Observation of the ν1 OH(OD) stretch of HOI and DOI by Fourier transform infrared emission spectroscopy

Article abstract of DOI:10.1063/1.471456

The spectra of vibrationally hot HOI formed in the reaction of alkyl iodides with oxygen atoms are observed by Fourier transform infrared emission spectroscopy. The v = 1-3 levels of the OH stretch are observed via the Δv = -1 and Δv = -2 sequence bands. The spectrum of DOI is observed by using 2,2,2-d₃-iodoethane as the precursor in the oxygen atom reaction. The v = 1-4 levels of the OD stretch are observed in the Δv = -1 sequence band, and the v = 1-5 levels of the OD stretch are observed in Δv = -2. Medium resolution spectra (0.031 cm^-1 apodized) are recorded and rotationally analyzed for the v₁ fundamental and 2v₁-v₁ hot band of HOI. An estimate of the HOI ground state structure is made by constraining the OH bond length to its value for HOCl and HOBr and calculating the HOI bond angle and the OI bond length by least squares fit to the ground state rotational constants.

Full text of DOI:10.1063/1.471456

Observation of the ν1 OH(OD) stretch of HOI and DOI by Fourier transform infrared
emission spectroscopy
Jody J. Klaassen, Jörg Lindner, and Stephen R. Leone
Citation: The Journal of Chemical Physics 104, 7403 (1996); doi: 10.1063/1.471456
View online: http://dx.doi.org/10.1063/1.471456
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/104/19?ver=pdfcov
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Observation of the ␯ OH(OD) stretch of HOI and DOI by Fourier transform
1
infrared emission spectroscopy
Jody J. Klaassen, J o¨ rg Lindner, and Stephen R. Leone
JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado
80309 and Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309
͑
Received 16 November 1995; accepted 7 February 1996͒
The spectra of vibrationally hot HOI formed in the reaction of alkyl iodides with oxygen atoms are
observed by Fourier transform infrared emission spectroscopy. The vϭ1–3 levels of the OH stretch
are observed via the ⌬vϭϪ1 and ⌬vϭϪ2 sequence bands. The spectrum of DOI is observed by
using 2,2,2-d -iodoethane as the precursor in the oxygen atom reaction. The vϭ1–4 levels of the
3
OD stretch are observed in the ⌬vϭϪ1 sequence band, and the vϭ1–5 levels of the OD stretch are
Ϫ1
observed in ⌬vϭϪ2. Medium resolution spectra ͑0.031 cm
apodized͒ are recorded and
rotationally analyzed for the ␯ fundamental and 2␯ Ϫ␯ hot band of HOI. An estimate of the HOI
1
1
1
ground state structure is made by constraining the OH bond length to its value for HOCl and HOBr
and calculating the HOI bond angle and the OI bond length by least squares fit to the ground state
rotational constants. © 1996 American Institute of Physics. ͓S0021-9606͑96͒02418-6͔
3
I. INTRODUCTION
formation in alkyl iodideϩO͑ P͒ reactions and analyze the
nascent vibrational distribution of HOI produced in pulsed,
time-resolved experiments,47 and in a closely related paper,
we report on the OH vibrational distribution produced in the
The hypohalous acids belong to the series HOX, where
X may be F, Cl, Br, or I. These are important atmospheric
species, particularly HOCl and HOBr, since they are in-
volved as intermediates in the catalytic destruction of
3
47
reaction of alkyl radicals with O͑ P͒.
In the following sections the fluorescence collection,
Fourier transform infrared ͑FTIR͒ spectrometer, and data
collection systems are described, as are the experimental de-
tails for producing HOI. Results are presented for the vibra-
tional analysis of the OH and OD stretches of HOI and DOI.
Rotation and distortion constants for the vibrational ground
state, v1ϭ1 and v1ϭ2 of HOI are determined by
combination-differences formed from the ␯1 fundamental
and 2␯ Ϫ␯ hotband.
1
–10
ozone.
Because of their importance in atmospheric chem-
istry and also because of their intrinsic, fundamental signifi-
cance, much work is available on the gas phase spectroscopy
of the first three acids in this series, HOF ͑Refs. 11–16͒,
HOCl ͑Refs. 17–28͒, and HOBr ͑Refs. 29–31͒ in both the
microwave and infrared regions. The number of investiga-
tions of the final member of this series, HOI, is far fewer,
although it too is regarded as an important species in the
1
1
chemistry of atmospheric iodine.3
2–35
Previous studies of
HOI include the characterization of the UV-VIS absorption
spectrum in the aqueous phase,3
6–37
and identification of the
II. EXPERIMENTAL DETAILS
IR absorption spectrum of HOI and its isotopic variants in N
2
3
8–39
and Ar matrices.
The first gas phase spectrum of HOI
Vibrationally hot HOI is observed as a product in the
reactions of oxygen atoms with iodoethane ͑C2H5I͒,
1-iodopropane ͑n-C3H7I͒, and 2-iodopropane ͑i-C3H7I͒, the
result of a novel, five-membered ring transition state:45
4
0
was reported by Barnes et al. They observed the ␯ OH
1
Ϫ1
stretch and the ␯ bend mode at a resolution of 1 cm
The paucity of investigations of HOI perhaps lies in the
difficulty of its synthesis. HOI has been speculated as a prod-
uct in the radical–radical reaction between HO and IO
Refs. 34 and 35͒ and also in the reaction of OH radical with
.
