Modugno et al.
Vol. 13, No. 8 / August 1996 / J. Opt. Soc. Am. B
1645
Precise measurement of molecular dipole
moments with a tunable far-infrared
Stark spectrometer: application to HOCl
G. Modugno, P. De Natale, M. Bellini, and M. Inguscio
European Laboratory for Nonlinear Spectroscopy (LENS) and Department of Physics, University of Firenze,
Largo E. Fermi 2, I-50125 Firenze, Italy
G. Di Lonardo and L. Fusina
Dipartimento di Chimica Fisica e Inorganica, University of Bologna, Viale Risorgimento 4, I-40136 Bologna, Italy
J. Vander Auwera
Université Libre de Bruxelles, CPi-160/09, Avenue F. D. Roosevelt 1050 Bruxelles, Belgium
Received August 7, 1995
Stark measurement of the electric dipole moment components of H16O35Cl is performed with a tunable farinfrared spectrometer at the European Laboratory for Nonlinear Spectroscopy, Firenze, Italy. Two pure rotational transitions are analyzed, namely, the 11,1 –00,0 at approximately 628 GHz and the asymmetry doublet
43,2 –32,1, 43,1 –32,2 at approximately 3.1 THz. The values obtained for ma and mb represent the first reported
measurement of dipole moments from far-infrared transitions with an accuracy up to several parts in 104.
© 1996 Optical Society of America.
1. INTRODUCTION
In recent years the development of laser-based heterodyne devices, combining continuous tunability with
metrological-grade sources, has made possible highly
precise frequency measurements of rotational spectra up
to the 6-THz region.1–3 However, line intensity measurements are also of crucial importance in a number of
fields including astrophysics and physics of the
atmosphere.4
Fourier transform spectrometers operating in the farinfrared (FIR) region and mounted on board stratospheric
balloon platforms have been increasingly used for in situ
measurements of the atmospheric composition.5,6 The
improving quality of data acquired in this way makes it
necessary to obtain new, accurate laboratory measurements. In order to retrieve precise concentration data
from the observed line intensities, one needs highly accurate measurements of dipole moments, and for this purpose Stark spectroscopy has proven to be a powerful tool.
Most molecules involved in atmospheric physics are
asymmetric rotors exhibiting a second-order Stark effect,
which gives rise to a quadratic dependence of the shifts on
the applied electric field. High resolution and accuracy
are required to resolve and analyze Stark patterns, which
are generally crowded. A few years ago the use of a tunable FIR (TuFIR) spectrometer for measurements of dipole moments was reported.7
Here we demonstrate that the high accuracy of frequency measurements permitted by the TuFIR spectrometer may be transferred to the determination of dipole
0740-3224/96/0801645-05$10.00
moments by using a Stark technique. The accuracy
achieved is comparable with that obtained in the microwave region, where high power and metrological-grade
sources are commonly available.
We report measurements of the permanent electric dipole moment components of hypochlorous acid (HOCl), a
molecule that is considered to play an important role in
the catalytic depletion of stratospheric ozone, acting as a
reservoir for active chlorine.8 Its FIR spectrum has been
the object of several studies9,10 that helped in the line selection for this work. Stark measurements of the dipole
moment for this molecule have been reported for three
transitions in the 30-GHz frequency region.11,12 We extend the observation to include two more transitions
in the FIR region, up to a frequency of approximately
3 THz.
2. EXPERIMENTAL APPARATUS
FIR radiation was produced with the TuFIR spectrometer
at the European Laboratory for Nonlinear Spectroscopy,
described in detail elsewhere.2,3 The generation of FIR
radiation is based on the mixing of radiation from two
frequency-stabilized CO2 lasers and microwaves from a
synthesizer in a metal–insulator–metal diode. To increase the amount of emitted FIR power and polarize the
beam, we have recently mounted a rooftop mirror close to
the metal–insulator–metal tungsten antenna. This
gives better collimation of the FIR beam, which is crucial
for Stark measurements. More than 95% of the power
turned out to be concentrated in a 15-mm-diameter colli-
© 1996 Optical Society of America
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J. Opt. Soc. Am. B / Vol. 13, No. 8 / August 1996
mated beam having a linear polarization that was
checked with a pair of crossed wire mesh polarizers. The
beam was more than 85% polarized in a plane containing
the antenna and the IR radiation direction. The collimated and polarized beam passed through a Stark cell
and was then detected at the modulation frequency of the
CO2 lasers (770 Hz) onto a pumped liquid-helium-cooled
bolometer. The detector was equipped with a cold, lowpass filter with a cutoff at 200 cm21. Two optically polished stainless-steel plates with rounded edges, 40 cm
long, 6 cm wide, and 2.5 cm thick, spaced with Zerodur
blocks equally distributed along the sides, were used as
Stark plates. The spacers were cut from a single étalon.
