Intracavity laser absorption spectroscopy of HOCI overtones. I. the 3v1+2v2 band and numbers of vibrational states

Article abstract of DOI:10.1063/1.471016

The near infrared high-resolution spectra of the a-type transitions of the weak 3v₁+2v₂ combination band of transient HO³⁵⁽³⁷⁾C1 at 12 600 cm^-1 has been recorded in an ultrasensitive titaniunrsapphire intracavity laser absorption spectrometer (ICLAS). We report line assignments, new and refined anharmonicity parameters, and the spectroscopic constants for the excited rovibrational states of 3v₁+2v₂. The Fermi resonance perturbations in this five quanta region, where the internal energy of the molecule is already more than 2/3 of the dissociation energy E₀, remain localized and they are the exception, while the extent of intermode mixing and thus intramolecular vibrational energy distribution (IVR) seems to be still small. A Dunham expansion is used for band origin predictions and representations of vibrational states N(E) of HO³⁵C1 up to the dissociation threshold. The results are compared with harmonic and anharmonic numbers of states from a recently proposed stretch-bend coupling model.

Full text of DOI:10.1063/1.471016

Intracavity laser absorption spectroscopy of HOCl overtones. I. The 3v 1+2v 2 band and
numbers of vibrational states
Bernd Abel, Hilmar H. Hamann, Alexander A. Kachanov, and Jürgen Troe
Citation: The Journal of Chemical Physics 104, 3189 (1996); doi: 10.1063/1.471016
View online: http://dx.doi.org/10.1063/1.471016
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Intracavity laser absorption spectroscopy of HOCl overtones.
I. The 3v1؉2v2 band and numbers of vibrational states
Bernd Abel, Hilmar H. Hamann, Alexander A. Kachanov,a) and Jurgen Troe
¨
¨
Abteilung Spektroskopie und Photochemische Kinetik, Max-Planck Institut fur biophysikalische Chemie, Am
¨
¨
¨
Fassberg, 37077 Gottingen, Germany and Institut fur Physikalische Chemie der Universitat Go¨ttingen,
¨
Tammannstrasse 6, 37077 Gottingen, Germany
͑Received 12 June 1995; accepted 12 October 1995͒
The near infrared high-resolution spectra of the a-type transitions of the weak 3 ϩ2
v1 v2
combination band of transient HO35͑37͒Cl at 12 600 cmϪ1 has been recorded in an ultrasensitive
titanium:sapphire intracavity laser absorption spectrometer ͑ICLAS͒. We report line assignments,
new and refined anharmonicity parameters, and the spectroscopic constants for the excited
rovibrational states of 3 ϩ2 2. The Fermi resonance perturbations in this five quanta region,
v1
v
where the internal energy of the molecule is already more than 2/3 of the dissociation energy E0 ,
remain localized and they are the exception, while the extent of intermode mixing and thus
intramolecular vibrational energy distribution ͑IVR͒ seems to be still small. A Dunham expansion is
used for band origin predictions and representations of vibrational states N(E) of HO35Cl up to the
dissociation threshold. The results are compared with harmonic and anharmonic numbers of states
from a recently proposed stretch–bend coupling model. © 1996 American Institute of Physics.
͓S0021-9606͑96͒02603-7͔
I. INTRODUCTION
laser spectroscopic techniques, such as vibrationally medi-
ated photodissociation and photofragment spectroscopy,7,8
9
The spectra of coupled vibrational overtone states in
polyatomic molecules are of fundamental interest for the un-
derstanding of ͑intra͒ molecular dynamics and related phe-
nomena, such as unimolecular reaction and internal vibra-
tional redistribution ͑IVR͒. High resolution spectra of these
highly excited molecular eigenstates probe the features of the
intramolecular potential, which are relevant to these
processes.1,2 While the line positions sample different parts
of the potential in general, the intensities may provide addi-
tional information on particular parts ͑e.g., the repulsive part͒
of the intramolecular potential surface.3 In addition to the
measured line positions and intensities, the density of levels,
and, in the case of predissociating states, their linewidths
provide a stringent test for theoretical models.4,5 In small
molecules at low internal energies a quasiperiodic motion of
the molecule can be inferred from the IR spectra, whereas
complete IVR at high ͑chemically significant͒ internal ener-
gies is often assumed in theories of unimolecular reaction.1,6
With our approach we would like to explore the spectros-
copy, perturbations, resonances ͑and the onset of IVR͒ and
numbers and densities of states in the intermediate energy
range and to study the competition of intramolecular energy
redistribution and state resolved unimolecular reaction at
much higher energies at a later stage.
‘‘ring down cavity’’ ͑RDC͒
and photoacoustic
spectroscopy,10 sensitive double resonance techniques,11,12 as
well as ultrasensitive intracavity laser absorption spectro-
13–18
meter ͑ICLAS͒
have been developed to overcome these
limitations. Especially the latter technique has proven to be
one of the most sensitive, powerful, and universal techniques
available.
In recent years, the classical ICLAS technique has been
extended into the near infrared using new solid state materi-
als like Ti:Sapphire.13,14,19 We have used this technology in
our vibronic solid state laser intracavity absorption spectrom-
eter. The spectral distribution and width of the laser emis-
sion, with an absorber inside the cavity, can be described
by13,14,16–19
2
ͱ
␥•tg /␲
⌫
Ϫ
v
v0
I
,t ͒ϭI
g
exp Ϫ
␥tg
͑v
ͫ ͫ
ͬ
ͬ
0
⌫
ϫexp Ϫ␴ ͒•C•l
,
͔
eq
͑1͒
͓
͑v
where ␥ is the cavity loss rate, ⌫ is the width of the gain
profile ͑HWHM͒, ␴͑ ͒ is the absorption cross section of an
v
absorber, C is the particle density, and tg is the generation
time. This technique can, in principle, provide absolute ab-
sorption cross sections at effective path lengths leqϭctg͑L/l͒
of several hundred kilometers ͑c is the speed of light; L is
the cell length; l is the laser cavity length͒ and highest sen-
sitivities of ␴ϫCϷ10Ϫ11 cmϪ1 at generation times of up to
several tens of milliseconds.19
For the investigation of the intra- and unimolecular dy-
namics in highly excited states in polyatomic molecules and
the probe of intramolecular potential energy surface param-
eters it is certainly important to measure the inherent weak
Direct absorption spectroscopy of overtones in the gas
phase has inherent limitations of sensitivity. Therefore, FTIR
techniques, even with multireflection cells, are currently still
limited to the infrared range.1 In the last decade sensitive
a͒
Also associated with the Institute for Spectroscopy, Russian Academy of
Science, 142092 Troitsk, Moscow Region, Russian Federation and the
Laboratoire de Spectrometrie Physique, Universite Joseph Fourier de
Grenoble, B. P. 87, 38402 Saint-Martin-d’Heres CEDEX, France.
