Determination of line strengths for selected transitions in the v2 band relative to the v1 and v5 bands of H2CO

Journal of Quantitative Spectroscopy & Radiative Transfer 90 (2005) 207 – 216

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Determination of line strengths for selected transitions in the v2 band relative to the v1 and v5 bands of H2CO Scott C. Herndona;∗ , David D. Nelson Jra , Yongquan Lib , Mark S. Zahnisera a

b

Aerodyne Research Inc., 45 Manning Road, Billerica, MA 01821, USA Atmospheric Sciences Research Center, University of Albany, State University of New York, 251 Fuller Road, Albany, NY 12203, USA Received 8 September 2003; accepted 13 March 2004

Abstract The spectral line strengths in the v2 band of H2 CO (segments spanning 1720–1780 cm−1 ) have been determined relative to two sets of spectral line groups in the v1 and v5 band, (∼ 2830 cm−1 ) using tunable diode laser spectroscopy. Simultaneous detection using a dual-diode instrument with a 150 m absorption cell was employed to assure identical H2 CO column density for the two spectral regions. The results in the selected regions of this study are in good agreement with the line positions and the relative intensities speci:ed in an unpublished complete line listing for the v2 band prepared by Linda Brown (see full text for reference). Based upon measurements of individual groups of spectral lines in the P, Q and R branches, the absolute band strength has been determined to be 76 ± 5 km mol−1 . ? 2004 Elsevier Ltd. All rights reserved. Keywords: H2 CO; Formaldehyde; Tunable Diode; Laser Spectroscopy

1. Introduction Formaldehyde (H2 CO) is made throughout the troposphere via photo-initiated oxidation of methane and several other hydrocarbons. It is also directly emitted by several combustion sources, including cold-start automobiles and other gasoline vehicles without a functioning oxidation catalyst. In the atmosphere, formaldehyde serves as a photolytic source of HOx , and is an important indicator of photochemical activity in the remote troposphere. Several measurement techniques have been used to measure H2 CO concentrations in the atmosphere [1]. Among the infrared techniques, two wavelength regions, ∼ 2800 cm−1 (v1 and v5 ) and ∗

Corresponding author. Tel.: +1-9786639500; fax: +1-9786634918. E-mail address: [email protected] (S.C. Herndon).

0022-4073/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2004.03.021

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Table 1 Formaldehyde infrared bands [6,22]

v1 v2 v3 v4 v5 v6

Band center (cm−1 )

Band strength (km mol−1 )

Local mode

2782 1746 1500 1167 2843 1249

75:5 ± 7:05 73:99 ± 2:4 11:15 ± 0:48 6:49 ± 0:64 87:6 ± 8:02 9:94 ± 0:97

CH sym. stretch CO stretch CH asym. stretch

∼ 1745 cm−1 (v2 ), are often used since the rotation–vibration spectra can be used to provide speci:c “:ngerprint” detection of H2 CO. The spectroscopy of the combined v1 and v5 bands has been studied extensively, and these bands are assigned in the HITRAN database [2,3]. An unpublished line list, generated by Linda Brown, [4] contains the transitions of H2 CO in the v2 band. These transitions have been used on a ship-borne measurement of H2 CO [5] but there have been no published measurements of the spectral line intensities for this band. Accordingly, the band has not yet been included in the HITRAN database. Table 1 shows the formaldehyde spectroscopic band assignments. The band strengths in Table 1 are taken from Nakanaga et al. [6]. The purpose of these experiments was to determine spectral line intensities in the v2 band by comparing individual rotation–vibration lines between the two wavelength regions, 1750 and 2830 cm−1 .

