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High sensitivity cavity ring down spectroscopy of the 4ν3 band of NO2 near 1.59 µm
Accepted Manuscript
High sensitivity cavity ring down spectroscopy of the 4ν 3 band of NO2 near 1.59 µm A.A. Lukashevskaya , S. Kassi , A. Campargue , V.I. Perevalov PII: DOI: Reference:
S0022-4073(17)30524-1 10.1016/j.jqsrt.2017.07.024 JQSRT 5791
To appear in:
Journal of Quantitative Spectroscopy & Radiative Transfer
Received date: Revised date: Accepted date:
30 June 2017 13 July 2017 13 July 2017
Please cite this article as: A.A. Lukashevskaya , S. Kassi , A. Campargue , V.I. Perevalov , High sensitivity cavity ring down spectroscopy of the 4ν 3 band of NO2 near 1.59 µm, Journal of Quantitative Spectroscopy & Radiative Transfer (2017), doi: 10.1016/j.jqsrt.2017.07.024
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ACCEPTED MANUSCRIPT Highlights First detection of the B-type band of 14N16O2 near 6276 cm-1 1630 lines corresponding to 1731 spin-rotation-vibration transitions are assigned Line positions are reproduced by an effective Hamiltonian model The (0,0,4) upper level is found mostly unperturbed Effective dipole moment and Herman-Wallis type parameters are determined
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High sensitivity cavity ring down spectroscopy of the 4ν3 band of NO2 near 1.59 µm
A.A. Lukashevskaya a, S. Kassi b,c, A. Campargue b,c*, V.I. Perevalov a a
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Laboratory of Theoretical Spectroscopy, V. E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, 1, Academician Zuev sq., 634055, Tomsk, Russia b Univ. Grenoble Alpes, LIPhy, F-38000 Grenoble, France c CNRS, LIPhy, F-38000 Grenoble, France
Number of pages: 15 Number of tables: 2
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Number of figures: 8
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Key words: Nitrogen dioxide, NO2; High resolution spectroscopy; Cavity ring down
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spectroscopy; Electron spin-rotation interaction; Effective Hamiltonian
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ACCEPTED MANUSCRIPT Abstract The very weak B-typeabsorption band of the nitrogen dioxide main isotopologue (14N16O2) is investigated between 6175 and 6350 cm-1. The absorption spectrum of this band was recorded by high sensitivity continuous wave-cavity ring down spectroscopy with noise equivalent absorption of min 1×10-10 cm-1. More than 1630 lines of the 4ν3 band are assigned with rotational quantum numbers N and Ka up to 55 and 7, respectively, what corresponds to 1731 spin-rotation-vibration transitions. The overall measured set of the line
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positions is used to fit the effective Hamiltonian parameters. The effective Hamiltonian takes explicitly into account the Coriolis interactions between the spin rotational levels of the (0,0,4) vibrational state and those of the nearby (0,2,3) bright state at 6183.61 cm-1 together with the electron spin-rotation interactions. The fitted set of the parameters reproduces the observed line positions with an rms of 2.2×10-3 cm-1. A selected set of the measured line
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intensities are used to determine the effective dipole moment parameters including the Herman-Wallis type parameters describing the line intensities of the 4ν3 band. The rms
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deviation of the fit is 5.7%.
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ACCEPTED MANUSCRIPT 1. Introduction This study completes the analysis of the very weak near infrared spectrum of nitrogen dioxide between 5855 and 6410 cm-1 recorded in Grenoble by cavity ring down spectroscopy (CRDS). The overview of this spectrum is presented in Fig. 1 of our recent paper [1] where the analysis of the 2 A-type band centered at 6350 cm-1 was reported. In Ref. [2], the 3 and 2 A-type bands lying in the 6100–6200 cm-1 region were assigned and modeled. The present contribution is devoted to the 4ν3 B-type band centered at 6275
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cm-1. This band is the most excited B-type “bright” band ever observed in NO2. Usually Btype bands have considerably smaller intensities compared to A-type bands with the same variation, ∑ |
| of the sum of the Vi vibrational quantum numbers (i= 1,2,3). Consequently,
above the 2ν3 B-type band centered at 3201 cm-1, only a few lines of five B-type “dark” bands were observed. They are all due to an intensity transfer from a nearby A-type band in local
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resonance interaction: (i) Two lines of the 2 band were reported in Ref. [3] due to the line intensity transfer from the 2 A-type band, (ii) Sixty lines of the band were assigned in Ref. [4]. They borrow intensity from the band, (iii) Five lines of the 2 band were reported in Ref. [5] due to the line intensity transfer from the
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2 band. Thirty six lines of the 2band and fifteen lines of the 5band were observed in Ref. [6] due to the line intensity transfer from the 2and 5
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bands, respectively. Practically all B-type bands borrow their line intensities via Coriolis interactions from the neighboring stronger A-type bands. It leads to the importance of the
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Herman-Wallis terms in the expansion of the transition dipole moment squared. Indeed, while in the case of A-type band, only the principal effective dipole moment parameter is generally
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sufficient to reproduce the line intensities with a reasonable accuracy, it is not the case for the B-type bands. This will be demonstrated below on the example of the studied 4ν3 band which has line positions mostly unperturbed while line intensities are greatly influenced by a non-
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resonant first-order Coriolis interaction from the considerably stronger A-type band. 2. Experimental details and line parameters retrieval The reader is referred to Refs. [7,8] for a detailed description of the used fiber-
connected cavity ring down spectrometer. The recording of the CRDS spectra under study is presented in details in Ref. [1]. Seven Distributed Feedback (DFB) laser diodes were used as light sources to cover the 6180–6350 cm-1 spectral region under study. The noise-equivalent absorption of the spectrum is min~ 1×10-10 cm-1. The frequency calibration was performed using a commercial Fizeau type wavemeter. We estimate an uncertainty of 1×10-3 cm-1 for the 4
ACCEPTED MANUSCRIPT position of well isolated lines as checked by comparison of the measured line positions of the 30013-00001 band of
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C O2 present as an impurity compared to those given by
HITRAN2012 database [9]. The filling pressure was 1.00 Torr and the temperature was 297.3±0.3 K. Taking into account the 2NO2↔ N2O4 dimerisation equilibrium, it corresponds to an NO2 partial pressure
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of 0.987 Torr [1].