pure overtone levels ͑n ͒, but spectroscopy on these rela-
v1
J. Chem. Phys. 104 (9), 1 March 1996
0021-9606/96/104(9)/3189/9/$10.00
© 1996 American Institute of Physics
3189
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3190
Abel et al.: Spectroscopy of HOCl. I
tively isolated stretching modes provides only restricted in-
formation. In order to have a complete view on intramolecu-
lar couplings and other dynamical processes it is important to
observe the much weaker combination bands as well. We
have developed a sensitive ICLAS spectrometer which can,
in contrast to most of the other above-mentioned techniques,
provide this sensitivity in combination with high spectral
resolution. The power of such a device and the technique in
general has already been proven in a number of high resolu-
tion studies of overtone spectra of gases.13,14,18 In this paper,
as a first example, we will present the measurement of a
fairly weak five quanta combination band of HOCl in the
energy range of 2/3 of its dissociation energy E0 , a band
which is hardly accessible by other techniques20–30 ͑like
FTIR spectroscopy͒. We have chosen this model system be-
cause it is a small triatomic molecule, for which accurate ab
initio calculations20 are feasible, which could be refined with
the available experimental data. HOCl overtones seem to be
mostly isolated and they do not show complicated ‘‘polyad
structure’’ such as observed for other molecules.1 These fea-
tures make it an excellent model system for studies of local
modes and intermode couplings in small molecules.
FIG. 1. Standing wave cavity configuration ͑OC:output coupler, FM1/FM2:
folding cavity mirror, AM: Ti:Sapphire crystalϩmount, HR: high reflector,
S: movable slit for wavelength tuning, triangles: movable prisms, PL: lens;
for details see text͒.
Ref. 35 we estimated the partial pressure of HOCl to be
around 10–15 Torr in the bulb after the synthesis. As, neither
H2O lines nor Cl2O lines interfered significantly with the
HOCl bands studied in this work, the mixture was used with-
out further separation. The pressure in the absorption cell
was 50 Torr in the measurements of the weak 3 ϩ2 band
v1 v2
and was kept constant during the measurements. The HOCl
sample consisted of a mixture of HO35Cl and HO37Cl in
natural abundance ͑ϳ75% HO35Cl͒.
The interest in high-resolution IR and near IR spectra for
the remote sensing of this molecule in the upper atmosphere
has also been stressed.31,32 For HOCl and its isotopomers
experimental data are available between 0 and 10 000 cmϪ1
͑Refs. 20–29͒ and, due to the limited sensitivity of the ap-
plied techniques, almost no data at relatively high excitation
energies ͑10 000–20 000 cmϪ1͒.30 The high-resolution IR
spectra of the fundamentals of this molecule have been re-
corded and assigned. After the first study of the infrared
spectrum of this molecule by Hedberg and Badger,21 and the
The laser spectrometer used in the experiments was
similar in design to that used in Ref. 14. The schematics of
the Ti:Sapphire cavity which has been used in the present
experiment is shown in Fig. 1. It was placed inside a sealed
box, which was flushed with nitrogen in order to remove the
strong atmospheric absorption from ͑oxygen and͒ water va-
por, which otherwise would have covered weak transitions.
For the description of the basic principles of ICLAS we will
refer to Ref. 19, where some specific questions of using solid
state lasers for this technique are considered. A flexible cav-
ity design, which allows to work at very different spectral
and sensitivity ranges, has been employed, which allowed to
use the same elements of the cavity in a standing-wave as
well as in a traveling-wave ring configuration, with any
known type of vibronic crystals ͑Ti:sapphire, Cr-doped for-
sterite, Cr4ϩ:YAG, Co:MgF2, etc.͒ and with many laser dyes.
Our present ICLA spectrometer consisted of a four mirror
standing wave astigmatically compensated linear cavity with
a flat high reflector HR, two highly reflecting folding mirrors
FM1 and FM2 with a radius of curvature of 150 mm and flat
output coupler OC ͑2% transmission͒. Two Brewster angle
prisms and a movable slit S were placed into the short arm of
the cavity in order to provide tuning of the broadband spec-
trum of the laser, as it is described in Ref. 14. The radiation
of a cw-argon ion laser ͑Innova 310, Coherent͒, operating on
all lines, was focused through one dichroic mirror with the
lens PL into a 11 mm long Brewster cut Ti:sapphire crystal
͑Science Solutions Inc.͒. The crystal was placed between the
folding mirrors with its Z axis oriented perpendicular to the
axis of the rod in the horizontal plane. The crystal mount had
two translation adjustments, one along the rod axis, another
parallel to the Brewster faces which was necessary for opti-
mization of the laser threshold and laser generation. It also
had a rotational adjustment normal to the face of the crystal
to avoid clustering of the spectrum due to the natural bire-
first results of Ashby27 on , high quality spectra of
,
,
v1
v1 v2
and
have been recorded and analyzed by Wells et al. and
v3
Juntilla et al.,24 Sams and Olson,28 and Deeley and Mills.25
Later, Lafferty and Olson22 made an improved analysis of the
and
bands with very good resolution. All these studies
v3
v2
provided an accurate set of molecular constants for the
ground state and for the fundamentals. The overtones and
combination bands have received much less attention in the
past. Deeley and Mills25 observed the 2 band and, very
v2
recently, Escribano, Fusina et al.26,30 assigned 2 , and 3
,
v1
v1
ϩ2 2 , all
and the combination bands 1ϩ
,
ϩ
,
v
v3 v1 v2 v1
v
accessible with FTIR spectroscopy. The latter group deter-
mined a large set of molecular parameters and anharmonicity
constants for the 35Cl and 37Cl isotopomers.26,30 Interest in
the UV photodissociation of the transient HOCl molecule
was kindled by its possible role in the stratospheric chlorine
balance33,34 and, hence, in ozone depletion.
