22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Peculiarities of O 2 (a1Δ g ) kinetics in reactions with H atoms
A. Chukalovsky, K. Klopovsky, A. Palov and T. Rakhimova
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia
Abstract: The comprehensive analysis of available data on the rate constant and channels
of reaction H+O 2 (a1Δ g )→products were carried out. The phenomenological mechanism of
the title reaction including Renner-Teller coupling between 2A' and 2A'' states of HO 2
molecule was presented. The estimation of the reaction H + O 2 (a1∆ g )(+M) → HO 2 *(+M)
rate constant was obtained.
Keywords: hydrogen, singlet oxygen, quenching, reaction mechanism
1. Introduction
Nowadays there is a fast growing interest in
application of non-equilibrium plasma for the plasmaassisted combustion (PAC). Excited molecules produced
in non-equilibrium plasma influence on combustion decreasing the ignition temperature and the induction
delay time and increasing the flame velocity [1]. Lowlying electronically excited states of the oxygen molecule
O 2 (1Δ g ) and O 2 (1Σ g ) attract special attention [1].
However, still there is a great lack of knowledge on the
reactions of hydrogen radicals (especially H and HO 2 )
with O 2 (1Δ g ) that hamper the development of adequate
kinetic schemes for needs of plasma-assisted combustion
and atmospheric chemistry [2].
In this paper, we analyzed currently existing
difficulties in description of reaction O 2 (1Δ g ) with Hatom H+O 2 (a1Δ g )→products and its channels in
temperature range 300 - 1000 K.
2. Data analysis
The branching channel (R1a) of this reaction plays the
key role in the acceleration of the chain oxidation and
ignition of hydrogen fuels [3]. A few data on the rate
constant and channels of reaction (R1) is available, that is
shown in Fig.1. But the reaction is a subject of debates to
date [4].
The title reaction was studied experimentally in
different temperature ranges: 300–423 K in [5]–[8] and
520–933 K in [9] (shown in Fig.1 with points and shaded
areas). These experimental data agree insufficiently well
in both the value of the pre-exponential factor in the rate
constant of the reaction and the value of the activation
energy. The important thing is that almost all the
experiments presented (see Fig.1) measured the total rate
of O 2 (a1Δ g ) deactivation [6]–[9] in the presence of Hatoms. The approximation for the total rate constant
reaction (R1) - k (R1) (T) = 6.5∙10-11×exp(-2530/T) [10],
based on this data is shown by curve 1 (Fig.1). Only in
experiment [5] the concentration of O-atoms was
measured which is a product of reaction (R1a) and then
the temperature dependence of k (R1a) (T) was restored.
According to this data the probability of branching
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channel (R1a) is not more than 10% of the total reaction
(R1) rate - see Fig.1.
Fig. 1. Available data on the rate constant and channels of
reaction H+O 2 (a1∆ g )→products. Points and shaded areas
- experimental data [5]–[9], lines - calculated temperature
dependences and approximations for rate constants of
(R1) reaction channels (see text).
Modern concepts of the reaction (R1) mechanism are
based on the fact that, as a result of collisions between
hydrogen atoms and O 2 (a1Δ g ) molecules, a long-lived
transition complex (НО 2 )± forms on the potential energy
surface (PES) of the HO 2 *(2A') radical [11], [12]. Recent
calculations of HO 2 *(2A') PES have shown that the value
of the input reaction barrier is about 0.26 eV [12]. This
complex could decay via branching channel (R1a) or be
stabilized in collisions with third particle (M) forming
electronically excited HO 2 *(2A') molecule - (R1b).
Quantum-mechanical calculations of the reaction (R1a)
dynamics by using the ab initio calculated PES of
HO 2 (A') radical [13] showed that the commonly used
statistical approach to determining the reaction constant
on the basis of the transition state theory (TST) [14], [15]
(curve 2 in Fig.1) overestimates the cross section of the
branching reaction channel in reaction (R1).
Using the cross section obtained in [13] for an
elementary process H+O 2 (a1∆ g )(ν i =0,j i =0)→O+OH,
1
(where ν i and j i are initial vibrational and rotational states
of O 2 (a1∆ g ) respectively) we calculated Boltzmann
averaged rate constant for reaction (R1a). Obtained
estimation - kth (R1a) (T) lies between curves 3 and 4 in Fig.
