Abstract. Using ab-initio calculations at the MP2/6-311++G(3df, 2pd), a very high level
theory, we obtained minimum energy structures for the C2H5O radical, products and
transition states of reactions on the potential energy surface. The decomposition reactions
of the C2H5O radical include three reactions: C2H5O → CH3 + HCHO (1); C2H5O →
CH3CHO + H (2) and C2H5O → CH2OCH2 + H (3). Remarkably, the TS-3 transition state
and (3) reaction are not found on the previous studies. The rate constants at the
high-pressure limit of the (1), (2) and (3) reactions were calculated using the transition
state theory (TST) and the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The
pressure-dependent rate constants of decomposition reactions were analyzed and solved
using the RRKM theory and the master equation method. The temperature and pressuredependent rate constant of three reactions were k(T, P) (1) = 1.072.108 x P0.873exp(-
2706.41/T); k(T, P) (2) = 5.379.103 x P1.774exp(-2902.8/T) and k(T, P) (3) = 3.849.10-33 x
P8.645exp(-5554.5/T). The result shows that, at low-temperature the rate constants of
reactions (1) and (2) depend on low-pressure and are nearly independent of high-pressure
while the rate constant of reaction (3) depends on both low and high pressure. At hightemperature, the rate constants of the three reactions depend on pressure

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JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2015-00077
Chemical and Biological Sci. 2015, Vol. 60, No. 9, pp. 44-50
This paper is available online at
Received September 28, 2015. Accepted December 17, 2015.
Contact Nguyen Ngoc Ha, e-mail address: hann@hnue.edu.vn
44
THEORETICAL STUDY OF TEMPERATURE-AND PRESSURE-
DEPENDENT RATE CONSTANT FOR UNIMOLECULAR
DECOMPOSITION REACTIONS OF C2H5O RADICAL
Nguyen Ngoc Tri1,2 and Nguyen Ngoc Ha1
1
Faculty of Chemistry, Hanoi National University of Education
2
Faculty of Chemistry, Quy Nhon University
Abstract. Using ab-initio calculations at the MP2/6-311++G(3df, 2pd), a very high level
theory, we obtained minimum energy structures for the C2H5O radical, products and
transition states of reactions on the potential energy surface. The decomposition reactions
of the C2H5O radical include three reactions: C2H5O → CH3 + HCHO (1); C2H5O →
CH3CHO + H (2) and C2H5O → CH2OCH2 + H (3). Remarkably, the TS-3 transition state
and (3) reaction are not found on the previous studies. The rate constants at the
high-pressure limit of the (1), (2) and (3) reactions were calculated using the transition
state theory (TST) and the Ric -Ramsperger-Kassel-Marcus (RRKM) theory. The
pressure-dependent rate constants of decomposition reactions were analyzed and solved
using the RRKM theory and the master equation method. The temperature and pressure-
dependent rate constant of three reactions were k(T, P) (1) = 1.072.108 x P0.873exp(-
2706.41/T); k(T, P) (2) = 5.379.103 x P1.774exp(-2902.8/T) and k(T, P) (3) = 3.849.10-33 x
P8.645exp(-5554.5/T). The result shows that, at low-temperature the rate constants of
reactions (1) and (2) depend on low-pressure and are nearly independent of high-pressure
while the rate constant of reaction (3) depends on both low and high pressure. At high-
temperature, the rate constants of the three reactions depend on pressure.
Keyword: Unimolecular reaction, RRKM, temperature- and pressure-d pendent rate constant.
1. Introduction
Alkoxy radicals are important immediates in reaction processes, organic chemistry
reactions, and atmospheric chemistry. Moreover, those are oxygen-containing compounds,
obtained from hydrocarbon combustion processes, reactions of hydrocarbon with species,
such as O, O2, OH, NO3 or from unimolecular decomposition reactions of ancol, peroxit or
dialkoxyl [1-6]. Recently, experimental and theoretical studies have been performed with
simple alkoxy radicals such as CH3O, C2H5O and C3H7O [6-8] but more interesting are the
unimolecular decomposition reactions with C-H and C-C bond dissociations. Among the
alkoxy radicals, C2H5O is the simplest radical contained in both C-C and C-H bonds.
Theoretical study of temperature-and pressure-dependent rate constant for unimolecular...