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Fig. 1. Spectrum and line list of NO2 near 6229 cm-1. The three lower panels show the CRDS spectrum recorded at 1.0 Torr, the simulation performed with a multiline fitting program and the corresponding (sim.- meas.) residuals. The two upper panels show the full line list and the stick spectrum limited to the assigned lines. The line parameter retrieval uses the multiline fitting computer code described in Ref.
[10]. The spectral line shape was modeled with the Voigt profile in which the calculated value for the Doppler line width was used and the collision broadening coefficient was fixed to the HITRAN value at 296 K (0.095 cm-1atm-1 [9]). Overall, the center and intensity of more than 3000 lines were retrieved in the 6180–6347 cm-1 interval. Note that in the case of unresolved spin-rotational doublets, we often fitted the absorption feature as a single line. Line intensities range between 10-28 and 10-26 cm-1/(molecule cm-2) at 296 K. The sample of spectrum 5
ACCEPTED MANUSCRIPT displayed in Fig. 1 illustrates the achieved spectrum reproduction with the retrieved line parameters. Because of the weakness and blending of the majority of the lines the averaged accuracy of the retrieved line intensities is estimated to be about 20% or even worse for the very weak or strongly blended lines. A selected set of 230 lines were used to derive effective dipole moment parameters (see below). The uncertainty of their intensities is estimated to be on the level of 5%.
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3. Spectrum assignment and modeling 3.1. Spectrum assignment
In the lower wavenumber region (6180-6200 cm-1), the 4ν3 band overlaps with the 3 and 2bands analyzed in Ref. [2]. In the upper wavenumber region (62906347 cm-1), it overlaps with the 2band studied in Ref. [1].
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For the considered 4ν3 B-type band, only the ΔKa= ±1 transitions are observable. The assignments were performed by comparison to a predicted spectrum with line positions calculated using an effective Hamiltonian (EH) of the (0,0,4) vibrational state. This EH takes into account both vibration-rotation and electron spin-rotation (SR) interactions. For the initial values of the (0,0,4) effective Hamiltonian parameters, the predictions of the global effective 14
N16O2 were adopted [11] except for the (0,0,4) initial vibrational energy
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Hamiltonian of
(6275.98 cm-1) which was taken from Ref. [12]. The ground state energy levels were
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calculated using the ground state parameters of Ref. [13]. In parallel the line intensity calculations were performed using the effective dipole moment parameters fitted to the
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selected values of the measured line intensities. The analyzed spectrum contains a number of doublets involving upper and lower SR energy levels with the same N value, but different J rotational quantum numbers (J=N±1/2).
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At the initial stage of the assignments, the dependence of the SR splitting versus N and Ka was a main criterion. Thus the preliminary assignment was performed basing on the agreement
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between the observed and calculated values of the splitting of the electron spin-rotation doublets as well as on the agreement between observed and calculated line intensities. Note that the measured values of the SR splittings were found in a very good agreement with their values predicted using the global effective Hamiltonian [11]. The newly assigned transitions were progressively included in the line position fitting and the refined effective Hamiltonian parameters were used to improve the prediction. In this way more than 1300 transitions of the 4ν3 band were assigned. In order to validate and extend the assignments, ground state combination differences (GSCD) relations were systematically 6
ACCEPTED MANUSCRIPT used with the help of the respective computer code [14]. Finally, 1731 spin-rotation-vibration transitions with N and Ka quantum numbers up to 55 and 7, respectively, were assigned that correspond to 616 SR energy levels of the (0,0,4) upper state. Fig.2 shows a portion of the RΔKa=1 (N, Ka=0) series of transitions in the 6291–6294 cm-1 spectral region. The displayed
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interval corresponds the band head of the RΔKa=1 (N, Ka=0) series.
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Fig.2. Portion of the RΔKa=1 (N, Ka=0) series of transitions in the 4ν3 band of NO2 in the 6292.8-6294.0 cm-1 spectral region. From top to bottom: stick spectrum of the assigned lines, CRDS spectrum (P= 1.0 Torr) and corresponding simulated spectrum.
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3.2. Effective Hamiltonian model The scheme of the effective Hamiltonian matrix in the basis of products of harmonic oscillator eigenfunctions (V1,V2,V3) and eigenfunctions of the rigid symmetric top |
〉 operators is given in Fig. 3. Here J, N and S are the total, rotational and electron
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spin |
〉 and
spin angular momentum quantum numbers, respectively, K and are the quantum numbers associated with the projection on the molecular-fixed z axis of the rotational and the electron spin operators, respectively. The reader is referred to Ref. [1] for the explicit expression of the Watson-type Hamiltonian (HVR) electron spin-rotation interaction operator (HSR) and second order Coriolis interaction operator (H2C) appearing in the effective Hamiltonian. As usual in the case of the NO2 molecule, the second-order Coriolis resonance interaction is expected to connect the (0,0,4) upper state with the (0,2,3) vibrational state. The 7
ACCEPTED MANUSCRIPT parameters of the (0,2,3) vibrational state were fixed to their values determined from the recent analysis of the 2band [2]. In total, 13 parameters of the (0,0,4) bright state, including 2 SR parameters and 3 Coriolis interaction parameters were fitted to the line positions of 1731 spin-vibration-rotation transitions. The obtained parameters are presented in Table 1. The high order EH parameters for both (0,0,4) and (0,2,3) vibrational states were fixed to the values obtained with the global model [11]. In some cases when the respective values determined with the global model looked less reasonable (change of sign or strong
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change in value compared to the ground state parameters), the parameters were fixed to the
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corresponding ground state values [13].
Fig. 3. Scheme of the effective Hamiltonian matrix for the {(0,2,3), (0,0,4)} interacting vibrational states of 14N16O2.
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The fitted value of the vibrational energy for the (0,0,4) state (6275.5753(13) cm-1), is in a good agreement with the value 6375.98 cm-1 determined in Ref. [12]. The initial values
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for the A rotational constant based on Ref. [11] are also included in Table 1 for comparison. The predicted [11] value of A rotational constant for the (0,0,4) vibrational state agrees within 0.04 % with the fitted value. The obtained set of the effective Hamiltonian parameters allows reproducing the 1731 experimental line positions with an rms deviation of 2.2×10-3 cm-1.
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ACCEPTED MANUSCRIPT Table 1. Effective Hamiltonian parameters for the (0,2,3) and (0,0,4) of interacting vibrational states 14 16 N O2. All values are in cm-1.
