Global modeling of NF3 line positions and intensities from far to mid-infrared up to 2200 cm−1

Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668

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Global modeling of NF3 line positions and intensities from far to mid-infrared up to 2200 cm−1 Oleg Egorov a,∗, Andrei Nikitin a, Michäel Rey b, Alena Rodina a, Sergei Tashkun a,c, Vladimir Tyuterev b,c a b c

Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, SB RAS 1, Akademician Zuev Sq., Tomsk 634055, Russian Federation Groupe de Spectrométrie Moléculaire et Atmosphérique UMR CNRS 7331, UFR Sciences, BP 1039, 51687, Reims Cedex 2, France Laboratory of Quantum Mechanics of Molecules and Radiative Processes, Tomsk State University, 36, Lenin Ave., Tomsk 634050, Russian Federation

a r t i c l e

i n f o

Article history: Received 31 July 2019 Revised 20 September 2019 Accepted 20 September 2019 Available online 23 September 2019 Keywords: Nitrogen trifluoride NF3 Line list Ab initio Potential energy surface Dipole moment surface Effective Hamiltonian Global modeling Greenhouse gas Global warming

a b s t r a c t In this work we report first global modeling of NF3 line positions and intensities up to the Tetradecad range of interacting bands (< 2200 cm−1 ). The calculations are based on our ab initio potential energy and dipole moment surfaces of NF3 which are used to compute initial theoretical line lists. The technique of six order contact transformations was then employed to build a global effective model for vibrational polyads. The purely theoretical parameters of this effective Hamiltonian were refined by fitting to assigned experimental line positions. The parameters of the effective dipole moment of vibrational bands were determined by fitting to our ab initio line intensities. The resulting global combined line list contains 41 cold and 683 hot sub-bands. It can be used for accurate simulating of NF3 radiative properties in the range 0–2200 cm−1 . The theoretical simulations of absorption were compared and validated to the experimental database of Pacific Northwest National Laboratory. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction Nitrogen trifluoride (14 NF3 hereafter NF3 ) is known as a potent greenhouse gas with a long lifetime [1–4]. Since NF3 is commonly used in microelectronics, its concentration has been increasing in the Earth’s atmosphere during the past decade as evaluated in [5,6]. Analyses of congested infrared spectra of NF3 are complicated by dense overlapping band patterns. For this reason, line lists of this molecule are yet lacking in widely used spectroscopic databases for atmospheric applications such as HITRAN [7] and GEISA [8] accessible via the VAMDC European portal [9,10]. NF3 is an oblate symmetric top molecule belonging to C3V symmetry point group. Experimental line positions of NF3 were studied in many works. Particularly, a series of works [11–17] was devoted to assignments of experimental transitions for the following infrared bands: v4 (E) [11]; v2 (A1 ), v2 +v4 (E), and 2v2 (A1 ) [12]; 2v4 (A1 , E) and v1 (E) [13]; v3 (E) [14]; v1 +v4 (E) [15,16]; 2v3 (A1 , E) and v1 +v3 (E) [17]. In these works an equivalence of various

∗

Corresponding author. E-mail address: [email protected] (O. Egorov).

https://doi.org/10.1016/j.jqsrt.2019.106668 0022-4073/© 2019 Elsevier Ltd. All rights reserved.

reduction schemes of the rovibrational Hamiltonian (D, Q, QD, etc.) was also analyzed by fitting the observed transitions. In recent work of Bolotova et al. [18], upper experimental energy levels were obtained from low and room temperature spectra both for six previously investigated NF3 states (2v4 (A1 , E), v1 (A1 ), v2 +v4 (E), v1 +v4 (E), 2v3 (A1 ,E), and v1 +v3 (E)) and for seven new ones (v2 +v3 (E), 2v1 (A1 ), v1 +v2 +v4 (E), v1 +v2 +v3 (E), v2 +2v3 (A1, E), 3v3 (E), and v1 +2v3 (A1 , E)). The spectroscopic parameters of the ground state were studied in [13,18–22] and the K = 3 splitting was considered in [21] and [22]. Hyperfine structure was observed in pure rotational region [23] and in [20] where the v1 (A) band was studied by laser side-band spectrometer. The first absorption cross-sections of NF3 were measured in [24] and then revisited in [1]. In our recent work [25], line intensities of NF3 were analyzed in the 1750–1950 cm−1 region where the cold 2v3 (A1 ,E) and v1 +v3 (E) bands are located. As a result, a good agreement was obtained between the measured absorption and simulation using our ab initio line intensities. In this work, we present calculations of line intensities for numerous cold and hot sub-bands of NF3 covering the region from 0 to 2200 cm−1 and propose a first NF3 complete line list for atmo-

2

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668

Fig. 1. The scheme of the NF3 global effective polyad model. The number of the vibrational states included in each polyad is given in brackets (on this scale, the splitting of vibrational sublevels is not shown).

