КИНЕТИКА И КАТАЛИЗ, 2013, том 54, № 6, с. 711-716
THEORETICAL STUDIES ON THE KINETICS AND MECHANISM OF THE REACTION OF ATOMIC HYDROGEN WITH CARBON DIOXIDE
© 2013 V. Saheb
Department of Chemistry, Shahid-Bahonar University of Kerman, Kerman 76169, Iran E-mail: email@example.com Received 31.10.2012
The potential energy surface for the reaction of hydrogen atom with carbon dioxide is explored by using various quantum chemical methods including W1BD, CBS-QB3, G4, G3B3, CCSD(T), QCISD(T), CCSD, M06-2X, and BB1K. Transition state theory and a modified strong collision/RRKM model are employed to calculate the thermal rate coefficients for the reaction. The results of calculation show that the overall rate constant for the reaction H + CO2 are pressure-independent over the temperature range of 300 to 3500 K. By using the energies at the W1BD level, the non-Arrhenius expression k = 9.8 J29 exp(—74.8 kJ/mol/RJ) L mol s-1 was found for the reaction.
The reaction of hydrogen atom with carbon dioxide plays an important role in hydrocarbon combustion
[I]. Several attempts have been made to obtain the kinetic parameters of this reaction [1—10]. For the first time, Fenimore and Jones determined the Arrhenius expression for the H + CO2 reaction by measuring the concentrations of H and CO2 on a cooled porous burner over the temperature range of 1217 to 1345 K [2, 3]. Dixon-Lewis et al. determined the Arrhenius parameters for the reaction at 1072 K by measuring the rate of reduction of CO2 to CO in the burnt gas region of a fuel-rich hydrogen-oxygen-nitrogen flame [4, 5]. Using a supersonic molecular beam sampling technique coupled with a mass spectrometric measurements in the reaction zone of a lean carbon monoxide-hydrogen-oxygen flame, Kochubei and Moin studied the kinetics of the reaction CO2 + H . In the latest study, the rate coefficient of the reaction H + CO2 ^ CO + OH was measured using OH concentration measurements in shock-heated N2O + H2 + CO2 mixture . The reverse process, that is the reaction of OH radicals with CO, producing H atom and CO2, was the subject of more than eighty experimental and theoretical studies
[II]. However, no theoretical kinetic study is reported on the reaction H + CO2. The potential energy surface (PES) of the reaction H + CO2 is essentially the same as that of the CO + OH reaction. In the present study, the PES of the reaction is re-investigated by various methods of high-level electronic structure calculation. The transition state theory and modified strong colli-sion/RRKM model are employed to calculate the thermal rate coefficients. The computed rate constants are compared with the available experimental data.
Electronic structure calculations
Various high-level quantum chemical calculations were employed to evaluate the accurate geometries, energies and rovibrational properties of all stationary points, i.e., minimum energy structures and saddle points. In order to compute accurate energies, the high-level composite methods CBS-QB3 , G3//B3LYP , G4  and W1BD  were employed. These methods are combinations of many single point energy calculations on the geometries optimized by B3LYP/CBSB7, B3LYP/6-31+G(d),B3LYP/GTBas3 and B3LYP/cc-pV(T + d)Z methods, respectively. G3//B3LYP is a variation of Gaussian-3 (G3) theory in which the geometries and zero-point energies are obtained from B3LYP method instead of geometries from MP2 method and zero-point energies from Hartree-Fock method. G4 is the most recent procedure in the Gaussian-n series of quantum chemical methods in which the average absolute deviation from experimental energies was significantly improved. W1BD theory is the unrestricted Brueckner doubles of the Weizmann-1 theory (W1) . W1 and W1BD methods are more expensive and more accurate than CBS-QB3, G3B3 and G4 methods and are often employed as benchmarks in the absence of accurate experimental data.
The hybrid meta density functional methods (HMDFT), BB1K , M06-2X  methods along with the 6-31 + G(d,p) and MG3S basis sets  were also used for the purpose of comparison. These methods are optimized against a representative database of very high-level calculations of saddle point geometries
and energies, and give remarkably accurate barrier heights with slight deterioration of reaction energetics.
The highest-level geometry optimizations performed here involve unrestricted coupled cluster method with single and double excitations (UCCSD) , employing the standard 6-311+G(2d,2p) basis set. Energies at all of the stationary points were then recalculated with the unrestricted coupled cluster method with single, double, and noniterative triple excitations UCCSD(T) and the unrestricted quadratic configuration interaction with single, double, and noniterative triple excitations UQCISD(T)  in combination with the standard augh-cc-pVTZ+2dfbasis set . All electrons were included in the correlation calculations.