II. EXPERIMENT
Fresh samples of HOCl were prepared before the mea-
surements by reacting Cl2 ͑Ϸ700 Torr͒ with a slurry of red
mercuric oxide22–24 ͑containing 5 g of HgO and 0.5–1 ml
H2O͒ in a separate gas handling setup ͑glass reactor͒. The
gas mixture at that time consisted of an equilibrium mixture
of Cl2O, H2O, and HOCl. With the equilibrium constant from
J. Chem. Phys., Vol. 104, No. 9, 1 March 1996
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Abel et al.: Spectroscopy of HOCl. I
3191
fringence of the rod.14 In order to minimize the amplitude of
the parasitic interference fringes, which are due to the scat-
tering on the intracavity surfaces,15,36 and back reflections
from external elements, only high quality mirrors on thick
substrates with a large wedge have been used. All optical
components ͑except the spherical mirrors͒ used in our setup
were 15 mm in diameter ͑Science Solutions Inc.͒ and have
Brewster angled rear faces such that no radiation could be
reflected back into the cavity. We worked at a generation
time tg equal to 300 ␮s ͑controlled by a simple mechanical
chopper͒ which corresponded to an absorption path equiva-
lent to 54 km in the absorption cell taking into account the
ratio of the cell length to the cavity length which was equal
to 0.6. Fused silica Brewster windows 2 in. in diameter hav-
ing 1° wedge were attached to the stainless steel cell holders
using O rings ͑Viton͒. The other side of each holder had a
standard O-ring vacuum tight connection to a Pyrex or quartz
tube of 30 mm diameter. Both Brewster window holders had
standard vacuum fittings to the vacuum pump, pressure
meter and the gas source. The overall cell length in our
present experiments was 95 cm. Intracavity absorption spec-
tra were recorded with a photodiode array ͑1024 diodes with
a 13 ␮ pitch and a height of 0.5 mm͒ which was placed into
the focal plane of an automated compact high resolution 1.3
m diffraction grating spectrometer ͓20ϫ7 cm, 75 lines/mm
echelle ͑‘‘echelette’’͒ grating working at the blaze angle of
64°͔. Throughout the experiments we worked in triple dif-
fraction in 30th order where the instrumental width of the
spectrograph was about 0.02 cmϪ1. The entire spectrum of
the molecule was automatically recorded in 14 fractions of
about 11 cmϪ1, each fraction was averaged 100 times and
had a small wavelength overlap with the previous one. The
control of the grating rotation and acquisition of the data
were done by a microcomputer. In the calibration procedure
water lines were used as an internal standard. Due to a small
nonlinearity of the spacing of the diodes in the CCD chip, a
linear interpolation could not be used for calibration, because
this might have resulted in an error of ϳ0.03 cmϪ1 ͑in the
worst case͒. Unfortunately, we did not have enough water
lines in each spectral window for the determination of
higher-order polynominal coefficients. Therefore, we re-
corded a spectral distribution of the laser for each of the 14
spectral windows of the HOCl spectrum with a fused silica
etalon inserted into the cavity, as well as the absorption spec-
trum of water vapor. The etalon fringe spectrum and the
water spectrum were processed and peak positions of fringes
and water lines were derived automatically using an algo-
rithm described by Snyder.37 The spectra were then cali-
brated with the water line data from the HITRAN database.
Subsequently a linear regression procedure was employed to
find expansion coefficients attributing absolute wave num-
bers to each pixel in each spectral window. The analysis of
residuals shows that the accuracy of the whole wavelength
calibration procedure was about 0.001–0.002 cmϪ1. Because
many HOCl lines were blended by intense water lines and
also because of the array diode spacing problem, we specify
FIG. 2. Overview of the 3 ϩ2 band of HO35Cl and HO37Cl in the
v1 v2
wavelength range between 12 560 and 12 650 cmϪ1. For clarity the posi-
tions of only four K sub-bands for the most abundant HO35Cl isotopomer
͑symmetric top notation͒ are shown. The water lines in the spectrum could
be easily identified in the spectrum and used for calibration.
III. RESULTS AND DISCUSSION
A. Spectra, Hamiltonian, and molecular parameters
Figure 2 shows a survey spectrum of the weak 3 ϩ2
v1
v2
band of the isotopomers HO 35Cl and HO37Cl in natural
abundance ͑ϳ75% HO35Cl͒ between 12 560 and 12 650
cmϪ1 together with assignments ͑only 4 Ka sub-bands͒ for
HO35Cl, wavelength calibration and some water lines in this
region used for calibration. The band origins are 12 612.5519
and 12 611.4757 cmϪ1 for HO35Cl and HO37Cl, respectively.
The observed band is approximately 20–50 times weaker
than the 4 band which we also recorded at around 13 430
v1
cmϪ1 ͑Ref. 38͒. The spectrum looks quite dense and unstruc-
q
q
tured due to many overlapping PKa(J) and RKa(J)
branches ͑symmetric top notation͒ up to Kϭ5 and Jϭ40
with a few intense water lines in between. The calculated
vibronic density of states in this wavelength range is
0.05/cmϪ1, so that we do not expect nor find other overlap-
ping vibrational overtone bands with appreciable intensity in
this particular region. In contrast to the appearance at first
sight, the spectrum represents a very clear example for a
weakly perturbed a-type parallel overtone band of an asym-
metric top molecule. A standard Watson-type Hamiltonian
39
͑in the S reduction and ⌫ representation͒ was used for the
analysis of the band. The molecular parameters of the excited
state were least-squares fitted to the experimental data, using
the ground state constants reported in Refs. 24 and 30. The
complete analysis of this combination band was possible due
to the excellent S/N ratio which allowed the measurement of
transitions up to KЉaϭ5 and JЉϭ45. For the final analysis of
the band, we fitted a set of Ϸ600 transitions for the most
abundant isotopomer and Ϸ200 for HO37Cl. Blended lines
and overlapping lines were excluded from the fit ͑see the
appendix and Ref. 46͒. Figures 3͑a͒ and 3͑b͒ show two K
branches for HO35Cl and HO37Cl ͑using symmetric top no-
tation͒ in two regions of the spectrum with very different
our accuracy of calibration to be better than 0.01 cmϪ1
.
