parti- tion function for a weakly bound species on surface takes the following form 2pmkB T 2D qtranslation ðA; TÞ5 A; h2 H0 5Eelectronic ZPE U0corrections (5) (6) (7) (8) G0 5H0 2TS0 (9) P where Eelectronic is the total electronic energy, ZPE5 i hcmi is the zero point energy, the correction to the internal energy, U0corrections , includes all thermal corrections at standard molar state, namely U0corrections 5U0translation 1U0rotation 1U0vibration (10) U02D2translation ðTÞ5RT (11) U02D2rotation ðTÞ5 RT (12) U0vibration ðTÞ5RT Nvib X i (2) where m is the species mass, kB and h are Boltzmann and Planck constants, respectively, and A is the surface area per binding site, which depends on surface site density characterizing for each single surface (a typical value of A for Ni(111) is 5.365 10220 m2 assuming for the p(2 2) cell and the fcc, hcp, and atop binding sites[16]) (4) bhcmi i exp kB T 21 (13) Transition state theory Conventional TST was applied to calculate rate constants for elementary reactions/steps which have intrinsic reaction barriers,[20] which can be depicted in Figure Within the TST framework, rate constant has the general form Journal of Computational Chemistry 2014, 35, 1890–1899 1891 FULL PAPER WWW.C-CHEM.ORG the surface If it is a strong binding case (e.g., adsorption energy is larger than DHrxn ) or direct adsorption, the molecules immediately land on the surface with only vibrational motion Translation and rotation are considered as frustrated motions and treated as harmonic vibrations.[16] In the case of weakly bound or indirect adsorption, the molecules are in a precursor state on the surface that translation on two dimensions and rotation about z-axis are considered.[16] Similar to the reaction on the surface, the adsorption process for molecule M in the gas-phase can be schematically eq KTS m presented as M hà MÃTS !Mà For direct adsorption, rate constant can be expressed as Figure Schematic representation of a surface reaction with an intrinsic barrier h* denotes an active surface site and A*, B*, and AB* are the adsorbed species, and ABÃTS are the adsorbed species at the TS [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.] kTST ðTÞ5 kB T q0TS DETS exp h q0R kB T The reaction scheme for reactions between adsorbed species (cf Figure 1) can be expressed as Reactions between adsorbed species eq KTS m kforward ðTÞ5 kB T qABÃTS DETS exp ð2 Þ; h qAà qBà kB T (16) where DETS is defined as DETS 5ðE1ZPABà ðE1ZPẪ ðE1ZPBà TS rdirect ðT Þ5 (21) (22) For indirect adsorption, TS is weakly bound to the surface The molecules can freely move on surface, thus they can contribute to translational, rotational and vibrational partition functions The rate constants can be described as indirect kadsorption ðTÞ5NA A2 indirect r ðT Þ5 sffiffiffiffiffiffiffiffiffiffiffiffi kB T indirect ðT Þ r 2pmM vib qrot Mà qMà TS TS vib qrot M qM DETS exp kB T (23) (24) As can be seen from (21) and (24), the indirect model takes into account the translation and rotation of the TS, while the direct model considers these degree of freedoms as vibration-like modes on the surface Therefore, it is important to determine the contribution of energetic degree of freedoms for the TS species The rate constant for desorption process can be calculated by equilibrium relation or using the following equation explicitly DETS; desorption kB T qMÃTS kdesorption ðTÞ5 exp ; h qMà kB T (25) where kforward ðTÞ DGrxn 5exp Keq ðTÞ5 reverse k ðTÞ kB T (18) and DGrxn 5DHrxn TDSrxn (19) Journal of Computational Chemistry 2014, 35, 1890–1899 TS TS (17) Two adsorption models, direct adsorption and indirect adsorption, are considered The main difference is in how strong or weak the molecules binding to 1892 DETS exp vib kB T qrot M qM qvib Mà  à DETS 5ðE1ZPEÞMà ðE1ZPEÞM 2ðE1ZPEÞhà To fulfill the thermodynamic consistency, the reverse rate constant is derived from Van’t Hoff equation, Adsorption of molecules (20) and (15) The rate constants as a function of temperature for the forward direction can be derived within the TST framework as follows sffiffiffiffiffiffiffiffiffiffiffiffi kB T direct ðT Þ; r 2pmM where (14) where q0TS , q0R are the partition functions for the transition state (TS) and reactants with respect to its own ground states, respectively The energy barrier DE TS TSTS (or Ea in the conventional notation) is the energy difference between the TS and the reactant(s) On the surface, it is divided into three individual processes to calculate rate constants, namely adsorption, desorption and reactions between adsorbed species Aà Bà ABÃTS !ABà hà NA h2 direct kadsorption ðTÞ5 2pmM kB T DETS; desorption 5ðE1ZPEÞMÃTS 2ðE1ZPEÞMà (26) Collision theory Within the simpler collision theory framework, the adsorption process can be written as following, with gas-phase M and WWW.CHEMISTRYVIEWS.COM FULL PAPER WWW.C-CHEM.ORG adsorbed species Mà , M hà Mà (hà is the active surface site) Collision theory is used to calculate the rate of adsorption processes with the general formula [14,15] collision radsorption À Á Ar T; hcoverage PM 2DEf pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp ; kB T 2pmM kB T (27) À Á where r T; hcoverage is the sticking coefficient for the collision process The estimation of sticking coefficients is discussed below PM is the partial pressure of gas-phase species M, and DEf is the activation energy for adsorption process It is essential to extract an adsorption rate constant depending only on temperature from the general adsorption rate It should be noted the site density is N0 NS A1 for a surface with N adsorption sites and total surface area of S, each with an area of A The sticking coefficient rðT; hcoverage Þ depends on the temperature T and the free-site surface coverage hcoverage The sticking coefficient can be written in the form of two factors, sticking coefficient of clean surface rðTÞ and a function of surface covÀ Á erage r hcoverage [21] The gas-phase species M is assumed as an ideal gas, the relation between pressure and concentration for ideal gas is widely known as PM hni V NA kB T (28) Substitute the expanded form of sticking coefficient and eq (28) into eq (27), the adsorption rate expression becomes sffiffiffiffiffiffiffiffiffiffiffiffi kB T 2DEf h n i exp 2pmM V kB T collision radsorption T; ẵMị5NA ArT ị (29) From eq (29), the adsorption rate constant can be extracted as sffiffiffiffiffiffiffiffiffiffiffiffi kB T 2DEf exp 2pmM kB T collision ðTÞ5NA ArðTÞ kadsorption (30) The adsorption processes are usually nonactivated,[14] that is, DEf 50, so the adsorption rate constant can be rewritten in a simpler form sffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffi k T rðTÞ kB T B collision kadsorption ðTÞ5NA ArðTÞ 2pmM C 2pmM (31) where C5 N1A A is the surface site density and the typical value of C is 3.095 1029 (mol/cm2) for Ni(111); NA is the Avogadro constant; A is the area of each adsorption site and the typical value of A is 5.365 10220 m2.[16] The desorption rate constants can be calculated through the equilibrium relations represented by eq (18) Sticking coefficient for barrierless adsorption Sticking coefficient for barrierless adsorption can be understood as the ratio of the rate of adsorption onto surface to the rate of collisions with surface The coefficient is controlled by both enthalpic and entropic contributions which have opposing effects on the variational behavior of the TST rate coefficient For most exothermic adsorption processes, the sticking coefficients are typically unity The entropic effect (the tendency of adsorbate migration on surface) will affect the value of sticking coefficient and make it less than unity For several reactions, the initial adsorption can be the rate controlling step; therefore, in this study, we tried to calculate the sticking coefficient for barrierless adsorption as a function of adsorbate–adsorbent perpendicular ˚ ) using formula proposed by Pitt et al.