Measurements of the absorption line strength of hydroperoxyl radical in the ν3 band using a continuous wave quantum cascade laser

Article abstract of DOI:10.1021/jp207477n

Mid-infrared absorption spectroscopy has been applied to the detection of the hydroperoxyl (HO₂) radical in pulsed laser photolysis combined with a laser absorption kinetics reactor. Transitions of the ν₃ vibrational band assigned to the O-O stretch mode were probed with a thermoelectrically cooled, continuous wave mid-infrared distributed feedback quantum cascade laser (QCL). The HO₂ radicals were generated with the photolysis of Cl₂/CH₃OH/O₂ mixtures at 355 nm. The absorption cross section at each pressure was determined by three methods at 1065.203 cm^-1 for the F₁, 13_1,13 ← 14_1,14 transition in the ν₃ band. From these values, the absolute absorption cross section at zero pressure was estimated. The relative line strengths of other absorptions in the feasible emitting frequency range of the QCL from 1061.17 to 1065.28 cm^-1 were also measured, and agreed with values reproduced from the HITRAN database. The ν₃ band absorption strength was estimated from the analytically obtained absolute absorption cross section and the calculated relative intensity by spectrum simulation, to be 21.4 ± 4.2 km mol^-1, which shows an agreement with results of quantum chemical calculations.

Full text of DOI:10.1021/jp207477n

ARTICLE
pubs.acs.org/JPCA
Measurements of the Absorption Line Strength of Hydroperoxyl
Radical in the ν3 Band using a Continuous Wave Quantum Cascade
Laser
Yosuke Sakamoto† and Kenichi Tonokura*,‡
†Department of Chemical System Engineering, Graduate School of Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku,
Tokyo 113-8656, Japan,
‡Department of Environment Systems, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwanoha 5-1-5, Kashiwa,
Chiba 277-8563, Japan
S Supporting Information
b
ABSTRACT: Mid-infrared absorption spectroscopy has been applied to the
detection of the hydroperoxyl (HO2) radical in pulsed laser photolysis
combined with a laser absorption kinetics reactor. Transitions of the ν3
vibrational band assigned to the OꢀO stretch mode were probed with a
thermoelectrically cooled, continuous wave mid-infrared distributed feedback
quantum cascade laser (QCL). The HO2 radicals were generated with the
photolysis of Cl2/CH3OH/O2 mixtures at 355 nm. The absorption cross
section at each pressure was determined by three methods at 1065.203 cmꢀ1
for the F1, 131,13 r 141,14 transition in the ν3 band. From these values, the
absolute absorption cross section at zero pressure was estimated. The relative
line strengths of other absorptions in the feasible emitting frequency range of the
QCL from 1061.17 to 1065.28 cmꢀ1 were also measured, and agreed with values
reproduced from the HITRAN database. The ν3 band absorption strength was
estimated from the analytically obtained absolute absorption cross section and the calculated relative intensity by spectrum
simulation, to be 21.4 ( 4.2 km molꢀ1, which shows an agreement with results of quantum chemical calculations.
structure assigned to electronic transitions, have been widely
examined.6ꢀ16 The line center absorption cross sections of
the 2ν1 absorption have been determined to be on the order
of 10ꢀ19 cm2 moleculeꢀ1 at several tens of Torr.6,7,11ꢀ14 The
1. INTRODUCTION
The hydroperoxy radical (HO2) is important intermediate in
both stratospheric and tropospheric chemistry.1 In the tropo-
sphere, the high reactivity of HO2 with NOx, itself, and alkylper-
oxy radicals, among others, keeps its concentration on the order
of 107 molecules cmꢀ3.2 The main fate of HO2 in the tropo-
sphere is to react either with NO to produce a hydroxyl radical
and nitrogen dioxide, or with itself to yield hydrogen peroxide. In
the stratosphere, HO2 reacts with ozone or an oxygen atom to
produce the hydroxyl radical, thus contributing to ozone loss
processes. HO2 is also an important intermediate in combustion
chemistry.3
Optical techniques have been widely used to monitor the HO2
radical directly in laboratory kinetic experiments. UV absorption
spectroscopy has been the most commonly used method to
detect the HO2 radical in the range 220ꢀ230 nm, because of its
strong cross sections (σ ≈ 10ꢀ18 cm2 moleculeꢀ1).4 However,
the broad and structureless absorption of HO2 in this region due
2
2
0
00
~
~
absorption cross-section of the A A r X A band is on the same
order of magnitude as the 2ν1 band.14
Although the mid-IR spectroscopic technique provides highly
selectivity and sensitive detection of HO2 due to the strong
fundamental rovibronic absorption, spectroscopic studies of
HO2 in the mid-IR region have been limited due to the lack of
a practical light source.17ꢀ25 There have been two experimental
reports on the line strength of the ν3 vibrational band by Zahniser
et al.23 and Buchanan et al.25 The estimated band strengths in
these two reports are in good agreement, and the reported value
by Zahniser et al. has been adopted by the HITRAN database.26
The band strength of the ν3 band of HO2 has also been estimated
by theoretical calculations27ꢀ31 showing a large discrepancy be-
tween experimental and theoretical values, in which the theore-
tical values were higher by a factor of about 2ꢀ6.
