Journal of Molecular Spectroscopy 207, 99–103 (2001)
doi:10.1006/jmsp.2001.8313, available online at http://www.idealibrary.com on
Molecular Constants for the v = 0, b1Σ+
g Excited State of O2 :
Improved Values Derived from Measurements of the Oxygen
A-Band Using Intracavity Laser Spectroscopy
Leah C. O’Brien,∗ Hong Cao,† and James J. O’Brien†
∗ Department of Chemistry, Southern Illinois University Edwardsville, Edwardsville, Illinois 62026-1652; and †Department of Chemistry,
University of Missouri—St. Louis, 8001 Natural Bridge Road, St. Louis, Missouri 63121-4499
Email: [email protected]
Received January 8, 2001; published online April 5, 2001
High-resolution intracavity laser spectroscopy (ILS) absorption measurements have been made on the b–X oxygen electronic
transition (the A-band) which has bandheads occurring in the region of 13 165 cm−1 . The positions of the lines were determined
to an accuracy that is based on calibration with I2 absorption lines using the Laboratoire Aimé Cotton (Orsay) Atlas as reference.
Based on the ILS measurements and the more accurately determined positions given by L. R. Brown and C. Plymate (J. Mol.
Spectrosc. 199, 166–179 (2000)) and with the 3 6g− ground state molecular constants fixed at the values determined by G. Rouillé
et al. (J. Mol. Spectrosc. 154, 372–382 (1992)), the following values (in cm−1 ) were found for the molecular constants: T0 =
13122.2524(1); B0 = 1.391244(2); D0 = 5.352(4) × 10−6 ; and H0 = −1.2(2) × 10−11 . These results are compared with values
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derived from fits of the line positions listed in several other studies of this transition. °
the oxygen spectra, Brown and Plymate referenced their line
positions to positions of lines in the 2–0 and 3–0 bands of CO.
In this investigation, all the lines listed in the Babcock and
Herzberg paper (14) were measured at high resolution using intracavity laser spectroscopy (ILS). We did not investigate the
region where the T S electric quadrupole branch of the A-band
occurs; this branch was observed with the FTS at the McMath
solar telescope at Kitt Peak by Brault using the atmosphere as
sample and a solar source at sunset (16). In this ILS study,
most of the lines were recorded at an oxygen vapor pressure of
0.8 Torr and the effective pathlengths employed ranged from 3
to 35 km. A similar methodology was employed by the Steinfeld
and Field groups (11) who recently reported intensity and collision broadening parameters for this band.
INTRODUCTION
The b16g+ –X 36g− electric dipole and spin-forbidden electronic
transition of O2 , long designated the atmospheric A band in the
solar spectrum, has been the subject of several recent studies
(1–11). These are motivated by various applications. Intensity,
pressure-broadening, and temperature dependence parameters
are used in remote sensing of conditions in the earth’s atmosphere and in the algorithm used in global ozone monitoring
(e.g., 12, 13). Line positions have been suggested as a convenient calibration standard for the visible region (9). This study
is relevant in the latter area.
Although line positions of the A-band have been determined
using improved techniques, the most extensive measurement
of the band remains that of Babcock and Herzberg (14). In that
study, where air sample pathlengths ranged from 30 m in a
laboratory study to a maximum on the order of 100 km in the
earth’s atmosphere, the accuracy of spectroscopic constants
reported surpassed that for any other molecule at the time. Many
of the more recent A-band studies list line positions but even
among efforts where serious attention was given to determining
line positions based on independent calibration, some disagreement remains concerning the absolute positions of the lines
(7, 9, 10, 15). In particular, there is a systematic 12-mK difference between positions reported by Phillips et al. (7) and those
of Brown and Plymate (9). Both these studies recorded spectra
using high-resolution FT spectrometers and whereas Phillips
et al. calibrated their spectra by interspersing iodine spectra with
EXPERIMENTAL DETAILS
The measurements were performed using a Ti : sapphire laserbased ILS system which has been described previously (17, 18).
A brief synopsis of the system employed and the method used
for determining the O2 absorption line positions follows.
In an ILS experiment, the enhanced sensitivity for observing
absorption by an intracavity species derives from the timemodulated operation of a homogeneously broadband laser.