45
Theoretical and experimental studies on the decomposition reaction of the C2H5O radical
were performed using different level of theory [2, 8-12]. However, these studies focused only
on the temperature-dependence of the rate constant while the pressure-de endent rate constant
waas examined in detail. Generally, the pressure factor has a significant role in the
unimolecular reaction rate, as has been stated in previous studies [13, 14]. Th refore, an
investigation learn more about the pressure-depend nt rate constant of the C2H5O radical is
important and more interesting.
2. Content
2.1. Computational method
The calculations were performed at the MP2/6-311++G(3df, 2pd) high level of theory
using Gaussian 03 program [15]. Geometry structures of the reactant, products and transiti n
states were optimized at the MP2/6-311++G(3df, 2pd) level. Single point energy of species
were carried out at the CCSD(T)/6-311++G(3df, 2pd) very high level of theory with geometry
obtained at the MP2/6-311++G(3df, 2pd) level. The kinetics of the reactions were observed
using TST and RRKM theory [16] and Chemrate program [17]. The reaction rate constant
was calculated in the temperature range of 200 - 2500 K, taking the quantum tunneling effect
by Wigner into account [8]. The pressure-d pendent rate constant was computed using the
master equation method [13, 18]. In the present work, pressure was measured in the range of
0.01 to 100 atm and the collisional rate between C2H5O and He bath gas was calculated using
parameters of Leonard-Jones (He: σ = 2.55 Å, ε/kT = 10 K; C2H5O: σ = 4.53A, ε/kT = 326.6 K),
with the transfer energy 1dE 200cm
[2, 10].
2.2. Results and discussion
2.2.1. Geometry structure of reactants, products and transition states
Optimized geometries for C2H5O radical, products and transition states calculated at the
MP2/6-311++G(3df, 2pd) high level of theory are shown in Figure 1. Some experimental data
for C2H5O radical and products are listed in Table 1.
C2H5O CH3 HCHO CH3CHO
CH2OCH2 TS-1 TS-2 TS-3
Figure 1. Geometry structure of C2H5O radical, products and transition states
(Length: Å, angle:
o
)
Nguyen Ngoc Tri and Nguyen Ngoc Ha
46
Calculated results show that geometry parameters for C2H5O radical and products are in
approximate agreement with experimental data in which the deviation of distance and angle is
about 0.001 - 0.011 Å and 0.02 - 1.740o, respectively (as shown in Table 1). Therefore, the
MP2/6-311++G(3df, 2pd) theory level is in good agreement for this investigated system.
In addition, structure parameters of the transition states obtained in our study were compared
with those in previous studies and the distance of C-C and C-H bonds in TS-1 and TS-2
transition states are in approximate agreement with the obtained results in previous papers
(RC-C in TS-1 in the range of 2.06 - 2.25 Å, RC-H in TS-2 in the range of 1.61 - 1.87 Å) [1, 2, 6, 8-10].
Remarkably, the decomposition reaction of the C2H5O radical through transition state TS-3 o
form CH2OCH2 has not been reported in previous papers. The degree of product formed and
passing through TS-3 reaction pathway is analyzed more clearly below.
Table 1. Experimental data of the C2H5O radical and products
C2H5O CH3CHO CH2OCH2 HCHO
rC1H2 1.086 rC1C5 1.501 rC1C4 1.459 rC1H2 1.111
rC1H3 1.085 rC5O7 1.216 rC1O7 1.425 rC1O4 1.205
rC1C5 1.521 rC1H3 1.086 rC1H2 1.084 aH2C1H3 116.1
rC5H6 1.088 rC5H6 1.114 aC1O7C4 61.6 aH2C1O4 121.9
rC5O8 1.388 aC1C5O7 123.9 aH2C1H3 116.8
aH2C1H4 108.1 aH3C1H4 108.3 aH2C1C4 119.1
aH2C1C5 110.8 aH6C5C1 117.5 aH2C1O7 114.7
aC1C5O8 114.4 aC1C4O7 59.2
(r: length, Å; a: angle,
0
) [19]
2.2.2. Thermodynamic parameters for decomposition reactions of the C2H5O radical
The most common reaction pathways for investigated systems with potential energy
barriers are shown in Figure 2. Decomposition reactions of C2H5O radical include:
C2H5O → CH3 + HCHO (1); C2H5O → CH3CHO + H (2)
and C2H5O → CH2OCH2 + H (3).
Thermodynamic parameters for these reactions were calculated at the same level and are
shown in Table 2.