spheric applications, particularly, for the global warming problem. For each spectral region, we give a comparison of the simulated absorption coefficient with the Pacific Northwest National Laboratory (PNNL) [26] measurements above 600 cm−1 . Our line list with the cutoff value in intensities of 10−25 (cm−1 /(molecule × cm−2 )) is given as supplementary material 1. In addition, we give the information on integrated intensities of the sub-bands included in this line list as supplementary material 2. In supplementary material 3 the quasi-continuum absorption (built using the “super-lines” compression technique) for the 0–2200 cm−1 region is supplied. All these materials will be freely accessible via TheoReTS information system [27] (http://theorets.tsu.ru) including both the line list with an intensity cutoff value of 10−26 (cm−1 /(molecule × cm−2 )) and the super-line library. 2. Global model up to five-quanta bands Our effective polyad model includes simultaneously six groups of the vibrational states (Fig. 1): “Ground”, “Dyad”, “Pentad”, “Octad”, “Tetradecad”, and “Icosad” providing a global spectra description up to five-quanta bands. This model was implemented in MIRS computational code [28,29] using the formalism of irreducible tensor operators (ITO) [30]. The similar calculation techniques have been applied for other symmetric top C3V molecules: CH3 D [31–34] and PH3 [35]. In this work, the parameters of the effective Hamiltonian of NF3 were obtained by the six-order contact transformation approach [36] and the MOL_CT computational code [37,38] from the ab initio potential energy surface (PES). A limited number of theoretical parameters were then empirically refined where it is possible using the experimental transitions of NF3 from published works. The effective transition moments of the refined bands were determined from fitting to our ab initio line intensities. The line positions and intensities of other bands were taken directly from ab initio line list. We refer to the resulting final line list as to a global combined one. It partially includes empirically refined line positions (when observed band assignments are available) with ab initio born line intensities in frame of an effective operator approach. As NF3 is a relatively heavy molecule, the total absorbance of the hot bands in its spectrum is comparable with that of the cold

bands even at room temperatures. We give a detailed description of the cold and hot bands when considering the absorption coefficient in each polyad. Although six polyads were included in the global model, we limited our line list up to the Tetradecad region (< 2200 cm−1 ). The highest polyad (Icosad) was used to compute the transitions of hot bands falling in the Tetradecad region. The importance of the hot bands in the absorption spectrum of NF3 is clearly seen in Fig. 2. To construct the ab initio PES of NF3 , the electronic structure calculations at CCSD(T)/cc-pVQZ level of the theory were carried out on the grid of 11697 nuclear configurations. The centers of four vibrational fundamental bands in our initial pure ab initio PES had the errors up to 14 cm−1 (–8.68 cm−1 , –2.68 cm−1 , –13.65 cm−1 , –1.45 cm−1 for v1 (A1 ), v2 (A1 ), v3 (E), and v4 (E) respectively). The ab initio calculations at the CCSD(T)/cc-CVQZ level did not significantly improve the results: –5.64 cm−1 , –1.83 cm−1 , –11.14 cm−1 , –0.93 cm−1 . Therefore accuracy of the PES was then improved by harmonic corrections and empirical equilibrium geometry optimization using the experimental band centers and the J = 1 rotational level. After these corrections, the errors of the fundamental band centers became −0.0 025, −0.0 039, −0.0 024 and −0.0 0 05 cm−1 , respectively. Ab initio dipole moment values were calculated by the CCSD(T) method with the basis sets AVTZ on a full grid of 11697 geometrical configurations and with AVQZ on a reduced grid of 2823 geometrical configurations. The surface for the dipole moment difference (AVQZ-AVTZ) was then constructed and added to the AVTZ dipole moment surface according to our approach described in Refs [39,40]. Previous extended tests for the methane molecule showed that the resulting DMS should be very close to the full AVQZ DMS up to about 50 0 0 cm−1 . We consider such combination of AVTZ and AVQZ basis sets for DMS as the most optimal one in terms of accuracy / computational time ratio. Our methods of variational normal mode calculations (particularly, homemade TENSOR code) described in Refs. [30,41,42] were then applied for the construction of a complete list of rovibrational transitions for NF3 . Although empirical harmonic corrections of the potential were made, the accuracies of some overtone and combination bands remained about ±0.5 cm−1 . This will be demonstrated by the comparison both with PNNL experimental data and our final global combined line list constructed using the effective operator approach (see below). According to our previous work [25], the accuracies of ab initio line intensities of the strong cold bands of NF3 are 5% in average, or maybe better. The accuracy of line intensities of weak and hot bands cannot be precisely evaluated from a comparison with observations because the most of such lines have never been experimentally measured. This is particularly caused by very dense spectrum of NF3 molecule. Nevertheless, we suppose that an average accuracy of ab initio line intensities for medium lines and hot bands could be about 5–10% except for weak lines perturbed by accidental resonances. This estimation is based on our previous works on methane-type molecules, for which much more experimental data are available to validate ab initio predictions (see, particularly, [40]). 3. Pure rotational region The effective Hamiltonian parameters of the ground state of NF3 were studied in many works, particularly by Ben Sari-Zizi et al. [13] Bolotova et al. [18] Cazzoli et al. [19] Hohe et al. [20] Breidung et al. [21] Cazzoli et al. [22]. In ref. [19] the microwave (60–520 GHz) and far infrared (700–1280 GHz) rotational spectrum were investigated up to J = 60 and three centrifugal distortion constants of the sixth order (HJ , HJJK , and HKKJ ) were determined for the first time. In [20] the pure rotational transitions from previous works were fitted together with new accurate

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668

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Fig. 2. The overview of the cold (solid lines) and hot (scattered color symbols) bands of NF3 emerging from the transitions between the polyads considered in this work.

Table 1 Statistics of the fit of the effective transition moments to the ab initio line intensities of the strongest pure rotational bands in the combined model.

Table 2 Integrated intensities (in cm−1 /(molecule × cm−2 )) of the strongest bands in the pure rotational region of NF3 at T = 296 K∗ .