2
2
00
00
~
~
to the predissociative B A r X A transition leads to overlaps
with the absorption of other species, such as hydrogen peroxide
(σ ≈ 10ꢀ19 cm2 moleculeꢀ1), the main product of the HO2 self-
reaction.4,5 Thus, the rovibrational absorption line is preferred for the
detection of HO2 in experimental studies of such reaction systems.
Recently, distributed feedback quantum cascade lasers (QCLs)
have gained wide use as a light source in mid-IR spectroscopy
Received: August 4, 2011
2
2
0
00
~
~
The A A r X A transition and the 2ν1 OH overtone
Revised:
December 9, 2011
transition of HO2, which occurs in the near-IR and has rovibronic
Published: December 09, 2011
r
2011 American Chemical Society
215
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|

The Journal of Physical Chemistry A
ARTICLE
because of their narrow line width, single-mode operation, high
output power, and thermoelectric-cooled operation. We pre-
viously reported a new experimental setup using mid-IR absorption
spectroscopy to monitor the HO2 using a continuous wave (cw)
QCL as a spectroscopic light source.32 In this study, we applied the
mid-IR absorption spectroscopy using a QCL to measure the
spectral line strength of the ν3 band of HO2. In addition, relative
line strengths to that at 1065.203 cmꢀ1 for other absorptions were
also measured and compared with the spectral simulation.
photolyzed with the third harmonics of a Nd:YAG laser at
355 nm (Continuum Surelite II). The photolysis laser was
expanded using a beam expander and shaped with a circular
orifice to 1.00 ( 0.05 cm diameter. The photolysis pulse energy
was 49 ( 3 mJ pulseꢀ1 cmꢀ2 (experimental error of 5% and
detector accuracy of 3%) as measured by a calibrated joule meter
of 3% power accuracy (OPHIR, 10A-P). Typical initial reactant
concentrations were [O2] = (0.2ꢀ1.3) ꢁ 1018 molecules cmꢀ3
(used as a buffer gas), [He] = 3.9 ꢁ 1016, [Cl2] = 3.8 ꢁ 1015,
[CH3OH] = 1.4 ꢁ 1015, and [1,4-c-C6H8] = 4.4 ꢁ 1014
molecules cmꢀ3. The concentrations of O2, He, and Cl2 were
obtained from the total pressure and flow rates, CH3OH was
directly measured, and 1,4-c-C6H8 was from the saturated vapor
pressure and flow rate.
Gas flows were regulated by four calibrated mass flow con-
trollers (KOFLOC, models 3660 and 3650, accuracy of <1.5%).
The total pressure was monitored by a capacitance manometer of
0.25% accuracy (MKS, Baratron 622B). The gases used in this
experiment were obtained from Nippon Sanso (Cl2, ca. 10% in
He; O2, > 99.999 95%). CH3OH and 1,4-c-C6H8 (Wako Co.)
were introduced into the reaction cell by passing O2, or as diluted
premixed gases stored in a 6 L canister coated with Silonite
(Entech Instruments, Inc., Simi Valley, CA). Spectroscopic and
kinetics experiments involving the photolysis laser were per-
formed at a repetition of 2 Hz to ensure removal of the reacted
mixture and replenishment of the gas sample between successive
laser shots, as the retention time of sample gas was 0.25 s. A slow
flow of O2 was introduced over the optical parts to protect probe
and photolysis beam entrance windows from deposition of
reaction products. Experiments were performed at room tem-
perature (298 ( 3 K).
2. EXPERIMENTAL SECTION
Mid-infrared absorption spectra of the ν3 band of the HO2
radical were measured using a pulse laser photolysis/cw direct
absorption spectroscopy. Since the apparatus used in this study is
described in detail elsewhere,32 herein will only be a brief outline.
The mid-infrared probe beam at around 1065 cmꢀ1 was provided
by a cw thermoelectrically cooled distributed feed-back QCL
(LC0069, Hamamatsu Photonics K.K., Hamamatsu, Japan). The
central laser wavelength can be selected by changing the device
temperature between ꢀ30 and +35 °C with a Peltier driver
(C10638-01, Hamamatsu Photonics K.K.). A laser driver
(C10336, Hamamatsu Photonics K.K.) was used to operate
the QCL. A Pyrex cell with an inner diameter of 21 mm with a
length of 650 mm was used to measure the absorption spectra of
the HO2 radical. Perforated quartz windows were attached to
each side of the cell. Antireflection (AR) coated ZnSe windows
were placed on the perforated quartz windows to allow the probe
beam. The probe beam was focused on the center of the cell using
an AR coated ZnSe lens with a 415 mm focal length. The optical
path length of probe beam was 89 ( 1 cm, and the length of the
overlap region between the photolysis and the probe beam was
40 ( 1 cm, both of which were directly measured. An off-axis
parabolic mirror (25.4 mm diameter, 50.7 mm focal length) was
used to collect the probe beam exiting the cell, which was focused
through an interference filter (SPECTROGON, center wave-
length 9400 nm, fwhm 220 nm) on a liquid nitrogen cooled
HgCdTe detector (Kolmar Technologies, KLD-1-J1/DC/11).
