DSpace at VNU: SurfKin: An Ab Initio Kinetic Code for Modeling Surface Reactions

Rate constants for elementary steps including adsorption, desorption, and chemical reactions on surfaces are calculated using the classi-cal collision theory and transition state theory.

SurfKin: An Ab Initio Kinetic Code for Modeling Surface

Reactions

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

classi-cal 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 implementa-tions 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 cata-lysts.V C 2014 Wiley Periodicals, Inc

DOI: 10.1002/jcc.23704

Introduction

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

essen-tially the starting point of developing a microkinetic model for

the understanding of the chemistry/physics occurring on

cata-lyst surfaces under realistic reaction conditions

Characteriza-tion 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

fit-ting 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

param-eters.[5,6] Due to its empirical nature, this practical method is

simple and effective to predict the energetics of surface

inter-mediates.[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

func-tional 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

advan-ces in DFT-based electronic structure calculations and

experi-mental techniques have validated the microkinetic models derived from the first-principles methods, which have become a bridge between microscopic properties and macroscopic per-formances.[12–18] Many microkinetic models have been devel-oped 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 thermo-dynamics,[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 first-principles calculations has become a powerful method for studying catalytic surface processes

In this article, we presented a C/C11 program called Surf-Kin (Surface Surf-Kinetics) for modeling gas–surface reactions from first-principles methods The code uses detailed kinetic mecha-nisms from DFT-based calculations Alternatively, it can be combined with the data obtained either from experiments or

[a] T N.-M Le , L K Huynh Molecular Science and Nano-Materials Laboratory, Institute for Computa-tional 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 Uni-versity, Vietnam National UniUni-versity, 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.)

V C 2014 Wiley Periodicals, Inc.

simulations (if available) to model complex chemical processes

in real conditions Statistical mechanics is used to estimate

ther-modynamic properties, such as entropies and enthalpies for

both gas-phase and adsorbed species Kinetic analyses are

per-formed 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

effec-tive tool that integrates quantum mechanical calculations and

statistical mechanics to study surface chemistry

Theoretical Methods

Statistical thermodynamic analysis

Thermodynamic properties (e.g., entropy and enthalpy) of the

reaction species were calculated using a well-established

statis-tical mechanical approach Details on thermodynamic property

calculations for gas-phase molecules can be found

else-where.[19] In this section, we only briefly describe the

imple-mentation 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

qtotal5qelectronic3qtranslation3qrotation3qvibration (1)

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

com-pared 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

parti-tion funcparti-tions to the total partiparti-tion funcparti-tion of a species of

interest

If a molecule strongly binds to the surface, translation and

rotation are considered as frustrated motions and thus

effec-tively 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 funcparti-tion for a weakly bound species on surface takes the

following form

q2DtranslationðA; TÞ5 2pmkBT

h2

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

character-izing for each single surface (a typical value of A for Ni(111) is

5.365 3 10220 m2 assuming for the p(2 3 2) cell and the fcc,

hcp, and atop binding sites[16])

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

q2Drotation5p

1=2

rh ðIZZÞ1=28p2kBT1=2

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 normal modes, the vibrational partition function is given by

qvibration5YN vib

i51

qvib

ð Þi5YN vib i51

1 12e2bhcm i

where b5 1

k B T, 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

S02D2translationðTÞ5R ln 2pmkBT

h2 A

11

(5)

S02D2rotationðTÞ5R ln p

1=2

rh ðIZZÞ1=28p2kBT1=2

11 2

(6)

S0vibrationðTÞ5RX

i

hcmi=kBT

ebhcm i212ln 12e

2bhcm i

(7)

H05Eelectronic 1 ZPE 1 U0corrections (8)

where Eelectronic is the total electronic energy, ZPE51

2

P

ihcmi is the zero point energy, the correction to the internal energy,

U0 corrections, includes all thermal corrections at standard molar state, namely

U0corrections5U0translation1U0rotation1U0vibration (10)

U02D2rotationðTÞ51

U0vibrationðTÞ5RTXN vib

i

bhcmi exp hcmi

k B T

 21

(13)

Transition state theory Conventional TST was applied to calculate rate constants for elementary reactions/steps which have intrinsic reaction bar-riers,[20] which can be depicted in Figure 1 Within the TST framework, rate constant has the general form

h

q0 TS

q0exp 2DETS

kBT

(14)

where q0

TS, q0 are the partition functions for the transition state (TS) and reactants with respect to its own ground states,

respectively The energy barrier DETSTSTS (or Ea in the

conven-tional notation) is the energy difference between the TS and

the reactant(s) On the surface, it is divided into three

individ-ual processes to calculate rate constants, namely adsorption,

desorption and reactions between adsorbed species

Reactions between adsorbed species The reaction scheme for

reactions between adsorbed species (cf Figure 1) can be

expressed as

A1 B

eq

ABTS m AB1 h (15)

