Calculation of Parameters of O (a1Δ ) Reactions 2 for … of Parameters of O 2 (a 1Δ g) ... g), 3...

21st

International Symposium on Plasma Chemistry (ISPC 21) Sunday 4 August – Friday 9 August 2013

Cairns Convention Centre, Queensland, Australia

Calculation of Parameters of O2(a1Δ g) Reactions

for Low-Temperature Mechanism of Methane Oxidation

Maxim Deminsky1,2

, Alexander Lebedev2, Andrey Zaitzevsky

2 and Boris Potapkin

1,2

1 National Research Centre "Kurchatov Institute", Moscow, Russia

2KintechLab, Moscow, Russia

Abstract: The important for low-temperature oxidation reactions of electronically excited

oxygen O2(a1Δg) with methyl radical are investigated theoretically by state-of-art quantum

chemical methods. It was found that the association reaction has a threshold with energy of

8.5 kcal/mole. The data obtained was used for kinetic analysis of excited oxygen formation

and reaction in non-equilibrium plasma.

Keywords: singlet oxygen, plasma

1. General

Singlet Oxygen O2(a1Δg) has lately become a

subject of intense research because of possible its capabil-

ity of significantly enhancing the combustion of hydro-

carbons. Although some efforts were made in modeling

methane combustion involving singlet oxygen [1], a reli-

able theoretical model based on first-principles calcula-

tions is required. The most interesting effect of O2(a1Δg)

is the involvement of this molecule into the reactions of

chain initiation and chain propagation. The potential effi-

ciency of O2(a1Δg) can be high for chain propagation,

because each excited oxygen molecule could stimulate the

production of a greater number of active radicals. At low

temperatures, the shift of the reaction equilibrium towards

the chain branched mechanism and the acceleration of

chain propagation may provide excited oxygen with an

additional possibility for enhancing HC combustion. This

effect could be achieved using, for example, cold

non-equilibrium plasmas [1]. Simulation of this effect

requires accurate information about the rates of elemen-

tary processes involving chain propagation. In fact, an

inaccuracy of 5 kcal mole in the energetic parameters of a

reaction at temperatures below 900 K changes the reac-

tion rate by about one order of magnitude and may be-

come a reason for the incorrect conclusions about the

pathways of oxidation in the mechanism. A kinetic model

of methane-air combustion in the presence of O2(a1Δg)

was proposed in several works. [1,2]. Theses models were

focused on the behavior of ignition time and flame veloc-

ity at elevated temperatures (T>1600K) when sensitivity

to accuracy of used rate constants with participation of

O2(a1Δg) is low. Presumably, this is why reactions in-

volving O2(a1Δg) are estimated within a rather rough ”vi-

bronic terms” model. Nevertheless, this model can be

regarded as a basis for the comprehensive theoretical de-

scription of combustion process stimulated by O2(a1Δg).

One of the key reactions of singlet oxygen in

an air-methane mixture is the reaction with the methyl

radical:

, which correlate with following channels of reaction of

CH3 with oxygen in the ground state:

Unfortunately, there are no experimental data on the rate

parameters of the process 1a. Only several ab initio cal-

culations of this reaction have been performed so far [3,

4]. However, the difference in approaches used for calcu-

lations of the Potential Energy Surface (PES) for CH3 +

O2(a1Δg) may lead to a contradiction in the conclusions

about the input of this reaction to the total oxidation

mechanism. The difference in conclusions about the ab-

sence [4] or presence [3] of a threshold of the reaction

together with the sufficiently great discrepancy for the

excitation energies (26.3 kcal/mole , 24.6 kcal/mole ) with

respect to the table value (22.5 kcal mole ) makes the ef-

fect of the error propagation of ab-initio calculations upon

the final value of the oxidation rate at low temperatures

strongly undetermined. Thus, the accuracy of the models

and calculations discussed above is not sufficient for

making an unambiguous conclusion about the role of

O2(a1Δg) in methane oxidation at low temperatures. The

aim of this study was to find out the principal reactions

involving excited oxygen, which provide the maximal

sensitivity with respect to the overall kinetic parameters

(induction time) and to evaluate the microkinetic charac-

teristics of the key elementary reactions using

state-of-the-art computational methods.

