J. Phys. Chem. 1996, 100, 1615-1621
1615
Reaction of Isocyanic Acid and Hydrogen Atom (H + HNCO): Theoretical Characterization Minh Tho Nguyen,* Debasis Sengupta, Luc Vereecken, Jozef Peeters, and Luc G. Vanquickenborne Department of Chemistry, UniVersity of LeuVen, Celestijnenlaan 200F, B-3001-LeuVen, Belgium ReceiVed: April 12, 1995; In Final Form: October 25, 1995X
The potential energy surface related to the H + HNCO reactions has been explored by means of an ab initio molecular orbital method at the PUMP4/6-311++G(d,p) and QCISD(TC)/6-311++G(2df,2pd)+ZPE levels. The addition of H to N is confirmed to be the dominant reaction channel, giving the H2NCO radical as the primary intermediate and H2N + CO as the fragment products. The contribution of both C- and O-additions to H2NCO formation is negligible. The hydrogen abstraction requires an activation energy larger than that of N-addition but smaller than that of C- and O-additions. Using a quantum statistical Rice-RamspergerKassel (QRRK) model, the kinetics of the N-addition and H-abstraction have been analyzed. The following rate constant expressions in the temperature range 300-3300 K and at a pressure of 1 atm are suggested: for H + HNCO f H2N + CO (via H2NCO*), K ) 3.59 × 104T2.49 exp(-1180/T); for H + HNCO f H2NCO, K ) 1.63 × 1011T-1.90 exp(-1390/T); for H + HNCO f H2 + NCO, K ) 1.76 × 105T2.41 exp(-6190/T); and for H2 + NCO f H + HNCO, K ) 1.63 × 104T2.58 exp(-2720/T) in cm3 mol-1 s-1. Kinetic calculations using the exact stochastic method coupled with RRKM theory have also been performed which fully support the simplified QRRK treatment. Overall, calculated rate constants are in excellent agreement with available experimental values. Some thermochemical parameters have also been predicted (at 0 K): ∆H°f,o(H2NCO) ) 3 ( 8 kJ mol-1, IEa(H2NCO) ) 7.19 ( 0.2 eV, ∆H°f,o(H2NCO+) ) 696 ( 8 kJ‚mol-1, and PA(HNCO) ) 723 ( 8 kJ mol-1.
Introduction The development of effective after-treatment processes aimed at the removal of nitric oxide from combustion products continues to attract considerable interest. In the RAPRENOX process proposed by Perry and Siebers,1 isocyanic acid, which is formed following thermal decomposition of the injected cyanuric acid, has been assumed to play an important role as an initiator and precursor of NH2, an NO-reducing agent (eqs a-d).
HNCO f HN + CO
(a)
HN + NO f H + N2O
(b)
H + HNCO f H2N + CO
(c)
H2N + NO f HN2 + OH
(d)
While eqs a and b constitute the initiation steps, eq c is presumably the key step of the entire process. Mertens and co-workers2 studied the kinetics of the H + HNCO reaction in a shock heated mixture of HNCO diluted in argon and measured the second-order coefficient over the temperature range 2340-3270 K. They attributed this to be the formation of H2N + CO. In a subsequent theoretical study, Miller and Melius3 considered both channels c and e of the H + HNCO reaction.
H + HNCO f H2 + NCO
(e)
NCO + H2 f HNCO + H
(f)
These authors calculated the rate coefficients of reactions c and X
Abstract published in AdVance ACS Abstracts, January 1, 1996.