The detected photocurrent signal was averaged with a digital
oscilloscope (Tektronix, TDS 520C) and transferred to a per-
sonal computer through a general purpose interface bus (USB-
GPIB, National Instruments).
3. RESULTS AND DISCUSSION
3.1. Determination of Absorption Cross Section of HO2
(σHO ) in the ν3 Band. The determination of the absorption cross
2
section of HO2 was done at an absorption line of F1 131,13
r
141,14 transition at 1065.203 cmꢀ1. Three methods were applied
to quantify the HO2 concentration: (1) initial absorbance, (2)
HO2 kinetics, and (3) comparison with the CH3OH absorption
intensity. In the feasible frequency range of the QCL from
1061.17 to 1065.28 cmꢀ1, the broadened methanol absorption
causes interference. The absorption line of HO2 in the ν3 band is
In the measurements of the absolute absorption cross section,
HO2 was produced by the pulse photolysis of chlorine in the
presence of CH3OH and oxygen. To measure the relative
intensities, HO2 was prepared by the pulse photolysis of chlorine
in the presence of 1,4-c-C6H8 and oxygen to avoid interfering
absorptions from methanol. The following reaction sequence
rapidly generates HO2:
1
split into F1 (J = N + 1/2) and F2 (J = N ꢀ /2) spin components,
where J is the total angular momentum and N is the rotational
quantum number. The absorption spectra of the F1 and F2 lines
interfere with each other.32 The neighboring absorption of F2,
131,13 r 141,14 transition at 1065.221 cmꢀ1 interferes with the
absorption of F1 131,13 r141,14 transition at 1065.203 cmꢀ1
.
Thus, a correction of the absorption intensity attributed to the
interference by CH3OH and HO2 was performed, the details of
which are described in the Supporting Information (S.1 and S.2).
3.1.1. Determination of σHO from Initial Absorbance. The
initial concentration of Cl produc2ed by photolysis of Cl2 at 355 nm
can be estimated from absorbed photolysis laser photon number
Cl2 þ hνð355nmÞ f 2Cl
ð1Þ
ð2Þ
ð3Þ
Cl þ CH3OH f CH2OH þ HCl
CH2OH þ O2 f HCHO þ HO2
or
Np
½Clꢂ0 ¼ 2½Cl2ꢂ
σCl
ð6Þ
2
0σL
Cl þ 1, 4-c-C6H8 f c-C6H7 þ HCl
c-C6H7 þ O2 f C6H6 þ HO2
ð4Þ
ð5Þ
where NP is the laser photon number per pulse calculated from the
laser pulse energy, σL is the laser beam cross section, σCl is the absorp-
2
The branching ratio of reactions 2, 3, and 5 is unity, while that
tion cross section of Cl2 at 355 nm (1.60 ꢁ 10ꢀ19 cm2 moleculeꢀ1).34
of reaction 4 is 0.38 ( 0.03.33 The chlorine molecule was
[Cl2]0 is calculated from the flow rates and total pressure. The
216
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The Journal of Physical Chemistry A
ARTICLE
Table 1. Reactions and Rate Constants Used in the Model
Simulation at 17 Torr Total Pressure
reaction
rate constant (298 K)a
ref
CH3OH + Cl f CH2OH + HCl
Cl f diffusion
5.5 ꢁ 10ꢀ11
68
9.1 ꢁ 10ꢀ12
2.9 ꢁ 10ꢀ11
6.6 ꢁ 10ꢀ10
1.5 ꢁ 10ꢀ11
73
34
this work
CH2OH + O2 f HO2 + CH2O
CH2OH + Cl2 f ClCH2OH + Cl
CH2OH + Cl f CH2O + HCl
CH2OH + CH2OH f products
CH2OH f diffusion
34
38
39
40
this work
HO2 + HO2 f H2O2 + O2
HO2 f diffusion
1.8 ꢁ 10ꢀ12
14
Figure 2. Absorption cross sections of HO2 at 1065.203 cmꢀ1 as a
function of total pressure. The dashed, solid, and dotted lines are the fit
using eq 9 to absorption cross sections obtained from the initial
absorbance (1, green), the HO2 kinetics (9, red), and the ratio of
absorption intensity to the CH3OH (2, blue), respectively.
71
this work
HO2 + CH2OH f products
HO2 + Cl f HCl + O2
6.0 ꢁ 10ꢀ11
3.2 ꢁ 10ꢀ11
9.1 ꢁ 10ꢀ12
41
34
34
HO2 + Cl f OH + ClO
a sꢀ1 for unimolecular reactions and cm3 moleculeꢀ1 sꢀ1 for bimolecular
reactions.