1. Because of lack of cross sections for reaction (R1a)
with excited states of O 2 (a1∆ g ) [13] our calculations were
based on the following. We assumed that cross sections
for (R1a) with O 2 (a1∆ g )(ν i >0,j i >0) have the same form as
for O 2 (a1∆ g )(ν i =0,j i =0), but their threshold either remains
the same (curve 3) or is shifted on the value of excitation
quantum towards lower energies (curve 4). As seen from
Fig. 1, estimation kth (R1a) (T) is in good agreement with
experiment [5] and does not exceed 25-30% of the total
rate (R1) [6]–[9].
The reaction channel (R1b) was estimated on the base
of Lindemann mechanism [16] on HO 2 *(2A') PES in [14].
It was shown that (R1b) could be ignored up to the
pressures about 100 Bar.
Another possible channel of reaction (R1) is
hypothetical O 2 (a1∆ g ) quenching - (R1c) [5], [6], [9].
Taking into account two channels (R1a) and (R1c) of the
title reaction kinetic calculations were carried in [10]
under conditions of the experiments [5], [6] at T = 300 K
and P ≈ 1 Torr. Later in [17] at the same assumptions
ignition in H 2 -O 2 -O 2 (a1∆ g ) mixture at T = 780 K and P =
10 Torr [18] were simulated. Both have shown low
probability about 10 - 20% for branching channel (R1a).
These results for values of the reaction (R1a) rate constant
are also shown in Fig. 1 with numbers 5 and 6
respectively. As seen, they are in agreement with obtained
estimation kth (R1a) (T) and data [5].
The mechanism of (R1c) reaction is still unknown direct collisional quenching is spin-forbidden. Authors of
paper [15] proposed the mechanism for (R1c) based on
the ability of non-adiabatic transition of the complex
(НО 2 )± from 2A' state (excited) to 4A" state (ground) and
following decay on H + O 2 products due to available
intersection of these PESs near the barrier of reaction
(R1) [15]. But calculations [15] showed rather low
probability and reaction rate constant for this channel curve 7 (see Fig.1).
Thus, theoretical estimations argue with experiments
on the total rate constant of reaction (R1) [6]–[9] - Fig. 1.
Another important issue that should also be analyzed
is the results of recent paper [19]. The paper reviewed the
measurements of shock-tube experiment on O 2 (a1∆ g )
quenching in lean H 2 -O 2 -O 2 (a1∆ g ) mixture [20]. Analysis
[19] showed that at temperatures above 850 K, the
O 2 (a1Δ g ) quenching is entirely due to the reaction (R1).
But for consistency with the experimental data [20] the
total rate constant of the title process (curve 1) should be
considerably reduced (by an order) [19]. This directly
contradicts with experimental data [9] - see Fig. 1.
Therefore, the mechanism of the title reaction requires
further clarification.
.
2
3. Discussion of reaction mechanism
It is well known that the HO 2 molecule has two lowlying electronic states: the ground state (2A'') and the first
excited state (2A'). Apparently, the studies of the reaction
(R1) and the dynamics of transition complex (НО 2 )± on
PES should take into account the interaction of these main
doublet states 2A" and 2A' of the radical HO 2 .
To date there are no results on quantum mechanical
calculations of the reaction (R1) dynamics that taking into
account the non-adiabatic coupling between doublet states
2
A' and 2A'' of HO 2 molecule. In this section we represent
phenomenological mechanism of the title reaction
including it.
Fig. 2 shows the slices of the HO 2 *(2A') and HO 2 (2A'')
PESs [12], [13] along the reaction coordinate R O-H and
R O-O for two bending angles θ = 100° (near the
equilibrium point of the molecule configuration [12]) and
θ = 180° (linear configuration of the molecule). The
cross-linking of the slices shown in Fig. 2 was held along
the coordinates R OH and R O-O at the equilibrium point of
the molecule configuration - R O-H =1.83 Bohr, R O-O =2.51
Bohr [12] (at origin point).