J. Chem. Phys., Vol. 104, No. 9, 1 March 1996
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3192
Abel et al.: Spectroscopy of HOCl. I
where B represents Bx , By , or Bz. ␣ and ␥ were obtained
from Ref. 30. The sextic centrifugal distortion constants
HKJ , HJK , HJ , and HK ͑and d1 , d2͒ were constrained to the
ground state values because their inclusion as free param-
eters did not improve the quality of our fit, which means that
we could not fit them sensitively enough. Nevertheless, the
overall fit appeared to be very good which manifested itself
in an average deviation of the residuals of less than 0.007
cmϪ1. All constants were determined with a high accuracy,
although those for the 37Cl species are less accurate than for
the other isotopomer. The 35Cl37Cl isotope shift for this band
for the two isotopomers appeared to be 1.076 cmϪ1, close to
the values for the ϩ2 and 2 bands.30 The tables of
v1
v2
v2
the assigned and calibrated transition wave numbers, the as-
signed molecular quantum numbers, and the residuals
⌬ ϭ
Ϫ
for the 3 ϩ2
v1
band of HO35Cl and
v2
v
vobs vcal
HO37Cl can be found in Ref. 46. While Table II lists the
derived excited state molecular parameters, Table I gives
fundamentals, harmonic frequencies, known overtones, and
anharmonicity parameters from a Dunham fit. In Table I we
compare our Dunham fit ͑fit 1 with y112 , and fit 2 with y11122
,
setting all other unknown coefficients to zero; ten fitted band
origins͒ with a previous fit from Ref. 30 ͑nine fitted band
origins͒. Because we have only fitted one additional band
origin most ͑but not all͒ of the constants did not change
͑within the error bars͒ compared to those from the previous
fit.30 However, including one additional parameter we could
predict the band origins of the 3 ϩ2 bands of HO35Cl
v1 v2
and HO37Cl much better. Because the impact ͑and the mag-
nitude͒ of a lower order anharmonicity constant, e.g., y112 , is
expected to be much larger than that of a high-order constant
͑e.g., y11122͒, we recommend fit 1 ͑Table I͒. Fit 1 was also
used for the state count in Sec. III C, although both ap-
proaches yielded results which were practically undistin-
guishable.
FIG. 3. Assignments for two K sub-branches for HO35Cl and HO37Cl ͑sym-
metric top notation͒ in two different regions of the spectrum with very
different appearance and congestion ͑a͒ and ͑b͒. For clarity only the qP0(J),
qP1(J), qR0(J), and qR1(J) sub-branches are shown. For further assign-
ments see tables in the Appendix.
B. Fermi resonance type perturbations in 3v1؉2v2 of
HO35Cl
appearance and congestion together with the precise assign-
ments ͑for clarity we show only two branches, but all lines in
this spectrum were assigned, see the Appendix and Ref. 46͒.
All along this spectrum intense water lines appear, which are
stronger than the HOCl lines, and thus can be easily identi-
fied and used for calibration. The refined molecular constants
and parameters obtained from these sets of data are listed in
Tables I and II. All refined parameters converged to values
close to the corresponding values for the ground state and the
lower overtones ͑Table II͒. The changes in rotational con-
stants with respect to their ground state values are in the
expected range and could be predicted with high accuracy
using the following expression40
In addition to a small additional anharmonic shift of the
origin ͑compared to the predictions͒ of the band, mainly due
to higher-order anharmonicity terms, we observed a local
perturbation of the Kaϭ4 sub-band which manifested itself
in
⌬ ϭ
v
a
systematic and considerable deviation of the
– cal values. While in the progress of assigning this
vobs v
band, it became apparent that the lines of this branch could
not be fitted using a conventional Hamiltonian. These lines
were omitted from the least-squares fitting of the upper state
molecular constants. In Fig. 4͑a͒ a small part of the consid-
q
ered HOCl spectrum with the affected R4(J) band ͑sym-
metric top notation͒ is shown. The perturbations are quite
obvious if one inspects the actual line positions of the
marked lines with respect to their predicted positions. In ad-
dition, the frequency shift ⌬ ϭ
Ϫ
͑residuals͒ is plot-
v
vobs vcal
B
B ϭB Ϫ
␣
rϩ1/2͒
͑v
͚
v
e
r
ted against the upper state JЈ quantum number for the
r
q
q
branches R4(JЈϪ1͒ and P4(JЈϩ1͒ in Fig. 4͑b͒. The lines
of transitions to JЈϽ10 were overlapped or blended, such
that the effect could not yet be analyzed quantitatively in this
B
rs
ϩ
␥
ϩ1/2͒ sϩ1/2͒ϩ...,
͑v
͑2͒
͑vr
͚
rрs
J. Chem. Phys., Vol. 104, No. 9, 1 March 1996
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Abel et al.: Spectroscopy of HOCl. I
3193
TABLE I. Harmonic frequencies, fundamentals, overtones, and anharmonicity ͑Dunham͒ parametersa for HO35Cl and HO37Cl ͑in cmϪ1͒.