Table 2. Summary of the Absorption Cross Sections for the
F1, 131,13 r 141,14 Transition of HO2 at Each Total Pressurea
absorption cross sections/10ꢀ18 cm2 moleculeꢀ1
initial
HO2
CH3OH absorption
cross section
total pressure/Torr absorbance
kinetics
7
1.87 ( 0.19
1.57 ( 0.16
1.23 ( 0.12
1.19 ( 0.12
1.00 ( 0.10
0.89 ( 0.09
0.81 ( 0.08
0.62 ( 0.06
0.58 ( 0.06
1.87 ( 0.12
1.49 ( 0.12
1.18 ( 0.08
1.28 ( 0.11
1.06 ( 0.09
0.94 ( 0.08
0.95 ( 0.08
0.74 ( 0.06
0.64 ( 0.05
1.73 ( 0.09
1.49 ( 0.07
1.11 ( 0.08
1.06 ( 0.04
0.91 ( 0.04
0.85 ( 0.03
0.74 ( 0.04
0.64 ( 0.03
0.51 ( 0.03
10
13
17
20
25
30
35
40
a The errors indicate 1σ.
The α is conversion factor of Cl to HO2, which is not unity because
Cl is consumed via reactions with CH2OH and HO2 and diffusion out
of the detection area, and was calculated by kinetic simulation for
each set of conditions. The reactions used for the simulation are
summarized in Table 1. Diffusion rates were determined in this
study, the details of which are described in Section 3.1.2. A typical
time profile of HO2 produced from the reaction of CH2OH + O2
at 20 Torr is shown in Figure 1. Sensitivity analysis shows that the
main reactions contributing to the rise of HO2 are reactions 2 and 3,
and the contributions of self-reactions and diffusion are negligible in
Figure 1. Upper panel: the simulated HO2 rise (solid line) and Cl decay
(dashed line) profile, and the observed absorbance of HO2 (open circle)
at 20 Torr total pressure. The simulation conditions were [Cl]0 = 1.37 ꢁ
1014, [Cl2]0 = 3.8 ꢁ 1015, [CH3OH]0 = 1.4 ꢁ 1015, and [O2] = 6.1 ꢁ
1017 molecules cmꢀ3. Lower panel: the sensitivity of the reactions:
CH3OH + Cl (solid line), CH2OH + O2 (dashed line), HO2 + HO2
(dotted line), and HO2 + Cl (shortened dashed line).
absorption of HO2 is measured in absorbance form, which obeys
Beer’s law
ꢀ
ꢁ
the range of ∼0.1 ms. Thus, AHO (max) can be regarded as AHO ,0
.
2
2
ΔI
A ¼ ꢀ ln 1 ꢀ
¼ σHO ½HO2ꢂl
ð7Þ
Figure 2 shows σHO obtained from AHO (max), which were
2 2
2
I0
corrected for the overlap of neighbor absorption of the F2, 131,13
r 141,14 transition (details are in Section S.2). The values were
summarized in Table 2 as a function of total pressure. Error bars
include measurement deviation and errors of the photolysis/probe
laser overlap length, photolysis laser cross section, estimation of
concentration, and photolysis laser power.
where I0 is the probe laser intensity without HO2 absorption, ΔI
is the differential HO2 absorption intensity, and l is the optical
path length. Then, σHO can be determined from eq 8.
2
AHO , 0
AHO ðmaxÞ
2
2
σHO
¼
¼
ð8Þ
The dependence of the peak absorption cross sections on the
total pressure can be represented by eq 9 derived from analytical
solution of the Voigt fZunction35
2
½HO2ꢂ0l
2αðNp=σLÞ½Cl2ꢂ0σ355
Cl2
Here AHO (max) is the maximum value for HO2 absorbance
2
after photolysis corrected for the methanol absorbance (details
are in Section S.1). The methanol absorbance refers to the
absorbance change by methanol loss via reaction 2 in this paper.
σ
2
pffiffiffi
π
2
¼
expðy Þ ∞expð ꢀ t2Þ dt
ð9Þ
σD
y
217
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The Journal of Physical Chemistry A
ARTICLE
where σ is the absorption cross section at each pressure, σD is the
Doppler absorption cross section at zero total pressure, and y is
the normalized pressure broadening parameter given by
Table 3. Summary of the Diffusion Rate Coefficients of
CH3OHa
total pressure/Torr
kdiff/sꢀ1
ꢀ
ꢁ
pffiffiffiffiffiffiffi
wL
7
272.6 ( 4.1
143.1 ( 1.6
113.6 ( 1.6
71.7 ( 0.7
48.9 ( 0.7
30.0 ( 0.6
28.0 ( 0.7
11.9 ( 0.6
7.4 ( 0.7
y ¼
ln 2
ð10Þ
wD
10
13
where wL is the Lorentz width of half-width at half-maximum
(HWHM) which is the sum of all broadening effect by itself and
other species and wD is the Doppler width (HWHM)
17
20
25
30
pi
wL ¼
γ ꢁ
ð11Þ
ð12Þ
∑
i
35
40
760
i
a The errors indicate 1σ.