2. Ab-initio calculation of rate constants of O2(a1Δg)

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reactions.

The Potential Energy Surface of the system

CH3 + O2(X3Σ; a

1Δg) was investigated at the

multireference configuration interaction (MRCI) level of

theory [5] in the triple-zeta basis set of Dunning and Hay.

To obtained accurate data, MRCI level of theory was used

with two different active space spans. The smaller active

space was consisted of 3 electrons on the 4 molecular

orbitals MRCI (3/4), while largest one was MRCI(7/5).

Results achieved with two different active spaces give

notably different values of the energy for reagents CH3

and O2(a1Δg) on the

2A′ term. Application of

size-extensivity corrections (Davidson’s, Pople’s meth-

ods) permits to smooth that difference and converges both

results to single energy point. It was concluded that

smaller (MRCI(3/4)) and larger active space (MRCI(7/5))

give regular under and overestimation of the results. Da-

vidson correction was applied to MRCI energies in order

to obtain the correct depth of the well on the ground

term( 2A′′). Finally, the potential energy surface obtained

by the MRCI(7/5) approach was selected for further anal-

ysis as the best fit for known thermodynamics data. For

example, calculated energy of the excitation (0.99 eV)

and the well depth of CH3O2 in ground state (1.301 eV)

are in good agreement with experimental values (0.98 and

1.34±0.04 eV respectively). Figure 1 presents the result-

ing PES. The activation energy of the process (1a) is as

high as 0.28 eV

Fig.1 PES for system CH3 + O2(X3Σ; a1Δg). 1- ground state 2A''

corresponds to reaction with O2(X3Σ), 2- excited state 2A' cor-

responds to reaction with O2( a1Δg), 3 - tems crossing and transi-

tion state (TS).

(0.36 eV taking ZPE energies into account).

The rate parameters of the reactions 1a, 1b, 2a, 2b, 1c, 2c

were computed from the data of quantum chemical calcu-

lations. Microcanonical variational Rice – Ramspergen –

Kassel – Marcus (RRKM) calculations were carried out

using the Khimera code [6]. A microcanonical loose vari-

ational transition state was used for the rate parameters 2a,

2c, 1c of reactions without a distinctive potential energy

barrier. A rigid transition state was used for the reactions

1a, 2b, 1b. The pressure dependence was computed using

the master equation method. Figure 2 presents the de-

pendence of the rate of association reaction via excited

state 2A’ vs. temperature and the parameters of rate con-

stant approximation in the quasi-Arrhenius form.

Fig. 2. Rate constants of reactions 1a, 2a. P = 1 atm. 1, 2 and

3-reactions through ground state in accordance with the works

[7], this study and [1] respectively, 4- reaction through excited

state in accordance with [1], 5-reaction through excited state in

accordance with this study.

The figure also includes the rate approximation used in

the work [1]. The confidence interval of the calculation

(dashed area) was estimated from the characteristic value

of the error of threshold calculation ±2 kcal/mole. The

reaction for the singlet state is several orders of magni-

tude slower than the reaction of the triplet state at the

characteristic pressure 1 atm. This effect can be explained

by the appearance of an energy barrier in the reaction path

and by the high probability for CH3 and O2(a1Δg)) reac-

tion directly into CH2O and OH, avoiding stabilization of

the way into the methylperoxy radical (CH3O2). The reac-

tion rate is three orders of magnitude lower than that from

[1], where intuitive suggestions about the PES behavior

were used in calculations within the ‘‘vibronic terms’’

approach.