Fundamentals/overtonesc
HO35Cl
HO37Cl
␯
␯
␯
1
2
3
22
22
25
24
30
30
30
26
30
͑0
͑0
͑0
͑1
͑1
͑1
͑1
͑2
͑3
͑3
0
1
2
0
0
1
2
0
0
2
1͒
0͒
0͒
0͒
1͒
0͒
0͒
0͒
0͒
0͒
͑asym. str͒
͑bend͒
724.358 07
1238.624 60
2461.21
3609.482 48
4331.9085
4820.4323
6013.8307
7049.8132
10322.2932
12 612.5519
718.165 69
1238.131 38
2460.24
3609.489 00
4325.7421
4819.9321
6012.7627
7049.8234
10 322.3778
12 611.4757
͑sym.str.͒
Fit 1d
with y112
Fit 2d
with y11122
Fit from
Ref. 30e
Fit 1d
with y112
Fit 2d
with y11122
Fit from
Ref. 30e
Dunham parameters
␻
3794.087
1267.722
725.324 079
Ϫ85.53649
Ϫ26.102
Ϫ1.93202
Ϫ7.642
Ϫ7.85
Ϫ6.63
0.216 859
Ϫ0.756
Ϫ0.0305
•••
3794.116
1267.745
725.324 079
Ϫ85.551 75
Ϫ26.163
Ϫ1.932 02
Ϫ7.644
Ϫ7.85
Ϫ6.63
0.21 7322
Ϫ0.750
3794.118 ͑26͒
1267.745 ͑66͒
725.324 079 ͑66͒
Ϫ85.551 75 ͑26͒
Ϫ26.163 ͑50͒
Ϫ1.932 02 ͑10͒
Ϫ7.642 ͑28͒
Ϫ7.85
3794.132
1267.143
719.121 97
Ϫ85.598 13
Ϫ26.028
Ϫ1.912 56
Ϫ7.599
Ϫ7.75
3794.152
1267.158
719.121 97
Ϫ85.608 27
Ϫ26.068
Ϫ1.912 56
Ϫ7.601
Ϫ7.75
3794.153 ͑26͒
1267.158 ͑66͒
719.121 97 ͑13͒
Ϫ85.608 27 ͑88͒
Ϫ26.068 ͑50͒
Ϫ1.912 56 ͑22͒
Ϫ7.599 ͑28͒
Ϫ7.75
1
␻2ϩ͑1/2͒x23
␻3ϩ2x33ϩ͑1/2͒x23 ͑Ref. 30͒
x11
x12
x13 ͑Ref. 30͒
x22
x23 ͑Ref. 20͒
x33 ͑Ref. 20͒
y111
y122
y112
y11122
⌬
Ϫ6.63
Ϫ6.52
Ϫ6.52
Ϫ6.52
0.216 859 ͑57͒
Ϫ0.756 ͑25͒
•••
•••
0.351
0.229 10
Ϫ0.805
Ϫ0.0203
•••
0.229 41
Ϫ0.801
•••
Ϫ0.001 23
0.000
0.229 10 ͑20͒
Ϫ0.805 ͑25͒
•••
•••
0.244
b
•••
b
Ϫ0.001 85
0.004
͑3 ϩ2
͒
Ϫ0.001
Ϫ0.005
v0 v1 v2
͑calc–obs͒
aWe determined the errors of the constants ␻i , xi , and yi of fit 1 and 2 to be comparable to those of Ref. 30. Standard errors in parentheses refer to the least
significant digits.
bDetermined by setting all other unknown high order y(ijk...) terms to zero;
cFor errors see Refs. 22, 24–26, and 30
d10 band origins fitted.
e9 band origins fitted.
range. The Kaϭ3 and Kaϭ5 sub-bands of HO35Cl, as well as
the Kϭ1-3 bands of HO37Cl, were found to be unperturbed.
The weak Kϭ4 band of HO37Cl is difficult to analyze, due to
the weakness of the lines, but it seems to be unperturbed as
well. As is usual in the case of medium local perturbations
where transitions to the perturbing level are not clearly ob-
served ͑extra lines͒ nor assignable, little can be done to quan-
titatively treat the resonance or the perturbing dark state. No
extra lines of the perturbing state were observed, and we did
not attempt to assign the perturber state quantitatively. The
molecular parameters and the anharmonicity parameters of
HO35͑37͒Cl are shown in Tables I and II. Band origins as well
as overtone bands can be predicted with a reasonable preci-
sion using a Dunham expansion and Eq. ͑2͒. Using the
known harmonic frequencies and the anharmonicities ͑Table
I͒ we calculated that there are about four vibrational levels
within Ϯ25 cmϪ1 of 3 ϩ2 2. Energetically, the most likely
possible to have simultaneous Fermi and Coriolis interac-
tions between two vibrational levels, as has been found for
HDO.43 Fermi resonances as well as Coriolis coupling be-
tween rovibrational levels are characterized by specific
⌬Kaϭ0,Ϯ2 or ⌬KaϭϮ1,Ϯ3 selection rules.41 We infer from
the J dependence of the perturbation, which can be inspected
in Fig. 4, that the 3 ϩ2 2 rovibronic levels are connected to
v1
v
the ‘‘dark’’ levels of the 2 ϩ3 ϩ3 state by Fermi-type
v1 v2 v3
interaction.38 Since the matrix elements for Coriolis coupling
interactions linking the two states would be proportional to
J(Jϩ1), we conclude that the observed decrease in the per-
turbation at increasing JЈ ͑upper state͒ can only be explained
by accidental Fermi resonance between the K sub-band of
3 ϩ2 and the ‘‘dark perturber.’’ Calculations show that
v1 v2
rovibrational levels of the Kϭ4 sub-band of 2 ϩ3 ϩ3
v1 v2 v3
and rovibrational levels of the 3 ϩ2 ͑Kϭ4͒ subband of
v1 v2
HO35Cl coincide partially ͑here ⌬Kaϭ0͒. The rotational con-
stants of neighboring states could approximately be predicted
using Eq. ͑2͒. The same calculations show that the sub-
branches of other possible overtones in the considered wave-
length region are too far away from the perturbed Kϭ4 band,
v1
v
candidate, which may act as
a
perturber, is the
2
3
ϩ3 ϩ3 3 overtone state, whose origin is slightly below
v
v1 v2
ϩ2 2. The selection rules for perturbations are ⌬ Jϭ0
v1
v
and only levels of the same overall rovibronic symmetry aЈ
or aЉ can interact.41,42 For molecules of Cs symmetry, it is
although the origins
may be quite close to that of the
v0
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3194
Abel et al.: Spectroscopy of HOCl. I
TABLE II. Molecular constants for the ground state and the 3 ϩ2 overtone state of HO35Cl and HO37Cl ͑in cmϪ1͒. Standard errors in parentheses refer
v1 v2
to the least significant digits. Parameters without error were fixed at their ground state values.