rffiffiffiffi
T
wD ¼ 3:581 ꢁ 10ꢀ7
ꢁ
ꢁ v0
M
7 Torr, 10 Torr, 13 Torr, and others, respectively. Then, from
these two parameters, σHO can be determined using the values
2
of kdiff and kself. The kself value of (1.75 ( 0.25) ꢁ 10ꢀ12 cm3
moleculesꢀ1 sꢀ1 at 298 K14 was used, which includes the
interference from CH3OH and shows no pressure dependence
in the range 0ꢀ30 Torr. The kdiff of HO2 was estimated by
measuring the kdiff of CH3OH and correcting it by the root of the
molar weight. The kdiff of CH3OH was directly determined by
measuring the absorbance time profile at 1065.180 cmꢀ1, where
CH3OH peak is present, which is affected by the removal of
CH3OH from probe region by reaction 2 and by the subsequent
inflow of CH3OH to the probe region. Approximating the
diffusion loss process as a first order reaction, and taking into
account the base validation by CH3OH mixing, the observed
decay can be written in absorbance form as the following
expression
where γi is the broadening coefficient by the species i, pi is the
partial pressure in Torr of the species i, M is the molecular weight
in atomic unit, and v0 is the frequency of spectrum peak center
in cmꢀ1. The partial pressure other than O2, almost of which was
He, was controlled to be 1.2 Torr. In this work, the total pressure
was approximately treated as O2 partial pressure. Figure 2 also
shows the fitting line for σHO by eq 9. Absolute absorption cross
2
section of HO2 was obtained as fitting parameter to be (3.0 (
0.1) ꢁ 10ꢀ18 cm2 moleculeꢀ1 (1σ). Considering the fitting
uncertainty (6%) originated from error of γO , and propagating
2
the error of absorption cross sections at each pressure (10%, see
Table 2), the final value was to be (3.0 ( 0.4) ꢁ 10ꢀ18 cm2
moleculeꢀ1 (1σ).
3.1.2. Determination of σHO from HO2 Kinetics. Under the
2
present experimental system, HO2 decay is mainly attributed to
its self-reaction
AðtÞ ¼ σCH OHΔ½CH3OHꢂ lfRD þ ð1 ꢀ RDÞexpð ꢀ kdiff tÞg
3
0
ð18Þ
HO2 þ HO2 f H2O2 þ O2
ð13Þ
where σCH OH is the absorption cross section of CH3OH at
3
1065.180 cmꢀ1, l is the length of photolysis/probe laser overlap
region, and RD is the ratio of the beam cross section of photolysis
laser to that of the reaction cell (0.227). The obtained kdiff values
are shown in Table 3. No dependence of kdiff on the initial Cl2
concentration was observed.
and secondarily to the diffusion loss from the probe region
HO2 f diffusion
ð14Þ
Approximating the diffusion loss process as a first order reaction,
HO2 loss rate can be written as following equation
The HO2 decay profiles, corrected for the absorption of
CH3OH, were analyzed by least-squares fitting of eq 17. Figure 3
shows an example of HO2 decay corrected for CH3OH and a
fitting line by eq 17. The CH3OH decay profile at 1065.203 cmꢀ1
was reproduced from the CH3OH decay at 1065.180 cmꢀ1 using
the absorption ratios, RAS (details in Section S.1). Figure 3 also
shows a reproduced CH3OH time profile.
d½HO2ꢂ
2
ꢀ
¼ 2kself ½HO2ꢂt þ kdiff ½HO2ꢂt
ð15Þ
dt
The time profile of [HO2] can be found by integration of eq 15
!
1
2kself
2kself
1
¼ ꢀ
þ
þ
expðkdiff tÞ ð16Þ
1065:203
CH3OH
A
ðtÞ ¼ RASA1065:180ðtÞ
ð19Þ
½HO2ꢂt
kdiff
kdiff
½HO2ꢂ0
Figure 2 shows the determined σHO from the HO2 decay profile
as a function of total pressures, which are corrected for the
2
At the short reaction times, exp(kdifft) can be approximated by
1 + kdifft. Then, eq 16 is modified to the following equation in
absorbance form
overlap with the neighboring absorption from the F2, 131,13
r
141,14 transition (details are in Section S.2), and a fitting line by
eq 9. The values were summarized in Table 2 as a function of total
pressures. The error bars include the error from measurement
deviation and the fitting, kself, l, and kdiff (see Table 3). The main
σHO ½HO2ꢂ l
2
0
AðtÞ ¼ σHO ½HO2ꢂ l ¼
ð17Þ
2
t
1 þ ðkdiff þ 2kself ½HO2ꢂ0Þt
source of error in the estimation of σHO is the error of kself. The
2
and σHO [HO2]0l and (kdiff + 2kself[HO2]0) are obtained as
fitting parameters. In the fitting procedure, the time ranges of 0 to
1.5 ms, to 3 ms, to 4 ms, and 5 ms were used for a total pressure of
absolute absorption cross section estimated by fitting was to be
2
(3.1 ( 0.1) ꢁ 10ꢀ18 cm2 moleculeꢀ1 (1σ). Considering the
fitting uncertainty (6%) originated from error of γO , and
2
218
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The Journal of Physical Chemistry A
ARTICLE
Figure 5. Absorption cross sections of CH3OH at 1065.180 cmꢀ1 as a
function of total pressure. The dashed line shows the reproduced
absorption cross section from the HITRAN values.26
Figure 3. Typical HO2 decay profile at 17 Torr total pressure with
[O2] = 5.1 ꢁ 1017, [CH3OH]0 = 1.4 ꢁ 1015, and [Cl2]0 = 3.8 ꢁ 1015
molecules cmꢀ3 corrected for CH3OH (blue line). The pink line shows
a fitting line for the corrected HO2 decay. The green line shows the
reproduced CH3OH decay from that at 1065.180 cmꢀ1. The red line
shows the HO2 decay without correction.