Band

RMS,%

Number of data

Jmax /Kmax

Band

Transition

Integrated intensity

0000(A1 )–0000(A1 ) v4 (E)–v4 (E)

0.12 0.28

2222 240

60/57 34/13

0000(A1 )–0000(A1 ) v4 (E)–v4 (E)

Ground–Ground Dyad–Dyad

1.33902E-020 2.29143E-021

∗

integrated intensities were calculated with an intensity cutoff value of 10−25 cm−1 /(molecule × cm−2 ).

transitions in the v1 (A1 ) fundamental band. The parameters of the ground state were reanalyzed including the K = 3 splitting in [21] and [22] from the pure rotational spectrum between 460 and 900 GHz, and between 450 and 810 GHz respectively. A discussion about the determination of the h3 0 and hJ 0 splitting parameters can be found in these two letter works. Because of the selection rule in dipole absorption spectra ࢞J = + 1 and ࢞K = 0, the K-dependent parameters (C0 , DK , HK etc.) cannot be determined directly from pure rotational transitions. At the same time, the J-dependent ground state parameters are well known. To determine the K-dependent parameters, the “loop-method” was applied in [13] that takes into account the correlation of the C0 rotational parameter with the DK 0 and HK 0 centrifugal distortion constants. The experimental transitions of two cold bands (v4 (E), 2v4 (E)) and one hot (2v4 (E)–v4 (E)) were combined in such manner to make an appropriate ground state combination difference (GSCD) from which the ࢞K parts were calculated by applying the well-known experimental values of J-dependent constants (see details in Ben Sari-Zizi et al. [13]). The ground vibrational state is well isolated, therefore it was not necessary to fit the corresponding parameters in our global model. Applying the expressions, relating the diagonal parameters of our global model with those of the effective Hamiltonian for an isolated state, we obtained the ground state parameters using the results of the previous work [13]. The effective dipole moment parameters for the pure rotational transitions were determined by a direct fit to the ab initio line intensities. Since the eigenvectors of the ground state are well defined, the corresponding ab initio line intensities were fitted with high accuracy (Table 1). For NF3 , the integrated intensity of the pure rotational transitions within the ground vibrational state has a relatively low value. The pure rotational transitions within the next first excited state at 296 K is approximately by one order

of magnitude lower (see Table 2). As a result, the absorption coefficient in this region does not exceed 3 × 10−6 cm−1 atm−1 (see Fig. 3). 4. Ground–Dyad region In the present polyad model of NF3 (Fig. 1), the Dyad includes two states: v4 (E) and v2 (A1 ). Spectroscopic parameters of these states were experimentally investigated with high accuracy by Boulaftali et al. [11] and Akkad et al. [12]. In Ref. [11] the high resolution IR spectra (400–720 cm−1 ) were complemented by the millimeter-wave (MMW) pure rotational transitions (140– 250 GHz, 340–470 GHz) as well as by the transitions measured in centimeter-wave (CMW) region (8–18 GHz, 18–26.5 GHz). The CMW rotational transitions enabled the observation of the A+ /A− splittings and they are crucial to determine the interaction parameters of the l-type intravibrational couplings while the IR data provide a complementary information on high order terms of the Hamiltonian. Since the notation of the assignment in our global model [43] differs from that given in experimental works, we could not take directly all bulk of experimental line positions to refine the theoretical parameters of the effective Hamiltonian. Using the information on J, K and total symmetry, the experimental transitions were then re-assigned to the theoretical ones in terms of the ITO formalism corresponding to the MIRS code. This assignment was repeated several times after each fit, making calculated and experimental transitions closer and closer. Finally the experimental line positions of quasi-isolated v4 (E) and v2 (A1 ) bands were fitted with relatively high accuracy for a global model (Table 3). A satisfactory fit for effective band transition moments using our ab initio line intensities was also obtained (Table 4).

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Fig. 3. Pure rotational region of NF3 . Table 3 Statistics of the fit of the experimental line positions in the Ground–Dyad region in the combined model. Band

RMS×103 , cm−1

Number of data

Jmax /Kmax

Source

v4 (E) v2 (A1 )

1.01 0.49

4202 3445

69/69 70/67

Boulaftali et al. [11] Akkad et al. [12]

Table 4 Statistics of the fit of the effective transition moments to the ab initio line intensities of the Ground–Dyad bands in the combined model. Band

RMS,%

Number of data

Jmax /Kmax

v4 (E) v2 (A1 )

2.23 1.45

1329 892

30/30 30/30

Although the absorption coefficient of NF3 in the Dyad region is stronger in comparison with the pure rotational band (Fig. 4 vs Fig. 3), it still requires an account of spectral lines with the intensities below 10−25 cm−1 /(molecule × cm−2 ) for a sufficiently complete simulation of the absorbance. For the simulation of the weak absorption intervals, a very small cutoff value for line intensities is necessary even at room temperature. In this case, the number of lines in the line list exceeds the total number of records in the whole room-temperature databases as HITRAN and therefore cannot be directly included in such compilations. Here, we apply the data compression based on the “super-lines” techniques [27] to simulate the NF3 absorption spectra. Recently, this approach has been successfully implemented for high-temperature CH4 spectra [44–46] and for crowded CF4 spectra [47]. Using the super-line approach, a reduced “light” list of strong lines with a moderate cutoff value (e.g. 10−25 cm−1 /(molecule × cm−2 )) was created as an intermediate step. The difference between the absorbance computed with this “light list” and that generated from the complete line list with the 10−30 cm−1 /(molecule × cm−2 ) and lower cutoff values is smoothed by an appropriate algorithm. This smoothed quasi-continuum difference is then simply added to the line-by-line absorption produced by the reduced line list. The super-line approach was applied for all “global combined line list” simulations of the NF3 absorption coefficient. An example is given in Fig. 4. The simulations using the “ab initio line list” were made with the cutoff value of 10−29 cm−1 /(molecule × cm−2 ) in line intensities. For NF3 , the quasi-continuum supplement at T = 298 K is needed especially in the wings of the bands while the absorption in the band centers is well described by our global combined line list with the 10−25 cm−1 /(molecule × cm−2 ) cutoff value. The low temperature spectra of NF3 particularly at T = 196 K