HO35Cl
HO37Cl
Origin
12 612.5519 ͑6͒
Ϫ0.9987
12 611.4757 ͑12͒
Ϫ0.9987
v0
␬
Ground state: ͑all values fixed; values from Refs. 23 and 26; errors: see Ref. 23͒
Rotational constants
Bx
By
BZ
0.504 241 880
0.491 199 240
20.463 610 3
0.495 357 294
0.482 764 156
20.462 856 4
Centrifugal distortion constants
DJϫ106
D
0.897 648 7
0.417 995 8
0.433 497 4
Ϫ0.208 780 4
Ϫ0.149 477
Ϫ0.485 0
0.866 692 2
0.406 524 6
0.433 298 0
Ϫ0.198 026 7
Ϫ0.138 152
Ϫ0.62 11
JKϫ104
DKϫ102
d1ϫ108
d2ϫ108
HJϫ1012
H
H
JKϫ109
KJϫ107
0.102 76
0.101 39
0.294 23
0.286 50
HKϫ105
0.384 753
0.382 545
Excited state:
␬
Ϫ0.9982
Ϫ0.9982
Rotational constants
Bx
By
Bz
0.501 219 41 ͑237͒
0.483 987 74 ͑238͒
19.376 498 ͑113͒
0.492 324 78 ͑584͒
0.475 684 97 ͑570͒
19.374 995 ͑510͒
Centrifugal distortion constants
DJϫ106
D
0.922 43
0.506 154
0.616 236
Ϫ0.208 7804
Ϫ0.149 477
Ϫ0.4850
͑136͒
͑897͒
͑393͒
0.858 69
0.462 49
0.631 55
Ϫ0.198 026 7
Ϫ0.138 152
Ϫ0.6211
͑420͒
͑473͒
͑491͒
JKϫ104
DKϫ102
d1ϫ107
d2ϫ108
HJϫ1012
H
H
JKϫ109
KJϫ107
0.102 76
0.101 39
0.294 23
0.286 50
HKϫ105
0.384 753
0.382 545
3
ϩ2 state. Obviously a special interplay between the
v1 v2
well-documented system in which substantial perturbations
are also absent in the spectrum, even at very high energies.3
Order in the spectrum can break down in different ways. One
positions of the sub-band origins and rotational constants is
needed to cause the perturbation in the Kϭ4 sub-band. These
calculations mainly exclude candidates other than
effective mechanism is a n ϫ Ϫn ϫ resonance which
vi vj
i
j
2
ϩ3 ϩ3 acting as a perturber, but our ‘‘assignment’’
may cause complicated ‘‘polyad structures,’’ energy ex-
change between the two oscillators, as well as an increase in
the density of observable lines in the spectrum. It may also
be possible that such a resonance tunes in at higher energies
due to different anharmonicies of the different modes. Our
calculations show that these effects will play a minor role in
the overtone spectra at higher energies. Our experiments in
the 5 or 6 quanta region, which are in progress, will
v1 v1
show at which energy efficient intramolecular energy redis-
tribution starts and which mechanisms are responsible for it.
v1 v2 v3
of the perturber can only be a recommendation at this point.
Due to the accidental coincidence of the two bands, we did
not expect nor find the same perturbations in the Kϭ4 sub-
band or HO37Cl.
With respect to intramolecular energy flow, it is clear
that Fermi-type resonance is one of the most effective
mechanisms causing IVR. In our case, Fermi resonance cer-
tainly causes the wave functions of the perturbing states to
be mixed, but, since the perturbations remain local in the
considered energy region as well as in the 3 1 energy region,
v
we do not yet expect effective overall intramolecular energy
flow in this range ͑other states in this energy range are cur-
rently under investigation to further proof this statement͒.
The absence of strong perturbations in the overtone spectrum
of HOCl is not surprising nor unique. An interesting question
is up to which energy this behavior persists. HCN is another
C. Numbers and densities of vibrational states of
HO35Cl
Numbers and densities of vibrationally highly excited
states provide a link between spectroscopy and reaction dy-
namics. Whenever intramolecular dynamics samples major
J. Chem. Phys., Vol. 104, No. 9, 1 March 1996
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Abel et al.: Spectroscopy of HOCl. I
3195
FIG. 5. Sums of states ͑integrated density of states͒ for HO35Cl from a
Dunham expansion ͑3͒ ͑see text͒, an ‘‘E3’’ extrapolation of the ‘‘exact’’
Dunham expansion between 0 and 12 600 cmϪ1 ͑2͒ ͑see text͒, from an
harmonic count ͑1͒, and from an empirical stretch–bend ͑4͒ coupling model
͑Ref. 4͒. All numbers of states above 12 600 cmϪ1 have been extrapolated
͑for details see text͒. Ez corresponds to the zero point energy.
With complete expressions for the potential energy surface,
all vibrational levels can, in principle, be determined by
quantum calculations or Monte-Carlo phase space integra-
tions with proper quantization. At present this has only been
possible for the Hϩ3 system ͑for references, see Ref. 4͒. In
most cases, however, the potential energy surface is not
known far from the potential minimum.
In this work we have calculated numerically the inte-
grated density of vibronic levels N(E) with the well-known
Dunham polynominal expansion given by
FIG. 4. ͑a͒ qR4(J) branch of the HOCl spectrum ͑symmetric top notation͒
showing the perturbation ͑shift of the marked lines with respect to their
predicted positions. ͑b͒ residuals for the qR (J Ϫ1͒ and the qR (J ϩ1͒
Ј
Ј
4
4
branches ͑Obs.–Calc.͒ are plotted against the upper state J quantum num-
Ј
1
2
E n ,n ,n ͒ϭ
␻ n ϩ ͒
͑
͑
ber ͑see text͒. The dotted lines show the maximum uncertainties of the
experiment ͑2ϫ␴͒. For an unperturbed band all Obs.–Calc. values should
fall into this range.
͚
1
2
3
i
i
i
1
2
1
2
ϩ
x
n ϩ ͒ n ϩ ͒ϩ
yijk n
͑
i
͑
͑
͚
͚
ij
i
j
iрj
iрjрk
parts or the complete phase space, statistical theories relate
rates with the corresponding phase space volumes. For ex-
ample, the specific rate constant k(E,J͒ of a unimolecular
reaction is given by
1
2
1
2
1
2
ϩ ͒ n ϩ ͒ n ϩ ͒ϩ•••
͑4͒
͑
͑
j
k
in the energy range between 0 and 13 000 cmϪ1, with the
parameters from Ref. 30 and those given in Table I ͑fit 1͒.