2. Experimental section 2.1. Tunable diode laser A dual laser mid-IR tunable diode laser (TDL) spectrometer with an astigmatic Herriot cell was used to conduct these measurements. This system has been described more completely elsewhere [7–10], but some general comments on how the apparatus works are warranted. Two Pb-salt laser diodes, one emitting at 2830 cm−1 , and one emitting at 1780 cm−1 , were housed in a single liquid nitrogen dewar. The output from each laser was collected with a reJecting microscope objective and directed into the multipass cell along one of two orthogonal paths. For the work presented here, the multipass cell was con:gured for 174 passes, equaling 153:5 m of total pathlength. The exit beams were directed to HgCdTe photoconductive detectors housed in the same dewar as the diodes. The data acquisition is based on a rapid current sweep of the diode laser with synchronous detection of the transmitted radiation. For the work presented here, spectra which spanned the features of interest were acquired using a data acquisition rate of 500 kHz with 150 point spectra. The sweep rate of ∼ 3:3 kHz is fast enough to minimize the impact of low frequency amplitude noise. The two diode lasers were deliberately run asynchronously in order to minimize cross talk between the two detection channels. The rotation–vibration spectra are averaged for 1 s and :t using line parameter data from a HITRAN-format [2] input :le and a Voigt lineshape model [11,12] to account for Doppler and

S.C. Herndon et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 90 (2005) 207 – 216

1.00

1.00

0.95

0.95

0.90

0.90

0.85

0.85

0.80

209

0.80 1774.76 1774.78 1774.80 1774.82 1774.84 TDLA Wavelength (cm-1)

2817.16

2817.20

2817.24

2817.28

2817.32

TDLB Wavelength (cm-1)

Fig. 1. Simultaneous transmission spectra in the v2 (left) and, v1 and v5 (right) bands of H2 CO (7:22 ppm) in air with a total pressure of ∼ 10 Torr and a path length of 153:5 m. The open circles are the acquired data, while the solid lines are the result of the Voigt lineshape :tting model which accounts for pressure and Doppler broadening.

pressure broadening of the lines. In the version of the :tting software used throughout these experiments, the laser linewidth could also be accounted for by assuming a Gaussian lineshape. For the purposes of this work, the line list provided by Brown [4] was adapted to this format and the nominal line strengths were used as “placeholders”. In order to derive a mixing ratio from the measured absorption pro:le additional measurements are required. They include pressure, temperature, and diode laser mode purity. The pressure inside the multipass cell was measured using a calibrated capacitance manometer and temperature was measured using a calibrated thermocouple. In the 2800 cm−1 region, strong methane lines were used to estimate the mode purity, while for the measurements in the 1700 band, water lines provided spectroscopic “black” absorption. H2 CO lines near 2817 and 2826 cm−1 were used in this work with the current ramp adjusted so that the laser frequency range spanned ∼ 0:3 cm−1 . This was wide enough to include several absorption features in a single laser sweep [13–17]. At the same time, the output from the second diode laser operating with a similar wavelength range (∼ 0:25 cm−1 ) at 1725, 1745 or 1774 cm−1 , was directed through the same multipass cell on an orthogonal coupling axis. Fig. 1 shows simultaneous transmission spectra taken while the diodes were operated near 1774 and 2817 cm−1 respectively. The left hand panel of Fig. 1 depicts a transmission spectrum in the R branch of the v2 band while the right hand panel shows the simultaneous absorption comprised of lines in the v1 and v5 bands. The simultaneous transmission spectra are both :tted and the resulting concentrations are compared. For the 2800 cm−1 region, linestrengths from the HITRAN database were used after corrections for an overestimate of the strengths of the doubly degenerate lines (see results for additional details). For the 1700 cm−1 region, the Brown [4] “placeholder” line strengths were used. A comparison of the resulting mixing ratios provides the ratio between the “placeholder” line strengths and the actual linestrengths for the 1700 cm−1 band based upon the line strengths in the 2800 cm−1 region.

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2.2. Estimate of band strength from individual spectral line intensities In order to compare any previously measured band strengths for the v2 band, it will be necessary to convert the individually measured spectral line strengths to an estimate of the band strength. The strength of a band is commonly de:ned as the sum of the individual spectral line intensities.
SAB ; (1) SBand = A;B

where the sum in (1) is taken over the lower states A and the upper states B. The spectral line strength for a transition from state A to state B can be written [18] as   8 3 N0 B vAB exp (−hcEA =kT )|RT |2 ; SA = (2) 3hc Q where N0 is Loschmidt’s Number (used in this context to express the spectral line strength in units of cm−2 STP atm−1 ), Q is the total partition function, vAB is the frequency of the transition between states A and B, EA is the lower state energy and |RT |2 is the square  of the dipole matrix element for the transition. Note that |RT |2 is computed by the double sum a;b | ¡ a||b ¿ |2 , where a and b are representative of the quantum numbers describing the degenerate sublevels of the A and B states. In (2) we have omitted the term which accounts for induced emission from higher populated vibrational states. The dipole matrix element, RT , may be assumed to be composed of independent rotational and vibrational components as in (3) |RT |2 = R2v Rrot 2 :