[22] In this position z (A approach, the reaction adsorption potential and the barrier height to migration on the surface as a function of z are needed and can be explicitly calculated from DFT calculations SurfKin Program Interpretation The structure of Surfkin program is schematically shown in Figure SurfKin program uses C/C11 language to take advantages of object-oriented programming pattern, which is convenient for defining properties of molecules, linking and processing data as well All molecules are held in a unique class type because of their similar data structure such as molecular names, masses, energies, vibration frequencies, geometries, and so forth The surface is a periodic structure, where reactions occur with active sites represented by h* In SurfKin, an active site is treated as a reaction species, so it also has the properties of a surface adsorbate molecule This concept can be conveniently adopted in SurfKin because it helps reduce processes for defining a new class, or creating linkage to others molecules The program is coded by a modulization method, which allows us to manipulate all the involving files properly Each module performs its individual functions, and then they are linked together for a specific calculation task The first step is to prepare the input data for the program, including a database and a control file The database is stored in a folder containing files of the information of all species, which characterizes the system of interest In the database, the files *.erg and *.freq contains information of molecular energies and frequencies, which is used to calculate energy barriers, partition functions, and thermodynamic quantities The ground state energy data of all species can be used to construct the potential energy surface (PES) Molecular geometries are stored in file *.geom, which is used to calculate moments of inertia for a specific species through its center of mass The control file is independent of the database It contains information of the databases for reactants, TSs, products as well as calculation parameters (e.g., temperatures and pressures) The program starts by reading input from the control file to get required information It is also directed to the current database path The program will check if the species of interest from the control file are in the designated database If that is the case, calculations are ready for the next steps in separate modules that calculate energy barriers, ZPE corrections, moments of inertia, partition functions, entropies, and enthalpies Using these precalculated quantities, the rate constants and equilibrium constants are calculated at the conditions of interest Journal of Computational Chemistry 2014, 35, 1890–1899 1893 FULL PAPER WWW.C-CHEM.ORG Figure Flowchart of calculation modules in SurfKin Case study 1: Methane Decomposition on Ni(111) 1894 Methane decomposition on metal-based catalysts is a crucial process for methane steam reforming used mainly for hydrogen production and fuel cell applications There are many successful microkinetic models developed from both semiempirical UBI-QEP method, in combination with experimental data[10,11] and DFTbased calculations,[16,23] to investigate methane steam reforming over nickel under realistic conditions These studies have constructed full microkinetic models for methane steam reforming with detailed reaction mechanisms Simulations of reforming reactor models have been performed as well In this study, this methane decomposition system was used as a test case for the SurfKin application Specifically, thermodynamic and kinetic analyses were performed in the framework of DFT periodic calculations and classical statistical mechanics approach relaxed for all geometry optimizations The surface Brillouin zone is sampled with a (6 1) mesh based on Monkhorst–Pack scheme.[32] The ionic relaxation was stopped until ˚ A Methfesthe forces on all free atoms are less than 0.02 eV/A sel–Paxton smearing of 0.2 eV was applied.[33] The total energies are then extrapolated to kBT eV The ZPE corrections were calculated from DFT vibrational analyses, and dipole corrections are also included.[34] The total energy of methane was ˚ The calculated in a box with dimensions of 18 19 20 A gamma-point k point sampling is used The Gaussian smearing parameter is 0.01 eV To account for the magnetic properties of Ni, all calculations were performed with spin polarizations The TS structures were initially estimated using the climbing image-nudged elastic band method.