The spacing, d, between the two plates was chosen to be
approximately 5 mm, taking into account both the FIR
beam diameter and the need to maintain a reasonable potential difference. Some Teflon was wrapped around the
external sides of the electrode plates to reduce the decomposition of the gas sample and to avoid electric breakdown. A Pyrex tube, equipped with two high-density
polyethylene windows and connected to the vacuum
pump, contained the Stark plates. The two plates were
tightened by three Teflon clamps to allow for rotation
along the longitudinal axis (parallel to the FIR beam) in
order to select DM 5 0 or DM 5 61 transitions. A highvoltage, stabilized power supply provided voltage to the
electrodes, whose value was measured by a precision digital voltmeter (Keithley Instruments, Inc., USA, model
199DM), after passing through a passive divider
(10,000:1). The divider (Jon Fluke Mfg. Co., Inc., USA,
model 80E), used high-stability resistors and, along with
the voltmeter, was calibrated to avoid systematic errors.
HOCl was produced by reacting Cl2 gas with a slurry of
red mercury oxide and water inside an evacuated flask.
Total pressures ranging from 2 to 20 Pa were used for the
measurements, with lower pressures being used at higher
electric fields, to avoid breakdown. We tried to maintain
a stable concentration of HOCl by streaming the gas at a
low rate. Electric fields up to 5 kV/cm could be reached
at low pressure, giving a maximum Stark shift of approximately 280 MHz, with a permissible degrading of the
signal-to-noise ratio. At these values of the shifts the
predominant contribution to the uncertainty on dipole
moment components is the uncertainty in the determination of the line center, which is due to the relatively low
signal-to-noise ratio.
Modugno et al.
last digit) for the spacing between the Stark plates,
in very good agreement with the mechanical measurements.
The measured line did not show any significant broadening with increasing values of the voltage, implying a
homogeneous field along the cell. The dipole moment reported in Ref. 13 was used for calibration, even though
our measurements were performed on a different rotational transition, at higher J and K values. This was
permissible because the dependence of the CH3F dipole
moment on J and K values is negligible14 and, in any
case, within the quoted uncertainty.
4. EXPERIMENTAL RESULTS AND DATA
ANALYSIS
HOCl is a planar near-symmetric rotor, and two classes of
transition arise from the two components of the electric
dipole moment, ma and mb , parallel to the principal axes
of inertia a and b. In Fig. 1 we present two experimental
recordings for the 43,2 –32,1, 43,1 –32,2 unresolved asymmetry transition doublet, at zero field and at approximately
5 kV/cm. The upper levels are split into a 10-MHz-wide
hyperfine structure. At zero field [Fig. 1(a)] the firstderivative line profile represents the overlap of the Doppler profiles that is due to the four hyperfine components
of these levels. The hyperfine structure is zero for the
lower levels, in the prolate symmetric-top approximation.
Figure 2 shows the frequency displacement versus the
electric field of the four components shown in Fig. 1(b).
Since the asymmetry splitting (1 MHz) is much smaller
than that induced by the electric field (up to approximately 120 MHz), the Stark splitting is linear with the
field and the data can be fitted to lines. With use of a
purely symmetric rotor model simultaneous fitting of all
data shown in Fig. 2 gives a reduced chi square value less
3. STARK CELL CALIBRATION
In order to determine accurately the static electric field
applied to the HOCl sample in the Stark cell, we needed
an accurate measurement of the plates’ separation. This
was achieved, after a preliminary mechanical estimation
of the thickness of the Zerodur spacers, by measuring the
Stark effect on a sample of CH3F gas for which a highly
accurate value of the dipole moment [ma 51.85840(8) D] is
available in the literature.13
We studied the M 5 (28)–(27) component of the 87 –77
transition at 408,111 MHz for values of the voltage ranging from 0 to 3200 V. After correction for second-order
effects the linear fit of frequency shifts versus voltages
gave a value of 0.5223(3) cm (3s uncertainty in the
Fig. 1. Experimental recordings of the 43,2 –32,1, 43,1 –32,2 asymmetry doublet at (a) zero electric field and (b) 4.9 kV/cm.