(3)

Furthermore, for H2 CO where the asymmetry is small (K = −0:96; minus implies prolate top), we may treat the molecule as a symmetric top for the evaluation of Rrot . The rotationally dependent non-vanishing dipole matrix element Rrot may be approximated by the HPonl–London factors for a symmetric top, following Dennison [19], Rrot 2 ∼ = (2J  + 1)HAB ; K  = 0;

(4)

where J  refers to the rotational quantum number in the A state and HAB is the HPonl–London factor for the A–B transition. It can be shown that substitution of (2) into (1) yields the following expression, where vQ is the average transition frequency. SBand =

8 3 N0 vR Q 2v : 3hc

(5)

It therefore follows, upon substitution of (5) into (2) that the spectral line intensity for a symmetric top molecule is related to the total band strength by SAB = SBand

vAB exp (−hcEA =kT ) (2J  + 1)HAB : vQ Q

(6)

Up to this point in this treatment, we have not considered the eSects of nuclear spin and the exchange of equivalent nuclei. If we assume the contribution to the total partition function due to higher vibrational levels is negligible, but account for the symmetry in H2 CO and the exchange of

S.C. Herndon et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 90 (2005) 207 – 216

equivalent spin

211

1 2

nuclei, (7) follows [20] (2I1 + 1)(2I2 + 1) = 2Qrot ; (7) Q = Qrot  where In is the spin of the nth H atom and  is the symmetry number. Because these experiments are conducted at room temperature, it is appropriate to approximate the rotational partition function as  Qrot = ( =ABC)=(kT=hc)3 : (8) In the case of the v2 parallel band of H2 CO, the spectral line strength is related to the total band strength through (9) vAB exp (−hcEA =kT )  (2J  + 1)(2I  + 1)HAB ; (9) SAB = SBand vQ 2 ( =ABC)=(kT=hc)3 where I is taken as the sum of I1 and I2 and is based on the parity of Ka , following Townes and Schawlow [21]. Eq. (9) will be used to estimate the v2 band strength, SBand , from the individually measured and assigned spectral line intensities. 3. Results Fig. 2 shows three pairs of simultaneous transmission spectra and their Voigt :ts. Those spectra on the upper portion of the :gure represent features in the P, Q and R branches of the v2 band, 1.00 0.90

Transmission

0.80 0.70 1725.50

1725.60 1745.80

1745.90

1774.7

1774.8

1.00 0.95 0.90 0.85 0.80 2826.62

2826.70

2826.62

2826.70

2826.6

2826.7

Wavelength (cm-1)

Fig. 2. Pairs of transmission spectra for H2 CO features in the v2 and, v1 and v5 bands. The open diamonds are the acquired data, while the solid lines are the result of the Voigt lineshape :tting model. The transmission spectra shown at the top are line(s) in the P, Q and R branches of the v2 band from left to right, while those below are the respective transmission spectra in the v1 and v5 band. The wavelength scales are consistent within the v2 and v1 and v5 spectral pairs.