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Fig. 3. Rate constants of reactions 1b, 2b. P = 1 atm. 1, 2 and


[8], this study and [1] 4-reaction through excited state in ac-

cordance with the study [1], 5-reaction through excited state in


In Fig. 3 the rate constant of reactions 1b, 2b is shown as

a function of temperature at atmospheric pressure. The

results are compared with the data of ab initio calculations

[8] and work [1]. Our calculations demonstrate a strong

effect of the potential energy surface features on the rate

behavior at low temperatures. Comparison of the three

possible channels for the reaction with excited oxygen

shows that the stabilization phenomena of the intermedi-

ate complex becomes significant at pressures greater than

300 atm. Therefore channels 1b and 1c are principal reac-

tions in wide range of pressures and temperature. As was

mentioned in the work [8], the production of CH2O and

OH requires PES hopping with a high transition probabil-

ity between the 2A’ and

2A” states. Using the results of

this study and the parameters of the saddle points from [8],

we came to the conclusion that the rate constant of reac-

tion to CH2O for the excited state is higher than that for

the ground one at low and moderate pressures.

Fig. 4. Rate constants of reactions 1c, 2c. P = 1 atm. 1, 2 and


[9], this study and [1] 4-reaction through excited state in ac-

cordance with the study [1], 5-reaction through excited state in


Figure 4 provides a comparison of the rates of the reac-

tions 1c and 2c. The rate of the reaction 1c is significantly

greater than the reaction through the ground term because

of the difference in the endothermicity of the reactions.

The graphs also present a comparison of the temperature

dependence of the calculated rate parameters with the

corresponding data from other works. The comparison of

the reaction rate of 2c with the corresponding data from

the Ref. [9] shows that the rate for the triplet state is well

reproduced by our model. A comparison of the rate 1c

with the curve from [1] exhibits a coincidence, which

probably indicates that the vibronic term approach is jus-

tified in this case. The results of approximation of the rate

constants of the reactions 1-2 (a-c) in quasi-Arenius form

for P=1 atm are presented in the Table 1.

Table 1. Rate constants of the reactions 1-2 (a-c)

The reaction for the singlet state in CH3O2 is several or-

ders of magnitude slower than the reaction of the triplet

state at the characteristic pressure 1 atm. This effect can

be explained by the appearance of an energy barrier in the

reaction path and by the high probability for CH3 and

O2(a1Δg) reaction directly into CH2O and OH, avoiding

stabilization of the way into the methylperoxy radi-

cal(CH3O2). The reaction rate is three orders of magnitude

lower than that from paper [1], where intuitive sugges-

tions about the PES behavior were used in calculations

within the ”vibrational term” approach.

3. Application for plasma assisted CH4 oxidation

The developed model was applied for the simulation of

plasma stimulated oxidation of CH4. According to com-

mon knowledge the most pronounced effect of plasma

discharge in air on kinetics is produced by generation of

the atomic oxygen [10]. In order to find out the efficiency

of the O2(a1Δg) we compare the influence of both particles

on the ignition delay. Since generation of O2(a1Δg) in air

is not effective [10] the generating this particle was ap-

plied to pure oxygen and after that the plasma compo-

nents were mixed with other part of the mixture. The ef-

fect of the atomic oxygen was simulated by the discharge

applied to both full mixture and oxygen alone. In all sim-

ulations the generation of the desired particle was pro-

moted by adjustment of the reduced electric field strength

to the conditions optimal for the desired particles. Gener-

ation of atomic oxygen is most effective if the reduced

electric field in the discharge is about 150 Td depending

on the composition of the gas processed by the plasma

while generation of singlet oxygen is most effective when

E/N is about 5-10 Td [10]. Since the rate of O2(a1Δg)

quenching is not well established the simulations were

performed both with and without the corresponding pro-

cesses in the kinetic model. The models of the nanosec-

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ond pulsed in case of high E/N and nonself-sustained

discharges in case of low E/N in frame work of computa-

tional environment Chemical Work Bench [6] were used.

The plasma chemical mechanism includes primary, sec-

ondary processes in the discharge volume and chemical

reactions of the heavy particles. Mechanism was validated

for wide range of the temperatures for methane combus-

tion including low temperatures T<1000 K [11]. The

sub-mechanism with participation of O2(a1Δg) was taken

from [1] and modified in accordance with this paper re-

sults.