[35,36] The dimer method was then used to further refine the determined TSs.[37,38] Vibrational frequencies were calculated Each TS was confirmed to have only one imaginary (negative) vibrational mode Computational details Reaction mechanism Periodic DFT calculations were performed using the VASP,[24–27] a periodic, plane wave-based code The ionic cores are described by the projector augmented wave method,[28,29] and the Kohn– Sham valence states were expanded in the plane wave basis sets up to 385 eV The exchange-correlation energy is described by the generalized gradient approximation with the revised PerdewBurke-Ernzerhof (RPBE) functional.[29,30] A three layer, close-packed Ni(111) surface with a vacuum of ˚ between successive metal slabs The DFT-determined lat12 A ˚ , which compares well with tice constant is found to be 3.52 A ˚ ).[31] A p(2 2) the experimental bulk lattice constant (3.52 A unit cell equivalent to 1/4 monolayer was used The top layer is The sequence of elementary steps is constructed within the Langmuir–Hinshelwood framework The detailed reaction mechanism is given in Table 1, with four elementary reaction steps (both directions on Table Elementary reaction steps for each step), including one methane dissociations on Ni(111) gas-phase species (i.e., CH4), five adsorbed speNo Reactions cies (i.e., CH3*, CH2*, CH*, CH4 2h* $ CH3* H* C*, and H*) and four TSs CH3* h* $ CH2* H* CH2* h* $ CH* H* (i.e., HACH3*, HACH2*, CH* h* $ C* H* HACH*, and CAH*) Note h* represents an active surface site that in this study we Journal of Computational Chemistry 2014, 35, 1890–1899 WWW.CHEMISTRYVIEWS.COM FULL PAPER WWW.C-CHEM.ORG Figure Calculated PES (ZPE correction included) at K for the decomposition of methane on Ni(111) The numbers in parentheses are the imaginary frequencies of the TSs The inset figure plots the free energies associated with methane decomposition on Ni(111) at 600 and 1073 K decomposition of methane From the energy differences between species in the PES, it is easily seen that the reactions via TS1, TS2, and TS4 are endothermic, while the reaction via TS3 is exothermic The temperature dependence will be discussed in the following sections The highest barrier occurs at the last step via TS4, breaking CAH bond; thus this step is probably the slowest step at K (113.0, 56.3, 29.9, and 127.4 kJ/mol for TS1, TS2, TS3, and TS4 routes, respectively) which is in good agreement with the trend proposed by Li et al.[39] However, the route via TS1 becomes the slowest step at higher temperature, which is consistent with earlier observations.[16,40,41] This issue will be discussed further in the kinetic analysis focus our effort on the decomposition of methane; thus subsequent important steps for the intermediate products in methane steam reforming, such as the formation and desorption of hydrogen, are not included These parameters are derived from DFT calculations The adsorption of methane is treated as a dissociative adsorption process to directly form CH3* and H* with a transition state (TS1 in Figure 3) The remaining adsorbed species, including the other TSs, are treated as strongly bound states with only vibrational contribution to thermodynamic properties Potential energy surface The calculated PES for methane decomposition over Ni(111) is shown in Figure 3, comparing to the values reported by Blaylock et al.,[16] where the gas-phase methane and clean Ni(111) surface is used as the reference state The vertical axis is the relative energies at K, the horizontal axis is the reaction coordinate The energies with ZPE corrections are used for discussion, otherwise it will be stated There are four TSs, that is, TS1 (HACH3*), TS2 (HACH2*), TS3 (HACH*), and TS4 (CAH*), for a complete Thermodynamic property analysis Table presents the thermodynamic properties, namely DHrxn , À Á 0 DSrxn , and Keq 5exp 2DGrxn =RT for each reaction step at 1073 K where the industrial steam methane reforming is actually performed If CH4* is treated as a weakly bound species, the DGorxn for the adsorption is highly positive of 131.8 kJ/ mol (or Keq is much smaller than unity) This indicates low Table Comparisons of thermodynamic and kinetic parameters calculated in this work and results from Blaylock et al.