Table 5. CH3OH Absorption Cross Sections at
1065.180 cmꢀ1 at Each Total Pressurea
Table 4. Summary of the Ratios of Absorbance of HO2 at
1065.203 cmꢀ1 to That of CH3OH at 1065.180 cmꢀ1a
total pressure/Torr
absorption cross section/10ꢀ18 cm2 moleculeꢀ1
7
1.43 ( 0.06
1.23 ( 0.04
1.03 ( 0.07
0.97 ( 0.03
0.84 ( 0.03
0.79 ( 0.02
0.68 ( 0.03
0.60 ( 0.02
0.50 ( 0.03
total pressure/Torr
RA
10
13
7
1.085 ( 0.032
1.087 ( 0.037
0.969 ( 0.020
0.985 ( 0.024
0.987 ( 0.026
0.980 ( 0.031
1.000 ( 0.035
0.996 ( 0.033
0.952 ( 0.037
17
10
20
13
25
17
30
20
35
25
40
30
a The errors indicate 1σ.
35
40
a The errors indicate 1σ.
Table 6. Summary of Absolute Absorption Cross Sections of
HO2 at 1065.203 cmꢀ1a
absolute absorption cross
method
initial absorbance
section/10ꢀ18 cm2 moleculeꢀ1
3.0 ( 0.4
3.1 ( 0.3
2.8 ( 0.3
3.0 ( 0.5
HO2 kinetics
CH3OH absorption cross section
recommendation value
a The errors indicate 1σ.
cross section of HO2 can be estimated by comparison of the loss
of CH3OH with the generation of HO2.
Figure 4. Example spectrum of the CH3OH/Cl2/O2 system at 7 Torr
total pressure. The peaks on the left and the right are CH3OH and HO2,
respectively.
1065:203
A
½CH3OHꢂ
½HO2ꢂ
½CH3OHꢂ
½HO2ꢂ
HO2
σ
¼ RA
σ
¼
σ
CH3OH
HO2
CH3OH
1065:180
CH3OH
A
ð20Þ
propagating the error of absorption cross sections at each
pressure (8%, see Table 2), the final value was to be (3.1 ( 0.3)
ꢁ 10ꢀ18 cm2 moleculeꢀ1 (1σ).
Here AHO is the absorbance of HO2 corrected for CH3OH, and
2
RA is the ratio of averaged absorbance from 0.1 to 0.3 ms of HO2
at 1065.203 cmꢀ1 to that of CH3OH at 1065.180 cmꢀ1, which
was obtained by measuring the spectra and is summarized
in Table 4. The ratio of [CH3OH] to [HO2] at 0.2 ms was
calculated to be 1.12 by kinetic simulation for each set of
3.1.3. Determination of σHO from Comparison with the
2
CH3OH Absorption Intensity. Since the absorption line of
CH3OH presents at 1065.180 cmꢀ1 near that of HO2 at
1065.203 cmꢀ1 in the CH3OH/Cl2/O2 system, the absorption
219
dx.doi.org/10.1021/jp207477n |J. Phys. Chem. A 2012, 116, 215–222

The Journal of Physical Chemistry A
ARTICLE
Figure 6. the HO2 relative intensity spectrum to the absorption intensity of 1065.203 cmꢀ1 at 13 Torr. The solid line shows experimental data. The red
line shows simulated spectrum from the parameters of HITRAN.26.