S.C. Herndon et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 90 (2005) 207 – 216 Placeholder [HCHO] via 1725, 1745, or 1774 cm-1 (ppm)

212

12 10 8 6 1:1 Line Data and Linear Fits Placeholder/Stan : 2826 cm−1 P Branch (1725.5 cm−1) 1.37 Q branch (1745.3 cm−1) 1.32 R branch (1774.73 cm−1) 1.42 : 2817 cm−1 R branch (1774.79 cm−1) 1.34

4 2 0 0

2

4

6

8

10

12

-1

[HCHO], via 2817 or 2826 cm (ppm)

Fig. 3. Fit H2 CO comparison using placeholder line strengths. The results of the Voigt :ts from the simultaneous v2 and, v1 and v5 spectra are depicted on the y and x-axis respectively. The (v1 and v5 ) spectra are :t using the HITRAN linestrengths while the v2 spectra are :t using the line list contributed by Linda Brown. This list is referred to as the placeholder [HCHO]. The results from several diSerent experiments and v2 , (v1 and v5 ) line combinations are shown.

from left to right. The three spectra on the lower half of the :gure are the simultaneously acquired transmission spectra where v1 and v5 transitions overlap. The :gure shows the ability of the dual diode laser coupled to a single multipass cell to compare transmission spectra in the 2800 cm−1 bands to those throughout the 1700 cm−1 band. The relative absorption intensities provided in the Brown [4] line list showed no deviation from experimental data. Likewise, absolute wavelength calibration using known weak water lines and germanium etalon fringes to calibrate the wavelength scale of the diode sweep found no diSerences between the assigned line positions in the narrow wavelength regions where the diode was operated. Fig. 3 shows the result of :tting multiple pairs of simultaneous spectra and comparing the resultant mixing ratios. The x-axis is the concentration using the HITRAN line strengths for the appropriate frequencies, in these experiments, 2817 and 2826 cm−1 . The y-axis is the concentration determined by :tting using the Brown [4] line list. The experimental conditions, for the data shown in the :gure and additional experiments are given in Table 2. The regions in the P, Q, and R branches of the v2 band which were compared can be found in Table 3. The v1 and v5 absorption features used as the ‘standard’ for these line strength assignments are also given in Table 3. Note that a second error in the HITRAN data base incorrectly assigns the full measured line strength to both of these degenerate transitions. 1 In order to properly :t the transmission spectra taken over this feature, the line strengths for both lines were halved. Though 1

Work is ongoing to correct several inconsistencies present in the HITRAN database in the v1 , v5 spectral region.

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213

Table 2 Line groupings intercomparison Description

Wavelength range (cm−1 )c;d;e

Standard P branch Q branch R branch Standard

2826.62–2826.75 1725.50–1725.6 1745.78–1745.9 1774.67–1774.83 2817.08–2817.32 1774.67–1774.83

Standard R branch

2817.16–2817.32 1774.76–1774.84

Concentration range (ppm)a

Ratiob

0.04–12 0.09–2.1 4–17

1.37 1.31 1.42

0.04–337 0.04–0.72

1.40 1.34

1.1–5.1

1.30

a

This concentration range is that of the ‘standard’. Concentration ratio [H2 CO]1700 =[H2 CO]2800∗ where 2800∗ is the noted ‘Standard’ in this table. c Mode purity of 2826 cm−1 laser is 86 ± 1%. d Mode purity of 2817 cm−1 laser is 85 ± 4%. e Mode purity of 1725, 1745 and 1774 cm−1 laser is ¿ 98:6 ± 0:5%. b

the ground state of these two lines will have diSering populations over the temperature ranges observed in this work, ±1 K, the error introduced by not formally apportioning the line strength will be negligible: 0.3% compared to other sources of error. Furthermore, some lines present in the original measurement paper [3] are not included in the HITRAN database detailing the v1 , v5 wavelength region. These lines have been added to account for weak H2 CO lines in this wavelength region which are not in either the v1 or v5 bands. 3.1. Band strength calculation The measured spectral line intensities given in Table 3 have been used along with Eq. (9), to provide an estimate of the band strength for the v2 transition in H2 CO. The band strength determined by the rescaled line intensities is 309 ± 20 cm−2 atm−1 or expressed in other units, 76 ± 5 km mol−1 , where the listed error is 2 based on the precision in the spectral line strength measurements. The individually determined band strengths in each of the P, Q, and R branches agree within 3 km mol−1 . This value provides an independent point of comparison to the assigned spectral line intensities and is compared to other measurements in the discussion section. 4. Discussion and conclusions The mixing ratios determined by using the “placeholder” line strengths from Brown in the 1700 cm−1 band are greater by a factor of 1:33 ± 0:09(2) than those determined using the HITRAN 2800 cm−1 features in each of the comparisons shown in Fig. 3 and Table 2. This factor has been calculated using a weighted :t of the resulting correction factors determined in the individual P, Q, and R branch experiments. A corrected line list which divides the “placeholder” linestrengths from Brown by this factor is available as supplemental material in HITRAN