0022-3654/96/20100-1615$12.00/0
e employing BAC-MP4/6-31G(d,p) energies (bond additive correction-fourth-order perturbation theory) in conjunction with UHF/6-31G(d,p) geometries and vibrational wavenumbers. They found that eq c is the dominant product channel over a wide range of temperature (300-3300 K) and involves the H2NCO intermediate, whose formation constitutes the rate-determining step. The kinetic analysis has been carried out by Miller and Melius3 with some adjustment on the vibrational wavenumbers in order to obtain a qualitative agreement with experiment. In fact, the out-of-plane bending wavenumber of the transition structure for addition obtained by Hartree-Fock calculations was found to be low and replaced the value estimated with the second-order perturbation (MP2) calculation. In addition, no geometrical and energetic information was presented. In principle, isocyanic acid exhibits four distinct reaction centers susceptible to attack by the hydrogen atom. Reactions c and e arise from the addition of hydrogen atom to the N of HNCO and abstraction of H from HNCO, respectively. To our best knowledge, the C- and O-additions have not been investigated yet. It is thus important to assess the influence of other product channels on the NH2 formation and thereby to ascertain the predominance of channel c. On the other hand, the rate constant for the reverse reaction involving the NCO radical (reaction f) has also been measured in shock tube4 and excimer laser photolysis5 experiments. The purpose of the present study is to re-examine the H + HNCO reaction system by considering the attack of H at four possible sites of HNCO. Kinetic parameters have also been determined for reactions c, e, and f, making the use of highlevel quantum chemical calculations and statistical treatments. Results and Discussion Ab Initio Molecular Orbital Calculations of the Potential Energy Surfaces. All the calculations were carried out using © 1996 American Chemical Society
1616 J. Phys. Chem., Vol. 100, No. 5, 1996
Nguyen et al.
Figure 2. UMP2/6-31G(d,p) geometries for stationary points relevant to the C-addition.
Figure 1. UMP2/6-31G(d,p) geometries for stationary points relevant to the N-addition and H-abstraction.
a local version of the Gaussian 92 set of programs.6 Initial exploration of the energy surface and vibrational analysis of all the stationary points were done with the dp-polarized 6-31G(d,p) basis set in the unrestricted Hartree-Fock (UHF) framework. Geometrical parameters of the relevant equilibrium structures and transition structures were subsequently refined using second-order perturbation theory (UMP2/(6-31G(d,p)). Single-point calculations with the full-fourth-order MøllerPlesset perturbation correction to the energy using the 6-311++G(d,p) basis set were performed on the UMP2/6-31G(d,p) geometries (++ indicates a set of sp-diffuse functions on C, N, and O and s-diffuse functions on H). To account for the slow convergence of the MP expansions due to the spin contamination present in UHF references, a spin projection technique was applied to perturbation energies (PUMP4SDTQ). The UMP2/6-31G(d,p)-optimized geometries are displayed in Figures 1-3. Table 1 records the computed total PUMP4/6311++G(d,p) energies for the portion of the H2NCO surface considered here. The relative energies for the four channels of the H + HNCO reaction are shown schematically in Figure 4 whereas those related to the conversion of an O-adduct to the final products are illustrated in Figure 5. Concerning the numbering of the structures (except for the reactants H + HNCO 1), the first letter H, N, C, or O of each structure indicates its correspondence to the H, N, C, or O reaction, respectively; TS stands for transition structure. Throughout this paper, bond lengths are given in angstroms, bond angles in degrees, total energies in hartrees, and zero point vibrational energies (ZPE’s) and relative energies in kilojoules per mole. All the H2NCO structures possess a 2A′ electronic ground state. It can be seen from Figure 4 that the addition of H to N is confirmed to be the most favorable process involving the
Figure 3. UMP2/6-31G(d,p) geometries for stationary points relevant to the O-addition.