[16] at 1073 K (800 C) DHrxn (kJ/mol) [a] [b] No Reactions Cal CH4 2h* ! CH3* H*[c] 57.9 59.8 CH3* h*! CH2* H* 5.1 CH2* h*! CH* H* CH* h* ! C* H* Ref DSrxn (J/mol-K) [a] Cal Ref Keq [b] 2123.3 2124.0 3.0 24.4 21.0 237.4 238.0 28.2 214.0 52.1 54.0 22.0 22.0 Cal 5.48 3.85 3.27 6.45 2.46 1.28 1.28 1.79 3 3 3 3 [a] 10210 10210[b] 1021 1021[b] 1021 1021[b] 1023 1023[b] A (1/s) Cal [a] Ea (kJ/mol) Ref [b] Cal.[a] Ref.[b] 2.95 1011 – 117 4.2 1012 5.1 1013 58 66 1.2 1013 9.0 1012 32 26 5.2 1013 2.2 1014 133 135 – [a] This work Arrhenius prefactors A and activation energies Ea are fitted from TST rate constants over a temperature range of 300–1500 K [b] Blaylock et al.[16] [c] Due to a small energy difference between [CH4 (g) h*] and CH4*, CH4* can be considered as a physisorbed state and the initial states are CH4* (translation, rotation in 2D) and h* Journal of Computational Chemistry 2014, 35, 1890–1899 1895 FULL PAPER WWW.C-CHEM.ORG Table Prefactors A, activation energies Ea, and rate constants for methane decomposition on Ni(111).[a] Rate constants No Reactions CH4 2h* ! CH3* H* CH3* h* ! CH2* H* CH2* h* ! CH* H* CH* h* ! C* H* A (1/s) 2.95 4.20 1.20 5.20 3 3 Ea (kJ/mol) 11 10 1012 1013 1013 117 58 32 133 300 K 29 1.32310 3.83 102 3.05 107 3.65 10210 600 K 1.98 3.22 1.74 1.21 3 3 1073 K 10 107 1010 102 6.04 6.12 3.17 1.67 3 3 105 109 1011 107 [a] Prefactors A and activation energies Ea are obtained by fitting calculated rate constants to the simple Arrhenius expression over a temperature range of 300–1500 K coverage for CH4* and the desorption is more favorable at this high temperature This is consistent with early observation by Lee et al.[40] When compared with Blaylock’s data, which treated methane as an dissociative adsorption species, our numbers are in a good agreement (e.g., 57.9 kJ/mol, 2123.3 J/mol-K for enthalpy and entropy change of CH4 2h* ! CH3* H* compared with the corresponding numbers of 59.8 kJ/mol, and 2124 J/mol-K, respectively) In addition, it can be seen that equilibrium constants of reactions 1–4 are the same orders of magnitude, similar to the results from Blaylock et al.[16] at the same temperature, 1073 K The differences are within a factor of two, which is likely due to the uncertainty of different DFT parameters used in the two studies Such a good agreement with available literature values for this well-defined system provides us more confidence on our calculated numbers and our implementation Kinetic analysis The kinetic data for methane decomposition on Ni(111) is given in Table The parameters A and Ea are derived from fitting TST rate constants to the simple Arrhenius expression, k5A3exp ð2Ea =RTÞ, in a temperature range of 300–1500 K Table lists kinetic parameters at different temperatures for methane decomposition process on Ni(111) In this process, the rate constants for all elementary reactions show a trend that the rate constants increase with temperature Because the decrease of the equilibrium constant for the adsorption/desorption with temperature (as discussed earlier), the methane adsorption favors at low temperature energetically Comparison of calculated values to Blaylock’s results was presented in Table The highest activation energy, about 133 kJ/mol, occurs when reactants are passing through TS4 (Reaction in Table 2) This result can be compared to the value 135 kJ/mol suggested by Blaylock et al.[16] Moreover, the forward rate constants are much smaller than the reverse ones with the variation of temperature Energetically, the channel via TS4, CH* ! C* H*, is expected to be the rate-limiting step, the slowest step in the reaction network, due to its highest barrier of 127.4 kJ/mol at K (cf Figure 3) However, it is noticed that the entropy contribution to the rate constants for this reaction is larger than that of reaction (CH4 2h* ! CH3* H*, via TS1), reflected by the A-factor of 5.20 1013 and 2.95 1011 for these two reactions, respectively This make the later reaction (reaction 1) the slowest step at high temperature (e.g., k(1073 K) 6.04 105 vs 1.67 107 for reactions and 4, respectively) This is a demonstration of the importance of kinetic analysis in order to explain and/or pre1896 Journal of Computational Chemistry 2014, 35, 1890–1899 dict surface reaction pathways This observation is consistent with previous study, where the first CAH bond cleavage of CH4 is the rate-limiting step.