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Table 3 Partial listing of line strength and positionsa Band

Line center (cm−1 ) Line strength (cm2 =molecule cm−1 ) Boltzman energy (cm−1 ) J  Ka Kc J  Ka Kc

v2 v2 v2 v2 v2 v2 v2 v2 v2 v2 v2 v2 v2 v2 v2 v2 v2 v2

1725.547 1745.786 1745.787 1745.804 1745.804 1745.82 1745.825 1745.825 1745.833 1745.844 1745.858 1745.863 1745.868 1745.868 1745.885 1745.885 1745.892 1745.909

6:50E − 20 2:60E − 20 2:60E − 20 1:17E − 20 1:17E − 20 6:12E − 21 3:84E − 20 3:84E − 20 1:92E − 20 3:68E − 21 4:69E − 21 2:93E − 21 3:39E − 20 3:39E − 20 1:52E − 20 1:52E − 20 6:12E − 21 8:33E − 21

98.4197 110.1092 110.1086 167.3146 167.3146 57.078 240.7772 240.7772 10.7001 83.7453 69.1824 100.7286 97.9578 97.9577 155.1694 155.1694 57.0425 47.3397

v2 v2 v2

1774.418 1774.696 1774.796

2:07E − 20 7:02E − 20 6:99E − 20

194.4175 173.3704 190.8431

v1 v1 v1 v 2 + v4 b v 3 + v6 b v1 v 3 + v6 b v5 v1 v1

2816.987 2817.129 2817.175 2817.19 2817.192 2817.214 2817.247 2817.273 2817.294 2817.44

3:82E − 20 2:88E − 20 3:94E − 20 3:61E − 21 3:68E − 21 2:32E − 20 3:52E − 21 7:10E − 21 2:89E − 20 1:32E − 20

v1 v1 d v1 d v5 v1 v1

2826.634 2826.682 2826.682 2826.71 2826.75 2826.765

1:76E − 20 1:26E − 20 1:26E − 20 3:52E − 20 6:74E − 21 6:90E − 21

a

7 5 5 5 5 5 5 5 1 6 5 7 4 4 4 4 4 3

1 3 3 4 4 2 5 5 1 2 2 2 3 3 4 4 2 2

6 3 2 2 1 3 1 0 1 4 3 5 2 1 1 0 2 2

8 5 5 5 5 4 5 5 1 6 5 7 4 4 4 4 4 3

1 3 3 4 4 2 5 5 1 2 2 2 3 3 4 4 2 2

7 2 3 1 2 2 0 1 0 5 4 6 1 2 0 1 3 1

12 2 12 1 13 1

10 11 2 11 11 1 13 12 1

9 10 12

253.822 329.042 235.646 666.40c 141.75c 495.797 363.19c 69.182 329.305 251.098

15 15 14 19 8 16 17 5 15 15

1 3 1 4 4 5 3 1 3 0

15 13 13 16 4 12 14 5 12 15

14 14 13 19 7 15 16 5 14 14

1 3 1 5 3 5 2 2 3 0

14 12 12 14 5 11 15 4 11 14

489.691 1013.411 389.306 203.284 665.893 665.891

19 23 18 12 20 20

3 7 1 0 5 5

17 17 17 12 15 16

18 22 17 12 19 19

3 7 1 1 5 5

16 16 16 11 14 15

Line strengths in the 1700 cm−1 band (measured in this work) are relative to the ∼ 2800 cm−1 lines from the HITRAN database [2]. b These lines have been added. The intensity and assignments are taken from Brown et al. [3]. c These energies have been calculated assuming a prolate top, following Hollas [23] and using the A, B and C rotational constants as 9.405, 1.295, 1:1342 cm−1 [24]. d The line strengths for these lines have been halved. See Text for additional details.