carbon-centered radical N2 (H2N-CO) as an intermediate. N2 turns out to be the most stable adduct and has a planar and strongly bent geometry. The associated barrier to the linearity of N2 via NTSc is substantial (141 kJ mol-1, Table 1). The barrier for addition to N via NTSa is smaller than that for fragmentation of N2 via NTSb giving H2N + CO. Nevertheless, NTSa lies higher in energy than NTSb, making the former the rate-controlling step. The hydrogen abstraction via HTS is characterized by a slightly larger barrier height than the N-addition and a small endothermicity. While the addition of H to the C of HNCO through CTSa giving C2 has an energy barrier similar to that of the H-abstraction, the addition to O requires a much larger activation energy (Figure 4). The energy ordering of the TS for N-, C-, and O-additions could be qualitatively understood on the basis of frontier orbitals. The addition is mainly controlled by the SOMO(H)-LUMO(HNCO) interaction. In
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J. Phys. Chem., Vol. 100, No. 5, 1996 1617
TABLE 1: Total, Zero Point, and Relative Energies of the Points Related to the H + HNCO Reaction structurea 1 (H + HNCO) N2 (H2NCO) N3 (H2N + CO) NTSa: 1 f N2 NTSb: N2 f N3 NTSc: N2 f N2 H2 (H2 + NCO) HTS: 1 f H2 C2 (HNCHO) C3 (HNCHO) CTSa: 1 f C2 CTSb: C2 f N2 O2 (HNCOH) O3 (HNCOH) OTSa: 1 f O2 OTSb: O2 f N2 OTSc: O3 f C2 OTSd: O3-inversion
PUMP4b ∆E 6-311++G(d,p) ZPEc PUMP4+ZPE 〈S2〉d -168.843 24 -168.891 09 -168.861 49 -168.830 27 -168.853 73 -168.835 67 -168.832 53 -168.815 95 -168.837 61 -168.839 79 -168.820 29 -168.803 74 -168.855 12 -168.856 16 -168.807 72 -168.787 53 -168.794 94 -168.793 79
53.9 84.2 61.5 58.9 74.0 79.8 49.5 47.7 83.6 83.7 60.6 67.4 83.4 82.9 59.7 70.8 67.4 75.4
40.3 -55.0 0.0 79.4 33.8 86.1 64.0 105.7 84.7 79.1 107.3 157.5 38.7 35.4 139.4 203.5 180.6 191.6
0.750 0.762 0.758 0.836 0.784 0.765 0.835 0.813 0.762 0.761 0.811 0.801 0.787 0.784 0.845 0.761 0.801 0.785
a On the basis of UMP2/6-31G(d,p) geometries. b Using spinprojected perturbation theory. c Zero point vibrational energies from UHF/6-31G(d,p) calculations and scaled by 0.90. d Expectation 〈S2〉 values of UHF references.
Figure 5. Schematic potential energy profile showing the conversion of an O-adduct to H2N + CO via a C-adduct and an N-adduct. Values obtained from PUMP4/6-311++G(d,p)+ZPE calculations.
mol-1) lie much higher in energy than that associated with the N-addition (79 kJ mol-1). This implies that the contribution of the C- and O- additions to the formation of the N-adduct N2 is expected to be negligible. In order to obtain reliable thermochemical and kinetic parameters, we have performed single-point energy calculations of the structures optimized at the UMP2/6-31G(d,p) level on both N-addition and H-abstraction reaction paths using the quadratic configuration method and the larger 6-311++G(2df,2pd) basis set. We have obtained the QCISD(TC) energies assuming the following additivity relationship:
TC ) E(QCISD(T)/6-311++G(d,p)) E(QCISD(6-311++G(d,p)) E(QCISD(TC)/6-311++G(2df,2pd)) ) E(QCISD/6-311++G(2df,2pd)) + TC
Figure 4. Schematic potential energy profiles showing the four H + HNCO reactions. Values obtained from PUMP4/6-311++G(d,p)+ZPE calculations. The ZPE’s were obtained from UHF/6-31G(d,p) wavenumbers and scaled by 0.9.