Equation ͑4͒ correctly predicts the positions of vibrational
levels at low energies,30 and in the overtone region of the
present work ͑prediction of term energies of vibrational lev-
els within a few wave numbers͒. The Dunham expansion has
also been used for extrapolation to higher energies ͑e.g., the
dissociation threshold͒, although it is known that the Dun-
ham expansion will diverge at high energies and ultimately
break down. Counting the numbers of levels N(E) gives the
results shown in Fig. 5 where N(E) has been extended up to
19 000 cmϪ1, i.e., near to the dissociation energy of 19 500
cmϪ1 ͑see below͒. The corresponding vibrational densities of
states ␳ ͑E͒ are displayed in Fig. 6.
k E,J͒ϭW E,J͒/ hϫ␳ E,J͒͒,
͑3͒
͑
͑
͑
͑
where W(E,J͒ denotes the number of open reaction channels
and ␳͑E,J͒ is the rovibrational density of states of the parent
molecule. Although ␳͑E,J͒, for a bond fission reaction, cor-
responds to unstable states in the dissociation contuum, it is
generally assumed to be given by a smooth continuation of
the density of states in the stable energy range.4 For this
reason, the determination of numbers N(E,J͒ and average
densities ␳͑E,J)ϭ ⌬N(E,J)/⌬E͘ of states at energies ap-
͗
proaching the dissociation limit is of great interest.
There are a variety of possibilities to determine N(E,J)
͓in the following we only consider the case Jϭ0 and abbre-
viate N(E,Jϭ0)ϭN(E)͔. Direct experimental determina-
tions of the positions of all vibrational levels below a given
energy E have only rarely been extended to sufficiently high
energies ͑the NO2 system is one of the rare examples5,13͒.
For the case of a triatomic molecule Nav͑E͒ can be esti-
mated using the classical expression6
n
EϩE ͒
͑
0
Nav E͒ϭ
,
͑5͒
͑
n!⌸niϭ1 ␻ ͒
͑
i
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3196
Abel et al.: Spectroscopy of HOCl. I
ϩ␻ E ,E ͒ n ϩ1/2͒,
͑6͒
͑
͑
31
1
2
3
where D is an average Morse dissociation energy of the two
stretches 1 and 2, and where the bending frequency ␻ de-
3
pends on the energies E1 and E2 of the adjacent stretches via
the coupling relation4
0.41
E1
D
E2
D
␻
E ,E ͒ϭ␻
3e
1Ϫ
1Ϫ
.
͑7͒
͑
ͩ
ͪͩ
ͪ
ͭ
ͮ
3
1
2
͑For energies above the average dissociation energy D, dif-
ferent expressions apply;4 anharmonic bend is used through-
out this work.͒ Equations ͑6͒ and ͑7͒ are not meant to repro-
duce precise level positions, but average positions such as
they are required for numbers and densities of states. For
practical applications, it is important to fit the parameters ␻1,
␻2, and ␻3, and D. In this case D corresponds to the geo-
metric average of the adjacent bonds dissociation energies
plus the harmonic zero point energy; the harmonic frequen-
cies ␻1, ␻2, and ␻ ͑which are slightly different, in general,
3
from those in Table I͒4 are fitted such that E͑1,00͒, E(0,1,0),
and E͑0,0,1͒ are identical with the three fundamental fre-
FIG. 6. Densities of states ␳͑E͒ for HO35Cl from a Dunham expansion ͑see
text͒, an ‘‘E3’’ extrapolation of the ‘‘exact’’ Dunham expansion between 0
and 12 600 cmϪ1 ͑see text͒, from an harmonic count, and from an empirical
stretch-bend coupling model ͑Ref. 4͒. All densities of states above 12 600
cmϪ1 have been extrapolated ͑for details see text͒. Ez corresponds to the
zero point energy.
quencies
,
, and
given in Table I. There is the prob-
v3
v1 v2
lem that the ⌬H00 values for the reactions
HOCl→OHϩCl,
͑8͒
͑9͒
HOCl→HϩOCl
are not known too well. Using a value of ⌬H00ϭ19 186 cmϪ1
for reaction ͑8͒ and of ⌬H00ϭ32 504 cmϪ1 for reaction ͑9͒
where E is the vibrational energy in excess of the zero point
from Ref. 44 one obtains ͗⌬H00͘ϭ͑32 504ϫ19 186͒
1/2
energy E0 and ␻ the n harmonic frequencies. From Eq. ͑5͒
i
cmϪ1ϭ24 972 cmϪ1, such that Dϭ27 308 cmϪ1. The har-
follows that Nav͑E͒ϰEn and in the case of HO35Cl n is equal
to 3. Therefore, an alternative extrapolation method uses ex-
pressions derived from Eq. ͑5͒.5 We have fitted the energy
levels from the Dunham expansion between 0 and 13 000
monic frequencies in this case have been fitted to
␻11ϭ741.374
cmϪ1
,
␻21ϭ3930.522
cmϪ1
,
and
␻31ϭ1283.558 cmϪ1, which reproduce the fundamentals of
Table I very well. The counted N(E) and ␳͑E͒ are then prac-
tically indistinguishable from the Dunham results, see Figs. 5
and 6. For EϪEz ͑Ez is the zero point energy͒ϭ10 000,
12 000, and 12 500 cmϪ1, the Dunham count gives N(E)
ϭ119, 197, and 219, whereas the present empirical method
gives 121, 197, and 220, respectively. The empirical method
cmϪ1
with
N(E)ϭaE3ϩbE6 ͓aӷb, aϭ1.411ϫ10Ϫ10 ͑cmϪ1 Ϫ3
bϭ1.221ϫ10Ϫ26 ͑cmϪ1 Ϫ6
an
energy
power
law
expansion
and
͔ and extrapolated N(E) and ␳͑E͒
͒
͒
up to 19 000 cmϪ1. The results for N(E) and ␳͑E͒, respec-
tively, are displayed in Figs. 5 and 6. They only slightly
differ from those obtained with the Dunham expansion. Fig-
ures 5 and 6 also include densities and integrated densities of
states from a harmonic count of energy levels using the har-
predicts N(E)ϭ777 and ␳͑E͒ϭ0.13 ͑cmϪ1 Ϫ1
at the disso-
͒
ciation energy, such that a threshold rate constant for unimo-
lecular dissociation of k(E)ϭ1/h␳(E)ϭ2.4ϫ1011 sϪ1 is pre-
dicted, in excellent agreement with the Dunham estimate
͓N(E0ϭdiss. energy͒ϭ780͔. In future ICLAS experiments in
the six and seven OH quanta region we will measure life-
times above the dissociation threshold from linewidth mea-
surements and re-examine this prediction. The uncertainty in
the dissociation energy does not influence the empirical re-
sults for N(E) near 13 000 cmϪ1, however, for ⌬H00ϭ19 500
monic frequencies ␻1, ␻2, and ␻ from Table I.