2
3
C H IϩO͑ P͒→HOIϩC H , ⌬ HϭϪ237 kJ/mol,
2
5
2
4
r
2
3
͑
n-C H IϩO͑ P͒→HOIϩC H , ⌬ HϭϪ245 kJ/mol,
i-C H IϩO͑ P͒→HOIϩC H , ⌬ HϭϪ236 kJ/mol.
3
7
3
6
r
40
iodine containing compounds ͑Refs. 41–44͒. Barnes et al.
made HOI by the reaction of OH radical with I , CH I, and
3
3
7
3
6
r
2
3
CH I . The yield of HOI from these reactions is quite small.
Grice and co-workers have also recently observed HOI for-
2
2
With a pathlength of 492 m they observed only a ϳ5% HOI
mation in molecular beam scattering experiments between
O͑ P͒ and iodoethane.
The HOI product is only formed for alkyl chains of two
carbon length or greater. Similar OH stretch vibrational dis-
tributions of the HOI product are observed for all three alkyl
3
48
absorption. We recently found the reaction between alkyl
3
iodides and O͑ P͒ to be an effective method of synthesizing
4
5
HOI. Furthermore, the HOI produced in this reaction is
found to be vibrationally very hot in the OH stretch, fluo-
rescing strongly in the mid IR. We use the emission from hot
HOI itself as the radiation source for the FTIR spectrometer.
By directly measuring the HOI fluorescence, we are able to
utilize a simple experimental arrangement and also exploit
the inherently greater sensitivity of emission spectroscopy.46
In forthcoming papers, we explore the mechanism of HOI
iodide precursors. Emission from v ϭ3 is observed in both
1
the ⌬vϭϪ1 and ⌬vϭϪ2 bands. This state has an energy of
Ϫ1
10 374 cm which corresponds to ϳ50% of the available
reaction exothermicity. 2-iodopropane is the precursor used
for the HOI spectroscopic measurements presented here. The
precursor for DOI is 2,2,2,-d -iodoethane.
3
J. Chem. Phys. 104 (19), 15 May 1996
0021-9606/96/104(19)/7403/9/$10.00
© 1996 American Institute of Physics
7403
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7404
Klaassen, Lindner, and Leone: The ␯ OH(OD) stretch of HOI
1
FIG. 2. Low resolution ͑1 cmϪ1͒ DOI emission spectrum with blackbody
background subtracted and intensities normalized to the instrument response
function. Emission is observed only for the OD stretch mode. Four quanta of
OD stretch are observed in the ⌬vϭϪ1 sequence band. In the ⌬vϭϪ2
FIG. 1. Low resolution ͑1 cmϪ1͒ HOI emission spectrum with blackbody
background subtracted and intensities normalized to the instrument response
function. Emission is observed only for the OH stretch mode. Three quanta
of OH stretch are observed in both the ⌬vϭϪ1 and ⌬vϭϪ2 sequence
Ϫ1
sequence band v1р5 is observed. A small amount of HOI emission is ob-
bands. The absorption feature at 2350 cm is due to atmospheric CO2 .
Ϫ1
served for the ␯ fundamental at 3625 cm . This can be attributed to some
1
minor contamination in the 2,2,2-d -iodoethane sample of other ethyl iodide
3
isotopes which are only partially deuterated at the beta-carbon.
Continuous HOI emission is produced with a flow tube
reactor. This consists of concentric quartz tubes, the outer
1
.27 cm in diameter, the inner, 0.64 cm. The inner tube en-
spectral responsivity of the InSb detector. Two times over-
sampling was used on all spectra. A commercial software
package was used to calculate the Fourier transforms. To
transform the higher resolution interferogram it was neces-
sary to break it up, by taking every third point from its origi-
nal 1.48 million points, into three interferograms of 494 660
points each. Each of these spectra were separately trans-
ters the outer tube approximately 1 cm from its outlet. Oxy-
gen atoms are made by microwave discharge ͑2.45 GHz,
ϳ90 W͒ in neat O ͑99.998%͒ in the outer tube of the reac-
tor. The backing pressure of O in the discharge is ϳ500 Pa.
The discharge is generated within an Evenson type cavity
located 15 cm before the outlet of the reactor. At the outlet of
the reactor, oxygen atoms formed in the discharge react with
2
2
Ϫ1
formed with a Nyquist frequency set to 5266.0033 cm , and
2
-iodoethane, which is fed through the inner concentric tube
the resulting spectra were coadded. No emission from the
HOI overtones was observed within the signal-to-noise ratio
of the higher resolution spectrum, so spectral folding prob-
lems were not encountered by this operation. Each interfero-
gram was corrected in phase from a small part of the inter-
ferogram itself.
at a backing pressure of ϳ300 Pa.
The quartz tube reactor is placed within a larger stainless
steel vacuum chamber containing Welsh cell fluorescence
collection optics which couple the emission into the FTIR
spectrometer. This chamber is evacuated by a blower pump,
however, the cross section of the vacuum line exiting the
chamber is reduced by a 2.5 cm diameter aperture in order to
throttle down the pumping speed and increase the residence
time of the hot HOI products in the observation region.