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(0,2,3) (0,0,4) a 6183.61 6275.98 a Ev 6183.925 b 6275.5753(13) c 8.160 7.141c A 8.0059492 b 7.138104(28) b (B+С)/2 0.4126903 0.411609(21) (B-С)/4 0.62987E-02 b 0.561(28)E-02 ΔK 0.34425E-02 b 0.21364(21)E-02 ΔJK -0.2825E-04 b -0.3805(27)E-04 ΔJ 0.324E-06 c 0.32810(13)E-06 δK 0.278E-04 c 0.40547E-05 d b δJ 0.7637E-07 0.399E-07 c c HK 0.938E-05 0.2279(33)E-05 HKJ -0.262E-07 c -0.57(11)E-08 c HJK 0.151E-10 0.151E-10 c HJ 0.112E-11 c 0.112E-11 c d hK 0.29297E-07 0.533E-07 c hKJ –0.3637E-10 d –0.3637E-10 d c hJ 0.246E-12 0.246E-12 c LK -0.203E-07 c -0.401E-08 c c LKKJ 0.302E-10 0.302E-10 c LKJk 0.138E-12 c 0.138E-12 c d PK 0.867E-11 0.597E-11 c d QK -0.844E-14 -0.392E-14 c Spin-rotation parameters εzz 0.18473 b 0.15058(18) (εxx +εyy)/2 0.853E-03 c 0.853E-03 c c (εxx –εyy)/4 -0.151E-02 -0.13345(40)E-02 ΔsK -0.282E-03 c -0.144E-03 c Coriolis interaction (0,2,3)↔(0,0,4) -0.628(19)E-01 [ ] -0.221(15)E-02 0.1389(22)E-02 [ ]
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Notes a From Ref. [12] b From recent CRDS analysis [2] c Value predicted with the global effective Hamiltonian [11] d Fixed to the ground state value [13].
3.3. Line intensity modeling The reader is referred to Ref. [1] for the explicit expression of the absorption line intensity, Sb←a(T) versus the transition dipole moment squared of a transition of NO2. The necessary equations are provided in Ref. [1] and not repeated here. In that paper, the measured line intensities of the 2A-type band 9
ACCEPTED MANUSCRIPT could be modeled with a good accuracy with only one principal effective dipole moment In the present case of the 4B-type band, the Herman-Wallis parameters are
parameter
necessary. This is due to the fact that, in spite of being mostly unperturbed, the 4B-type band borrows its intensity from the strong band through non-resonant first-order Coriolis interaction The Herman-Wallis parameters account for this regular vibration-rotation interactions. In the case of a B-type band such as the studied 4band, the observed transitions
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correspond to ΔKa= ±1. The Herman-Wallis type functions contained in the equations of the respective matrix elements are given by the following expressions [15,16]: |
(
|
)
(
)
(
) ,
)
(
( Here m
)
(
)
for P-branch and m
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(1)
(
)
(
for R-branch,
are Herman-Wallis-type parameters.
) .
(2) and
A selected set of measured line intensities were used to fit the effective dipole moment
doublets. The
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parameters. We have chosen 230 mostly isolated lines and 15 mostly isolated spin-rotation parameter f the principal matrix element of the effective dipole moment
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operator and three corresponding Herman-Wallis parameters could be determined. The parameter was fixed to the value 0.3738×10-4 Debye obtained in Ref. [2]. No weighting was
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used in the fit. The fitted set of the effective dipole moment parameters (Table 2) allows reproducing the selected measured line intensities with an rms deviation of 5.7%. The results
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of the fit are provided as Supplementary Material.
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Table 2. Fitted effective dipole moment parameters. Parameter
Value 0.1701 (87)×10-4 Debye 0.3738×10-4 Debye [2] 0.14465(25) -0.07021(13) -0.008214(83)
As one can see from Table 2, the Herman-Wallis type parameters have very large 10
ACCEPTED MANUSCRIPT values. It is very interesting to compare them with the theoretical values. The principal contribution to these parameters gives the first-order Coriolis interaction. The perturbation theory leads to the following equation for this contribution to the (
is the rotational const,
parameters:
)
(
where
and
(3)
)
is the Coriolis interaction constant,
are the
and
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harmonic frequencies of the first and third vibrational modes,
and
are the dipole moment derivatives. The numerical values for the modulo of the dipole moment derivatives can be obtained using the parameter RE. [4] for the band and the parameter
(
)(
)
0.17×10-4 Debye presently derived for
band: (
| |
)(
√
|
√
)
Debye,
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|
Debye derived in
Debye.
Supposing that the dipole moment derivatives have different signs and taking cm-1,
=1325.673 cm-1,
=0.45 from Ref. [17] we
= 0.1335. This value is very close to the fitted one (0.1447) from Table 2 and the
fitted values of the
and
parameters satisfy approximately to the theoretical equation
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obtain
=1633.066 cm-1 from Ref. [11] and
= 0.41044
The comparison between the experimental and simulated spectra included in Fig. 4
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illustrates the achieved quality of the spectrum reproduction. The vast majority of the lines are well reproduced but a number of additional lines with significant intensity are present in the experimental spectrum. They may be due to hot bands of
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N16O2, minor isotopologues or
band of
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impurities. The most important absorption features due to an impurity is the 30013-00001 12 16
C O2 observed in the 6160-6260 cm-1 range. As a result of the high reactivity of
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NO2, other trace species may be present in the sample and detectable as a result of the sensitivity of the CRDS recordings [1].
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Fig. 4. Comparison of the CRDS spectrum of the 4ν3 band of 14N16O2 recorded at 1 Torr to a simulation based on the effective operator approach. 4. Some characteristics of the 4ν3 spectrum of 14N16O2
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4.1. Spin-rotation splitting The SR doublets are a characteristic feature of the NO2 spectrum due to the electron ground electronic state has S= ½ electronic spin). The SR
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spin–rotation interaction (the ̃
splitting depends on vibrational and rotational quantum numbers. Within the same vibrational band, the SR splitting generally increases with increasing Ka values and decreases with increasing N values. Note that we use the following labeling of the spin-rotation states |N Ka Kc J> (with
) or simply |N Ka Kc ±>. Calculated spin–rotation splittings of the
levels of the (0,0,4) upper state are displayed in Fig. 5. The largest SR splitting reaches a value of 0.66 cm-1 for Ka= 5 and N= 5 (Fig. 5). The SR splitting in the Ka= 1 and Ka= 2 series reflects the perturbation due to the local resonance with the (0,2,3) state.