The rate constants as a function of temperature for the forward

direction can be derived within the TST framework as follows

kforwardðTÞ5kBT

h

q0

AB  TS

qAqB

expð2DETS

kBTÞ; (16) where DETS is defined as

DETS5ðE1ZPEÞAB

TS2 ðE1ZPEÞA2 ðE1ZPEÞB (17)

To fulfill the thermodynamic consistency, the reverse rate

constant is derived from Van’t Hoff equation,

KeqðTÞ5k

forwardðTÞ

kreverseðTÞ5exp 2

DGrxn

kBT

(18) and DGrxn5DHrxn2 TDSrxn (19)

Adsorption of molecules Two adsorption models, direct

adsorption and indirect adsorption, are considered The main

difference is in how strong or weak the molecules binding to

the surface If it is a strong binding case (e.g., adsorption energy is larger than DH0

rxn) 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 pro-cess for molecule M in the gas-phase can be schematically presented as M 1 h

eq

M TS m

M For direct adsorption, rate constant can be expressed as

kdirectadsorptionðTÞ5 NAh

2 2pmMkBT

ffiffiffiffiffiffiffiffiffiffiffiffi

kBT 2pmM

s

rdirectð Þ;T (20)

where

rdirectð Þ5T q

vib

M  TS

qrot

Mqvib M

exp 2DETS

kBT

(21)

and

DETS5ðE1ZPEÞM

TS2ðE1ZPEÞM2ðE1ZPEÞh

(22) For indirect adsorption, TS is weakly bound to the surface The molecules can freely move on surface, thus they can con-tribute to translational, rotational and vibrational partition functions The rate constants can be described as

kindirectadsorptionðTÞ5NAA2

ffiffiffiffiffiffiffiffiffiffiffiffi

kBT 2pmM

s

rindirectð ÞT (23)

rindirectð Þ5T q

rot

M 

TSqvib

M  TS

qrot

Mqvib M

exp 2DETS

kBT

(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

kdesorptionðTÞ5kBT

h

q0

M  TS

qM exp 2DETS; desorption

kBT

; (25)

where

DETS; desorption5ðE1ZPEÞM

TS2ðE1ZPEÞM (26)

Collision theory Within the simpler collision theory framework, the adsorption process can be written as following, with gas-phase M and

Figure 1 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 ABTSare the adsorbed species at the TS [Color

fig-ure can be viewed in the online issue, which is available at

wileyonlineli-brary.com.]

adsorbed species M, M 1 h M(h is the active surface

site) Collision theory is used to calculate the rate of

adsorp-tion processes with the general formula[14,15]

radsorptioncollision 5Ar T; hcoverage

PM ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pmMkBT

kBT

where r T; h coverage

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

DEfis the activation energy for adsorption process It is

essen-tial to extract an adsorption rate constant depending only on

temperature from the general adsorption rate It should be

noted the site density is N05N

S51for a surface with N adsorp-tion sites and total surface area of S, each with an area of A

The sticking coefficient rðT; hcoverageÞ depends on the

tempera-ture 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

cov-erage r h coverage

.[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

PM5 n V

h i

Substitute the expanded form of sticking coefficient and eq

(28) into eq (27), the adsorption rate expression becomes

radsorptioncollision ðT;½MÞ5NAAr Tð Þ

ffiffiffiffiffiffiffiffiffiffiffiffi

kBT 2pmM

s exp 2DEf

kBT

V

h i (29)

From eq (29), the adsorption rate constant can be extracted

as

kcollision

adsorptionðTÞ5NAArðTÞ

ffiffiffiffiffiffiffiffiffiffiffiffi

kBT 2pmM

s exp 2DEf

kBT

(30)

The adsorption processes are usually nonactivated,[14] that

is, DEf50, so the adsorption rate constant can be rewritten in

a simpler form

kadsorptioncollision ðTÞ5NAArðTÞ

ffiffiffiffiffiffiffiffiffiffiffiffi

kBT 2pmM

s

5rðTÞ C

ffiffiffiffiffiffiffiffiffiffiffiffi

kBT 2pmM

s

(31)

where C5 1

N A A is the surface site density and the typical value

of C is 3.095 3 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 3 10220 m2.[16] The desorption rate

con-stants can be calculated through the equilibrium relations

rep-resented 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 adsorb-ate migration on surface) will affect the value of sticking coeffi-cient 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 position z (A˚) using formula proposed by Pitt et al.[22]