4
9–50
Infrared emission is collected by a Welsh cell
main chamber and is f/number-matched by a telescope
f ϭ150 mm, f ϭ150 mm, CaF ͒ to the FTIR spectrometer.
in the
͑
1
2
2
The modulated IR fluorescence signal is detected by a 77 K
InSb detector, amplified with current and voltage amplifiers
and sent to a homebuilt data acquisition system based on a
commercial 16-bit A/D card in a PC and original software.
Three sets of emission spectra were recorded, one low
resolution scan for both HOI and DOI and a higher resolu-
tion scan for HOI. We were not able to make a high resolu-
tion scan for DOI due to the limited quantity of the deuter-
ated compound. The low resolution scans are 500
Ϫ1
coadditions each recorded at 1 cm
resolution and are
shown in Figs. 1–3. The higher resolution scan for HOI,
shown in Figs. 4–6, is 970 coadditions. Triangular apodiza-
tion was used resulting in an apodized resolution of 0.031
Ϫ1
FIG. 3. Expanded portion of low resolution ͑1 cm ͒ HOI spectrum show-
Ϫ1
Ϫ1
ing the ␯1 fundamental, 3625 cm and the 2␯ Ϫ␯1 hotband, 3458 cm
The b-type band Q branches for the fundamental are clearly evident and are
.
1
Ϫ1
cm . The frequency range recorded was only limited by the
labeled in symmetric top notation.
J. Chem. Phys., Vol. 104, No. 19, 15 May 1996
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Klaassen, Lindner, and Leone: The ␯ OH(OD) stretch of HOI
7405
1
Ϫ1
FIG. 4. A portion of the high resolution ͑0.031 cm apodized͒ HOI spec-
Ϫ1
FIG. 6. A portion of the high resolution ͑0.031 cm apodized͒ HOI spec-
trum showing the QR branch of the 2␯ Ϫ␯ hotband with rotational assign-
trum showing the QR branch of the ␯ fundamental with rotational assign-
ments indicated. Many of the transitions for the different Ka subbands over-
lap each other, although for each Ka there is some value of J at which the
1
1
1
ments indicated. Resolved K ϭ1 asymmetry doublets are indicated by the
a
Wang symmetry parameter ␥. The transition marked with an asterisk is an
OH emission line which was used as an internal check on the frequency
calibration.
transition is not blended. Resolved K ϭ1 asymmetry doublets are indicated
a
by the Wang symmetry parameter ␥.
OH emission, which likely comes from the reaction se-
quence
III. DESCRIPTION OF THE SPECTRA AND
ASSIGNMENTS
3
i-C H IϩO͑ P͒→IOϩi-C H •, ⌬ Hϭ9 kJ/mol
Figures 1 and 2 show the low resolution ͑1 cmϪ1͒ HOI
3
7
3
7
r
3
and DOI emission spectra obtained from the alkyl iodideϩO
reactions. The intensity of these emission spectra are normal-
ized by first subtracting out the background, room tempera-
ture blackbody spectrum, and dividing the result by the in-
strument response function of the FTIR optics and the InSb
detector. The instrument response function is determined
from the observed emission of a calibrated blackbody source
compared with the theoretical emission of an ideal black-
body. In both spectra the only vibrational bands observed
belong to the ⌬vϭϪ1 and ⌬vϭϪ2 sequence bands of the
OH͑OD͒ stretch. In the HOI spectrum, Fig. 1, emission is
observed in both sequence bands for vр3. In the DOI spec-
trum, Fig. 2, emission from vр5 is observed in the ⌬vϭϪ2
sequence band, and for vр4 for the ⌬vϭϪ1 sequence band.
An expanded portion of the HOI low resolution spec-
C H •ϩO͑ P͒→OHϩC H , ⌬ HϭϪ283 kJ/mol,
3
7
3
6
r
is observed in the higher resolution HOI spectrum. These
radical–radical reactions are investigated in more detail by
pulsed laser photolysis experiments.47 The OH emission al-
lows a convenient check to the calibration of the interfero-
gram with respect to the reference HeNe laser of the FTIR.
Twenty-two OH emission lines were observed over the fre-
Ϫ1
quency range 3330–3680 cm . Comparison of observed
OH line positions to those reported in the literature5
1–52
shows randomly distributed deviations of less than Ϯ0.004
cm . The observed spectra are not recalibrated.
Ϫ1
trum is shown in Fig. 3. Prominent in Fig. 3 are the ␯ fun-
1
Ϫ1
damental at 3626 cm and the 2␯ Ϫ␯ hot band at 3459
cm . As is the case for the ␯ fundamentals of HOF ͑Ref.
