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

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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:
[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

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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 5

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
1
;
qvibration 5 ðqvib Þi 5
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
1
ðIZZ Þ1=2 8p2 kB T
S02D2rotation ðTÞ5R ln
2
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 1 ZPE 1 U0corrections

(5)
(6)
(7)
(8)

G0 5H0 2TS0

(9)
P
1

where Eelectronic is the total electronic energy, ZPE5 2 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)

1
U02D2rotation ðTÞ5 RT
2

(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 3 10220 m2 assuming for the p(2 3 2) cell and the fcc,
hcp, and atop binding sites[16]).

(4)

bhcmi
 
i
exp hcm
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 1. Within the TST
framework, rate constant has the general form
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the surface. If it is a strong binding case (e.g., adsorption
0
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 1 hÃ

MÃTS ƒ!MÃ
For direct adsorption, rate constant can be expressed as
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 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
2
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

0
kB T qABÃTS
DETS
exp ð2
Þ;
h qAÃ qBÃ
kB T

(16)

where DETS is defined as
DETS 5ðE1ZPEÞABÃ 2 ðE1ZPEÞAÃ 2 ðE1ZPEÞBÃ
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
MÃ qMÃ
TS

TS

vib
qrot
M qM



DETS
exp 2
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


0
DETS; desorption
kB T qMÃTS
kdesorption ðTÞ5
exp 2
;
h qMÃ
kB T

(25)

where



kforward ðTÞ
DGrxn
5exp 2
Keq ðTÞ5 reverse
k

ðTÞ
kB T

(18)

and DGrxn 5DHrxn 2 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
2
vib
kB T
qrot

M qM
qvib
MÃ

Â
Ã
DETS 5ðE1ZPEÞMÃ 2 ðE1ZPEÞM 2ðE1ZPEÞhÃ

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.

AÃ 1 BÃ
ABÃTS ƒ!ABà 1 hÃ

NA h2
direct
kadsorption
ðTÞ5
2pmM kB T

DETS;

desorption 5ðE1ZPEÞMÃTS 2ðE1ZPEÞMÃ

(26)

Collision theory
Within the simpler collision theory framework, the adsorption
process can be written as following, with gas-phase M and
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adsorbed species MÃ , M 1 hÃ
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
5

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 5 NS 5 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 5

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
ðT; ½MŠÞ5NA ArðT Þ

(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
5
2pmM
C
2pmM

(31)

where C5 N1A 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 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 2. 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.
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Figure 2. 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 3 6 3 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 5 0 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 3 19 3 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 3 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 1. 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*,
1
CH4 1 2h* $ CH3* 1 H*
C*, and H*) and four TSs
2
CH3* 1 h* $ CH2* 1 H*
3
CH2* 1 h* $ CH* 1 H*
(i.e., HACH3*, HACH2*,
4
CH* 1 h* $ C* 1 H*

HACH*, and CAH*). Note
h* represents an active surface site.
that in this study we

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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 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 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.

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 0 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
0
Table 2 presents the thermodynamic properties, namely DHrxn
,
À
Á
0
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 2. 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.

1

CH4 1 2h* ! CH3* 1 H*[c]

57.9

59.8

2

CH3* 1 h*! CH2* 1 H*

5.1

3

CH2* 1 h*! CH* 1 H*

4

CH* 1 h* ! C* 1 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
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 3 1011

–

117

4.2 3 1012

5.1 3 1013

58

66

1.2 3 1013

9.0 3 1012

32

26

5.2 3 1013

2.2 3 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) 1 h*] and CH4*, CH4* can be considered as a physisorbed state and the initial states are
CH4* (translation, rotation in 2D) and h*.