the LUMO of HNCO the N atom bears, in fact, the larger MO coefficient followed by those of C and O.7 Both adducts C2 and O2 could be directly converted to their more stable isomer N2 by 1,2- and 1,3-shift of the hydrogen, respectively. The associated energy barriers are rather high, especially for the one-step O2 f OTSb f N2 process. Nevertheless, there exists a lower-energy multistep reaction path connecting an O-adduct to the final products. Figure 5 shows the minimum energy route O3 f OTSc f C2 f CTSb f N2 linking the O-, C-, and N-adducts. The energetics illustrated in Figures 4 and 5 clearly show that, even in the most favorable case, the transition states associated with the formation and transformation of the O- and C-adducts (at 181 and 157 kJ
Figure 6 shows the relative schematic potential energy diagrams for the N-addition and H-abstraction at the QCISD(TC)/6-311++G(2df,2pd)+ZPE level; the available experimental values for the fragments8 are also included for comparison. The ZPEs have also been recalculated using the UMP2/631G(d,p) level and scaled by 0.95. Note that the heat of formation of the NdCdO radical is actually not well established.9 It is also useful to estimate some energetic quantities associated with the H2NCO adduct N2. It is calculated to be 73 and 105 kJ mol-1 more stable than the reactants H + HNCO and products H2N + CO, respectively. Combination of these values and the experimental heats of formation (namely, ∆H°f at 0 K in kJ mol-1: H, 216; HNCO, -109; H2N, 192; and CO, -1148) leads to the two values 2 and 5 kJ mol-1 for the heat of formation of H2NCO at 0 K. Another way of deriving the latter value requires the knowledge of its ionization energy and the heat of formation of the corresponding cation. At the QCISD(TC)/6-311++G(2df,2pd)+ZPE level, its adiabatic ionization energy amounts to 7.19 eV. Regarding the standard heat of formation of the H2NCO+ cation, there are actually two different experimental values. While the first of 700 kJ mol-1 was given in the compilation of Lias et al.8 (using PA(HNCO) ) 725 kJ mol-1), the second value of 672 kJ mol-1 was originally reported by Wight and Beauchamp10 and recently confirmed by Hop et al.11 (giving PA(HNCO) ) 759 kJ mol-1). Our results rather advocate the smaller value of the two reported proton affinities. In fact, calculations at the same level of theory provide PA-
1618 J. Phys. Chem., Vol. 100, No. 5, 1996
Nguyen et al. SCHEME 1 H + HNCO
H2NCO*
H2N + CO N3
H2NCO N2
Figure 6. Schematic potential energy profile showing the H-abstraction and N-addition using higher-level QCISD(TC)/6-311++G(2df,2pd)+ZPE calculations. The ZPE’s were obtained from UMP2/6-31G(d,p) wavenumbers and scaled by 0.95.
TABLE 2: Unscaled Vibrational Wavenumbers of HNCO, H2NCO (N2), and Transition Structures for the H + HNCO f H2NCO (NTSa), H2NCO f H2N + CO (NTSb), and H + HNCO f H2 + NCO (HTS) Processesa HNCO N2 NTSa NTSb HTS a
564.4, 617.4, 791.9, 1315.0, 2376.1, 3792.3 133.3, 531.7, 634.7, 1107.7, 1268.4, 1656.9, 1912.0, 3654.8, 3842.6 2716.6i, 324.6, 516.7, 665.7, 846.9, 1155.0, 1325.9, 2265.5, 3788.4 531.2i, 100.9, 352.6, 790.7, 860.6, 1600.0, 2050.2, 3477.6, 3589.1 1598.7i, 287.5, 593.6, 650.2, 656.2, 829.6, 1295.2, 2406.8, 2569.8
i refers to the imaginary frequency; at the UMP2/6-31G(d,p) level.