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0.8 0 1 2 3 4 5 6 7
-1
SR splitting (cm )
Ka
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0.2
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20
30
40
50
N
4.2. Resonance interactions
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Fig. 5. Calculated spin–rotation splitting of the energy levels of the (0,0,4) vibrational state. The plot is limited to the levels experimentally determined.
The mixing coefficients of the rovibrational eigenfunctions of the (0,0,4) vibrational
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state with those of the (0,2,3) bright state are small (Fig. 6). The maximum value is limited to 3.5% at N= 50 and Ka= 5. Nevertheless the inclusion of the Coriolis interaction terms into the
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effective Hamiltonian slightly improves both line position and intensity fits. A sharp leap upward of the mixing coefficients for Ka= 6 at N = 44 is caused by the accidental coincidence
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of two energy levels with different N values (ΔN=1) and different spin components interacting through the second order Coriolis + SR interactions. The scheme of this resonance
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perturbation is presented in Fig. 7. The observed alternation of the values of the mixing coefficients of the (0,0,4)
vibrational state with the (0,2,3) vibrational state in the cases of Ka= 1 and Ka= 2 at high N values is connected with the different energy spacing between interacting levels for even and odd N values.
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4 Ka
Mixing, %
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0 0
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Fig. 6. Mixing coefficients of the rovibrational eigenfunctions of the (0,0,4) vibrational state with the (0,2,3) vibrational state. The plot is limited to the maximum observed N value for each Ka.
Fig. 7. Scheme of the perturbation of the {44 6 38 -} rotational level of the (0,0,4) vibrational state by the level {43 7 36 +} of the (0,2,3) vibrational state.
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5. Conclusion
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Fig. 8. Overview of the different 14N16O2 bands analyzed by CRDS between 6050 and 6450 cm-1 [1, 2 and This work]. Line intensities are given at 296 K. With the present study of the 4ν3 B-type band of
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N16O2, we have achieved the
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analysis of the weak bands newly detected by CRDS between 6050 and 6450 cm-1. An overview of the line lists obtained in this region is presented in Fig. 8. The 4ν3 band is the
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only mostly unperturbed B-type band observed above 3500 cm-1. The positions of 1731 vibration-rotation transitions were modeled using the vibration-rotation Hamiltonian which explicitly takes into account electron spin-rotational interaction, as well as a weak Coriolis
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resonance interactions of the (0,0,4) vibrational state with the nearby (0,2,3) vibrational state. An rms deviation of 0.0022 cm-1 was achieved for the residuals between the observed and calculated line positions. The modeling process was helped by reasonable predictions of the rotational, centrifugal distortion, and SR constants provided by a recent global fit of the observed vibration-rotation NO2 transitions up to 7916 cm-1 [11]. The assignment was also supported by the reasonable agreement between the observed and calculated line intensities based on the fitted value of the effective dipole moment parameters. The maximum line intensity of the 4ν3 band is 2.17×10-26 cm-1/(molecule cm-2). 15
ACCEPTED MANUSCRIPT The importance of Herman-Wallis coefficients for the satisfactory reproduction of the measured intensities is interpreted as resulting from a non-resonant coupling to the 1+33 band at 5984.7 cm-1. This strong A-type band, recently reported by Fourier transform spectroscopy [4], has an intensity more than three orders of magnitude higher than the presently 4ν3 band. In the future, an extended analysis of the 1+33 band together with additional recordings will allow completing our previous studies by CRDS up to 8000 cm-1
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Acknowledgements This work is jointly supported by RFBR (Russia, grant N 16-55-16017) and CNRS (France) in the framework of the Laboratoire International Associé SAMIA (Spectroscopie d’Absorption des Molécules d’Intérêt Atmosphérique).
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References Lukashevskaya AA, Kassi S, Campargue A, Perevalov V.I. High sensitivity cavity ring down spectroscopy of the 2band of NO2 near 1.57 µm. J Quant Spectrosc Radiat Transf 2017;200:17–24, doi:10.1016/j.jqsrt.2017.05.017. Lukashevskaya AA, Naumenko OV, Kassi S, Campargue A. First detection and analysis of the 3ν1+ν2+ν3 band of NO2 by CRDS near 6156 cm-1. J Mol Spectrosc http://dx.doi.org/10.1016/j.jms.2017.06.005 Stephen TM, Goldman A, Perrin A, Flaud JM, Keller F, Rinsland CP. New high resolution analysis of the 33 and 2bands of nitrogen dioxide (NO2) by Fourier transform spectroscopy. J Mol Spectrosc 2000;201:134–42. Miljanic S, Perrin A, Orphal J, Fellows CE, Chelin P, New high resolution analysis of the 1+33 band of nitrogen dioxide. J Mol Spectrosc 2008;251:9–15. Raghunandan R, Perrin A, Ruth AA, Orphal J. First analysis of the 21+33 band of NO2 at 7192.159 cm-1. J Mol Spectrosc 2014;297:4–10. Lukashevskaya AA, Naumenko OV, Perrin A, Mondelain D, Kassi S, Campargue A. High sensitivity cavity ring down spectroscopy of NO2 between 7760 and 7917 cm-1. J Quant Spectrosc Radiat Transf 2013;130:249–59. Kassi S, Campargue A. Cavity ring down spectroscopy with 5×10-13 cm-1 sensitivity. J Chem Phys 2012;137:234201. Mikhailenko SN, Le Wang, Kassi S, Campargue A. Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS. J Mol Spectrosc 2007;244:170–8. Rothman LS, Gordon IE, Babikov Y, Barbe A, Benner DC, Bernath PF, et al. The HITRAN2012 molecular spectroscopic database. J Quant Spectrosc Radiat Transf 2013;130:4– 50. Lyulin OM. Determination of spectral line parameters from several absorption spectra with the MultiSpectrum Fitting Computer Code. Atmospheric and Oceanic Optics 2015;28:387–95. Lukashevskaya AA, Lyulin OM, Perrin A, Perevalov VI. Global modelling of NO2 line positions. Atmospheric and Oceanic Optics 2015;28:216–31. doi:10.1134/S1024856015030094 Delon A, Jost R. Laser induced dispersed fluorescence spectra of jet cooled NO2: the complete set of vibrational levels up to 10,000 cm-1 and the onset of the Ã2B2– X 2 A1 vibronic interaction. J Chem Phys 1991;95:5686–700. Semmoud-Monnanteuil N, Colmont JM, Perrin A, Flaud JM, Camy-Peyret C. New measurements in the millimeter wave spectrum of NO2. J Mol Spectrosc1989;134:176–182. Bykov AD, Naumenko OV, Pshenichnikov AM, Sinitsa LN, Shcherbakov AP. An expert system for identification of lines in vibrational-rotational spectra. Opt Spectrosc 2003;94: 528– 37. Perevalov VI, Lukashevskaya AA. Parameterization of the effective dipole moment matrix elements in the case of the asymmetric top molecules. Application to NO 2 molecule. Atmospheric and Oceanic Optics 2015;28:17–23. Lukashevskaya AA, Lavrentieva NN, Dudaryonok AS, Perevalov VI. NDSD-1000: Highresolution, high-temperature Nitrogen Dioxide Spectroscopic Databank. J Quant Spectrosc Radiat Transf 2016;184:205-17. Speirs GK, Ŝpirko V. Application of the Monte Carlo method to anharmonic force constant calculations: The anharmonic potential functions of some nonlinear symmetrical triatomic molecules. J Mol Spectrosc 1975;56:104-123. Perrin A, Kassi S, Campargue A. First high resolution analysis of the 41+3 band of nitrogen dioxide near 1.5 µm. J Quant Spectrosc Radiat Transf 2010;111:2246–55. Mondelain D, Perrin A, Kassi S, Campargue A. First high resolution analysis of the 53 band of nitrogen dioxide near 1.3 µm. J Quant Spectrosc Radiat Transf 2012; 113:1058–65. Lukashevskaya AA, Naumenko OV, Perrin A, Mondelain D, Kassi S, Campargue A. High sensitivity cavity ring down spectroscopy of NO2 between 7760 and 7917 cm-1. J. Quant. Spectrosc. Radiat. Transf 2013;130: 249–59.