Hyperfine structure is evident at zero field (see the text).
Modugno et al.
Vol. 13, No. 8 / August 1996 / J. Opt. Soc. Am. B
1647
In the other transition investigated, 11,1 –00,0, the separation of the level 11,1 from the nearest 11,0 is approximately 390 MHz. This value is much larger than that
observed in the transition analyzed above and requires a
perturbative theory for an asymmetric rotor with the addition of a near degeneracy.15 An energy-level diagram
illustrating the interacting levels is shown in Fig. 3. As
can be seen, even if the main contribution to the levels’
shift still comes from ma , through the near degeneracy of
the 11,1 and 11,0 levels, second-order contributions that
are due to mb are also present. According to the model
proposed in Ref. 16, in the presence of hyperfine structure
the energy matrix may be divided in blocks, each one
characterized by a fixed value of u M I 1 M J u . The simplest case is for u M I u 5 I and u M J u 5 J because a 2 3 2
matrix has to be diagonalized:
Fig. 2. Frequency displacement of the Stark components of the
43,2 –32,1, 43,1 –32,2 doublet, obeying the DM J 5 21 and DM I 5 61
selection rules. The assignment (referring to the upper level) is
given in the high-field approximation: I: M J 5 24, M I 5 63/2;
II: M J 5 24, M I 5 61/2; III: M J 5 2 3, M I 5 63/2, 61/2; IV:
M J 5 22, M I 5 63/2, 61/2.
than 1 (x2 5 0.8), which suggests that the adopted model
is adequate. The statistical weight assigned to each datum was proportional to the inverse of its squared estimated uncertainty.
Some components have been fitted only at field values
for which the Stark energy is much larger than the hyperfine energy so that the total angular momentum J and
the nuclear spin I become ‘‘good’’ quantum numbers. In
this case the quadrupole energy is a constant additive
term in the Hamiltonian.14 Only the component with the
maximum value of u M I 1 M J u has a linear behavior for
every field because the quadrupole energy is independent
of the electric field.
From measurements on this transition, only the dipole
component along the a axis can be determined. In fact,
Stark shifts are due to the interactions between the two
pairs of near-degenerate levels, which give rise to the
asymmetry doublet and have nonzero matrix elements
only for ma (DK a 5 0, DK c 5 61). The result for the ma
dipole moment component is reported in Table 1. Negligible contribution has been calculated from the secondorder Stark effect, which is due to the interaction with the
nearest levels through mb .
F
E 1 1,1 1 E e 1 E Q
ES
G
ES
8 .
E 1 1,0 1 E 8e 1 E Q
(1)
The diagonal terms refer to the two near-degenerate levels and have the following meaning: E 1 1,1 and E 1 1,0 are
the rotational energies, E e and E e8 represent the second8 refer to the quadruorder Stark energies, and E Q and E Q
pole energies. The off-diagonal element E S is the Stark
interaction matrix element.15,16
A total of four components have been analyzed for the
11,1 –00,0 transition, numerically diagonalizing matrices of
size up to 636. The experimental points, as well as the
fits, are shown in Fig. 4. A reduced chi square value of
approximately 1 was obtained for this transition, too.
The results for the two components of the dipole moment
are presented in Table 1, which also summarizes previous
measurements. A meaningful comparison should be
made only between the results from two-parameter fittings of ma and mb . The values corresponding to the
10,1 –00,0 transition at 29,842 MHz (Refs. 11 and 12) are in
agreement with the present result for the 11,1 –00,0 transition, which differs only in the K a value of the upper level.
As for the uncertainties, the values quoted in Ref. 11 are
far less precise than our measurements; the present mb
estimation has an uncertainty similar to that quoted in
Ref. 12, and the uncertainty in ma is lowered by a factor of
approximately 4. The relative uncertainty in mb is more
than 1 order of magnitude larger than that in ma because,
as explained above, the mb contribution to the Stark shift
Table 1. Electric Dipole Components of H16O35Cl
along the Principal Axes a and b
Transition
171,17 –180,18
200,20 –191,19
10,1 –00,0
10,1 –00,0
10,1 –00,0
4 3, K c – 3 2, K c
11,1 –00,0
ma (D)a
mb (D)a
Reference
[0.3627]b
[0.3627]b
0.3627(9)
0.3627(9)c
0.367(24)
0.3546(18)
0.36295(25)c
1.4708(60)
1.4707(60)
[1.4708]b
1.472(36)c
1.3(9)
12
12
12
12
11
present work
present work
1.463(30)c
a
Numbers in parentheses represent 3s uncertainties in the least significant digits.
b
This quantity is kept fixed in the fit.
c
Results from a two-parameter fit in which both ma and mb are refined.