3
Anharmonicities in general will be specific properties of
the particular molecule considered. Nevertheless, one may
compare exactly measured or calculated N(E), or values de-
duced from Dunham expansions, such as done in the present
work, with the empirical ‘‘universal’’ anharmonicity model
proposed recently by Troe.4 In this local mode model,
stretching vibrations are represented by Morse oscillators
and bending vibrations are coupled to adjacent stretches. For
a nonlinear triatomic molecule, energy levels are approxi-
mated by
cmϪ1 45
of course, a somewhat larger N(E) and a smaller
,
k(E) results. The changes are easily estimated. For the
present molecule, it will be possible to inspect even higher
overtones in the 14 000–18 000 cmϪ1 range, approaching the
dissociation threshold. Even without doing this, the present
work shows that the empirical method of Ref. 4 within a few
percent gives good agreement with Dunham counts of level
numbers N(E), up to 2/3 of the dissociation energy. The
E n ,n ,n ͒ϭE ϩE ϩE
3
͑
1
2
3
1
2
2
ϭ␻ n ϩ1/2͒Ϫ␻ n ϩ1/2͒2/4D
͑
11
͑
1
1
11
2
ϩ␻ n ϩ1/2͒Ϫ␻ n ϩ1/2͒2/4D
͑
21
͑
2
2
21
J. Chem. Phys., Vol. 104, No. 9, 1 March 1996
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Abel et al.: Spectroscopy of HOCl. I
3197
differences in the state densities are smaller than the fluctua-
tions of the average densities of states, which are illustrated
in Fig. 6.
͑1988͒; S. L. Coy and K. K. Lehmann, Spectrochim. Acta A 45, 47 ͑1989͒.
13 A. Campargue, D. Permogorov, and A. Charvat, Chem. Phys. Lett. 223,
567 ͑1994͒; A. Campargue, D. Permogorov, and R. Jost, J. Chem. Phys.
102, 5910 ͑1994͒; R. Georges, A. Delon, F. Bylicki, R. Jost, A. Campar-
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͑1995͒.
IV. CONCLUSIONS
14 A. Charvat, A. A. Kachanov, A. Campargue, D. Permogorov, and F. Sto-
eckel, Chem. Phys. Lett. 214, 495 ͑1993͒.
In this article we have demonstrated that the intracavity
absorption technique with a Ti:sapphire laser system pro-
vides a powerful technique for high-resolution spectroscopy
on weak overtones and combination bands of small transient
molecules in the near infrared. The high sensitivity, linear
response, high-resolution, loss compensation ͑in case of win-
dow deposits͒, and the multiplex advantage makes this tech-
nique highly competitive ͑maybe superior͒ to ring-down cav-
ity absorption and the classic photoacoustic technique and
certainly superior to long path FTIR spectroscopy. This tech-
nique is also complementary to the classical double reso-
nance techniques ͑e.g., Ref. 11͒, because the level positions,
densities, and widths, as well as perturbations investigated
with this technique also provide direction information about
intramolecular and unimolecular dynamics.
15 E. N. Antonov, P. S. Antsiferov, A. A. Kachanov, and V. G. Koloshnikov,
Opt. Commun. 41, 131 ͑1982͒.
16 S. E. Vinogradov, A. A. Kachanov, S. A. Kovalenko, and E. A. Sviriden-
kov, JETP Lett. 55, 581 ͑1992͒.
17 E. N. Antonov, V. G. Koloshnikov, and V. R. Mironenko, Opt. Commun.
¨
15, 99 ͑1975͒; V. M. Baev, G. Gaida, G. Schroder, and P. E. Toschek, ibid.
38, 309 ͑1981͒.
18 M. A. Melieres, M. Chenevier, and F. Stoeckel, J. Quant. Spectrosc. Ra-
diat. Transfer 33, 337 ͑1985͒.
19 A. Kachanov, A. Charvat, and F. Stoeckel, J. Opt. Soc. Am. B 11, 2412
͑1994͒.
20 L. Halonen and T. K. Ha, J. Chem. Phys. 88, 3775 ͑1988͒; P. Botschwina,
Chem. Phys. 40, 33 ͑1979͒.
21 K. Hedberg and R. M. Badger, J. Chem. Phys. 19, 508 ͑1951͒.
22 W. J. Lafferty and W. B. Olson, J. Mol. Spectrosc. 120, 359 ͑1986͒.
23 M. Carlotti, G. Di Lonardo, L. Fusina, A. Trombetti, and B. Carli, J. Mol.
Spectrosc. 141, 29 ͑1990͒.
24 J. S. Wells, R. L. Sams, and W. J. Lafferty, J. Mol. Spectrosc. 77, 349
͑1979͒; M. L. Juntilla, W. J. Lafferty, and J. B. Burkholder, ibid. 164, 164
͑1994͒.
ACKNOWLEDGMENTS
25 C. M. Deely and I. M. Mills, J. Mol. Spectrosc. 114, 368 ͑1985͒.
26 F. Cavazza, G. Di Lonardo, R. Escribano, L. Fusina, P. C. Gomez, and J.
Ortigoso, J. Mol. Spectrosc. 159, 395 ͑1993͒.
Financial support of this work by the Deutsche Fors-
chungsgemeinschaft ͑SFB357 ‘‘Moleculare Mechanismen
unimolecularer Reaktionen’’͒ is gratefully acknowledged.
The authors thank David Luckhaus for providing the WANG
͑asymmetric rotor fitting͒ program, as well as the Grenoble
ICLAS group for providing the source code which was used
for some of our data processing and calibration algorithms.
We also thank N. P. Ernsting for his support, and Dr. J. Baur
͑Science Solutions Inc.͒ for providing the high resolution
spectrometer.
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APPENDIX
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2223, e-mail: janis@aip.org. The price is $1.50 for each microfiche ͑98
pages͒ or $5.00 for photocopies of up to 30 pages, and $0.15 for each
additional page over 30 pages. Airmail additional. Make checks payable to
the American Institute of Physics.
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