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Table 3. Prefactors A, activation energies Ea, and rate constants for methane decomposition on Ni(111).[a]
Rate constants
No.
1
2
3
4

Reactions
CH4 1 2h* ! CH3* 1 H*
CH3* 1 h* ! CH2* 1 H*
CH2* 1 h* ! CH* 1 H*
CH* 1 h* ! C* 1 H*

A (1/s)
2.95
4.20
1.20
5.20

3
3

3
3

Ea (kJ/mol)
11

10
1012
1013
1013

117
58
32
133

300 K
29

1.32310
3.83 3 102
3.05 3 107
3.65 3 10210

600 K
1.98
3.22
1.74
1.21

3
3
3
3

1073 K
1

10
107
1010
102

6.04
6.12
3.17
1.67

3
3
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 1 2h* ! 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 calculated numbers and our implementation.
Kinetic analysis
The kinetic data for methane decomposition on Ni(111) is given
in Table 3. 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 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 calculated values to Blaylock’s results was presented in Table 2. The
highest activation energy, about 133 kJ/mol, occurs when reactants 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. Energetically, 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
(CH4 1 2h* ! CH3* 1 H*, via TS1), reflected by the A-factor of
5.20 3 1013 and 2.95 3 1011 for these two reactions, respectively. This make the later reaction (reaction 1) the slowest step
at high temperature (e.g., k(1073 K) 5 6.04 3 105 vs. 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 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) 1 H2O(g)
Nið111Þ
CO2(g) 1 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 4. Elementary reaction steps of
is the main channel,
water–gas shift reaction on Ni surface.
showing in Table 4.
No.
Reactions
There are four gas-phase
1
H2O(g) 1 h* $ H2O*
species including CO(g),
2
CO(g) 1 h* $ CO*
H2O(g), CO2(g), and H2(g);
3
H2O* 1 h* $ H* 1 OH*
six adsorbates, that is,

4
CO* 1 OH* $ COOH* 1 *h
CO*, H2O*, H*, OH*,
5
COOH* 1 h* $ COO* 1 H*
6
H2(g) 1 2h* $ 2H*
COOH*, and COO*; and
7
CO2(g) 1 h* $ CO2*
three TSs, that is,
h* represents an active surface site
HAOH*, COAOH*, and
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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.

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 0 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 4 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 0 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 5.
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 5. Thermodynamic data at standard molar state for WGSR on Ni(111) at 600 and 1073 K.

No.

Reactions

1

H2O 1 h* ! H2O*

2

CO 1 h* ! CO*

3

H2O* 1 h* ! H* 1 OH* (via TS1)

4

CO* 1 OH* ! COOH* 1 h* (via TS2)

5

COOH* 1 h* ! COO* 1 H* (via TS3)

6

H2 1 2h* ! 2H*

7

CO2 1 h* ! CO2*

T (K)

0
(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
3
3
3
3
3
3
3

1026
1026
108
101
1021
1022
10210
1026
109
106
1021
1024
1023
1023

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Table 6. Prefactors (A),[a] activation energies (Ea)[a] and rate constants for WGSR on Ni(111).
Rate constants
No.
1
2
3
4
5
6
7

Reactions
H2O 1 h* ! H2O*
H2O* ! H2O 1 h*
CO 1 h* ! CO*
CO* ! CO 1 h*
H2O* 1 h* ! H* 1 OH*
H* 1 OH* ! H2O* 1 h*
CO* 1 OH* ! COOH* 1 h*
COOH* 1 h* ! CO* 1 OH*
COOH* 1 h* ! CO2* 1 H*
CO2* 1 H* ! COOH* 1 h*
H2 1 2h* ! 2H*

2H* ! H2 1 2h*
CO2 1 h* ! CO2*
CO2* ! CO2 1 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
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
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. 3 10
2.64 3 1013
5.76 3 1012
2.37 3 1021
2.17 3 102
7.93 3 102
1.63 3 101
4.94 3 1010
1.89 3 106
6.95 3 1024
2.02 3 1013
2.32 3 109
4.59 3 1012
3.93 3 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
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 3 108 at 600 K) and decreases by seven orders of
magnitude at a temperature of real steam reforming condition (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 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 4. 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 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.

Kinetic analysis

Conclusions

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 carboxyl 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 3 106 1/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 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

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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

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

Journal of Computational Chemistry 2014, 35, 1890–1899

1899