Table 7. Relative Absorption Intensities to the Absorption at
1065.203 cmꢀ1 at 13 Torr Total Pressure
Table 8. Summary of the Absorption Band Strength of HO2
in the ν3 Band
relative
relative
method
Sband/km molꢀ1
ref
wavenumber intensitya HITRAN wavenumber intensitya HITRAN
laser photolysis
21.4 ( 4.2
7.8 ( 1.9
6.7
this work
1061.291 0.203(17)
1061.659 0.532(76)
1061.903 0.976(44)
1061.913 1.084(31)
1061.945 0.789(29)
1062.090 0.737(48)
1062.102 0.695(46)
1062.165 0.677(51)
1062.171 0.674(46)
1062.236 0.664(57)
0.170
0.425
0.932
0.987
0.780
0.738
0.684
0.684
0.720
0.619
1064.179 0.492(27)
1064.216 0.202(29)
1064.452 1.070(42)
1064.464 1.043(48)
1064.469 0.977(34)
1064.631 0.847(95)
1064.639 0.785(54)
1064.696 0.788(41)
1064.710 0.742(30)
1064.768 0.742(17)
1064.910 1.137(86)
0.445
0.171
1.090
1.060
1.006
0.844
0.766
0.739
0.690
0.671
1.254
discharge flow
23
flash lamp photolysis
B3LYP/aug-cc-pVQZ
CCSD(T)/TZ2PF
CCSD/aug-cc-pVTZ
BP/TZVPD
25
26.5
this work
31.7
29
31
30
32.2
16.8
estimation error of the absorption cross section of methanol (see
Table 5). The absolute absorption cross section was estimated by
fitting to be (2.8 ( 0.1) ꢁ 10ꢀ18 cm2 moleculeꢀ1 (1σ).
Considering the fitting uncertainty (7%) originated from error
1062.393 1.064(100) 1.181
of γO , and propagating the error of absorption cross sections at
2
1062.395 1.093(78)
1062.700 0.895(25)
1062.716 0.856(33)
1063.806 0.205(41)
1.222
0.918
0.861
0.183
1064.913 1.219(136) 1.305
each pressure (5%, see Table 2), the final value of (2.8 ( 0.3) ꢁ
10ꢀ18 cm2 moleculeꢀ1 was determined (1σ), and summarized in
Table 6 with the values from other methods. Taking the results of
three different methods into account, the recommended value
was to be (3.0 ( 0.5) ꢁ 10ꢀ18 cm2 moleculeꢀ1, which is an
averaged value of three methods, and its error was determined to
cover all range of three methods.
3.2. Absorption Spectrum and Band Strength of the HO2
ν3 Band. The absorption spectrum of HO2 was measured over
the range 1061.17ꢀ1065.28 cmꢀ1 at 13 Torr total pressure in the
1,4-c-C6H8 system. Over 7000 points were measured. Each data
point was the average of 20 laser shots at the mean absorbance
between 0.1 and 0.3 ms after photolysis with a repetition rate of
2 Hz. The wavelength was calibrated with CH3OH and HO2 peaks.
Figure 6 shows the HO2 absorption spectrum at 13 Torr between
1061.17 and 1065.29 cmꢀ1. Table 7 summarizes the comparison
between the measured relative intensities and those reproduced
with use of the parameters listed in HITRAN.26 The measured
relative peak intensities are in good agreement with those
reproduced from HITRAN.26
1065.203 1.000
1.000
0.926
1065.221 0.931(17)
a Numbers in parentheses represent the deviation (1σ) in last digits.
conditions. An example spectrum of HO2 and CH3OH at a total
pressure of 7 Torr averaged between 0.1 to 0.3 ms is shown in
Figure 4. σCH OH at 1065.180 cmꢀ1 was directly determined by
3
measuring the absorbance of the premixed CH3OH/O2 sample
of the concentration range from 0.8 to 1.9 ꢁ 1015 mole-
cules cmꢀ3, the range through which the contribution from
self-broadening is negligible. The obtained σCH OH at
1065.180 cmꢀ1 is shown in Figure 5 and summarized in3Table 5
as a function of total pressure and shows the close agreement
with the values calculated with integrated absorption cross
section and air broadening coefficient recommended in the
HITRAN database.26 Error (1σ) included the experimental
deviation, the estimation error of the optical path length, and
methanol sample concentration.
The line strength can be calculated from the absolute absorp-
tion cross section as follows:
The determined σHO values, which are corrected for the
2
overlap with the neighboring F2, 131,13 r 141,14 transition (as
described in Section S.2), and the fitting line from eq 9, are shown
in Figure 2. The values were summarized in Table 2. The error
bars include measurement deviation of RA (see Table 4) and
Z
a
Sline
¼
σ dv ¼ σD ꢁ
ð21Þ
h
220
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The Journal of Physical Chemistry A
ARTICLE
Table 9. Summary of the HO2 Geometry and Frequencies
geometrya
frequency/cmꢀ1
Sband/km molꢀ1
level of theory
R(OꢀO)
R(OꢀH)
θ(OꢀOꢀH)
ν3
ν2
ν1
ν3
ν2
ν1
B3LYP/aug-cc-pVQZb
CCSD(T)/TZ2PFc
CCSD/aug-cc-pVTZd
BP/TZVPDe
1.325
1.333
1.321
1.347
1.331f
0.975
0.977
0.966
0.995
0.971f
105.55
104.20
104.63
104.8
1166
1138
1183
1118
1098g
1435
1439
1473
1377
1392g
3598
3696
3655
3391
3436h
26.5
31.7
32.2
16.8
39.8
39.8
41.9
33.8
24.7
36.9
36.2
11.8
experimental
104.29f
a R/Å, θ/deg. b This work. c Ref 29. d Ref 31. e Ref 30. f Ref 42. g Ref 36. h Ref 43.