1
1
Ϫ1
1
1
6͒, HOCl ͑Refs. 18 and 26͒, and HOBr ͑Ref. 31͒ the ␯ of
1
HOI is a hybrid band consisting of both a-type and b-type
transitions. HOI is an accidental, prolate symmetric top,
␬
ϭϪ0.9996, and except for the K ϭ1 subbands, where
a
asymmetry doubling is observed, its transitions are those of a
prolate symmetric top. The Q bandheads of the perpendicu-
lar b-type band are very obvious in Fig. 3. The A constant
Ϫ1
for HOI is greater than 20 cm , so these Q bandheads
Ϫ1
spread over ϳ500 cm and are immediately assignable by
inspection. They are labeled in Fig. 3 using symmetric top
notation. The parallel a-type transitions of the fundamental
are much more congested and lie near the band center. They
are not resolved in the low resolution spectrum of Fig. 3,
however, in the higher resolution spectrum individual rota-
tional lines in the parallel band are resolved. A small portion
FIG. 5. The ␯1PP3 branch of HOI taken from the high resolution ͑0.031
cm apodized͒ spectrum. The transitions indicated here are the only indi-
vidual rovibrational transitions of the perpendicular b-type band from the
high resolution spectrum which could be observed in the spectrum. The two
transitions marked with an asterisk are OH emission lines which were
among those used as an internal calibration reference.
Ϫ1
J. Chem. Phys., Vol. 104, No. 19, 15 May 1996
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7406
Klaassen, Lindner, and Leone: The ␯ OH(OD) stretch of HOI
1
Q
TABLE I. Band centers and vibrational parameters ͑in cmϪ1͒ for HOI and
DOI ⌬v ϭϪ1 and ⌬v ϭϪ2 sequence bands. Band centers are taken from
of the R branch of the fundamental is shown in Fig. 4 along
1
1
with lines indicating the rotational assignments. At our
apodized resolution of 0.031 cm , many rotational lines of
the 1 cm spectra as the minimum between the P and QR branches. Their
Ϫ1
Q
Ϫ1
Ϫ1
errors are Ϯ5 cm
.
the different K subbands are overlapped.
a
The majority of assignable lines in the ␯ band belong to
HOI
DOI
1
the parallel type transition. However, it is fortunate that ␯ is
1
⌬v ϭϪ1
1
a
a hybrid band, since without the perpendicular type transi-
tions it would be possible to obtain only the difference in the
rotational A constants for the upper and ground states, not
their absolute values. Fitting of the spectrum began with the
1-0
2-1
3625
2674
2585
2498
2409
3458a
3292
3
4
-2
-3
⌬
7081
v ϭϪ2
P
R
1
Q and Q bandheads of the perpendicular transition. These
a
2-0
5258
5084
4910
4739
alone quite well define the band center and A rotational con-
3-1
4-2
6751
stants in the ground state and in ␯ . A reasonable initial
1
5-3
estimate of the B and C rotational constants is obtained by
setting them to one half the spacing between the strong
Vibrational Parameters
3789.37͑40͒
2759.35͑38͒
x12
x13
K ϭ2 transitions evident in Fig. 4. Fitting proceeds
a
ͩ
␻1ϩ
ϩ
ͪ
2
2
smoothly by simulating a stick spectrum, making new as-
signments, including them in the fit, and simulating a new
stick spectrum. A criterion for the correct assignment is that
the new fit predicts additional lines of the band not included
in the previous fit.
x
Ϫ82.825͑97͒
Ϫ43.445͑61͒
11
aSee Table III for band centers determined from fit to rotationally resolved
spectra.
While the PQ and RQ bandheads are strong, no indi-
vidual rotational lines of the perpendicular band were ob-
x12
x13
1
2
1
2
GЈ ϪGЉ ϭ
ͩ
␻ ϩ
ϩ
ͪ
͑vЈϩ ͒ϩx ͑vЈϩ ͒
1 1
11
v
v
1
2
served within the signal-to-noise of the spectrum with the
1
1
2
2
P
exception of the P K ϭ3 subband. Here individual rota-
a
x12
x
13
tional transitions with JЉϭ3–30 are assignable. This portion
of the spectrum is displayed in Fig. 5.
1
2
1
2
Ϫ
ͩ
␻ ϩ
ϩ
ͪ
͑vЉϩ ͒Ϫx ͑vЉϩ ͒ . ͑2͒
1 1
11
1
2
2
2
The 2␯ Ϫ␯ hot band is also a hybrid having both a-type
1
1
From a fit of Eq. ͑2͒ to the observed transitions, the
vibrational anharmonicity constant, x , for the OH͑OD͒
stretch is determined. For HOI we obtain x ϭϪ82.825͑97͒
cm , and for DOI, Ϫ43.445͑61͒ cm . Because we observe
only transitions which involve the OH͑OD͒ stretch, the vi-
and b-type transitions. From the low resolution spectrum it is
11
P
possible to identify Q bandheads of the b-type perpendicu-
11
R
lar band having K р6. The Q bandheads having K Ͼ2 are
Ϫ1
Ϫ1
a
a
difficult to identify as they overlap with the congested a-type
parallel transitions of the ␯ fundamental. From the higher
1
brational equilibrium frequency, ␻ , cannot be determined
1
resolution HOI spectrum it is also possible to identify and
independent of the cross anharmonicity terms x12 and x13.