can be simulated without super-lines as it can be seen from our previous work [25]. Starting from the Dyad-band region, a typical feature for heavy molecules is observed: there are numerous hot bands located closely to the fundamental cold band transitions. The integrated intensities of some strong hot bands from the Dyad region as well as their centers can be seen in Table 5. The 2v4 (E)–v4 (E) hot band produced by Dyad-Pentad transition has the position closed within 0.22 cm−1 to the center of the v4 (E) band. The peak around 540 cm−1 on Fig. 4a and b corresponds to the absorption of the v1 (A1 )–v4 (E) band with the center of 538.58 cm−1 which line intensities are comparable with those of the v4 (E) band in this region. Another strong hot band v3 (E)–v4 (E) at 414.12 cm−1 is the extension of the left wing of the v4 (E) band (Fig. 4a). In the Q branch region of the v2 (A1 ) band at 647.13 cm−1 (Fig. 4c) there are two major hot bands – 2v2 (A1 )–v2 (A1 ) and v2 +v4 (E)–v4 (E) centered at 645.12 cm−1 and 644.85 cm−1 . The Q branches of these hot bands significantly overlap with the P branch lines of v2 (A1 ). As a result, this region is too congested to see individual rovibrational peaks especially when comparing with the PNNL spectra at 0.1 cm−1 resolution. In [12] the experimental transitions of the fundamental v2 (A1 ) band were analyzed up to Jmax = Kmax = 70 from the room temperature IR spectra (600– 1160 cm−1 ) complemented with MMW transitions measured in the same region as in the case of v4 (E). The lines from the P and R branches of the v2 (A1 ) band have an obvious clustered structure with K increasing to higher wavenumbers. According to [11] and [12], the RK (J) lines are stronger in the v4 (E) and v2 (A1 ) bands in comparison with PK (J) lines (this also can be seen from Fig. 4) and only the transitions with the certain K numbers can be extracted from the measured spectra in the latter case. Since the experimental records from the PNNL library start approximately from 600 cm−1 , the agreements with the simulated absorption coefficient can be analyzed in the v2 (A1 ) region. Though both the ab initio line list and global combined line list simulations agree very well with PNNL in most of spectral intervals, there are two exceptions. The first one is the Q branch region where the effective polyad model shows a better match than the ab initio line list (Fig. 4c). The second one is the region of the hot bands at

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Fig. 4. Absorption coefficient of NF3 in the Dyad region: a – an overview simulation from 350 to 720 cm−1 ; b – v4 (E); c – v2 (A1 ).

642–643 cm−1 where both simulations depict some discrepancies. Currently, for the upper states of these hot bands (Table 5) there are no experimental data, therefore the line positions in our global combined line list correspond to those from the ab initio calculations. 5. Ground–Pentad region In the Pentad, the following five states of NF3 were included in the global effective polyad model (Fig. 1): v3 (E), 2v4 (A1 , E), v1 (A1 ), v2 +v4 (E), and 2v2 (A1 ). These states were investigated experimentally in references: [12–14,18,20] and [12] respectively. The Pentad region is important for atmospheric applications because this includes the strongest v3 (E) band of NF3 at 907.54 cm−1 where there is no significant absorption of water vapor. On the

contrary, the second overtone 2v2 (A1 ) band located at 1292 cm−1 is very weak with the absorption of 10−8 –10−7 cm−1 atm−1 . The contributions from the hot bands to the total absorption are more significant in this region than in the previous Dyad range. The combination v2 +v4 (E) band is relatively strong in comparison with the weak v4 (E) and v2 (A1 ) bands. The rovibrational transitions of this band were analyzed in details in [12]. In the latter work [12], 2363 lines with ࢞K = +1 and 2568 with ࢞K = – 1 were assigned. Although, the rovibrational patterns of the v2 +v4 (E) band is similar to that of v4 (E). However, there are several differences. The ࢞K = – 1 transitions of the P branch form strong clusters with pronounced heads at J = K and decreasing intensities for small K values. In the Q branch the transitions with ࢞K = – 1 have the K-resolved cluster structure. For low J values, the line position go down in wavenumbers with increasing K.

6

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668 Table 5 Integrated intensities (in cm−1 /(molecule × cm−2 )) of the strongest bands of NF3 in the Dyad region at T = 296 K∗ . Center

Band

Transition

Integrated intensity

414.1189493 488.1608478 490.0502162 490.2787639 491.1430718 492.9647166 493.2003965 493.4223349 493.4227759(89)1 538.5788781 640.9943438 642.4969626 642.6379512 642.7347240 643.0704590 643.5459430 644.8547291 645.1217158 647.1339922 647.1340617(73)2

v3 (E)–v4 (E) v3 +v4 (E)–v3 (E) 3v4 (E)–2v4 (A1 ) 2v4 (A1 )–v4 (E) v2 +v4 (E)–v2 (A1 ) 3v4 (A2 )–2v4 (E) 2v4 (E)–v4 (E) v4 (E)

Dyad–Pentad Pentad–Octad Pentad–Octad Dyad–Pentad Dyad–Pentad Pentad–Octad Dyad–Pentad Ground–Dyad

1.26373E-020 1.53441E-021 2.24831E-021 1.36833E-020 6.55183E-021 2.81066E-021 2.46282E-020 1.40809E-019

v1 (A1 )–v4 (E) v2 +v3 (E)–v3 (E) v2 +2v4 (E)–2v4 (E) v2 +2v4 (A1 )–2v4 (A1 ) 2v2 +v4 (E)–v2 +v4 (E) 3v2 (A1 )–2v2 (A1 ) v1 +v2 (A1 )–v1 (A1 ) v2 +v4 (E)–v4 (E) 2v2 (A1 )–v2 (A1 ) v2 (A1 )

Dyad–Pentad Pentad–Octad Pentad–Octad Pentad–Octad Pentad–Octad Pentad–Octad Pentad–Octad Dyad–Pentad Dyad–Pentad Ground–Dyad

3.15127E-021 5.03198E-021 3.37821E-021 1.73792E-021 3.28075E-021 1.13388E-021 1.40659E-021 5.75058E-020 1.97922E-020 2.36272E-019

∗ integrated intensities were calculated with an intensity cutoff value of 10− 25 cm−1 /(molecule × cm−2 ); 1 and 2–measured data from Boulaftali et al. [11] and Akkad et al. [12].