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215

format and has been submitted to the HITRAN project for inclusion in the next edition of that data base. 2 There are several sources of systematic error present in this work, but some of the usual suspects can be ruled out. Generally, any error in measuring the pressure, temperature and path length contributes directly to the measurement of a line strength. In these experiments, however, because the identical pressure, temperature, path length and :tting protocol is employed for both the ‘standard’ and ‘placeholder’ spectra :tting, the direct inJuence of the uncertainty in P and T is eliminated. Though the path length in the astigmatic multipass cell is well known [9] (¡ 0:1%), this potential uncertainty also factors out in this intercomparison. The principal uncertainties in this work are the diode laser lineshape model and the diode mode purity. The notes to Table 2 give the measured mode purity for the 2800 cm−1 laser (∼ 85% ± 4%) and for the 1700 cm−1 laser (98:6% ± 0:5%). The combined uncertainty of this source results in a 4% systematic error directly associated with the mode purity of the diode pairs. The pressure broadening coeXcient used through out this work for the v2 band was 0:1 cm−1 atm−1 at 296 K, however pressures in this work never exceeded 10 Torr. Because mixing ratios of H2 CO typical of this work were less than 10 ppm, the contribution to the overall pressure broadening due to a self-broadening mechanism is negligible. Estimating the uncertainty due to improperly modeling the laser line-width is less direct. Transmission spectra of H2 O lines taken at ∼ 2 Torr in the vicinity of 1775 cm−1 show an apparent Gaussian HWHM of 0:00265 cm−1 compared to a calculated Doppler width of 0:00257 cm−1 . If the Doppler component is removed from the apparent spectrum, this results in an eSective Gaussian laser linewidth of less than 0:001 cm−1 . Using low pressure transmission spectra of a CH4 singlet at 2826:88 cm−1 , the apparent lineshape is well simulated by a Gaussian pro:le with a HWHM of 0:0048 cm−1 compared to the Doppler width for CH4 at room temperature of 0:0043 cm−1 . Thus we infer a laser linewidth of 0:002 cm−1 . The uncertainty associated with the assumption that a pure Gaussian pro:le represents the laser lineshape has been estimated by using numerical simulations with the pressure broadening and Doppler widths constrained to values typical of the experiments presented in this work. For the case where the laser lineshape is represented by a Lorentzian half-width of 0:001 cm−1 , and allowing for negligible pressure broadening, the :tting procedures used in this work underestimate the H2 CO mixing ratio (using v1 , v5 ) by 3%. This uncertainty estimate represents a worst case within the measurement conditions; generally the :ts appear to recover over 99% of the absorption area. Analogous simulations for the determination of the H2 CO mixing ratio in the v2 band indicate a potential underestimate of only 0.5%. Due to the relatively poor spectral characteristics of the 2800 cm−1 diode used in these experiments, the combined mode purity and laser lineshape uncertainties associated with :tting the two transmission spectra is 5%. The systematic uncertainty in the original determination [3] of the v1 , v5 spectral line strengths is 5%. The v2 band strength estimated from the measured line intensities is 76 ± 5 km mol−1 , which compares favorably to that of Nakanaga et al., 74±2:4 km mol−1 . This comparison is an independent check of the spectral line strengths measured relative to the v1 , v5 values. Ongoing work in our laboratory is using this spectral region to measure ambient concentrations of this atmospherically important species. 2

At the time of submission this data is available via ftp, at ftp.aerodyne.com/herndon/h2co/h2co 1700.par.