The comparison of following effects was performed:

-discharge in pure oxygen (E/N = 100 Td).

-discharge in air (E/N = 150 Td).

- discharge in pure oxygen (E/N = 10 Td).

- discharge in pure oxygen (E/N = 10 Td) without

quenching.

- input of the energetically equivalent amount of heat

The results of the comparison with different

total plasma energy input are given in Fig. 5.

Fig.5 Ratio of induction time at mixture heating to induction

times at different scenario: solid line – non self-sustained dis-

charge at 10Td in O2, dashed line – discharge in O2 at 100 Td,

dotted line - non self-sustained discharge at 10Td in O2 without

quenching, dash-dotted line - dashed line – discharge in Air at

150 Td

One can see that the efficiency of O2(a1Δg) is

sensitive to the rate of quenching and could potentially be

competitive to the reaction with atomic oxygen. The in-

fluence of the O2(a1Δg) is occur due to participation in the

initiation reaction and reaction 1b. It is important to note

principal consequence of the modification of the rate con-

stants of the reactions 1a and 1b. The lowering of rate

parameter of the reaction 1a leads to reducing of ignition

delay time. It is explained by fact that CH3O2 produced in

reaction 1a then mainly dissociates into CH3 + O2(X3∑)

(that is property of the [1] mechanism).So, the overall

effect of this reaction is the dissipation of the excitation

energy into heat O2(a1Δg)=> O2(X

3∑)+Q. Since the in-

termediate states of the excited and ground CH3O2 corre-

sponds to actually different species with different elec-

tronic configurations, the correctness of the reaction

pathway CH3+O2(a1Δg)=> CH3O2(

2A’)=> CH3O2(

2A’’)=>

CH3 + O2(X3∑) seems questionable.

In all simulations application of plasma pro-

duced greater impact on the ignition delay than heating of

the mixture. One can see that in the optimal regime (low

E/N value, pure oxygen) the effect of the O2(a1Δg) can be

compatible with effect of the atomic oxygen (discharge in

the air-methane mixture at high E/N).

The results of the kinetic simulations show

high sensitivity of the model results to the rate of

quenching of O2(a1Δg) and peculiarities of the chemical

O2(a1Δg) sub-mechanism. Thus, further development of

the kinetic model should be performed focusing on the

evaluation of the rates of O2(a1Δg) quenching on the vari-

ety of particles present in the mixture and analysis of the

reaction pathways with participation of excited oxygen.

4. References

[1] A. Starik, V. Kozlov, and N. Titova, Combustion and

Flame, 157, 313–327 (2010).

[2] A. Starik and N. Titova, Kinetics and Catalysis, 47,

487–496 (2006).

[3] S. P. Walch, Chemical Physics Letters, 215, 81–86

(1993).

[4] R. Zhu, C.-C. Hsu, and M. Lin, Journal of Chemical

Physics, 115, 195–203 (2001).

[5] M. Dallos, H. Lischka, E. V. do Monte, M. Hirsh, and

W. Quapp, Journal of Computational Chemistry, 23,

576–583 (2002).

[6] M. Deminsky, e.a Computational Materials Science,

28, 169 (2003)

[7] D.L. Baulch, e.a., J. Phys. Chem. Ref. Data

34,757-1397 (2005).

[8] R. Zhu, C.-C. Hsu, M. Lin, J. Chem. Phys. 115 ,

195–203 (2001).

[9] C.-L. Yu, C. Wang, M. Frenklach, J. Phys. Chem.

99 ,14377–14387 (1995).

[10] A. Starikovskiy and N. Aleksandrov, Progress in

Energy and Combustion Science, 39, 61–110 (2013).

[11] M.Deminsky, e.a, Russian Journal of Chemical

Physics, 32, 1-15 (2013)

Calculation of Parameters of O (a1Δ ) Reactions 2 for … of Parameters of O 2 (a 1Δ g) ... g), 3...

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