Figure 2. Correlation energy for reactions calculated
at the MP2/6-311++G(3df,2pd) level
Theoretical study of temperature-and pressure-dependent rate constant for unimolecular...
47
As shown in Table 2, the reaction energy (ΔE0, ΔEZPE) and Gipps energy at 298 K
(ΔG0298) of the (1), (2) and (3) reactions are quite positive. Therefore, (1), (2) and (3)
reactions are unlikely to occur at 298 K thermodynamically. In particular, ΔE0, ΔEZPE and
ΔG0298 values in the reactions increase in the order (1) < (2) <(3), thus in (1) via (2) final (3)
reactions, the possibility of reaction decreases. Moreover, enthalpy energies calculated at 298 K
(ΔH0298) for these reactions are positive and therefore endothermic reactions. Correlation
energies calculated for the transition states in the reactions increase in the order (1) < (2) < (3),
so the occurring degree of reactions decreases in the order (1) > (2) > (3). As a result, the (3)
reaction is very unlikely to occur. On the other hand, in previous studies, the range of ΔE, ΔE#
and ΔH# energies values for (1) reaction are 5.24 - 8.16 kcal.mol-1, 16.19-23.66 kcal.mol-1
and about 17.21 kcal.mol-1, respectively; for (2) reaction about 20.00 kcal.mol-1, 13.17 - 14.99
kcal.mol-1 and about 20.27 kcal.mol-1, respectively [2-5, 8, 9]. Thus, thermodynamic
parameters obtained in this study are in good agreement with those presented in previous
studies.
Table 2. Thermodynamic parameters for reactions at the MP2/6-311++G(3df,2pd) level
(kcal.mol
-1
)
Reaction ΔE0 ΔEZPE ΔH298
0 ΔG298
0
ΔE# ΔH# ΔG#
(1) 14.81 8.99 10.78 0.19 18.57 18.77 18.24
(2) 20.34 13.75 13.67 14.26 21.97 22.05 21.95
(3) 46.76 41.55 40.99 42.58 55.44 55.09 55.85
(
#
for transition states)
3.3. Dependence of the rate constant on temperature and pressure for
decomposition reactions of the C2H5O radical
Using transition state theory (TST) with quantum tunnel effect followed by the Wigner,
we obtained rate constants for decomposition reactions of the C2H5O radical, as shown in
Figure 3.
Figure 3. The temperature-dependent rate constant k(T)
for (1), (2) and (3) reactions at the MP2/6-311++G(3df, 2pd) level
Nguyen Ngoc Tri and Nguyen Ngoc Ha
48
Using the Origin program, we analyzed temperature-dependent rate constants of reactions
following the three parameters Arrhenius expression: k∞(T) = A'xT
n x exp(-Ea/RT) (with T in
the given range of 200 - 2500 K). Analysis results by TST obtained rate constants of reactions
such as: k∞(T) (1) = 8.371. 0
9 x T0.482exp(-8995.0/T) s-1 (R2 = 1.000); k∞(T) (2) =
9.497.109 x T0.469exp(-10577.7/T) s-1 (R2 = 1.000); k∞(T) (3) = 9.639.10
9 x T0.468exp(-
27635.7/T) s-1 (R2 = 1.000). From these obtained expressions, we found that, the k(T) rate
constant depends on T temperature with the high linear correlation. For the (3) reacti n, at
low-temperature, thereaction rate constant is much smaller than its in (1) and (2) reactions.
However, at high temperature, the rate constant of the (3) reaction is quite large. Thus, the (3)
reaction should be more closely investigated and considered at high temperatures, som thing
which in previous studies.
Using the RRKM theory and master equation method, the pressure-d pendent rate
constant at different temperatures of the (1), (2) and (3) reactions carried out at the MP2/6-
311++G(3df, 2pd) level with He bath gas used to invoke particle collision are illustrated in
Figure 4.
Figure 4. Pressure-dependent rate constant at some temperatures
for the (1), (2) and (3) reactions
As shown in Figure 4, the rate constant of the (1) reaction is greater than in the (2)
reaction and is much larger than in the (3) reaction. Moreover, calculating about the
temperature-and pressure-d pendent rate constants for these reactions we obtained three
expressions: k(T, P) (1) = 1.072.108 x P0.873exp(-2706.4/T) atm.s-1; k(T, P) (2) = 5.379.103 x P1.774
exp(-2902.8/T) atm.s-1 and k(T, P) (3) = 3.849.10-33 x P8.645exp(-5554.5/T) atm.s-1. The results
in this study show that, at low temperatures (ranging from 200-500K) the rate constant of (1)
and (2) reactions depend linearly on pressure when the pressure range is low (0.01-1atm), and
are almost independence of pressure when the pressure range is high (about 100 atm). In the (3)
reaction, the rate constant depends strongly on pressure in this entire temperature range. In the
high temperature range (1000 - 2500 K), the rate constants for three reactions are linearly
dependent on pressure.