[16,40,41] The good agreement with available data on thermodynamic properties and kinetics of methane dissociation on Ni(111) suggests SurfKin is an effective tool that integrates quantum mechanical calculations and statistical mechanics to study reactions on surfaces Case study 2: Water-Gas Shift Reaction on Ni(111) Water–gas shift reaction (WGSR), CO(g) H2O(g) Nið111Þ CO2(g) H2(g), plays a key role in reducing the side product, carbon monoxide, as well as boosting hydrogen production in steam reforming of methane This reaction has been studied extensively on a wide range of transition metal systems showing overall energetic trends,[42] singly on Cu,[43,44] Cu- based,[45] Pt,[46] Ni,[47] or coupling in steam reforming process on Ni.[10,16,48] Among these candidates, it has been shown that Ni is a good catalyst for this reaction though the reaction mechanism and kinetics on this surface are not fully understood.[47] In this second test case, the reaction mechanism, based on DFT calculations, for WGSR on Ni(111) is proposed and the thermodynamic and kinetic properties are analyzed using the SurfKin program Because there is no research developing full microkinetic model for WGSR on Ni(111) surface, our results will be compared to DFT calculations from Catapan et al.,[47] and the results extracting from the work of Blaylock et al.[16] Reaction mechanism The WGSR mechanism is described within Langmuir–Hinshelwood framework The sequence of elementary reactions (both forward and reverse directions) via the carboxyl species Table Elementary reaction steps of is the main channel, water–gas shift reaction on Ni surface showing in Table No Reactions There are four gas-phase H2O(g) h* $ H2O* species including CO(g), CO(g) h* $ CO* H2O(g), CO2(g), and H2(g); H2O* h* $ H* OH* six adsorbates, that is, CO* OH* $ COOH* *h CO*, H2O*, H*, OH*, COOH* h* $ COO* H* H2(g) 2h* $ 2H* COOH*, and COO*; and CO2(g) h* $ CO2* three TSs, that is, h* represents an active surface site HAOH*, COAOH*, and WWW.CHEMISTRYVIEWS.COM FULL PAPER WWW.C-CHEM.ORG Figure Calculated PES at K for WGSR on Ni(111) with the carboxyl formation pathway ZPE correction is included The free energy profiles along the reaction coordinate at different temperatures are shown on the right subfigure HACOO* For the adsorption of gas-phase species apart from H2(g), which is dissociative adsorption, the adsorption energies (including ZPE corrections) for CO(g), H2O(g), CO2(g) on Ni(111) surface, comparing to Blaylock’s results[16] given in the parentheses, are 2197.65 (2144.75), 20.34 (21.93), 0.82 (2.89) kJ/mol, respectively Small binding energies of H2O(g) and CO2(g) suggesting that these surface species will be treated as the free translational and rotational species on Ni(111) forward WGSR, the highest barrier occurs at the step via TS2, forming COOH* from CO* and OH* This is probably the slowest step at K (i.e., 127.63, 88.4, and 78.0 kJ/mol for TS2, TS1, and TS3 routes, respectively) It is worth mentioning that the finding on the lowest reaction step is via the carboxyl formation and energetic trend of the PES for WGSR on Ni(111) is in agreement with the recent DFT results from Catapan et al.