(HNCO) ) 723 kJ mol-1 and, thereby, ∆H°f,o(H2NCO+) ) 696 kJ mol-1 at 0 K, with a probable error of about (8 kJ mol-1 (using ∆H°f,o(H+) ) 1528 kJ mol-1). Using the calculated ) 7.19 eV and values IEa(H2NCO) ∆H°f,o(H2NCO+) ) 696 kJ mol-1, we obtain ∆H°f,o(H2NCO) ) 2 kJ mol-1, a value consistent with those derived above from the energies of the fragments. It is thus reasonable to propose an average value, ∆H°f,o ) 3 ( 8 kJ mol-1 at 0 K. Table 2 displays the unscaled vibrational wavenumbers for a few important species involved in the reactions H + HNCO to NH2 + CO (via addition of H to the N of HNCO) and H2 + NCO (via direct hydrogen abstraction) which have been utilized later to calculate the frequency factors. In summary, the addition of H to the N center of HNCO is confirmed to be the most favorable reaction channel via the primary formation of the H2NCO radical. In the following section, a kinetic analysis of the formation of H2N + CO will be considered. Moreover, the formation of H2 + NCO and its reverse process by direct hydrogen abstraction will also be analyzed. Quantum Statistical Analysis of Reactions c, e, and f. In this part, we calculate the rate constants for the various reaction
pathways arising from the addition of H to the nitrogen center of HNCO using the quantum statistical Rice-RamspergerKassel (QRRK) theory.12 We use the chemical activation process13 to treat the nonequilibrium situation that arises due the very high energy release during the formation of the adduct radical, H2NCO. The amount of excess energy is stored as quantized vibrational energy in the adduct molecule and can be utilized to overcome the barrier for further reaction. The RRK theory14 takes into account the probability of localization of a certain amount of energy, which is necessary to cross the barrier, in the appropriate vibrational mode. The reactions in Scheme 1 involve the competition between the stabilization and dissociation of the energized adduct and should not be treated as elementary single-step reactions. Recent publications12,15 reveal that the formation of the energized adduct with a non-Boltzmann distribution can be accurately treated by the QRRK theory. The details about the methodology and algorithm are discussed in refs 12 and 14. Dean12 has developed a useful scheme for the calculation of the apparent rate constant for a recombination reaction as a function of temperature and pressure. We consider the following scheme: k1
R + R′
A*
k2(E)
products
k–1(E) βks[M]
A
which is very similar to Scheme 1 and where M is the bath gas (argon for the present study), A* the energized adduct, and the ki(E)’s are the energy dependent rate constants calculated according to RRK theory.14 The input data required are (1) frequency factors and (2) activation barriers. The frequency factors (AF) were obtained from the following equation:
AF )
kbT Q# h Q
(1)
where Q# and Q are the complete partition functions of the transition state and reactants, respectively, T is the temperature in Kelvin, and h is Planck’s constant. It can be shown that with this frequency factor, the high-pressure limit of the RRK expression for a dissociation reaction, is equal to the transition state theory equation. The partition functions were obtained from the ab initio calculated harmonic vibrational wavenumbers and moments of inertia calculated at the UMP2/6-31G(d,p) level. As the MP2-calculated vibrational wavenumbers are in general higher than the observed values, a constant scaling factor of 0.95 has been used. The activation barriers and the energy released during the formation of H2NCO have been taken from the calculation at the QCISD(TC)/6-311++G(2df,2dp)+ZPE level, as shown in Figure 6. The collisional stabilization rate constant, ks, has been calculated following the equation given by Troe16 using the Lennard-Jones collision rate. This author17 proposed a simple and now widely used approximation for calculating the collisional stabilization efficiency, β. The equation is given by
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J. Phys. Chem., Vol. 100, No. 5, 1996 1619
-〈E〉 β ) F EkbT 1 - xβ
(2)
where -〈E〉 is the average energy transferred per collision (220 cm-1 for Ar18) and FE is a factor which reflects the energy dependence of the density of states. FE has been calculated using the expression suggested by Gardiner and Troe18 which uses the vibrational density of states according to the Whitten and Rabinovitch approximation.19 Equation 2 is valid only when 1 e FE e 3,18 but at very high temperature FE may exceed 3. For this reason β has been calculated following the equation suggested by Gilbert et al.20