During the initial evolution period of the laser, absorption lines
of an intracavity species appear superimposed on the spectrally
broad output of the laser. If the output of the laser is observed
during this time period with a high-resolution spectrograph,
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100
O’BRIEN, CAO, AND O’BRIEN
analyzer. Detector dark current data are subtracted from each acquired spectrum. Broadband tuning of the laser is accomplished
using two Brewster-angle prisms and a movable slit.
As illustrated in Fig. 1, the resonator of the laser is isolated
from the atmosphere to avoid atmospheric contributions to the
absorption spectrum. Oxygen pressures are measured using 10and 100-Torr capacitance manometers. Immediately following
the acquisition of an oxygen spectrum, the absorption cell is
evacuated and a background spectrum is obtained using identical
generation time conditions. Division of the two dark-currentcorrected spectra yields the resultant oxygen spectrum.
Spectra are recorded as a series of overlapping ∼7 cm−1
wide spectral profiles. Wavenumber calibration is accomplished
by alternatively measuring the oxygen spectrum as described
above and an I2 absorption spectrum (e.g., see Fig. 2) recorded
FIG. 1. Schematic diagram for the intracavity laser spectrometer. Legend:
AOM = acoustooptic modulator; HR = high reflector; FM = fold mirror; OC =
output coupler. The iodine cell is empty when the oxygen spectra are collected
and vice versa.
quantitatively accurate information for the absorption lines
(intensities, widths, positions) can be obtained. The dynamic
range for the measurements depends on the selected observation
time (∼100 µs–1 ms). The time period used is termed the
generation time, tg .
The observed transmittance at a particular frequency, Iobs (ν),
is related to tg via the Beer–Lambert relationship for ILS,
Iobs (ν) = I0 (ν) exp[−σ (ν)N (`/L)ctg ],
[1]
where I0 (ν) is the intensity of the laser in the absence of absorption and indicates the 100% transmittance level, σ (ν) is the
absorption cross section, N is the number density for the intracavity absorber, `/L (=0.74) is the fraction of the laser cavity of
length L (2.17 m) occupied by the absorber, and c is the speed
of light. The combination (`/L)ctg represents the effective absorption pathlength for the experiment.
The spectrometer employed is shown schematically in Fig. 1.
A standing wave, four mirror (HR, FM, FM, OC in Fig. 1),
Ti : sapphire laser is pumped by the visible lines of an argon ion
laser. Spectra are acquired at a specific generation time that is
obtained by the sequential operation of two acoustooptic modulators, AOM1 and AOM2. Modulated operation of AOM1 causes
the pump power directed into the laser crystal (from Crystal Systems) to be alternatively above (for a period just longer than tg )
and below (for a relatively brief “off” period for the Ti:sapphire
laser) the threshold value required for laser operation. At the selected tg value, activation of AOM2 diverts ∼70% of the output
of the Ti:sapphire laser into a high-resolution spectrograph for
a time period (∼0.1 µs) much shorter than tg . Dispersed light
exciting the spectrograph is focused (×3 magnification ratio)
onto the 1024 channels of a diode-array detector. The sequence
is repeated at an approximately 10-kHz rate. Spectral data are
accumulated for 30 scans of 0.6 s duration using a multichannel
FIG. 2. ILS spectral profile recorded in vicinity of the bandhead for the O2
A-band. Conditions are: effective pathlength = 5.67 km; pressure = 30.0 Torr;
temperature = 296.5 K. Also shown are: (2nd panel) the corresponding I2 absorption spectrum; (3rd panel) an étalon spectrum; and (4th panel) the dispersion
of the array detector calibrated for this region from the asterisked pair of I2 absorption lines.