The anharmonicities for the OH͑OD͒ stretches of
HOF͑DOF͒ ͑Refs. 54 and 55͒, HOCl͑DOCl͒ ͑Ref. 56͒, and
OH͑OD͒ ͑Ref. 57͒ radical are also known. x11 for HOI and
DOI is very similar to that found for hydroxyl ͑Ϫ84.881
assign lines belonging to the a-type band of 2␯ Ϫ␯ . A por-
1
1
Q
tion of the R branch of the parallel band is shown in Fig. 6
along with the rotational assignments.
Ϫ1
Ϫ1
cm ͒ and deuterated hydroxyl ͑Ϫ44.055 cm ͒ radicals,
Ϫ1
IV. VIBRATIONAL ANALYSIS
and also to that for HOF ͑Ϫ85.24 cm ͒ and DOF ͑Ϫ45.14
cm ͒. The x11 anharmonicities for HOCl and DOCl,
Ϫ97.50 cm and Ϫ51.72 cm , respectively, are ϳ15%
Ϫ1
The band centers of the vibrational transitions for the
Ϫ1
Ϫ1
⌬
vϭϪ1 and ⌬vϭϪ2 sequence bands observed in the low
higher.
resolution spectra of HOI and DOI are listed in Table I. The
band center frequencies are taken as the minimum between
the P and R branch contours of the lower resolution spec-
Q
Q
V. RO-VIBRATIONAL ANALYSIS
tra. This is a crude estimate of the band center and is as-
signed an appropriate error of Ϯ5 cm . These vibrational
transitions, which are only observed for the OH͑OD͒ stretch,
are fit to the vibrational term value expression for a poly-
atomic, anharmonic oscillator,53 Eq. ͑1͒.
Because this is the first investigation of the rotational
structure of HOI, there are no highly accurate microwave
data to assist in determining the ground state constants of
this molecule. To avoid any difficulties which might arise
from correlations in lower and upper state rotational con-
stants when both sets are simultaneously determined by fit-
ting transition frequencies, and also to produce error esti-
mates which more accurately reflect the quality of the data,
we use the technique of combination differences to deter-
mine the rotation and distortion constants for the ground
state, ␯ ϭ1, and ␯ ϭ2 levels. In determining the rotational
Ϫ1
1
2
1
2
1
2
G
v v v3ϭ͚r
␻ ͑v ϩ ͒ϩ
x ͑v ϩ ͒͑v ϩ ͒ϩ••• . ͑1͒
rs r s
r
r
͚
1
2
rрs
Terms involving v and v , which are always zero in
2
3
this case, cancel out, leaving a simplified expression, Eq. ͑2͒,
for the vibrational transitions observed for the OH͑OD͒
stretch,
1
1
constants for ␯ ϭ1, combination differences can be made
1
J. Chem. Phys., Vol. 104, No. 19, 15 May 1996
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Klaassen, Lindner, and Leone: The ␯ OH(OD) stretch of HOI
7407
1
TABLE II. Range of JЉ and KЉ for observed transitions in HOI ␯ funda-
fourth order are included. The rotational wave functions are
expanded in terms of a symmetric rotor basis set. The Hamil-
tonian is taken from Eqs. ͑8.110͒–͑8.112͒ of Ref. 58. The
diagonal and off-diagonal matrix elements as used in the
fitting procedure are given in
a
1
mental and 2␯ Ϫ␯ hotband.
1
1
Single Ro-vibrational
transitions
␯1 Fundamental
JЉ range
2␯ Ϫ␯ hotband
1
1
JЉ range
Q
P0
P1 ␥ ϭ0
P1 ␥ ϭ1
P2
P3
2–45
4–15, 17–34
4–14, 16–29
4–8, 10–14, 16–29
4–36
4–24
4–29
6–22, 24–30
6–8, 10–30
8–15, 17–27, 29–35
17–35
Q
Q
Q
Q
Q
Q
Q
Q
Q
a
14–27, 29–38
14–18, 21–38
3–4, 6–45
4–38
2–40
10–37
10–37
3–40
4–28, 30–32
3–30
1
2
2
a
͗
v,J,ka
͉
H͉
v,J,ka
͘
ϭ␯ ϩ
͑B ϩC ͓͒J͑Jϩ1͒Ϫk ͔
0
v
v
a
2
a
2
2
ϩA k ϪD J ͑Jϩ1͒
v
J
R0
2
a
4
ϪDJKJ͑Jϩ1͒k ϪD k ,
͑3͒
K
a
a
R1 ␥ ϭ0
R1 ␥ ϭ1
R2
R3
a
1
4
1/2
͗
͗
v,J,ka
͉
͉
H
͉
͉
v,J,k Ϯ2
͘
ϭ
͑B ϪC ͓͒ f ͑0͒f ͑1͔͒
a
v
v
Ϯ
Ϯ
Ϫd J͑Jϩ1͓͒ f ͑0͒f ͑1͔͒1/2, ͑4͒
1 Ϯ Ϯ
PP3
H
v,J,k Ϯ4
͘
ϭd ͓ f ͑0͒f ͑1͒f ͑2͒f ͑3͔͒1/2,
v,J,ka
a
2 Ϯ Ϯ Ϯ Ϯ
Q bandhead
␯1 Fundamental
2␯ Ϫ␯ hotband
1
1
͑
5͒
͑6͒
In Eqs. ͑3͒–͑6͒, v and J are the vibrational and total
transitions
KЉ range
KЉ range
a
a
PQ
Q
1–7
0–5
1–6
0
f ͑l͒ϭ͓J͑Jϩ1͒Ϫ͑k Ϯl͒͑k ϮlϮ1͔͒.