Here a/h = 2.43 ꢁ 10ꢀ3 cmꢀ1 is the area to height ratio of the
Doppler absorption line profile at zero pressure. The band strength
is the summation of the line strength for all rotational transitions
16.8 km molꢀ1 with BP/TZVPD,30 and 32.2 km molꢀ1 with
CCSD/aug-cc-pVTZ level of theory,31 respectively. In this study,
we performed the frequency analysis with B3LYP/aug-cc-pVQZ
level of theory, resulting in the value of 26.5 km molꢀ1. The cal-
culated ν3 absorption band strengths are also summarized in
Tables 8, and the HO2 geometry and frequencies are in Table 9.
Our experimental value of 21.4 ( 4.2 km molꢀ1 is in fair
agreement with those theoretical values based on the quantum
chemical calculation. It is noteworthy that the band strength
determined in the present work includes the systematic error
because the absolute absorption cross section at zero pressure was
estimated from the absorption cross sections at higher pressures.
Sband
¼
Sline ¼ SlineðF, 131, 13 r 141, 14Þ ꢁ
RI
∑
∑
ka, kc, F
ka, kc, F
ð22Þ
where RI is the relative intensity to the F1, 131,13 r 141,14
transition. The summation of the relative intensity of 4.9 ꢁ 102
was estimated in our temperature condition from the reproduced
spectrum with molecular parameters of HO2 radical reported by
Nelson and Zahniser36 using the PGOPHER software.37 Since
the HO2 radical is a near symmetric prolate top with k = ꢀ0.993,
the effects of a small asymmetry on the transition intensity are
very small. Therefore, we calculated relative rovibrational inten-
sities using the symmetric top H€onlꢀLondon factors and no
other factors. Nelson and Zahniser calculated the relative in-
tensities of HO2 ν3 band with the H€onlꢀLondon factors and
showed an agreement with experimental relative intensities within
10% error.36 Our calculation is essentially the same with Nelson and
Zahniser. Considering the uncertainty of the relative intensities of
10%, the ν3 band strength was estimated from our recommendation
4. CONCLUSION
A QCL as mid-IR laser source has been used to determine the
absolute absorption cross section of HO2 ν3 band. The absolute
absorption cross sections of the F1, 131,13r141,14 transition at
1065.203 cmꢀ1 were estimated by three methods. These three
estimated values are in good agreement with each other. The
absorption spectrum of HO2 ν3 band was also measured from
1061.17 to 1065.28 cmꢀ1. The measured spectrum features show
an agreement with that reproduced from the reported molecular
parameters. The determined absorption cross section was con-
for absolute absorption cross section to be 21.4 ( 4.2 km molꢀ1
.
verted to the ν3 absorption band strength to be 21.4 (4.2 km molꢀ1
,
The band strength is represented by the following equation24
in agreement with results of the frequency analysis of quantum
chemical calculations.
2π2ν
2
Sband
¼
jμj
ð23Þ
3ε0hcQvib
’ ASSOCIATED CONTENT
where ε0 is the vacuum permittivity, h is the Planck’s constant, c is
the velocity of light, ν is the wavenumber at band center, Qvib is the
vibrational partition function, and |μ| is the vibrational transition
dipole moment. For the ν3 band with 1097.625 cmꢀ1, eq 23 gives
|μ| = 0.088 ( 0.009 D.
S
Supporting Information. Full description of the materi-
b
al. This material is available free of charge via the Internet at
http://pubs.acs.org.
There are two previous experimental studies reporting the
band strength of the HO2 ν3 band, as summarized in Table 8.
Buchanan et al.25 reported the value of 6.7 km molꢀ1 using the
single mode diode laser combined with the flash lamp photolysis.
Zahniser et al.23 reported 7.8 ( 1.9 km molꢀ1 using the multi-
mode diode laser with monochromator in the discharge flow
system. The previously reported values are small compared to
our value of 21.4 ( 4.2 km molꢀ1. The value by Buchanan et al.25
was measured with the low signal-to-noise ratio (S/N) of <5.
They analyzed their value as the Doppler limit, while their
measurements were done in 7ꢀ20 Torr total pressure. This
would cause underestimation. Considering the pressure broad-
ening effect, their value should have been corrected to be about
2ꢀ3 times higher.
’ AUTHOR INFORMATION
Corresponding Author
*Phone: +81-4-7136-4706. E-mail: tonokura@k.u-tokyo.ac.jp.
’ ACKNOWLEDGMENT
This work was supported in part by a Grant-in-Aid for
Scientific Research from the Ministry of Education, Culture,
Sports, Science and Technology (19350004). Y.S. thanks the
JSPS Research Fellowship for Young Scientists for financial support.
The authors thank Dr. K. Tanaka for a proofreading.
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