Table 6 Statistics of the fit of experimental line positions in the Ground–Pentad region in the combined model. Band

RMS×103 , cm−1

Number of data

Jmax /Kmax

Source

v3 (E) 2v4 (A1 ) 2v4 (E) v1 (A1 ) v 2 +v 4 ( E ) 2 v 2 ( A 1 )∗

0.97 0.95 1.57 0.03 0.93 1.10

2831 669 1077 347 4438 3276

55/44 39/39 41/40 41/35 68/68 61/61

Najib et al. [14] Ben Sari-Zizi et al. [13] Ben Sari-Zizi et al. [13] Hohe et al. [20] Akkad et al. [12] Akkad et al. [12]

∗ the experimental transitions of the 2v2 (A1 )–v2 (A1 ) hot band from Akkad et al. [12] were included in the fit.

Table 7 Statistics of the fit of the effective transition moments to the ab initio line intensities of the Ground–Pentad bands in the combined model. Band

RMS,%

Number of data

Jmax /Kmax

v3 (E) 2v4 (A1 ) 2v4 (E) v1 (A1 ) v 2 +v 4 ( E ) 2v2 (A1 )

4.63 3.96 3.50 4.23 2.65 1.51

1387 595 1264 618 972 1365

25/24 25/24 25/25 25/25 25/25 25/25

For J above 18, the line positions go up with increasing K. The strongest ࢞K = + 1 transitions belong to the R and P branches where the clusters with heads at J = K were observed. Generally, the v2 +v4 (E) band is rather isolated one. Both the experimental transitions and ab initio line intensities were well fitted by our global model up to Jmax = Kmax = 68 (Table 6) and Jmax = Kmax = 25 (Table 7) respectively. The experimental transitions of the 2v2 (A1 ) band were analyzed in [12]. Because of very weak line intensities, the spectroscopic parameters are better determined from the transitions of the 2v2 (A1 )–v2 (A1 ) hot band. According to the supplementary material 2 of this paper, the integrated intensity of the 2v2 (A1 ) band is approximately by one order of magnitude lower than that of the above mentioned hot band. Experimental data for the R branch of the 2v2 (A1 ) band is completely lacking while the transitions from Q and P branches can be observed at room temperature. Following the work [12], the parameters of the 2v2 (A1 ) state in our global

model was also refined from the fit to the experimental transitions of the 2v2 (A1 )–v2 (A1 ) hot band (Table 6). The upper state of 2v4 contains two vibrational sublevels with A1 and E symmetries. The 2v4 (A1 ) and 2v4 (E) bands are located at 983.70 cm−1 and 986.62 cm−1 – in the region between the strongest v3 (E) and v1 (A1 ) bands. In the 2v4 (A1 ) band, the P branch lines can be well determined experimentally [13]. However, the Q branch is compressed within 2 cm−1 and the lines of the R branch overlap with clusters of the strong v1 (A1 ) band. The clusters in the P branch of 2v4 (A1 ) extend to low wavenumbers when K increases. The Q branch of the 2v4 (E) band is more sparse than that of the v4 (E) one, and the certain series of the transitions with ࢞K = +1 can be resolved at room temperature [13]. The ࢞K = +1 transitions corresponding to the P branch are vanishingly weak, whereas in the R branch these transitions form well observable clusters. The strong ࢞K = –1 transitions, on the contrary, are observed in the P branch while in the R branch they are quite weak. The 2v4 (E) band is 1.5 times stronger than 2v4 (A1 ) (Table 8). In this work, both the experimental transitions and ab initio line intensities of these sub-bands were fitted with approximately the same accuracy (Tables 6 and 7). To refine the parameters of the effective Hamiltonian of the v1 (A1 ) band, we used the experimental transitions from [20], where the FTIR spectra were complemented with the high accuracy saturation technique using CO2 laser side-band as tunable infrared source. The P and R branch regions of the v1 (A1 ) band have a regular structure and the corresponding lines can be assigned unambiguously from the FTIR spectra. Although, the line density in the Q branch is higher, the individual transitions were resolved in [20] with the help of side-band spectrometer

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Table 8 Integrated intensities (in cm−1 /(molecule × cm−2 )) of the strongest bands of NF3 in the Pentad region at T = 296 K∗ . Center