Ϯ
a
a
R
aWang asymmetry parameter.
angular momentum quantum numbers. The pseudo-quantum
number k corresponds to the signed value of K in the sym-
a
metric rotor basis. A , B , and C are the effective rota-
v
v
v
from transitions involving both the ␯ fundamental and the
tional constants, and D , D , D , d , and d are the quar-
1
J JK K 1 2
2
␯ Ϫ␯ hotband. Due to the better signal-to-noise ratio for
tic centrifugal distortion constants of the symmetric top
reduced Hamiltonian.
1
1
the spectrum of the ␯ fundamental only these transitions are
1
used for determining the ␯ rotation and distortion constants.
For each J the Hamiltonian matrix is written in the sym-
metric top basis and is subjected to a Wang transformation.58
The resulting four Wang submatrices are diagonalized inde-
1
The transitions used in forming combination differences are
taken from both the low and higher resolution spectra. The
range of J and Ka quantum numbers observed for the ␯1
fundamental, and also the 2␯ Ϫ␯ hot band, are listed in
pendently. Only for the K ϭ1 subbands is the asymmetry
a
doubling observed. For all other K subbands the splitting
1
1
a
Table II.
between the asymmetry doublets is less than the instrumental
Q
In the higher resolution HOI spectrum, 370 transitions
are assigned in the ␯ fundamental. Of these, approximately
resolution. For example, the calculated splitting at R ͑30͒ is
2
Ϫ1
only 0.006 cm . For all K Ͼ1 subbands where asymmetry
1
a
one third are blended lines. Blended lines are given a greater
uncertainty than unblended lines in the fitting procedure. A
ro-vibrational line assigned to only one transition is given an
doubling is not observable, the term values are taken as the
mean of those calculated for the symmetric, ␥ϭ0, and anti-
symmetric, ␥ϭ1, Wang functions.
Ϫ1
uncertainty of 0.01 cm . Lines which can be assigned to
The rotation and distortion constants for the ground state
Ϫ1
two transitions are given an uncertainty of 0.02 cm , and
and ␯ ϭ1 of HOI are determined from fitting the Hamil-
1
lines which can be assigned to more than two transitions are
omitted from the fit. The same criteria for assigning uncer-
tainties are applied to transitions in the 2␯ Ϫ␯ hotband.
tonian given above to combination differences of the ␯ fun-
1
damental. The rotation constants for ␯ ϭ2 are determined
1
from combination differences of the 2␯ Ϫ␯ hotband. From
1
1
1
1
Of the 370 transitions taken from the higher resolution
the 370 transitions observed for the ␯ fundamental, 226
1
HOI spectrum for the ␯ fundamental, only 28 belong to the
combination difference pairs are derived for the ground state
1
P
perpendicular transition. These are all from the P K ϭ3
and 223 for ␯ ϭ1. For ␯ ϭ2, there are 109 combination dif-
a
1
1
subband. To obtain the A rotational constants with greater
ferences derived from 259 assigned transitions in the 2␯ Ϫ␯1
1
accuracy it is necessary to include more ⌬K ϭϮ1 transi-
hotband. Each combination difference is given an uncer-
tainty equal to the square root of the sum of squares of the
uncertainties for the transitions from which it is made. The
four Wang submatrices are diagonalized numerically, and
computed combination differences are least squares fit to the
measured values. Iteration of fit parameters is continued until
the reduced chi-squared varies by less than 0.001. The d2
off-diagonal centrifugal distortion term is found to be not
statistically significant with this data set and is therefore con-
strained to zero. Likewise, inclusion of centrifugal distortion
terms higher than fourth order did not significantly improve
the quality of the fit. The centrifugal distortion terms for
v1ϭ2 are not well determined from the combination differ-
a
R
tions from the perpendicular band. The perpendicular Q and
P
Q bandheads are easily identified from the low resolution
spectrum. Thirteen of these bandheads for K р7 are in-
a
cluded in the fit and are given an appropriately greater un-
Ϫ1
certainty of Ϯ0.5 cm . The perpendicular Q bandheads are
a convolution of all the overlapping ⌬Jϭ0 transitions having
⌬
K ϭϮ1. In the fit, the Q bandheads are treated as a single
a
transition assigned a median J value, Jϭ15.
The rotational analysis of HOI is based on the Hamil-
r
tonian of a near prolate asymmetric rotor, type I represen-
tation. The symmetric top reduction (S) of the molecular
Hamiltonian is used.58 Centrifugal distortion terms up to the
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7408
Klaassen, Lindner, and Leone: The ␯ OH(OD) stretch of HOI
1
TABLE III. Spectroscopic constants determined by combination differences for HOI ground state, v ϭ1, and
1
Ϫ1
v1ϭ2 ͑in cm ͒, S Reduction; IЈ representation.