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ACCEPTED MANUSCRIPT Lukashevskaya AA, Naumenko OV, , Mondelain D, Kassi S, Campargue A. High sensitivity Cavity Ring Down spectroscopy of the 3ν1+3ν2+ν3 band of NO2 near 7587 cm-1 J. Quant. Spectrosc. Radiat. Transf 2016;177:225–233 doi:10.1016/j.jqsrt.2015.12.017
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High sensitivity cavity ring down spectroscopy of the 4ν 3 band of NO2 near 1.59 µm A.A. Lukashevskaya , S. Kassi , A. Campargue , V.I. Perevalov PII: DOI: Reference:
S0022-4073(17)30524-1 10.1016/j.jqsrt.2017.07.024 JQSRT 5791
To appear in:
Journal of Quantitative Spectroscopy & Radiative Transfer
Received date: Revised date: Accepted date:
30 June 2017 13 July 2017 13 July 2017
Please cite this article as: A.A. Lukashevskaya , S. Kassi , A. Campargue , V.I. Perevalov , High sensitivity cavity ring down spectroscopy of the 4ν 3 band of NO2 near 1.59 µm, Journal of Quantitative Spectroscopy & Radiative Transfer (2017), doi: 10.1016/j.jqsrt.2017.07.024
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ACCEPTED MANUSCRIPT Highlights First detection of the B-type band of 14N16O2 near 6276 cm-1 1630 lines corresponding to 1731 spin-rotation-vibration transitions are assigned Line positions are reproduced by an effective Hamiltonian model The (0,0,4) upper level is found mostly unperturbed Effective dipole moment and Herman-Wallis type parameters are determined
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High sensitivity cavity ring down spectroscopy of the 4ν3 band of NO2 near 1.59 µm
A.A. Lukashevskaya a, S. Kassi b,c, A. Campargue b,c*, V.I. Perevalov a a
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Laboratory of Theoretical Spectroscopy, V. E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, 1, Academician Zuev sq., 634055, Tomsk, Russia b Univ. Grenoble Alpes, LIPhy, F-38000 Grenoble, France c CNRS, LIPhy, F-38000 Grenoble, France
Number of pages: 15 Number of tables: 2
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Number of figures: 8
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Key words: Nitrogen dioxide, NO2; High resolution spectroscopy; Cavity ring down
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spectroscopy; Electron spin-rotation interaction; Effective Hamiltonian
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ACCEPTED MANUSCRIPT Abstract The very weak B-typeabsorption band of the nitrogen dioxide main isotopologue (14N16O2) is investigated between 6175 and 6350 cm-1. The absorption spectrum of this band was recorded by high sensitivity continuous wave-cavity ring down spectroscopy with noise equivalent absorption of min 1×10-10 cm-1. More than 1630 lines of the 4ν3 band are assigned with rotational quantum numbers N and Ka up to 55 and 7, respectively, what corresponds to 1731 spin-rotation-vibration transitions. The overall measured set of the line
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positions is used to fit the effective Hamiltonian parameters. The effective Hamiltonian takes explicitly into account the Coriolis interactions between the spin rotational levels of the (0,0,4) vibrational state and those of the nearby (0,2,3) bright state at 6183.61 cm-1 together with the electron spin-rotation interactions. The fitted set of the parameters reproduces the observed line positions with an rms of 2.2×10-3 cm-1. A selected set of the measured line
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intensities are used to determine the effective dipole moment parameters including the Herman-Wallis type parameters describing the line intensities of the 4ν3 band. The rms
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deviation of the fit is 5.7%.