Fig. 2. Slices of adiabatic PESs of the electronically
excited 2A' (solid lines) and ground 2A'' (dashed lines)
states of HO 2 molecule for bent - θ = 100° (black) and
linear θ = 180° (blue) configuration.
The transition (НО 2 (2A'))± complex which is formed
at the peak of the energy barrier of the reaction (R1) is
highly vibrationally excited (ν' O-H ≈ 7, E ≈ 2.75 eV). This
leads to intense intramolecular vibrational energy
redistribution, which leads to pumping bending and O - O
stretch vibrations of HO 2 (2A') state. The character time of
this process is about 10-12 - 10-11 s [21]. As seen from
Fig.2, the electronic states 2A' and 2A'' are degenerate in
the linear geometry. This can lead to non-adiabatic
transitions between two Born–Oppenheimer states of the
HO 2 molecule due to the Renner–Teller effect [22] in
case of highly excited bending mode. This gives the
possibility to fast internal conversion of the vibrationally
excited 2A' state into the 2A'' state and back (i.e. 2A' ↔ 2A'')
during the lifetime of the highly excited (НО 2 )± complex.
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This process will compete with the decay channel, which
forming O and OH - (R1a).
Note that in [22] the interaction between 2A' and 2A''
states of HO 2 molecule was investigated taking into
account the Renner-Teller effect and tunneling between
two isomeric states H-O-O and O-O-H. It was shown that
even at low excitation of 2A' state, which equals about a
quantum of bending vibration of the molecule HO 2, the
Renner-Teller effect leads to a mixing of states 2A' and
2
A''. This means that there is a possibility to find a
molecule HO 2 in both excited 2A', and ground 2A''
electronic state. This probability increases with the
density of rovibronic states of the molecule HO 2 , i.e. with
energy increase.
The fast internal conversion "opens" an additional
channel of reaction (R1) leading to the decay of
(НО 2 (2A''))± complex into H-atom and oxygen O 2 (3Σ) in
ground state, i.e. quenching (R1c). Besides, the transition
(НО 2 )± complex could be stabilized in collisions forming
vibrationally excited HO 2 molecule in both excited (2A')
and ground (2A'') electronic states. As a result, reaction
(R1) can have several output channels - (R1a,b,c).
4. Calculations behind the shock
In this section we re-analyzed the results of recent
paper [19] in which the modelling of experiment [20] was
carried out. In [20] using a combined discharge
flow/shock apparatus the effective rate constant (K eff ) of
O 2 (1Δ g ) deactivation was obtained by measuring the
changes of dimol emission intensity (634 nm) in lean H 2 O 2 -O 2 (a1∆ g ) mixture. The measurements were performed
behind the falling shock at temperatures of 500–1020 K
and pressures of 26–90 Torr. The data obtained is shown
in Fig. 3.
The modeling of this experiment was carried in analogy
with paper [19]. For parametric studies we used the zerodimensional kinetic model. The kinetic mechanism for
H 2 -O 2 -O 2 (a1∆ g ) chemistry was taken from [4]. It
included 47 reverse reactions for 12 reactive species: H 2 ,
O 2 , H, O, OH, H 2 O, HO 2 , H 2 O 2 , O 3 , O 2 (a1Δ g ), HO 2 *,
HO 2 *(ν). The parameters behind the shock front (P sh ,T sh )
and fractions of the components (obtained earlier in [4])
were specified as input data for calculations. As earlier,
for k (R1) (T) we used approximation from [10] (curve 1 in
Fig.1). The probability for (R1a) channel was taken to be
- α = k (R1a)/ k (R1) ×100% = 10%, in accordance with [17].
The probability for (R1b) - β = k (R1b)/ k (R1) ×100% , was
varied.
To correctly compare the calculations with the data
[20] the effective rate constant of O 2 (a1∆ g ) quenching
was defined in (1).