Ground state
v1ϭ1
3625.84͑1͒a
v1ϭ2
7084.74͑5͒a
␯0
A
B
20.934 75͑109͒b
0.278 939 8͑285͒
0.275 070 8͑271͒
0.235 76͑314͒
20.032͑306͒
5.727 6͑824͒
Ϫ18.54͑648͒
0.0
20.079 60͑235͒
0.278 457 1͑337͒
0.274 461 0͑326͒
0.236 09͑375͒
19.536͑405͒
5.508͑180͒
Ϫ23.03͑768͒
0.0
19.257 2͑237͒
0.277 992 3͑226͒
0.273 946 8͑209͒
C
6
c
D ϫ10
0.236 09
J
6
19.536c
DJKϫ10
3
c
D ϫ10
5.508
K
9
Ϫ23.03c
0.0
d ϫ10
1
d
d2
No. of comb. diff.
226
0.25
223
0.32
109
0.66
2
e
␹
␯
aBand origins are determined in a separate fit to transition frequencies constraining rotational constants to values
determined by combination differences. The number in parentheses is an estimate of the uncertainty for the
band center.
b
One standard deviation in parentheses.
c
v ϭ2 distortion constants are constrained to the values determined for v ϭ1.
1
1
d
e
The d term is constrained to zero.
2
2
␯
2
␹
ϭ␹ /␯, where ␯ is the number of observations less the degrees of freedom.
ences of the 2␯ Ϫ␯ hotband alone. In the final fit, these
The inertial defect for the ground vibrational state of HOI is
indeed small. From the inverse of the rotational constants in
Table III, the calculated inertial defect for the ground vibra-
1
1
terms are constrained to the values determined for v ϭ1 and
1
only the A, B, and C rotational constants for v ϭ2 are al-
1
2
lowed to vary. The constants derived for these three states
tional state of HOI is 0.0026͑5͒ cm or 0.045͑8͒ amu Å . The
are listed in Table III.
ground state inertial defect for HOI is similar in magnitude
The band centers for ␯ and 2␯ cannot be determined by
and sign to those determined for HOCl ͑Ref. 24͒, 0.0642͑1͒
amu Å , and HOBr ͑Ref. 31͒, 0.067 175͑16͒ amu Å .
1
1
2
2
combination differences. In order to obtain these constants,
transition frequencies are fit instead of combination differ-
ences. Two techniques are used. In the first, the lower and
upper state constants are fixed to those determined by com-
bination differences and only the band center for the upper
state is treated as an adjustable parameter. In the second
technique, only the lower state constants are fixed to those
determined by combination differences while all rotation and
distortion constants for the upper state are allowed to float in
the fit. The difference in the band centers determined by the
two techniques is used as an estimate in the error for the
band center. In addition to determining the band center, fit-
ting the transitions also provides a consistency check on the
constants determined by combination differences. The rota-
tion and distortion constants determined by fitting transitions
are the same as those determined in the combination differ-
ence fit within the more conservative confidence interval for
the combination difference fit.
VI. DISCUSSION
With the work presented here, rotationally resolved
spectroscopic observations have been made of all the hypo-
halous acids. In Table IV the ground state constants and
molecular structures which have been determined for this
series are summarized. In the current work no rotational con-
stants for the isotopically substituted species DOI were de-
termined, so the structure of HOI can not be evaluated di-
rectly. However, the consistency of the ground state
rotational constants found for HOI can be compared with
known structures of the other molecules in this series by
constraining one of the molecular parameters. In their recent
31
work on the ␯ fundamental of HOBr, Cohen et al. noted
1
that the OH bond length is nearly the same in HOCl and
HOBr. They constrained the OH bond length in HOBr to that
determined for HOCl and calculated the corresponding bond
angle and OBr bond length by best least squares fit to their
rotational constants. In a similar manner we also constrain
the OH bond length in HOI to 0.9643 Å ͑the value deter-
mined for HOCl and used by Cohen et al.31 for HOBr͒ and
calculate the HOI bond angle and OI bond length from a
least squares fit to the three ground state rotational constants;
these are reported in Table IV. Although the molecular pa-
rameters determined in this way for HOI have large uncer-
tainties, the values are quite consistent with those known for
the other hypohalous acids. Ruscic and Berkowitz59 have
compared the OX bond length in HOX to that of the di-
atomic molecule and noted that the ratio is nearly constant in
Calculation of the inertial defect for HOI in its ground
vibrational state is also a valuable tool in checking the valid-
ity of the rotational constants. The inertial defect, Eq. 7, is
the difference between the largest moment of inertia, that
about the c axis, and the sum of the moments of inertia about
the a and b axes:
␯
c
␯
b
␯
a
I Ϫ͑I ϩI ͒ϭ⌬ .
͑7͒
␯
For planar rigid rotors the inertial defect is zero, and any one
of the moments of inertia is determined by the other two.
However, vibrational effects cause the inertial defect to be
nonzero in real molecules, although for a necessarily planar
molecule such as HOI the deviation is expected to be small.
J. Chem. Phys., Vol. 104, No. 19, 15 May 1996
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Klaassen, Lindner, and Leone: The ␯ OH(OD) stretch of HOI
7409
1
TABLE IV. Comparison of ground state constants and vibrational frequencies ͑in cmϪ1͒ and molecular struc-
tures for the hypohalous acids.