β)
〈E〉d/(〈E〉d + FEkbT) F kT E -E ∫0E0f(E) 1 - 〈E〉 +E Fb k T exp - F0EkbT d E b
[
(
)]
(3)
where 〈E〉d is the average energy transferred per collision in the down transition, E0 is the threshold energy for the dissociation of the adduct, and f(E) is the density of states. The denominator of eq 3 has been calculated by a numerical method, and the Whitten-Rabinovitch approximation19 was used to calculate f(E). The value of 〈E〉d for Ar has been taken from ref 21 (260 cm-1). Values of 〈E〉 and 〈E〉d are assumed to be temperature independent. The rate constants for the direct hydrogen abstraction processes (i.e., for processes e and f) have been calculated following the equation given by
( )
k ) AF exp -
E0 kbT
(4)
The role of tunneling during hydrogen transfer reactions, especially in the low-temperature region, is well established.22 Since all the reactions under investigation involve the transfer of hydrogen, it is essential to include a tunneling correction for the rate constants. The symmetric Eckart potential23 is often used24 to include the contribution of hydrogen tunneling to the rate constant. The symmetric Eckart potential is given by23
V(x) )
V* cosh [xx(F*/2V*)] 2
(5)
where x is the reaction coordinate, V* is the activation barrier, and F* is the curvature at the potential energy maximum. The Schro¨dinger equation for the Eckart potential can be solved, and for an incident particle of mass µ and energy E, the probability of tunneling is given by23
K(ζ) )
cosh(2Rxζ) - 1 cosh(2Rxζ) + coshx4R2 - π2
(6)
where ζ ) E/V*, R ) 2πV*/hν*, and ν* is the absolute value of the imaginary frequency at the saddle point. The tunneling correction (qc), which is the ratio of the quantum mechanically calculated rate constant to that calculated classically, is given by the following equation22
( )∫
qc ) exp
E0 kbT
( )
1 -E dE K(ζ) exp kbT kbT
∞
0
(7)
The integration in eq 7 was solved by a numerical method.
Figure 7. Variation, with temperature, of the rate constants for all the reaction pathways arising from the reaction of H + HNCO. Experimental plots taken from ref 2 are also shown (see text for definitions).
In the present case, the tunneling correction, qc, has been multiplied by the rate constants for the processes H + HNCO f NH2CO and H + HNCO f H2 + NCO to include the tunneling effect. We define the rate constants as
Kc
H + HNCO f NH2 + CO (via NH2CO*)
Ks
H + HNCO f NH2CO
Ke
H + HNCO f H2 + NCO
Kf
H2 + NCO f H + HNCO
The total rate constant (Kt) for the disappearance of the reactants (i.e., H and HNCO) can be written as
Kt ) Kc + Ks + Ke The energy interval of hν was chosen for the calculation of rate constants by the QRRK method, where ν is the geometrical mean of the scaled vibrational wavenumbers of H2NCO. The variation of Kc, Ks, and Ke with temperature at 1 atm of pressure as shown in Figure 7 reveals that the tunneling is important in the lower temperature region. At higher temperatures, the tunneling corrections for all the reactions approach unity. The rate constant for the formation of H2 + NCO is much lower than that for NH2 + CO. Formation of the stabilized adduct, NH2CO, remains unimportant almost within the entire temperature range studied here (300-3300 K). The lower value of Ks is due to the very low collision efficiency, β. The value of β changes from 6.9 × 10-5 to 3.4 × 10-6 as the temperature increases from 300 to 3300 K. At higher temperatures, both Kc and Ke attain nearly the same value. For example, at 3300 K, Kc ) 1.2 × 1013 cm3 mol-1 s-1 and Ke ) 7.5 × 1012 cm3 mol-1 s-1. Experimental values of the total rate constant (Kt) for H + HNCO are available only in the temperature range 2340-3270 K.2 For comparison, the experimental values of Kt are also plotted in Figure 7. It can be seen that our calculated values are in excellent agreement with the available experimental results.2 For example, at 3200 K, our calculated value of Kt is 1.82 × 1013 cm3 mol-1 s-1, which compares well with the experimental value of 1.47 × 1013 cm3 mol-1 s-1. The rate constants Kc and Ke vary between 1.47 × 109 to 1.24 × 1013 and 3.0 × 102 to 7.48 × 1012 cm3 mol-1 s-1, respectively, in the temperature range 300-3300 K. Figure 7 also indicates
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Figure 8. Variation of Kc (H + HNCO f H2N + CO) and Ks (H + HNCO f H2NCO) with respect to pressure at 1000 K.