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ACCEPTED MANUSCRIPT 1. Introduction This study completes the analysis of the very weak near infrared spectrum of nitrogen dioxide between 5855 and 6410 cm-1 recorded in Grenoble by cavity ring down spectroscopy (CRDS). The overview of this spectrum is presented in Fig. 1 of our recent paper [1] where the analysis of the 2 A-type band centered at 6350 cm-1 was reported. In Ref. [2], the 3 and 2 A-type bands lying in the 6100–6200 cm-1 region were assigned and modeled. The present contribution is devoted to the 4ν3 B-type band centered at 6275
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cm-1. This band is the most excited B-type “bright” band ever observed in NO2. Usually Btype bands have considerably smaller intensities compared to A-type bands with the same variation, ∑ |
| of the sum of the Vi vibrational quantum numbers (i= 1,2,3). Consequently,
above the 2ν3 B-type band centered at 3201 cm-1, only a few lines of five B-type “dark” bands were observed. They are all due to an intensity transfer from a nearby A-type band in local
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resonance interaction: (i) Two lines of the 2 band were reported in Ref. [3] due to the line intensity transfer from the 2 A-type band, (ii) Sixty lines of the band were assigned in Ref. [4]. They borrow intensity from the band, (iii) Five lines of the 2 band were reported in Ref. [5] due to the line intensity transfer from the
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2 band. Thirty six lines of the 2band and fifteen lines of the 5band were observed in Ref. [6] due to the line intensity transfer from the 2and 5
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bands, respectively. Practically all B-type bands borrow their line intensities via Coriolis interactions from the neighboring stronger A-type bands. It leads to the importance of the
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Herman-Wallis terms in the expansion of the transition dipole moment squared. Indeed, while in the case of A-type band, only the principal effective dipole moment parameter is generally
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sufficient to reproduce the line intensities with a reasonable accuracy, it is not the case for the B-type bands. This will be demonstrated below on the example of the studied 4ν3 band which has line positions mostly unperturbed while line intensities are greatly influenced by a non-
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resonant first-order Coriolis interaction from the considerably stronger A-type band. 2. Experimental details and line parameters retrieval The reader is referred to Refs. [7,8] for a detailed description of the used fiber-
connected cavity ring down spectrometer. The recording of the CRDS spectra under study is presented in details in Ref. [1]. Seven Distributed Feedback (DFB) laser diodes were used as light sources to cover the 6180–6350 cm-1 spectral region under study. The noise-equivalent absorption of the spectrum is min~ 1×10-10 cm-1. The frequency calibration was performed using a commercial Fizeau type wavemeter. We estimate an uncertainty of 1×10-3 cm-1 for the 4
ACCEPTED MANUSCRIPT position of well isolated lines as checked by comparison of the measured line positions of the 30013-00001 band of
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C O2 present as an impurity compared to those given by
HITRAN2012 database [9]. The filling pressure was 1.00 Torr and the temperature was 297.3±0.3 K. Taking into account the 2NO2↔ N2O4 dimerisation equilibrium, it corresponds to an NO2 partial pressure
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of 0.987 Torr [1].
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Fig. 1. Spectrum and line list of NO2 near 6229 cm-1. The three lower panels show the CRDS spectrum recorded at 1.0 Torr, the simulation performed with a multiline fitting program and the corresponding (sim.- meas.) residuals. The two upper panels show the full line list and the stick spectrum limited to the assigned lines. The line parameter retrieval uses the multiline fitting computer code described in Ref.
[10]. The spectral line shape was modeled with the Voigt profile in which the calculated value for the Doppler line width was used and the collision broadening coefficient was fixed to the HITRAN value at 296 K (0.095 cm-1atm-1 [9]). Overall, the center and intensity of more than 3000 lines were retrieved in the 6180–6347 cm-1 interval. Note that in the case of unresolved spin-rotational doublets, we often fitted the absorption feature as a single line. Line intensities range between 10-28 and 10-26 cm-1/(molecule cm-2) at 296 K. The sample of spectrum 5
ACCEPTED MANUSCRIPT displayed in Fig. 1 illustrates the achieved spectrum reproduction with the retrieved line parameters. Because of the weakness and blending of the majority of the lines the averaged accuracy of the retrieved line intensities is estimated to be about 20% or even worse for the very weak or strongly blended lines. A selected set of 230 lines were used to derive effective dipole moment parameters (see below). The uncertainty of their intensities is estimated to be on the level of 5%.
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3. Spectrum assignment and modeling 3.1. Spectrum assignment
In the lower wavenumber region (6180-6200 cm-1), the 4ν3 band overlaps with the 3 and 2bands analyzed in Ref. [2]. In the upper wavenumber region (62906347 cm-1), it overlaps with the 2band studied in Ref. [1].
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For the considered 4ν3 B-type band, only the ΔKa= ±1 transitions are observable. The assignments were performed by comparison to a predicted spectrum with line positions calculated using an effective Hamiltonian (EH) of the (0,0,4) vibrational state. This EH takes into account both vibration-rotation and electron spin-rotation (SR) interactions. For the initial values of the (0,0,4) effective Hamiltonian parameters, the predictions of the global effective 14
N16O2 were adopted [11] except for the (0,0,4) initial vibrational energy
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Hamiltonian of
(6275.98 cm-1) which was taken from Ref. [12]. The ground state energy levels were
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calculated using the ground state parameters of Ref. [13]. In parallel the line intensity calculations were performed using the effective dipole moment parameters fitted to the
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selected values of the measured line intensities. The analyzed spectrum contains a number of doublets involving upper and lower SR energy levels with the same N value, but different J rotational quantum numbers (J=N±1/2).
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At the initial stage of the assignments, the dependence of the SR splitting versus N and Ka was a main criterion. Thus the preliminary assignment was performed basing on the agreement
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between the observed and calculated values of the splitting of the electron spin-rotation doublets as well as on the agreement between observed and calculated line intensities. Note that the measured values of the SR splittings were found in a very good agreement with their values predicted using the global effective Hamiltonian [11]. The newly assigned transitions were progressively included in the line position fitting and the refined effective Hamiltonian parameters were used to improve the prediction. In this way more than 1300 transitions of the 4ν3 band were assigned. In order to validate and extend the assignments, ground state combination differences (GSCD) relations were systematically 6
ACCEPTED MANUSCRIPT used with the help of the respective computer code [14]. Finally, 1731 spin-rotation-vibration transitions with N and Ka quantum numbers up to 55 and 7, respectively, were assigned that correspond to 616 SR energy levels of the (0,0,4) upper state. Fig.2 shows a portion of the RΔKa=1 (N, Ka=0) series of transitions in the 6291–6294 cm-1 spectral region. The displayed
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interval corresponds the band head of the RΔKa=1 (N, Ka=0) series.
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Fig.2. Portion of the RΔKa=1 (N, Ka=0) series of transitions in the 4ν3 band of NO2 in the 6292.8-6294.0 cm-1 spectral region. From top to bottom: stick spectrum of the assigned lines, CRDS spectrum (P= 1.0 Torr) and corresponding simulated spectrum.