Band

Transition

Integrated intensity

875.4336780 875.9071928 889.9538206 892.5434290 892.8754532 895.2773710 895.5886188 896.4181600 896.9606126 897.1492556 898.7972681 899.5637640 899.8822452 900.6284150 901.4016358 902.2797971 902.8845268 906.5489901 907.5412842 907.5413300(72)1 980.3289801 983.7010988 983.701767(34)2 986.1651131 986.6227314 986.622364(18)2 1024.0236928 1025.5995890 1026.3017660 1027.0880106 1027.3060312 1028.4131638 1029.6188501 1032.0012130 1032.00123750(47)3 1055.1132931 1135.6973591 1138.2770640 1138.276629(10)4

v1 +2v4 (E)–v2 +v4 (E) v1 +v4 (E)–v2 (A1 ) v3 +2v4 (E)–2v4 (E) v2 +v3 +v4 (A2 )–v2 +v4 (E) v3 +2v4 (E)–2v4 (A1 ) 2v2 +v3 (E)–2v4 (A1 ) 2v3 (A1 )–v3 (E) v2 +v3 +v4 (E)–v2 +v4 (E) v3 +2v4 (A2 )–2v4 (E) v3 +2v4 (A1 )–2v4 (E) v3 +v4 (A2 )–v4 (E) v1 +v3 (E)–v1 (A1 ) v3 +2v4 (A2 )–2v4 (A1 ) v2 +v3 +v4 (A1 )–v2 +v4 (E) v2 +v3 (E)–v2 (A1 ) v3 +v4 (E)–v4 (E) 2v3 (E)–v3 (E) v3 +v4 (A1 )–v4 (E) v3 (E)

Pentad–Tetradecad Dyad–Octad Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Dyad–Octad Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Dyad–Octad Dyad–Octad Pentad–Tetradecad Dyad–Octad Ground–Pentad

2.35396E-020 3.14482E-019 4.44810E-019 8.37178E-020 3.82370E-019 7.98154E-020 6.04005E-019 1.69734E-019 1.42979E-019 1.95185E-019 2.35141E-018 3.11483E-019 1.27725E-020 8.29164E-020 1.95770E-018 4.35073E-018 1.14926E-018 2.02445E-018 4.74639E-017

3v4 (E)–v4 (E) 2v4 (A1 )

Dyad–Octad Ground–Pentad

4.32864E-020 1.05085E-019

3v4 (A2 )–v4 (E) 2v4 (E)

Dyad–Octad Ground–Pentad

3.52051E-020 1.60248E-019

v1 +v3 (E)–v3 (E) v1 +v2 +v4 (E)–v1 +v3 (E) 2v1 (A1 )–v1 (A1 ) v1 +2v4 (E)–2v4 (E) v1 +2v4 (A1 )–2v4 (A1 ) v1 +v2 (A1 )–v2 (A1 ) v1 +v4 (E)–v4 (E) v1 (A1 )

Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Pentad–Tetradecad Dyad–Octad Dyad–Octad Ground–Pentad

9.76758E-020 2.83084E-020 5.06757E-020 5.28428E-020 2.73078E-020 1.66133E-019 6.82061E-019 3.91208E-018

v2 +v3 (E)–v4 (E) v2 +2v4 (E)–v4 (E) v 2 +v 4 ( E )

Dyad–Octad Dyad–Octad Ground–Pentad

4.38844E-020 1.69975E-020 1.01371E-019

∗ integrated intensities were calculated with an intensity cutoff value of 10− 25 cm−1 /(molecule × cm−2 ); 1, 2, 3 and 4 – experimental values from Najib et al. [14], Ben Sari-Zizi et al. [13], Hohe et al. [20] and Akkad et al. [12]. The total list of the bands is given as supplementary material 2.

(resolution 250 kHz). Information on the fit to experimental line positions [20] is collected in Table 6. The line positions of the strongest v3 (E) band were studied with a resolution of 0.0025 cm−1 in [14] combining IR measurements (850–950 cm−1 ) with MMW pure rotational transitions (150–550 GHz). Because of high density of lines, the rotational patterns are not resolved in the low-wavenumber part. Nevertheless, from the high-wavenumber part some strong clusters of the R branch can be revealed. In the Q and P branches the single lines corresponding to a constant value of J – K have been assigned in [14]. The clusters in the R branch are blended at high J values due to a significant overlapping. However, the transitions with low K values have been experimentally resolved in [14]. Finally, the IR transitions of the v3 (E) band were fitted in this work up to Jmax = 55 and Kmax = 44 with quite good accuracy (Table 6). The v1 (A1 ) band of NF3 is the second strongest one after v3 (E). The third place among the most absorbance bands belongs to 2v4 (A1 ,E) and v2 +v4 (E) with approximately equivalent integrated intensities (Table 8). The left wing of the v3 (E) band overlaps with hot bands whose total absorption is approximately comparable with that of v3 (E) at room temperature. Because of high density of lines in this region, there are no any prominent peaks and the absorption coefficient gradually decreases to its minimum (Fig. 5a and b). Though our ab initio line list includes line intensities with the cutoff of 10−29 (cm−1 /(molecule × cm−2 )), the simulated absorption in the Q and R branches of the 2v4 (A1 , E) bands are

slightly lower than the experimental one. At the same time, the P branch region is properly described (Fig. 5c). This difference can be caused by a lack of the contributions from hot bands with V4 = 2 selection rule in this region, because we limited our calculations by the upper states of Icosad polyad (≈30 0 0 cm−1 ). On the other hand, in this region the Q and R branches of 2v4 band overlap with the P branch lines of the stronger v1 (A1 ) band [13], however no experimental analyses of the resonance interactions between these two bands were published so far. The PNNL absorption spectrum in the region of the v1 (A1 ) band is perfectly described by our global combined line list (Fig. 5d). Note that ab initio shift of about 0.5 cm−1 at 1029.62 cm−1 was removed in our global combined model. This peak corresponds to the hot v1 +v4 (E)–v4 (E) band (Table 8) whose pure ab initio line positions were refined with the help of the effective polyad method. On the contrary, the v2 +2v4 (E)–v4 (E) hot band located near the cold v2 +v4 (E) does not match with the measured absorption because of lacking experimental transitions to refine the parameters of the v2 +2v4 (E) state (Fig. 5e). Nevertheless, the absorption in the P and R branches of the cold v2 +v4 (E) band agrees well with the PNNL experimental spectrum. According to [12], the R branch of the 2v2 (A1 ) band is completely absent at room temperature. This is also confirmed by the PNNL measurements in which the P and Q branches of the 2v2 (A1 ) band can be only seen (Fig. 2f). Our global combined model rather accurately describes the ab initio line intensities of this band (Table 7). However, the experimental