Fig. 3. Schematic drawing of the levels giving predominant contribution to the Stark shift of the 11,1 and 00,0 levels. The asymmetry splittings have been exaggerated for clarity.
1648
J. Opt. Soc. Am. B / Vol. 13, No. 8 / August 1996
Modugno et al.
eral components, each having a Doppler width up to 2 orders of magnitude larger than that observed in Refs. 11
and 12. In addition, a good resolution of such a pattern
would require large Stark shifts, which are difficult to obtain in the presence of a predominant second-order Stark
effect governed by mb matrix elements. Alternatively,
measurements could be made on transitions with different J and K values to calculate the dependence of ma on
these quantum numbers, and this dipole component
would then be kept fixed to a more reliable value in fitting
the transitions of more direct interest.
5. CONCLUSIONS
Fig. 4. Frequency displacement of the Stark components, obeying the DM 5 61 selection rule, of the 11,1 –00,0 transition. The
assignment (referring to the upper level) is given, respectively, in
the low-field and the high-field approximations: I: F 5 1/2,
M F 5 61/2; M J 5 61, M I 5 63/2. II: F 5 5/2, M F 5 65/2;
M J 5 61, M I 5 63/2. III: F 5 5/2, M F 5 63/2; M J 5 61,
M I 5 61/2. IV: F 5 5/2, M F 5 61/2; M J 5 61, M I 5 61/2.
The two other components, for which only the experimental
points are shown, correspond for high fields to M J 5 0 and therefore are forbidden according to the DM 5 61 selection rule.
results from the much weaker second-order interaction
only.
It is worth noting that the present technique enables us
to obtain an uncertainty in mb similar to that obtained
from the 10,1 –00,0 transition,12 even if the ma interaction
for the 11,1 –00,0 transition is 1 order of magnitude larger.
This can be deduced from the level separation in Fig. 3
and by taking into account the fact that the Stark interaction matrix element E S [see matrix (1)] has approximately the same value whether evaluated between the
levels 11,1 –11,0 or 10,1 –00,0.
From the data reported in the first three rows of Table
1 there is no chance of revealing any dependence of ma
and mb on J, K a , and K c , since either ma or mb was kept
fixed at values obtained from other transitions, involving
very different quantum numbers.
The value of ma from the 4 3, K c – 3 2, K c transition differs
by a few percent from those obtained from the 11,1 –00,0
and 10,1 –00,0 transitions. This variation is well beyond
the uncertainties and suggests an effective dependence of
the dipole moment components on J, K a , and K c ; however, more data are needed to give a trend.
A more precise determination of the b dipole component, which is the one involved in FIR transitions and
hence the more important for intensity calculations,
could, in principle, be obtained by choosing transitions for
which the largest contribution to the interaction with
neighboring levels comes from mb . In practice, this is difficult, since the main interaction among levels comes from
the asymmetry splitting, which gives nonzero matrix elements containing ma only. Transitions between high-J
and low-K levels could be selected in order to have larger
splittings and a reduced contribution from the a dipole
component.
However, high-J transitions imply a
crowded Stark pattern, which would also be difficult to
analyze because the line intensity is shared among sev-
The two dipole moment components of hypochlorous acid
(HOCl) have been measured for two transitions in the
FIR region, up to a frequency of approximately 3.1 THz.
Our results suggest a dependence of the HOCl dipole moment on the quantum numbers involved in the investigated transitions. The accuracy of our results is comparable with that obtained from previous microwave data
and is limited by the uncertainty in the frequency measurements. This work may pave the way to accurate
studies of dipole moments with an almost continuous coverage of the 0.3–6-THz spectral range, giving access to intensity measurements for transitions directly observed in
related research fields.
ACKNOWLEDGMENTS
This work was accomplished in the frame of Infrared
Spectroscopy of Ozone Related Atmosphere Constituents
(ISORAC2) collaboration, supported by the European
Commission (EC) under contract EV5V-CT92-0076,
which is gratefully acknowledged. The project was also
partially supported by the EC through contract
GE1*CT92-0046. We are also grateful to K. M. Evenson
and L. R. Zink for useful discussions about the setup of
the corner reflector used in this work.
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