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Acknowledgements This work was funded by NASA Grant NAG5-7656. The authors would also like to thank Ken Demerjian for the use of the dual wavelength TDL system. References [1] Gilpin T, Apel E, Fried A, Wert B, Calvert J, Genfa Z, Dasgupta P, Harder JW, Heikes B, Hopkins B, Kleindienst HW, Lee Y-N, Zhou X, Lonneman W, Sewell S. Intercomparison of six ambient [CH2 O] measurement techniques. J Geophys Res 1997;102:21161–88. [2] Rothman LS, Rinsland CP, Goldman A, Massie ST, Edwards DP, Flaud J-M, Perrin A, Camy-Peyret C, Dana V, Mandin J-Y, Schroeder J, McCann A, Gamache RR, Wattson RB, Yoshino K, Chance KV, Jucks KW, Brown LR, Nemtchinov V, Varanasi P. The Hitran Molecular Spectroscopic Database and Hawks (HItran Atmospheric Workstation): 1996 Edition. JQRST 1998;60:665–710. [3] Brown LR, Hunt RH, Pine AS. Wavenumbers, linestrengths and assignments in the doppler—limited spectrum of formaldehyde from 2700 to 3000 cm−1 . J Mol Spectrosc 1979;75:406–28. [4] Brown, LR. Linelist for H2 CO in the 1700 cm−1 band. 2000, personal communication. [5] Wagner V, Schiller C, Fischer H. Formaldehyde measurements in the marine boundary layer of the Indian Ocean during the 1999 INDOEX cruise of the R/V Ronald H. Brown. J Geophys Res 2001;106:28528–38. [6] Nakanaga T, Kondo S, SaPeki S. Infrared band intensities of formaldehyde and formaldehyde-d2. J Chem Phys 1982;76:3860–5. [7] Li Y, Schwab J, Roychowdhury U, Ren X, Brune W, Karcher R, Zahniser MS, Nelson DDJ, Herndon SC, Demerjian KL. Intercomparison of formaldehyde, sulfur dioxide and nitrogen dioxide measurement techniques during the PMTACS—NY Summer 2002 Campaign at Whiteface Mountain, 2003. (in press). [8] Horii CV, Zahniser MS, Nelson DDJ, McManus JB, Wofsy SC. Nitric acid and nitrogen dioxide Jux measurements: a new application of tunable diode laser absorption spectroscopy. Proceedings of the SPIE Conference on Atmospheric Sensing. 1999. [9] McManus JB, Kebabian PL, Zahniser MS. Astigmatic mirror multipass absorption cells for long-path-length spectroscopy. Appl Opt 1995;34:3336–48. [10] Zahniser MS, Nelson DD, McManus JB, Kebabian PL. Measurement of trace gas Juxes using tunable diode laser spectroscopy. Phil Trans Roy Soc Lond A 1995;351:371–82. [11] Humlicek. JQSRT 1979;21:309–13. [12] Armstrong BH. Spectrum line pro:les: the Voigt function. JQSRT 1967;7:61–88. [13] Saito S, Matsumura C. J Mol Spectrosc 1980;80:34–40. [14] Paukert TT, Johnson HS. J Chem Phys 1972;56:2824–38. [15] Buchanan JW, Thrush BA, Tyndall GS. Chem Phys Lett 1983;103:167–8. [16] Zahniser MS, McCurdy KE, Stanton AC. Quantitative spectroscopic studies of the HO2 radical: band strength measurements for the v1 and v2 vibrational bands. J Phys Chem 1989;93:1065–70. [17] Nelson DD, Zahniser MS. Diode laser spectroscopy of the v3 vibration of the HO2 radical. J Mol Spectrosc 1991;150:527–34. [18] Pugh LA, Rao KN. Intensities from infrared spectra, Molecular Spectroscopy: Modern Research, Vol. 2. Academic Press, New York; 1976. pp. 172–3. [19] Dennison DM. The infrared spectra of polyatomic molecules. Rev Modern Phys 1931;3:280–345. [20] Hertzberg G. Infrared and Raman spectra of polyatomic molecules, Molecular Spectra and Molecular Structure, Vol. 2, D. Van Norstrand Company Inc., New York, 1945. [21] Townes CH, Schawlow AL. Microwave spectroscopy. New York, 1975. p. 698. [22] Smith MAH, Rinsland CP, Fridovich B, Rao KN. Intensites and collision broadening parameters from infrared spectra. Chapter 3, Molecular Spectroscopy: Modern Research. Academic Press, Inc. 1985. [23] Hollas MJ. Modern Spectroscopy, John Wiley & Sons, Chichester, 1993. p. 407. [24] Muller HSP, Winnewisser G, Demaison J, Perrin A, Valentin A. The ground state spectroscopic constants of formaldehyde. J Mol Spectrosc 2000;200:143–4.