In this 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 Fig-ure 2 SurfKin program uses C/C11 language to take advan-tages 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, geo-metries, 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, par-tition 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 inter-est from the control file are in the designated database If that

is the case, calculations are ready for the next steps in sepa-rate modules that calculate energy barriers, ZPE corrections, moments of inertia, partition functions, entropies, and enthal-pies Using these precalculated quantities, the rate constants and equilibrium constants are calculated at the conditions of interest

Case study 1: Methane Decomposition on

Ni(111)

Methane decomposition on metal-based catalysts is a crucial

cess for methane steam reforming used mainly for hydrogen

pro-duction 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

DFT-based calculations,[16,23]to investigate methane steam reforming

over nickel under realistic conditions These studies have

con-structed 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

anal-yses were performed in the framework of DFT periodic

calcula-tions and classical statistical mechanics approach

Computational details

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

Perdew-Burke-Ernzerhof (RPBE) functional.[29,30]

A three layer, close-packed Ni(111) surface with a vacuum of

12 A˚ between successive metal slabs The DFT-determined

lat-tice constant is found to be 3.52 A˚, which compares well with

the experimental bulk lattice constant (3.52 A˚ ).[31]

A p(2 3 2) unit cell equivalent to 1/4 monolayer was used The top layer is

relaxed for all geometry optimizations The surface Brillouin zone is sampled with a (6 3 6 3 1) mesh based on Mon-khorst–Pack scheme.[32] The ionic relaxation was stopped until the forces on all free atoms are less than 0.02 eV/A˚ A Methfes-sel–Paxton smearing of 0.2 eV was applied.[33] The total ener-gies are then extrapolated to kBT 5 0 eV The ZPE corrections were calculated from DFT vibrational analyses, and dipole cor-rections are also included.[34]The total energy of methane was calculated in a box with dimensions of 18 3 19 3 20 A˚ The 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] Vibra-tional frequencies were calculated Each TS was confirmed to have only one imaginary (negative) vibrational mode

Reaction mechanism 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 each step), including one gas-phase species (i.e.,

CH4), five adsorbed spe-cies (i.e., CH3*, CH2*, CH*, C*, and H*) and four TSs (i.e., HACH3*, HACH2*,

HACH*, and CAH*) Note that in this study we

Figure 2 Flowchart of calculation modules in SurfKin.

Table 1 Elementary reaction steps for methane dissociations on Ni(111).

h* represents an active surface site.

focus our effort on the decomposition of methane; thus

sub-sequent 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

meth-ane 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

contri-bution 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 0 K, the horizontal axis is the reaction coordinate

The energies with ZPE corrections are used for discussion,

other-wise it will be stated There are four TSs, that is, TS1 (HACH3*),

TS2 (HACH2*), TS3 (HACH*), and TS4 (CAH*), for a complete

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 dis-cussed in the following sections The highest barrier occurs at the last step via TS4, breaking CAH bond; thus this step is prob-ably the slowest step at 0 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

Thermodynamic property analysis Table 2 presents the thermodynamic properties, namely DH0

rxn,

DS0 rxn, and Keq5exp 2DG0

rxn=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 spe-cies, the DGo

rxnfor the adsorption is highly positive of 131.8 kJ/

mol (or Keq is much smaller than unity) This indicates low

Figure 3 Calculated PES (ZPE correction included) at 0 K for the decomposition of methane on Ni(111) The numbers in parentheses are the imaginary

fre-quencies of the TSs The inset figure plots the free energies associated with methane decomposition on Ni(111) at 600 and 1073 K.

Table 2 Comparisons of thermodynamic and kinetic parameters calculated in this work and results from Blaylock et al.[16]at 1073 K (800  C).

3.85 3 10210[b]

6.45 3 10 21[b]

1.28 3 1021[b]

1.79 3 10 23[b]

[a] This work Arrhenius prefactors A and activation energies E a 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) 1 h*] and CH4*, CH4* can be considered as a physisorbed state and the initial states are

CH4* (translation, rotation in 2D) and h*.

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

meth-ane 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 CH412h*! CH3* 1 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

calcu-lated numbers and our implementation

Kinetic analysis

The kinetic data for methane decomposition on Ni(111) is given

in Table 3 The parameters A and Eaare derived from fitting TST

rate constants to the simple Arrhenius expression,

k5A3expð2Ea=RTÞ, in a temperature range of 300–1500 K

Table 3 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

calcu-lated values to Blaylock’s results was presented in Table 2 The

highest activation energy, about 133 kJ/mol, occurs when

reac-tants are passing through TS4 (Reaction 4 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

Ener-getically, the channel via TS4, CH*! C* 1 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 0 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 1