that the rate constant for the disappearance of the reactants (Kt) is primarily due to the formation of the H2N + CO channel. At this stage it will be interesting to judge the validity of the collisional stabilization process, βks[M] (β from eq 3), by comparing it with the more rigorous biexponential model of Troe.25 For this purpose RRKM calculations were carried out using the Monte Carlo simulation technique, based on the exact stochastic method.26 The biexponential model was used to calculate the collisional energy transfer. The whole calculation was performed using the URESAM program.27 The detailed algorithm will be published elsewhere. As far as we are aware, the stochastic method is applied here for the first time to model the time evolution of a chemically activated system. Calculations were performed at two different temperatures, namely 300 and 1500 K, with a pressure of 1 atm. Results of the RRKM calculations show that a negligible amount of the stabilized adduct is formed from the energized H2NCO. For example, about 0.001% and 0.0002% of the total H2NCO* formed from H + HNCO are stabilized at 300 and 1500 K, respectively. This clearly supports the use of βks[M], a simpler approach, to calculate the rate constant for stabilization of the energized adduct. Figure 8 displays the variation of the rate constants Kc and Ks with respect to pressure at 1000 K. It shows that Ks does not reach its high-pressure limit even at a pressure of ∼103 atm. The rate constant of the formation of NH2 + CO (Kc) is independent of pressure within the pressure range studied and remains always higher than Ks. This indicates that, even at very high pressure, the disappearance of the reactants is primarily due to the formation of NH2 + CO. It should be noted that the pressure dependence of Ke cannot be shown, as the high-pressure Arrhenius equation has been used (eq 4). To our knowledge, there is no experimental data available for Ke, but there are two experimental reports4,5 on the kinetic study of the reaction NCO + H2 f H + HNCO, which is the reverse process of reaction e. In order to compare the results of our calculation with experiment, we also calculated the rate constant for the reaction NCO + H2 f H + HNCO following eq 4. Figure 9 shows the variation of the calculated values of Kf as a function of temperature and compares the experimental values within the available temperature range (i.e., 592-913 and 1490 K). The calculated values of Kf fall well within the uncertainty of the experimental results. Finally, we have fitted our calculated rate constants for the various pathways with the following modified Arrhenius
Nguyen et al.
Figure 9. Variation, with temperature, of the rate constant for the H2 + NCO reaction. Experimental results shown are taken from ref 5.
equation
(
k ) ATn exp -
E RT
)
(8)
to obtain the exponent n, the effective frequency factor A, and the activation barrier E/R. Hence we suggest the following expressions for the rate constants at a pressure of 1 atm (in cm3 mol-1 s-1) in the temperature range 300-3300 K:
( 1180 T ) 6190 exp(T )
Kc ) 3.59 × 104T2.49 exp Ke ) 1.76 × 105T2.41
(
Ks ) 1.63 × 1011T(-1.90) exp -
(
Kf ) 1.63 × 104T2.58 exp -
1390 T
)
2720 T
)
Conclusions The potential energy surface corresponding to several possible pathways arising from the reaction H + HNCO has been calculated using higher-level ab initio molecular orbital theory. The results of our calculation confirm that the addition of H atom to the nitrogen center of HNCO, forming the H2NCO radical intermediate, is the dominating pathway. A detailed kinetic analysis in the framework of QRRK theory has been carried out for the addition of H atom to the nitrogen center of HNCO and the hydrogen abstraction reaction NCO + H2. While the formation of NH2 + CO is much faster than that of H2 + NCO at lower temperatures, their rate converge at higher temperatures. The contribution of tunneling was found to be unimportant at the higher temperatures. Formation of the stabilized adduct, H2NCO, is unimportant at all temperatures and pressures. A similar conclusion regarding the stabilization of the energized adduct is drawn via more rigourous RRKM calculation with a biexponential model of collisional stabilization. The calculated values of the rate constants for the various pathways are in good agreement with the experimental results. The expressions for the rate constants, based on a modified Arrhenius equation, have been suggested over a wide range of temperatures. Finally, the ionization energy and heat of formation of the H2NCO radical have been predicted; the heat of formation of the H2NCO+ cation and the proton affinity of HNCO have also been re-evaluated.
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