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MOLECULAR CONSTANTS FOR THE O2 A-BAND FROM ILS
using an extra-cavity cell. In the latter case, the ILS spectral
output serves as the broadband spectral source; the I2 spectrum
is obtained by dividing the spectrum obtained with I2 present
in the external cell by that obtained when I2 is absent from the
cell. Reference positions for the I2 lines were obtained from the
S. Gerstenkorn et al. (Laboratoire Aimé Cotton) Iodine Atlas
(19, 20). To correct for small changes in the dispersion (≤1.6%)
of a spectrum across the diode array detector, spectra recorded
from a 14.7-mm-thick intracavity étalon provide a source of
equally spaced fringes. A series of étalon spectra recorded at a
specific spectrograph position enables a polynomial fit that describes the change in the dispersion with channel position to be
obtained. An example of such a spectrum is shown in Fig. 2. Peak
positions (absorption peaks and fringe positions) are determined
from the zero crossing-points of the first derivative spectra using
Savitzky–Golay polynomial smoothing. This procedure allows
line positions to be determined to an accuracy of better than
±0.002 cm−1 ; the major source of uncertainty is found to be the
values provided for the reference lines.
101
TABLE 1
3 −
Line Positions for the b 1Σ+
g –X Σg Transition (the A-band)
16
of O2 Observed Using Intracavity Laser Spectroscopy
RESULTS AND DISCUSSION
Figure 2 shows a segment of the oxygen A-band spectrum in
the vicinity of the band heads and Fig. 3 shows a spectrum for
the major portion of the band. The latter was assembled from
a number of overlapping separate spectral profiles. In order to
measure the positions of the lines, collection conditions (i.e., tg
value and pressure) were adjusted to give lines of reasonable
transmittance throughout the region of the O2 A-band. Effective
pathlengths between 2.5 and 35.2 km were employed and pressures between 0.8 and 30 Torr were used. Most of the lines positions were obtained from spectra acquired at oxygen pressure of
Note. Also listed are the assignments and residuals for the fit of this data.
The asterisks indicate blended lines.
FIG. 3. ILS spectrum for the strongest portion of the O2 A-band
{the b 16g+ –X 36g− transition}. This spectrum was formed from a number of
overlapping spectral profiles observed for an oxygen pressure of 0.8 Torr. The
effective pathlength was normalized to 3.0 km.
0.80–0.82 Torr. Given the accuracy at which line positions could
be determined and pressures at which the spectra were recorded,
no pressure shift corrections were applied. Line positions are
given in Table 1.
Because of previous work, assignment of the lines was
straightforward. A nonlinear least-squares program was used
to fit the line positions to standard energy level expressions.
For the 16g+ state the expression was E = T0 + B0 J (J + 1) −
D0 J 2 (J + 1)2 + H0 J 3 (J + 1)3 , while for the 3 6g− ground state
the energy level expressions given in Rouillé et al. (20) were
employed. The ground state rotational constants have been determined to high precision by rotational Raman spectroscopy
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102
O’BRIEN, CAO, AND O’BRIEN
TABLE 2
16
Molecular Constants for the b 1Σ+
g State of O2 Obtained in This Work Using Intracavity Laser
Spectroscopy (ILS) Compared with Values Obtained by Other Workers
Note. The ground state constants were held fixed to the values determined by G. Rouillé et al. (21). The constants provided in
the last row were obtained by combining the data of Brown and Plymate (9) with the ILS data for lines of higher J values (please
see text for details).
a Published transition frequencies were refitted using fixed ground state constants so that comparison is straightforward.
b Held fixed (see text for details).
c Two reassignments of lines as noted in the text.
d Varied weights used in fit; uncertainty is given for the low J lines.
and the values used in the fit were fixed at the values determined
in that work by Rouillé et al. (21). A total of 80 lines with J 0 = 0
to 40 were fitted to produce three molecular constants for the
b 16g+ state that are shown in Table 2.
Many research workers have analyzed this transition. Different Hamiltonians for the ground state have been employed,
however, which impedes direct comparison of molecular constants (e.g., see Table 7 in Cheah et al. (10)). In order to conduct
a more direct comparison with the results obtained by other authors, the line positions that are listed in other papers (where line
positions were obtained from independent calibration) were refit using the same energy level expressions and fixed values for
the ground state constants (as per Rouillé et al.) as employed
in our fit. Lines with observed − calculated values greater than
twice the estimated experimental uncertainty were deweighted
in these fits. The resulting molecular constants from the refits
are shown in Table 2. Also indicated in Table 2 are the number
0
values and the average uncerof lines included in each fit, Jmax
tainty of the individual rotational lines, σfit , as determined from
the standard deviation of the fits. During the refits, it was discovered that two sets of lines were misassigned in the work of Cheah
et al. (10). Using their notation, the assignments for the following lines should be interchanged in their paper: rQ(17) ↔ rR(19)
and rQ(21) ↔ rR(25). This greatly improves the quality of the fit
to their data.