8

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668

Fig. 5. Simulated absorption coefficient of NF3 in comparison with the measured PNNL spectrum in the Pentad region: a – an overview region from 820 to 1300 cm−1 ; b – v3 (E); c – 2v4 (A1 , E); d – v1 (A1 ); e – v2 +v4 (E); f – 2v2 (A1 ); g – NF3 +CF4 mixture simulation in the region of 2v2 (A1 ).

absorption does not match the simulations in this region because there is lacking band at 1282.50 cm−1 in the calculations. On the contrary, this peak corresponds to the strong v3 (F2 ) band of CF4 at 1283.66 cm−1 [47]. As can be seen in Fig. 5g, the simulated absorption coefficient rather well describes experimental data if the mixture of NF3 and CF4 is considered with partial pressures 0.9978 atm and 0.0022 atm respectively. 6. Ground–Octad region The Ground–Octad bands cover the region from approximately 1300 to 1700 cm−1 . This NF3 polyad includes eight vibrational levels (Fig. 1). Unfortunately, there is much less experimental information on the transitions of the Octad bands in comparison with the previous Pentad polyad. This can be explained by a

coincidence of the NF3 Octad region with the strong v2 band of H2 O. Moreover, the Octad bands of NF3 are weaker than those of the Pentad region. We refined the parameters of two upper states of the v1 +v4 (E) and v2 +v3 (E) bands. In our combined model (Table 9) we have also fitted the ab initio line intensities of six Octad bands (Table 10). The experimental transitions of the v1 +v4 (E) band have been studied in [15,16,18]. The first high resolution spectrum of the v1 +v4 (E) band was recorded in the 1450–1600 cm−1 region with a resolution of 0.0025 cm−1 at room temperature [15]. According to [15] this band has the strong Q branch covering the region of about 1.5 cm−1 . The ࢞K = +1 and ࢞K = –1 components of the Q branch clusters almost coincide and overlap at different K-numbers. In the R branch region the strong ࢞K = +1 and weak ࢞K = –1 transitions are blended by lines. The ࢞K = +1 transitions of the P branch are,

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668

Fig. 5. Continued

9

10

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668 Table 9 Statistics of the fit of experimental line positions in the Ground–Octad region in the combined model. Band

RMS×103 , cm−1

Number of data

Jmax /Kmax

Source

v 1 +v 4 ( E ) v 2 +v 3 ( E )

1.86 5.71

1199 378

39/39 49/49

Hmimou et al. [15] Bolotova et al. [18]

Table 10 Statistics of the fit of the effective transition moments to the ab initio line intensities of the strongest Ground–Octad bands in the combined model. Band

RMS,%

Number of data

Jmax /Kmax

v 3 +v 4 ( A 2 ) v 3 +v 4 ( E ) v 3 +v 4 ( A 1 ) v 1 +v 4 ( E ) v 2 +v 3 ( E ) v 1 +v 2 ( A 1 )

1.34 1.31 1.19 4.35 4.94 3.66

840 387 777 2291 2569 666

30/30 30/30 30/30 30/30 30/30 30/30

Table 11 Integrated intensities (in cm−1 /(molecule × cm−2 )) of the strongest bands of NF3 in the Octad region at T = 296 K∗ . Center

Band

Transition

Integrated intensity

1383.1542171 1392.2196030 1395.7021320 1399.9713250 1516.7426608 1517.5847951 1520.2884071 1523.0411850 1523.040783(34)1 1537.3981581 1540.3990868 1541.2728891 1545.4831441 1548.5356280 1548.27178122 1546.303 1675.5471560

v3 +2v4 (E)–v4 (E) v 3 +v 4 ( A 2 ) v 3 +v 4 ( E ) v 3 +v 4 ( A 1 ) v1 +v2 +v4 (E)–v2 (A1 ) v1 +2v4 (A1 )–v4 (E) v1 +2v4 (E)–v4 (E) v 1 +v 4 ( E )

Dyad–Tetradecad Ground–Octad Ground–Octad Ground–Octad Dyad–Tetradecad Dyad–Tetradecad Dyad–Tetradecad Ground–Octad

1.50679E-021 2.59760E-021 5.15485E-021 4.28983E-021 3.40185E-021 4.72664E-021 8.43498E-021 5.47606E-020

v2 +v3 +v4 (A2 )–v4 (E) 2v2 +v3 (E)–v2 (A1 ) v2 +v3 +v4 (E)–v4 (E) v2 +v3 +v4 (A1 )–v4 (E) v 2 +v 3 ( E )

Dyad–Tetradecad Dyad–Tetradecad Dyad–Tetradecad Dyad–Tetradecad Ground–Octad

2.25313E-021 3.53872E-021 3.35135E-021 1.58559E-021 4.50582E-020

Ground–Octad

4.15842E-021

v 1 +v 2 ( A 1 )

∗

integrated intensities were calculated with an intensity cutoff value of 10 Hmimou et al. [15], Bolotova et al. [18], and Najib et al. [48].