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3.2. Effective Hamiltonian model The scheme of the effective Hamiltonian matrix in the basis of products of harmonic oscillator eigenfunctions (V1,V2,V3) and eigenfunctions of the rigid symmetric top |
〉 operators is given in Fig. 3. Here J, N and S are the total, rotational and electron
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spin |
〉 and
spin angular momentum quantum numbers, respectively, K and are the quantum numbers associated with the projection on the molecular-fixed z axis of the rotational and the electron spin operators, respectively. The reader is referred to Ref. [1] for the explicit expression of the Watson-type Hamiltonian (HVR) electron spin-rotation interaction operator (HSR) and second order Coriolis interaction operator (H2C) appearing in the effective Hamiltonian. As usual in the case of the NO2 molecule, the second-order Coriolis resonance interaction is expected to connect the (0,0,4) upper state with the (0,2,3) vibrational state. The 7
ACCEPTED MANUSCRIPT parameters of the (0,2,3) vibrational state were fixed to their values determined from the recent analysis of the 2band [2]. In total, 13 parameters of the (0,0,4) bright state, including 2 SR parameters and 3 Coriolis interaction parameters were fitted to the line positions of 1731 spin-vibration-rotation transitions. The obtained parameters are presented in Table 1. The high order EH parameters for both (0,0,4) and (0,2,3) vibrational states were fixed to the values obtained with the global model [11]. In some cases when the respective values determined with the global model looked less reasonable (change of sign or strong
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change in value compared to the ground state parameters), the parameters were fixed to the
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corresponding ground state values [13].
Fig. 3. Scheme of the effective Hamiltonian matrix for the {(0,2,3), (0,0,4)} interacting vibrational states of 14N16O2.
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The fitted value of the vibrational energy for the (0,0,4) state (6275.5753(13) cm-1), is in a good agreement with the value 6375.98 cm-1 determined in Ref. [12]. The initial values
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for the A rotational constant based on Ref. [11] are also included in Table 1 for comparison. The predicted [11] value of A rotational constant for the (0,0,4) vibrational state agrees within 0.04 % with the fitted value. The obtained set of the effective Hamiltonian parameters allows reproducing the 1731 experimental line positions with an rms deviation of 2.2×10-3 cm-1.
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ACCEPTED MANUSCRIPT Table 1. Effective Hamiltonian parameters for the (0,2,3) and (0,0,4) of interacting vibrational states 14 16 N O2. All values are in cm-1.
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(0,2,3) (0,0,4) a 6183.61 6275.98 a Ev 6183.925 b 6275.5753(13) c 8.160 7.141c A 8.0059492 b 7.138104(28) b (B+С)/2 0.4126903 0.411609(21) (B-С)/4 0.62987E-02 b 0.561(28)E-02 ΔK 0.34425E-02 b 0.21364(21)E-02 ΔJK -0.2825E-04 b -0.3805(27)E-04 ΔJ 0.324E-06 c 0.32810(13)E-06 δK 0.278E-04 c 0.40547E-05 d b δJ 0.7637E-07 0.399E-07 c c HK 0.938E-05 0.2279(33)E-05 HKJ -0.262E-07 c -0.57(11)E-08 c HJK 0.151E-10 0.151E-10 c HJ 0.112E-11 c 0.112E-11 c d hK 0.29297E-07 0.533E-07 c hKJ –0.3637E-10 d –0.3637E-10 d c hJ 0.246E-12 0.246E-12 c LK -0.203E-07 c -0.401E-08 c c LKKJ 0.302E-10 0.302E-10 c LKJk 0.138E-12 c 0.138E-12 c d PK 0.867E-11 0.597E-11 c d QK -0.844E-14 -0.392E-14 c Spin-rotation parameters εzz 0.18473 b 0.15058(18) (εxx +εyy)/2 0.853E-03 c 0.853E-03 c c (εxx –εyy)/4 -0.151E-02 -0.13345(40)E-02 ΔsK -0.282E-03 c -0.144E-03 c Coriolis interaction (0,2,3)↔(0,0,4) -0.628(19)E-01 [ ] -0.221(15)E-02 0.1389(22)E-02 [ ]
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Notes a From Ref. [12] b From recent CRDS analysis [2] c Value predicted with the global effective Hamiltonian [11] d Fixed to the ground state value [13].
3.3. Line intensity modeling The reader is referred to Ref. [1] for the explicit expression of the absorption line intensity, Sb←a(T) versus the transition dipole moment squared of a transition of NO2. The necessary equations are provided in Ref. [1] and not repeated here. In that paper, the measured line intensities of the 2A-type band 9
ACCEPTED MANUSCRIPT could be modeled with a good accuracy with only one principal effective dipole moment In the present case of the 4B-type band, the Herman-Wallis parameters are
parameter
necessary. This is due to the fact that, in spite of being mostly unperturbed, the 4B-type band borrows its intensity from the strong band through non-resonant first-order Coriolis interaction The Herman-Wallis parameters account for this regular vibration-rotation interactions. In the case of a B-type band such as the studied 4band, the observed transitions
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correspond to ΔKa= ±1. The Herman-Wallis type functions contained in the equations of the respective matrix elements are given by the following expressions [15,16]: |
(
|
)
(
)
(
) ,
)
(
( Here m
)
(
)
for P-branch and m
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(1)
(
)
(
for R-branch,
are Herman-Wallis-type parameters.
) .
(2) and
A selected set of measured line intensities were used to fit the effective dipole moment
doublets. The
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parameters. We have chosen 230 mostly isolated lines and 15 mostly isolated spin-rotation parameter f the principal matrix element of the effective dipole moment
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operator and three corresponding Herman-Wallis parameters could be determined. The parameter was fixed to the value 0.3738×10-4 Debye obtained in Ref. [2]. No weighting was
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used in the fit. The fitted set of the effective dipole moment parameters (Table 2) allows reproducing the selected measured line intensities with an rms deviation of 5.7%. The results
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of the fit are provided as Supplementary Material.
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Table 2. Fitted effective dipole moment parameters. Parameter
Value 0.1701 (87)×10-4 Debye 0.3738×10-4 Debye [2] 0.14465(25) -0.07021(13) -0.008214(83)
As one can see from Table 2, the Herman-Wallis type parameters have very large 10
ACCEPTED MANUSCRIPT values. It is very interesting to compare them with the theoretical values. The principal contribution to these parameters gives the first-order Coriolis interaction. The perturbation theory leads to the following equation for this contribution to the (
is the rotational const,
parameters:
)
(
where
and
(3)
)
is the Coriolis interaction constant,
are the
and
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harmonic frequencies of the first and third vibrational modes,
and
are the dipole moment derivatives. The numerical values for the modulo of the dipole moment derivatives can be obtained using the parameter RE. [4] for the band and the parameter
(
)(
)
0.17×10-4 Debye presently derived for
band: (
| |
)(
√
|
√
)
Debye,
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|
Debye derived in
Debye.