[47] Potential energy surface Thermodynamic analysis Figure presents the PES for WGSR in the free energy landscape The gas-phase species, CO(g), and H2O(g), and the clean Ni(111) surface are used as the reference state The vertical axis is the relative electronic energies at K (including ZPE correction), the horizontal axis is the reaction coordinate There are three TSs, namely TS1 (HAOH*), TS2 (COAOH*), and TS3 (COOAH*) for the carboxyl energetic pathway From the energy difference between species in the PES, it is shown that the reaction via TS2 is endothermic, while the reactions via TS1 and TS3 are exothermic For the Thermodynamic properties for the WGSR on Ni(111) at the practical condition of steam reforming are shown in Table Only the carboxyl formation step via TS2 (reaction 4) is endothermic while the other reactions are exothermic The positive entropy change and negative enthalpy change for COO* forming via TS3 (reaction 5) indicated that this reaction is the most thermodynamically favorable reaction on the Ni(111) surface in the current selected pathway There is large entropy loss, and large negative enthalpy change associated with CO adsorption, resulting in stable adsorbed CO species Table Thermodynamic data at standard molar state for WGSR on Ni(111) at 600 and 1073 K No Reactions H2O h* ! H2O* CO h* ! CO* H2O* h* ! H* OH* (via TS1) CO* OH* ! COOH* h* (via TS2) COOH* h* ! COO* H* (via TS3) H2 2h* ! 2H* CO2 h* ! CO2* T (K) (kJ/mol) DHrxn DS0rxn (J/mol-K) DG0rxn (kJ/mol) 600 1073 600 1073 600 1073 600 1073 600 1073 600 1073 600 1073 23.2 21.5 2195.0 2187.0 220.8 212.4 93.8 91.8 292.0 2104.0 270.2 263.5 24.5 26.8 2106.6 2104.5 2159.0 2152.0 245.5 235.0 225.1 227.7 32.8 17.7 2131.6 2126.0 258.3 263.6 60.7 110.6 2100.0 224.0 6.4 25.3 108.9 121.6 2112.0 2123.0 8.7 71.7 30.5 61.5 Keq 5.14 4.10 4.59 1.47 2.75 5.86 3.30 1.20 5.44 1.02 1.74 3.23 2.21 1.02 3 3 3 3 3 3 3 1026 1026 108 101 1021 1022 10210 1026 109 106 1021 1024 1023 1023 Journal of Computational Chemistry 2014, 35, 1890–1899 1897 FULL PAPER WWW.C-CHEM.ORG Table Prefactors (A),[a] activation energies (Ea)[a] and rate constants for WGSR on Ni(111) Rate constants No Reactions H2O h* ! H2O* H2O* ! H2O h* CO h* ! CO* CO* ! CO h* H2O* h* ! H* OH* H* OH* ! H2O* h* CO* OH* ! COOH* h* COOH* h* ! CO* OH* COOH* h* ! CO2* H* CO2* H* ! COOH* h* H2 2h* ! 2H* 2H* ! H2 2h* CO2 h* ! CO2* CO2* ! CO2 h* A 1.23 2.26 9.86 1.19 3.78 5.82 1.35 3.06 3.84 2.66 3.43 2.17 7.86 1.07 [b] 3 3 3 3 3 3 3 Ea (kJ/mol) 13 10 1013 1012 1016 1010 1012 1012 1013 1013 1012 1013 1015 1012 1011 2.7 0.5 2.7 194.6 93.3(89.0[c]) 113.0 125.9 (111.0[c]) 31.8 83.3(97.0[c]) 176.5 2.4 69.5 2.7 4.6 300 K 4.19 1.79 3.36 1.42 3.81 1.28 1.53 9.98 1.52 1.40 1.43 1.66 2.68 2.01 3 3 3 3 3 3 3 600 K 12 10 1013 1012 10218 1026 1027 10210 107 1021 10218 1013 103 1012 1010 1073 K 12 7.18 10 2.64 1013 5.76 1012 2.37 1021 2.17 102 7.93 102 1.63 101 4.94 1010 1.89 106 6.95 1024 2.02 1013 2.32 109 4.59 1012 3.93 1010 9.10 2.47 7.30 5.55 1.05 1.80 1.08 8.96 3.35 6.56 2.71 9.39 5.82 6.38 3 3 3 3 3 3 3 1012 1013 1012 106 106 107 106 1011 109 103 1013 1011 1012 1010 [a] Prefactors A and activation energies Ea (kJ/mol) of the simple Arrhenius expression, kðTÞ5A3exp ð2Ea =RTÞ, are fitted from the calculated rate constants over a temperature range of 30021500 K unless otherwise noted [b] For the adsorption reactions 1, 2, 6, and 7, the rate constants (cm3/mol-s) are calculated from collision theory [cf eq (31)] For desorption processes, the rate constants (1/s) are derived from equilibrium constants and the adsorption rate constants, to which normalizing factor [RT/p] is added [c] From Blaylock et al.[16] 1898 on Ni(111) The equilibrium constant for this reaction is very large (4.59 108 at 600 K) and decreases by seven orders of magnitude at a temperature of real steam reforming condition (1.47 101 at 1073 K), showing that CO conversion is favorable at low temperature For the adsorption of H2O, H2, and CO2, there is much entropy lost at the reaction conditions comparing to enthalpy, which is equivalent to the increase of free energy with increasing temperatures This means that these processes are unfavorable at higher temperatures, which can be seen clearer at free energy profiles at 600 and 1073 K (cf Figure 4) The dissociation of H2O* via TS1 (reaction 3) seems to be disadvantageous at a higher temperature, but this reaction also has a rather high barrier and the increasing temperature is favorable for the kinetics The predicted thermodynamic properties are further confirmed by kinetic analysis quickly than V reaches the reaction enthalpy, DH00 [22] Within the collision theory, the calculated rate constant values for