For each data set investigated, we examined whether or not
the quality of the fit was improved by the addition of a fourth
molecular constant, H0 , for the excited state. Only the fit of the
data from Brown and Plymate improved significantly with the
0
values
addition of the fourth parameter. However, the low Jmax
of their data did not yield an accurate value for H0 , as determined
by its comparison to the H0 value obtained from the combined
fit (see below). Hence for the final fit of their data set, the H0
value was held fixed to the value of H0 determined from the
combined fit.
One of the primary objectives of this study was to investigate
a 0.012 cm−1 discrepancy in the T0 values between the data
of Brown and Plymate (9) and that of Phillips et al. (7), as
was noted in the Brown and Plymate publication. Our analysis
based on calibration from an iodine spectrum acquired within
a few minutes of the corresponding oxygen spectrum and with
zero adjustment to the spectrograph or laser beam optical path,
supports the calibrated line positions of Brown and Plymate
(9) and also those of Kanamori et al. (15). Indeed, the slight
difference between our T0 value and the T0 value of Brown and
Plymate (see Table 2) is not statistically significant.
The best line positions according to the lowest average uncertainty of the individual rotational line positions are those of
Brown and Plymate, though considerably fewer line positions
are involved in the fit. Accordingly, in order to obtain the best
set of constants for this band, the Brown and Plymate line positions (up to J 0 = 20) were combined with our additional line
positions (from J 0 = 20 to 40). The line positions of Brown
and Plymate were weighted with an experimental uncertainty
of 0.0004 cm−1 and our line positions were weighted with an
experimental uncertainty of 0.004 cm−1 ; the resultant refit to
this data yielded the molecular constants for the 16g+ that are
listed in the final row of Table 2. The positions and residuals for
the fit of the combined data are shown in Table 3. Due to the
high precision of the Brown and Plymate data and our high J 0
values, it was necessary to add a fourth molecular constant, H0 ,
in order to better fit the data. We believe this is the most accurate
and precise set of parameters that is currently available for the
v = 0 16g+ state.
We also investigated using a global fit where the molecular
constants for both states were varied. However, this fit yielded
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MOLECULAR CONSTANTS FOR THE O2 A-BAND FROM ILS
TABLE 3
3 −
Line Positions for the b 1Σ+
g –X Σg Transition (the A-Band)
16
of O2 Observed Using the Lines of Low J Observed
by Brown and Plymate (9) and the Lines of High
J Observed in This Study
103
ity of this experimental approach enabled 80 lines of the band
to be included in the fit. The line positions were calibrated
from I2 absorption lines observed within a few minutes using the same apparatus. The largest source error for the line
positions is found to be the values of the I2 reference positions. Since the majority of the line positions were obtained
from spectra recorded at 0.8 Torr, no pressure shift corrections
(∼ −0.005 cm−1 /atm) were applied. The molecular constants
obtained were compared with results obtained by other workers. In order to make direct comparison possible, much of that
data were refit using the same approach as employed in our fits.
By combining the best set of data for lines of low J with our
lines of high J , we obtained what we believe is the most accurate
and precise set of molecular constants for the v = 0, b 16g+ state
that is currently available.
ACKNOWLEDGEMENTS
Supported in part by NASA’s Planetary Atmospheres Program under Grants
NAGW-2474 and NAG5-6091. Acknowledgement is made by LCO to the donors
of The Petroleum Research Fund, administered by the ACS, for partial support
of this research.
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Note. Also listed are the assignments and residuals for the fit of this
combined data. The asterisks indicate blended lines.
the same excited state constants which had the same uncertainty
associated with them as indicated in Table 2 for the fit to the
combined data, and the quality of the fit did not improve.
CONCLUSION
The molecular constants for the 16g+ excited state of the oxygen A-band have been determined based on spectra obtained
by intracavity laser spectroscopy, a different type of experimental approach from that employed by previous investigators
concerned with the line positions of this band. The sensitiv-
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