Supposing that the dipole moment derivatives have different signs and taking cm-1,
=1325.673 cm-1,
=0.45 from Ref. [17] we
= 0.1335. This value is very close to the fitted one (0.1447) from Table 2 and the
fitted values of the
and
parameters satisfy approximately to the theoretical equation
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obtain
=1633.066 cm-1 from Ref. [11] and
= 0.41044
The comparison between the experimental and simulated spectra included in Fig. 4
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illustrates the achieved quality of the spectrum reproduction. The vast majority of the lines are well reproduced but a number of additional lines with significant intensity are present in the experimental spectrum. They may be due to hot bands of
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N16O2, minor isotopologues or
band of
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impurities. The most important absorption features due to an impurity is the 30013-00001 12 16
C O2 observed in the 6160-6260 cm-1 range. As a result of the high reactivity of
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NO2, other trace species may be present in the sample and detectable as a result of the sensitivity of the CRDS recordings [1].
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Fig. 4. Comparison of the CRDS spectrum of the 4ν3 band of 14N16O2 recorded at 1 Torr to a simulation based on the effective operator approach. 4. Some characteristics of the 4ν3 spectrum of 14N16O2
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4.1. Spin-rotation splitting The SR doublets are a characteristic feature of the NO2 spectrum due to the electron ground electronic state has S= ½ electronic spin). The SR
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spin–rotation interaction (the ̃
splitting depends on vibrational and rotational quantum numbers. Within the same vibrational band, the SR splitting generally increases with increasing Ka values and decreases with increasing N values. Note that we use the following labeling of the spin-rotation states |N Ka Kc J> (with
) or simply |N Ka Kc ±>. Calculated spin–rotation splittings of the
levels of the (0,0,4) upper state are displayed in Fig. 5. The largest SR splitting reaches a value of 0.66 cm-1 for Ka= 5 and N= 5 (Fig. 5). The SR splitting in the Ka= 1 and Ka= 2 series reflects the perturbation due to the local resonance with the (0,2,3) state.
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0.8 0 1 2 3 4 5 6 7
-1
SR splitting (cm )
Ka
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0.2
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20
30
40
50
N
4.2. Resonance interactions
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Fig. 5. Calculated spin–rotation splitting of the energy levels of the (0,0,4) vibrational state. The plot is limited to the levels experimentally determined.
The mixing coefficients of the rovibrational eigenfunctions of the (0,0,4) vibrational
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state with those of the (0,2,3) bright state are small (Fig. 6). The maximum value is limited to 3.5% at N= 50 and Ka= 5. Nevertheless the inclusion of the Coriolis interaction terms into the
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effective Hamiltonian slightly improves both line position and intensity fits. A sharp leap upward of the mixing coefficients for Ka= 6 at N = 44 is caused by the accidental coincidence
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of two energy levels with different N values (ΔN=1) and different spin components interacting through the second order Coriolis + SR interactions. The scheme of this resonance
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perturbation is presented in Fig. 7. The observed alternation of the values of the mixing coefficients of the (0,0,4)
vibrational state with the (0,2,3) vibrational state in the cases of Ka= 1 and Ka= 2 at high N values is connected with the different energy spacing between interacting levels for even and odd N values.
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4 Ka
Mixing, %
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0 0
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40
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Fig. 6. Mixing coefficients of the rovibrational eigenfunctions of the (0,0,4) vibrational state with the (0,2,3) vibrational state. The plot is limited to the maximum observed N value for each Ka.
Fig. 7. Scheme of the perturbation of the {44 6 38 -} rotational level of the (0,0,4) vibrational state by the level {43 7 36 +} of the (0,2,3) vibrational state.
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5. Conclusion
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Fig. 8. Overview of the different 14N16O2 bands analyzed by CRDS between 6050 and 6450 cm-1 [1, 2 and This work]. Line intensities are given at 296 K. With the present study of the 4ν3 B-type band of
14
N16O2, we have achieved the
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analysis of the weak bands newly detected by CRDS between 6050 and 6450 cm-1. An overview of the line lists obtained in this region is presented in Fig. 8. The 4ν3 band is the
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only mostly unperturbed B-type band observed above 3500 cm-1. The positions of 1731 vibration-rotation transitions were modeled using the vibration-rotation Hamiltonian which explicitly takes into account electron spin-rotational interaction, as well as a weak Coriolis
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resonance interactions of the (0,0,4) vibrational state with the nearby (0,2,3) vibrational state. An rms deviation of 0.0022 cm-1 was achieved for the residuals between the observed and calculated line positions. The modeling process was helped by reasonable predictions of the rotational, centrifugal distortion, and SR constants provided by a recent global fit of the observed vibration-rotation NO2 transitions up to 7916 cm-1 [11]. The assignment was also supported by the reasonable agreement between the observed and calculated line intensities based on the fitted value of the effective dipole moment parameters. The maximum line intensity of the 4ν3 band is 2.17×10-26 cm-1/(molecule cm-2). 15
ACCEPTED MANUSCRIPT The importance of Herman-Wallis coefficients for the satisfactory reproduction of the measured intensities is interpreted as resulting from a non-resonant coupling to the 1+33 band at 5984.7 cm-1. This strong A-type band, recently reported by Fourier transform spectroscopy [4], has an intensity more than three orders of magnitude higher than the presently 4ν3 band. In the future, an extended analysis of the 1+33 band together with additional recordings will allow completing our previous studies by CRDS up to 8000 cm-1
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Acknowledgements This work is jointly supported by RFBR (Russia, grant N 16-55-16017) and CNRS (France) in the framework of the Laboratoire International Associé SAMIA (Spectroscopie d’Absorption des Molécules d’Intérêt Atmosphérique).
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ACCEPTED MANUSCRIPT Lukashevskaya AA, Naumenko OV, , Mondelain D, Kassi S, Campargue A. High sensitivity Cavity Ring Down spectroscopy of the 3ν1+3ν2+ν3 band of NO2 near 7587 cm-1 J. Quant. Spectrosc. Radiat. Transf 2016;177:225–233 doi:10.1016/j.jqsrt.2015.12.017
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