The rate constants for those reactions calculated in this work are quite consistent with
experimental and theoretical results shown in previous studies. Specifically, the experimental
result for the (1) reaction calculated by Caralp et al. [2] was k∞(T) = 1.10
13exp(-8455.0/T) s-1
in the temperature range 391- 471 K with He collision particles; according to Batt [2] it was
k∞(T) = 8.0.10
13exp(-10825.4/RT) s-1; according to Fenter e al. [2] it was k490K(T) = 7.10
4 s-1
Theoretical study of temperature-and pressure-dependent rate constant for unimolecular...
49
in 760 Torr with N2 collision particles; according to Leggett and Thyme [8] it was k(T) =
1.41.1012exp(-11102.2 ± 890.8/T) s-1 in the temperature range 422 - 429 K and according to
Batt and Milne [8] it was k(T) = 1.0.1015exp(-10900.9 ± 543.5/T) s-1 in the temperature range
435 - 491 K. At 298 K, the experimental rate constant for the (1) reaction obtained by Baulch
et al. was k298K = 1.9.10
-2 s-1 while according to Heicklen it was k298K = 0.13 s
-1, according to
Choo and Benson it was k298K = 0.76 s
-1 and according to Baldwin et al. it was k298K = 6.5.10
-3 s-1 [8].
In the (2) and (3) reactions, we obtained experimental result regarding reaction rate
constants. Our results obtained at the MP2/6-311++G(3df, 2pd) level are in good agreement
with those of previous studies. Particularly, the rate constant of the (2) reaction obtained by
Caralp et al. [2] at the QCISD(T)/6-311+G(3df, 2p) level was k(T) = 1.3.1013exp(-10103.4/T) s-1;
according to Hoyermann et al. [5], at MP2/6-311+G**//MP2/6-31G* it was k(T) =
6.31.1013exp(-12100.1/T) s-1; according Rauk et al. [6] at the B3LYP/6-31G(d) level it was
k(T) = 2.45.1013exp(-10536.4/T) s-1; according to Viskolcz et al. [9] at the QCISD(T)/6-
311+G(3df, 2p) level it was k(T) = 1.49. 0-2, 2.29.104 and 2.94.107 at temperatures of 298,
500 and 750 K, respectively; according to M. C. Lin et al. [11], in 1atm, in the temperature
range 300 - 1000 K it was k(T) = 1.331038 x T-8.61exp(-12839/T) s-1 and according to Zhang
et al. [12] at QCISD(T)/aug-cc-pVTZ//MPWIK/6-31+G(d, p) with temperatures in the range
of 200 - 2500 K it was k(T) = 1.30. 09 x T1.42exp(-10.300/T) s-1.
3. Conclusion
Performing calculations at the MP2/6-311++G(3df, 2pd) high level of theory we obtained
the minimum-energy structures for the C2H5O radical, products and transition states on the
potential energy surface. It is notable that, the reaction pathway through the TS-3 t ansition
state to form CH2OCH2 has never before been reported before. Single point energies of the
species in this study were carried out at the CCSD(T)/6-311++G(3df, 2pd)//MP2/6-311
++G(3df, 2pd) high level. Rate constants for decomposition reactions of the C2H5O radical
were calculated using the transition state theory (TST) and the RRKM theory. The results
show a high linear correlation between rate constant and temperature. In addition, the
temperature-and pressure-dependent reaction rate constants obtained using the master
equation method vielded three expressions: k(T, P) (1) = 1.072.108 x P0.873exp(-2706.4/T);
k(T, P) (2) = 5.379.103 x P1.774exp(-2902.8/T) and k(T, P) (3) = 3.849.10-33 x P8.645
exp(-5554.5/T). Accordingly, the (1) reaction occurs stronger than the (2) reaction and much
stronger than the (3) reaction. All results calculated in this paper are in good agreement with
experimental and theoretical results of previous studies.
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