Vibrational frequencies were computed at the B3LYP/CBSB7, BB1K/MG3S and CCSD/6-311+ +G(2d,2p) levels of theory. All of the quantum chemical calculations were performed with the Gaussian 09 package of programs .
As it will be discussed in detail in the next section, the reaction proceeds via the saddle points TS1 and TS2, leading to the chemically activated intermediates INT1 and INT2, respectively. These intermediates decompose to yield the reactants and products, or can be activated by molecular collisions. In this research, RRKM theory is used to compute the rate constants for the decomposition of these vibrationally excited adducts to different products [23, 24]. According to the RRKM theory, the energy-specific rate constant for unimolecular reaction is given by the following equation:
obtained the following expression for the overall rate coefficient :
k(E) = a
Qi hp (E)'
k = _2iL_e(-EJRT) x h QaQb
J+ k (E v+r )}e (-E+/RT )dE +
n 1(0 + ke + K\
where G(E+r) is the sum of active vibrational and rotational states for the transition state, p(E) is the density
of active quantum states for reactant, Q+ and Q1 are the partition functions for the adiabatic rotations in the
transition state and reactant. Values of G(Ev+r) and p(E) are computed by the Beyer—Swinehart direct count algorithm . In this investigation, the values of
k(E), p(E) and G(Ev+r) are calculated by using RRKM program from Zhu and Hase . Transition state theory with the application of RRKM theory to the uni-molecular decomposition of the chemically activated intermediates, was used to compute the rate constants for the reaction channels R1 and R2. By applying steady-state approximation to the activated intermediates in such reaction mechanisms, Berman and Lin
Here, ke and k'e are the energy-specific rate constants for unimolecular decomposition of the intermediates to the reactants and products, respectively. The total partition functions for reactants A and B excluding electronic degrees of freedom are given by qA and qB
while qfr is the product of translational and rotational partition functions for the transition state of entrance channels. a is the reaction path degeneracy and Be is the quotient of electronic partition functions oftransition state and reactants. To compute the integral in the equation (2), a step size AE+ = 0.4 kJ/mol up to 400 kJ/mol was used. The rate constant for de-energization of the activated adducts (®) is given by
® = Pc^coll, (3)
where Zcoll is the collision frequency and Pc is the collision efficiency. Here, the data for the viscosity of gaseous molecules are used to estimate the collision diameters and the collision frequencies. Troe  has obtained the following expression for Pc:
Pc = (((down/((( down + W))2, (4)
where FE is the energy dependence of the density of states and (AE) down is the average energy transferred in a deactivating collision. No experimental data is available for ZaE of the intermediates studied in the
\ / down
present research. In fact, energy transfer parameters are poorly known for many molecules. Joshi and Wang  found that a value of 260 cm-1 reproduces the experimental data for pressure dependences of OH + CO reaction. This value is employed to compute the integral (2). We found that using the values 30 cm-1 higher or lower than 260 cm-1 in the equation (2) does not affect meaningfully the calculated rate coefficients.
Here, the tunneling for Eckart potential barrier  is used to compute the tunneling correction factor, which can be expressed as an integral over the energy E,
expVi/R T ) J K exp (—E/ kBT ) dE/kBT,
where V1 is the height of the potential barrier, and K is the transmission probability for tunneling. K depends on E and some parameters, which are determined by the shape of the barrier and effective mass for the sys-
180.0 180.0 180.0
1.160 1.148 1.159
1.160 1.148 1.159
157.8 158.8 157.6
118.4 118.0 114.9
1.167 1.153 1.163
1.206 1.192 1.208
1.355 1.329 1.340
109.4 110.8 108.8
0.958 ' O 0.962
, O6 \ 1.364 1.176 129.3 1.339
1.173 129.7 1.369
91.5 93.5 95.8
n \ / 0.975
O / 2.249O
/ 2.180 124.1 1.976
0.977 0.965 ...
1.325 1.308 1.333
109.8 130.3 J08.4130.7 / , 130.3
99.6 100.1 99.6
1.542 H1.480 1.541
1.182 1.172 1.182
160.6 159.9 160.6 TS4
1.182 1.172 1.182
99.7 100.1 99.6
0.965 O 0.954
1.183 1.170 1.180
126.7 127.5 127.3
1.175 1.161 1.172
106.0 100.3 109.3
1.299 1.277 1.299
1.226 1.275 O 1.225 1.178 1.165 1.175
1.164 H1.128 1.168
108.2 109.3 108.0
1.217 1.182 1.224
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