The modeling results in compare with the data [20] are
shown in Fig. 3. As seen, calculations of K eff demonstrate
good agreement with experiments at T ≤ 600 K, where
O 2 (a1∆ g ) quenching is determined by the processes
involving HO 2 /HO 2 * radicals [10], [19]. On the contrary,
at T ≥ 850K the results for K eff significantly depend on
the value of parameter β. In this region the reaction (R1)
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plays the key role in O 2 (a1∆ g ) quenching [10], [19]. At
β=0% calculations significantly overestimate the rate of
O 2 (a1∆ g ) quenching, like it was obtained in [19].
However, even low value β = 10% allows to decrease K eff
by 2.5 times in compare with case, when (R1b) is not
included. A further increase in the probability of the
channel (R1b) up to the value of β = 50% allows to reach
the full agreement with averaged experimental
dependence K exp (T) [20]. Note that the calculation results
do not depend on which of two electronic states 2A' or 2A"
the excited radical HO 2 is stabilized in the reaction (R1b).
Fig. 3. Effective rate constant K eff of O 2 (a1∆ g ) quenching
as a function of the gas temperature behind the shock
front. The symbols - experimental data [20], and the
dashed line is least-squares averaging of the data K exp (T)=(2.16±1.66)·exp(-(2600±200)/T) см3/с) with its
confidence interval (hatched area) [20]. Solid curves calculation results.
Thus,
the
rate
constant
of
reaction
H+O 2 (a1∆ g )(+M)→HO 2 (2A',2A")(+M), corresponding to
the value of β = 10 - 50%, could be estimated as (0.5 ÷
2.6)∙10-12 cm3/s at temperature of about 1000 K and
pressure of 70 - 90 Torr.
Theoretical analysis based on Lindemann mechanism
[16] taking into account the obtained estimation for k (R1b)
have shown that reaction (R1b) demonstrate rather strong
pressure dependence in compare with previous
consideration [14]. Besides it requires a long lifetime of
the transition complex (НО 2 )± of about 10-10 s. Such a
value lies within the uncertainty of the characteristic time
of unimolecular decomposition of HO 2 molecule with
energy near the dissociation threshold [23] and consistent
with the experimental data [24], however, exceeds the
estimates from RRKM-theory [23].
5. Conclusions
The comprehensive analysis of available data on the
rate
constant
and
channels
of
reaction
H+O 2 (a1Δ g )→products were carried out. It was shown
that theoretical estimations based on examination of the
reaction (R1) only on PES of HO 2 (2A') state argue with
3
experiments on the total rate of O 2 (a1Δ g ) decomposition
in the title reaction. Besides the kinetic studies show
significant value (80 - 90%) for quenching probability
which has not been confirmed theoretically.
The phenomenological mechanism of the title reaction
including Renner-Teller coupling between 2A' and 2A''
states of HO 2 molecule was presented. It allows to
explain qualitatively the data reviewed on the ratio
between probabilities of quenching and branching
channels of the title reaction. Besides, it makes possible to
stabilize the complex in the excited electronic 2A' and
ground 2A'' state of HO 2 . The proposed mechanism
requires substantial verification and extensive quantummechanical calculations of the dynamics of highly excited
states of HO 2 *(2A',ν') taking into account the RennerTeller coupling between states 2A' and 2A'', tunneling
between the two isomeric geometries H-O-O and O-O-H,
and consider all possible dissociation channels.
Re-analysis of the experiment on O 2 (a1∆ g ) quenching
behind the shock in lean H 2 -O 2 -O 2 (a1∆ g ) mixture
allowed to estimate the rate constant of the reaction
H+O 2 (a1∆ g )(+M)→HO 2 (2A',2A")(+M). The obtained
estimate equals (0.5 ÷ 2.6)∙10-12 cm3/s at temperature of
about 1000 K and pressure of 70 - 90 Torr. This result
demonstrate rather strong pressure dependence of the title
reaction that could limit applicability of O 2 (a1∆ g ) for
PAC by the pressure range up to hundreds of Torr.
6. Acknowledgements
We would like to thank Professor Hua Guo from the
University of New Mexico who kindly provided the
calculated data of HO 2 PESs for us.
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8. Equations
( R1a )
O + OH

 (+ M )
→ HO2* (ν ) ( R1b )
H + O2 (1 ∆ g ) → products ⇒  

 H + O2
( R1c ) − ?
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