HOFa
HC Clb
35
HO Brc
79
HOId
A0
B0
C0
19.534 564
0.892 724 1
0.850 833 4
3.176 8
80.41
2.750 5
20.463 616
0.504 241 82
0.491 199 20
0.897 19
41.793
4.388 0
20.470 159
0.352 797 66
0.346 341 65
0.429 5
25.04
4.6018
20.935
0.278 94
0.275 07
0.236
20.0
5.73
6
D ϫ10
J
6
DJKϫ10
3
D ϫ10
K
9
d1ϫ10
d2ϫ10
␯1
␯2
␯3
H–OX Å
HO–X Å
ЄH–O–X/°
Ϫ142.3
Ϫ20.90
Ϫ7.08
Ϫ19
9
Ϫ11.8
Ϫ1.482
Ϫ0.39
3614.902 41
e
3609.482 48g
1238.624 60h
i
3625.84d
3577.925 8
1353.404 66f
1162.570 4
i
1068
k
f
h
j
l
889.079 74
724.358 07
620.18
575
0.964m
0.9643n
0.964 3o
1.827 9o
103.0o
0.964 3p
1.991
105.4
m
n
1.442
1.6891
m
102.96n
97.2
aHOF rotational constants from Ref. 14. The values listed here have been converted to the symmetric top
reduction (S) using the relations in Ref. 58.
b
HOCI rotational constants from Ref. 26.
c
HOBr rotational constants from Ref. 31.
d
From Table III.
e
Reference 16.
f
Reference 14.
g
Reference 26.
Reference 23.
h
i
Reference 31.
Reference 30.
j
k
Reference 40.
l
Reference 39.
m
Reference 11.
Reference 24.
Reference 31.
n
o
p
H-OI bond length constrained to value used for HOBr and HOCI.
the series from HOF to HOBr. Using this fact they predicted
an OI bond length in HOI of 1.995 Å which is in reasonable
agreement with our value of 1.991 Å.
Like the simple case for diatomic molecules, the distor-
tion constants of asymmetric rotors can be derived from
force constants and the derivatives of the inverse moment of
inertia tensor with respect to internal coordinates;5
8,64
thus it
It can be seen from Table IV that the quartic centrifugal
distortion constants, D , D , and D , show a monotonic
is not surprising to find an empirical relationship between the
distortion constants of a series of chemically similar mol-
ecules. Demaison et al.65 noted an empirical relationship be-
tween distortion and rotation constants which is broadly ap-
plicable to a large group of molecules and is helpful for
obtaining initial estimates of at least the order of magnitude
of the distortion constants. From Table IV, it is seen that the
J
JK
K
variation with the changing mass of the halogen atom. If the
HOX molecule is considered as a pseudodiatomic with the
OH group treated as a single composite atom, then the DJ
distortion constant for all of the hypohalous acids is well
approximated by the relation linking the force constant and
moment of inertia of a diatomic molecule to its centrifugal
distortion constant,5
8,60
DJK and D constants for the hypohalous acids also show a
K
monotonic variation with the varying mass of the halogen
3
4
Be
atom. Using the functional form given in Eq. ͑7͒ as a guide,
D ϭ
e
.
͑8͒
3
x
2
i
2
we have plotted in Fig. 7 log D (iϭJ,JK,K) vs log 4B /␻
␻e
i
where
for
D ,B ϭ(BϩC)/2
and
␻ ϭ␯ ;
for
J
x
i
3
The D distortion constants predicted by this simple re-
DJK ,B ϭ(BϩC)/2 and ␻ ϭ␯ ; and for D ,B ϭA and
J
x i 2 K x
lationship when ␻ is the HO–X vibrational frequency and
␻ ϭ␯ . These combinations of rotational constants and vi-
i 1
e
B is taken as the mean of the measured ground state B and
brational frequencies were chosen so that the plots all
showed straight lines. Interestingly, the plots of the distortion
e
C rotational constants, (B ϩC )/2, are in fair, quantitative
0
0
agreement ͑ϳ5%͒ with the measured values for all the hy-
constants done in this manner all have a common intersec-
pohalous acids and also for HOD.6
1,62
The applicability of
tion. Also plotted in Fig. 7 are the points for HOD,
61,62
which
Eq. ͑8͒ to other polyatomic molecules which can be treated
as pseudodiatomics was noted by Thomas et al. in their early
study of the methyl halides.63
were calculated as for the hypohalous acids. The HOD cen-
trifugal distortion terms are well predicted by the straight
lines falling through the data for the hypohalous acids.
J. Chem. Phys., Vol. 104, No. 19, 15 May 1996
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7410
Klaassen, Lindner, and Leone: The ␯ OH(OD) stretch of HOI
1
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FIG. 7. Plot for all the hypohalous acids and also HOD of log D ͑i
i
23
24
25
3
x
2
i
ϭJ,JK,K͒ vs log 4B /␻ , where for D , B ϭ(BϩC)/2 and ␻ ϭ␯ ; for
J
x
i
3
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x
i
2
K
x
i
1
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᭹͒; HOF ͑᭺͒; HOCl ͑ϩ͒; HOBr ͑ϫ͒; and HOI ͑*͒.
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