these adsorption processes seem to have similar orders of magnitude The calculated activation energies are compared to results from Blaylock et al.,[16] which are the values in the parentheses The maximum difference of activation energy is about 15 kJ/mol (125.9 vs 111 kJ/mol for this work and the literature, respectively), occurring at the reaction This discrepancy is much due to the DFT-calculated results for electronic energy barriers, that is, 124.7 versus 111.4 kJ/mol for this work and the literature, respectively In comparing between prefactors, the largest difference (3.78 1010 vs 1.4 1011 for this work and the literature, respectively) occurs at the breaking step of OH group from H2O* (reaction 3) This difference is in the acceptable range that gives the same order in the rate constant Kinetic analysis Conclusions Calculated kinetic information for WGSR on Ni(111) is given in Table The Arrhenius parameters, A and Ea, are independent of temperature and derived from fitting rate constants to Arrhenius expression in the temperature range of 300–1500 K The highest activation energy (125.9 kJ/mol) occurs at the carboxyl forming step (reaction 4), corresponding to a low rate constant (1.08 106 1/s) at 1073 K This rate constant is the same order of the one for breaking OH group (1.05 106 1/s) from H2O* (reaction 3), which makes reactions and the lowest reactions at the real reaction conditions The sticking coefficients for barrierless adsorption of gas-phase species, that is, CO, CO2, and H2O, were derived with the calculated adsorption potential (V) and the barrier height to migration (V0 ) on the surface with the similar assumptions made by Grabow et al.[46] Our calculation results are consistent with the common assumption of unity for all flat metal crystal faces as V0 is much smaller than V and goes to zero much more The C/C11 SurfKin program has been successfully developed in an attempt to construct microkinetic models for gassurface reactions Thermodynamic properties of reaction species were estimated based on ab initio calculations and statistical mechanics Rate constants for elementary steps (including adsorption, desorption and chemical conversion on surfaces) can be obtained using kinetics/dynamics models from, that is, collision theory and TST The good agreement with available data in the literature for the methane decomposition and WGSR on Ni(111) surface suggests this is a powerful tool using DFT calculation data to explore complex gas-surface reactions in a wide range of conditions and it opens a possibility to effectively construct detailed microkinetic mechanisms for modeling real complex processes The code currently does not include simulation on reactor models, as well as a graphical user interface (GUI) These features are being developed Journal of Computational Chemistry 2014, 35, 1890–1899 WWW.CHEMISTRYVIEWS.COM FULL PAPER WWW.C-CHEM.ORG Acknowledgments The authors greatly appreciate the computing resources and support provided by the Institute for Computational Science and Technology—Ho Chi Minh City, International University—VNU-HCMC, the high performance computing clusters hosted by Golden Energy Computing Organization (GECO) at Colorado School of Mines, and Fusion, a 320-node computing cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory Keywords: gas-surface reaction Á thermodynamics Á rate constant Á microkinetic mechanism Á methane decomposition Á water gas shift reaction How to cite this article: T Nguyen-Minh, B Liu, L K Huynh J Comput Chem 2014, 35, 1890–1899 DOI: 10.1002/jcc.23704 [1] R W McCabe, J Catal 1983, 79, 445 [2] G Papapolymerou, V 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statistical mechanics to study surface chemistry Rotational... acceptable range that gives the same order in the rate constant Kinetic analysis Conclusions Calculated kinetic information for WGSR on Ni(111) is given in Table The Arrhenius parameters, A and... with available literature values for this well-defined system provides us more confidence on our calculated numbers and our implementation Kinetic analysis The kinetic data for methane decomposition