(CH412h* ! CH3* 1 H*, via TS1), reflected by the A-factor of

5.20 3 1013 and 2.95 3 1011 for these two reactions,

respec-tively This make the later reaction (reaction 1) the slowest step

at high temperature (e.g., k(1073 K) 5 6.04 3 105vs 1.67 3 107

for reactions 1 and 4, respectively) This is a demonstration of

the importance of kinetic analysis in order to explain and/or

pre-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)1H2O(g) Nið111Þ

CO2(g)1H2(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 show-ing 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 mecha-nism 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

is the main channel, showing in Table 4 There are four gas-phase species including CO(g),

H2O(g), CO2(g), and H2(g); six adsorbates, that is, CO*, H2O*, H*, OH*, COOH*, and COO*; and three TSs, that is,

HAOH*, COAOH*, and

Table 3 Prefactors A, activation energies E a , and rate constants for methane decomposition on Ni(111).[a]

Rate constants

[a] Prefactors A and activation energies E a are obtained by fitting calculated rate constants to the simple Arrhenius expression over a temperature range of 300–1500 K.

Table 4 Elementary reaction steps of water–gas shift reaction on Ni surface.

h* represents an active surface site

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,

compar-ing 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

spe-cies on Ni(111)

Potential energy surface

Figure 4 presents the PES for WGSR in the free energy

land-scape 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 0 K

(includ-ing ZPE correction), the horizontal axis is the reaction

coor-dinate 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

forward WGSR, the highest barrier occurs at the step via TS2, forming COOH* from CO* and OH* This is probably the slowest step at 0 K (i.e., 127.63, 88.4, and 78.0 kJ/mol for TS2, TS1, and TS3 routes, respectively) It is worth mention-ing that the findmention-ing 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]

Thermodynamic analysis Thermodynamic properties for the WGSR on Ni(111) at the practical condition of steam reforming are shown in Table 5

Only the carboxyl formation step via TS2 (reaction 4) is endo-thermic while the other reactions are exoendo-thermic The posi-tive entropy change and negaposi-tive 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

Figure 4 Calculated PES at 0 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.

Table 5 Thermodynamic data at standard molar state for WGSR on Ni(111) at 600 and 1073 K.

rxn (kJ/mol) DS 0

on Ni(111) The equilibrium constant for this reaction is very

large (4.59 3 108at 600 K) and decreases by seven orders of

magnitude at a temperature of real steam reforming

condi-tion (1.47 3 101 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

condi-tions comparing to enthalpy, which is equivalent to the

increase of free energy with increasing temperatures This

means that these processes are unfavorable at higher

tem-peratures, 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

con-firmed by kinetic analysis

Kinetic analysis

Calculated kinetic information for WGSR on Ni(111) is given in

Table 6 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

car-boxyl forming step (reaction 4), corresponding to a low rate

constant (1.08 3 106 1/s) at 1073 K This rate constant is the

same order of the one for breaking OH group (1.05 3 1061/s)

from H2O* (reaction 3), which makes reactions 3 and 4 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

Gra-bow 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

quickly than V reaches the reaction enthalpy, DH0.[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 lit-erature, respectively), occurring at the reaction 4 This discrep-ancy 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 prefac-tors, the largest difference (3.78 3 1010 vs 1.4 3 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

Conclusions

The C/C11 SurfKin program has been successfully developed

in an attempt to construct microkinetic models for gas-surface reactions Thermodynamic properties of reaction spe-cies were estimated based on ab initio calculations and statis-tical 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 decom-position 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 microki-netic mechanisms for modeling real complex processes The code currently does not include simulation on reactor mod-els, as well as a graphical user interface (GUI) These features are being developed

Table 6 Prefactors (A),[a]activation energies (E a )[a]and rate constants for WGSR on Ni(111).

Rate constants

[a] Prefactors A and activation energies Ea(kJ/mol) of the simple Arrhenius expression, kðTÞ5A3exp ð2E a =RT Þ, are fitted from the calculated rate con-stants over a temperature range of 30021500 K unless otherwise noted [b] For the adsorption reactions 1, 2, 6, and 7, the rate concon-stants (cm 3 /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]

The authors greatly appreciate the computing resources and

sup-port provided by the Institute for Computational Science and

Tech-nology—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 reactionthermodynamicsrate

con-stantmicrokinetic mechanismmethane decompositionwater

gas shift reaction

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Received: 21 January 2014 Revised: 13 July 2014 Accepted: 15 July 2014 Published online on 11 August 2014

in an attempt to construct microkinetic models for gas -surface reactions Thermodynamic properties of reaction spe-cies were estimated based on ab initio calculations and statis-tical mechanics... 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...

for reactions and 4, respectively) This is a demonstration of

the importance of kinetic analysis in order to explain and/or

pre-dict surface reaction pathways This observation