on the contrary, weaker than the corresponding ࢞K = –1 ones. As in the case of the v3 (E) band, the (J – K = constant) rule can be applied to reveal the clusters in the R and P regions and their heads at J = K. In higher wavenumber range, the transitions of the v1 +v4 (E) band are blended by strong P branch lines of the v2 +v3 (E) band. The center of the v2 +v3 (E) band is rather close to that of v1 +v4 (E): 1548 cm−1 and 1523 cm−1 respectively. The experimental transitions of this band could not be assigned in [15]. In [18] the upper states of v1 +v4 (E) and v2 +v3 (E) have been considered as isolated ones. In [18], the transitions of the v2 +v3 (E) band have been assigned up to Jmax = 49 from the low temperature spectrum (T = 80 K). The calculated center of the v1 +v4 (E) band fits well to 0.0 0 04 cm−1 with the experimental value in our combined model (Table 11). At the same time, there is some ambiguity in the center of the v2 +v3 (E) band. According to the unpublished FTIR measurements [48], this band would have the center at 1546.30 cm−1 whereas the recent study [18] reports the band center at 1548.2717812 cm−1 . The Q branch of the v2 +v3 (E) band is congested in both the R branch of the cold v1 +v4 (E) band as well as in the hot bands. Note that the theoretical parameters in our combined effective model calculated using the ab initio PES were rather poorly fitted to the experimental energy levels of [18] (Tables 9 and 11). Since there is no experimental information on the transitions in the v3 +v4 (E), v3 +v4 (A1 ), and v1 +v2 (A1 ) cold bands, the sim-

−25

cm

−1

/(molecule×cm

−2

); 1, 2, and 3 – experimental values from

ulations on Fig. 6a, b and e correspond essentially to the pure ab initio calculations. We included these bands in the combined model because they are the next strongest ones in the Octad region after v1 +v4 (E) and v2 +v3 (E) (Table 11). The experimental rotational patterns of the absorption coefficient in the region of the v3 +v4 (E) and v3 +v4 (A1 ) bands were not well resolved and somewhat noisy in the wings. Our simulations underestimates the PNNL measurements that probably can be caused by the absence of some hot band transitions among the highest polyads in our ab initio line list. Although there is a mismatch in the Q branch of the v1 +v2 (A1 ) band, but the corresponding R branch agrees well with our simulations (Fig. 6e). In the v1 +v4 (E) and v2 +v3 (E) bands, the results of empirical correction of the line positions in our global combined line list are clearly seen (Fig. 6c and d). The corresponding shifts between the pure ab initio line list and the PNNL measurements, particularly in the P, Q, and R branches of the v1 +v4 (E) band, are reduced after the fit to the experimental line positions [15]. Nevertheless, some mismatches remain in our global line list. These mismatches correspond to the line positions of two hot bands: v1 +2v4 (A1 )–v4 (E) and v1 +2v4 (E)–v4 (E). The cold v1 +2v4 (A1 ) and v1 +2v4 (E) bands are very weak at room temperature (with integrated intensity ∼10−23 –10−22 cm−1 /(molecule × cm−2 )) and their line positions have been not studied yet. Consequently, we used the effective Hamiltonian parameters for these two states computed from the PES via the contact transformation method [36–38]. On the

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668

contrary, the peak of the v1 +v2 +v4 (E)–v2 (A1 ) hot band at 1516.74, agrees well with the PNNL measurements as the spectroscopic parameters of the upper v1 +v2 +v4 (E) state were empirically refined (see below). In region of the v2 +v3 (E) band (Fig. 6d), the positions of the absorption peaks generally coincide very well with the measurements. For three hot bands at 1540.40 cm−1 , 1541.27 cm−1 , and 1545.48 cm−1 (Table 11) the rotational patterns were blended at 0.1 cm−1 resolution. 7. Ground–Tetradecad region As the Tetradecad region is located in the wing of the v2 band of H2 O – from 1700 to 2200 cm−1 , this region is more appropriate for detecting NF3 in atmospheric applications in comparison with the Octad range (∼ 1500 cm−1 ). Among the 14 vibrational levels

11

(25 including sublevels) of NF3 of the Tetradecad (Fig. 1), the line intensities of three bands (2v3 (A1 ), 2v3 (E), and v1 +v3 (E)) were studied in our recent work [25]. In ref. [25] a good agreement was obtained between the simulated absorption in the regions of the 2v3 (A1 , E), and v1 +v3 (E) bands and FTIR measurements at 0.005 cm−1 resolution at T = 196 K. In this section, we will give a more detailed analysis of the absorption coefficient of NF3 in the 1700 – 2200 cm−1 region in comparison with the PNNL measurements at T = 298 K. Particularly, the absorption of the hot bands will be discussed below. The 2v3 (A1 , E), and v1 +v3 (A1 ) bands are the strongest ones in the Tetradecad region. As can be seen from Fig. 2, the absorption produced by these bands in 1700–1970 cm−1 region is stronger than the absorption of the Octad bands (Fig. 6). To refine the effective Hamiltonian parameters of the upper states of 2v3 (A1 ), 2v3 (E),

Fig. 6. Simulated absorption coefficient of NF3 in comparison with the measured PNNL spectrum in the Octad region: a – overview region from 1300 to 1700 cm−1 ; b – v3 +v4 (E, A1 ); c – v1 +v4 (E); d – v2 +v3 (E); e – v1 +v2 (A1 ).

12

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Fig. 6. Continued Table 12 Statistics of the fit to the experimental line positions and energy levels in the Ground– Tetradecad region in the combined model. Band

RMS×103 , cm−1

Number of data

Jmax /Kmax

Source

2v3 (A1 ) 2v3 (E) v 1 +v 3 ( E ) 2v1 (A1 ) v 1 +v 2 +v 4 ( E )

1.80 1.19 1.31 0.81 1.24

449 2974 2962 664 59

42/30 65/63 63/50 35/19 15/15

Najib et al. [17] Najib et al. [17] Najib et al. [17] Bolotova et al. [18] Bolotova et al. [18]

Table 13 Statistics of the fit of the effective transition moments to the ab initio line intensities of the strongest Ground–Tetradecad bands in the combined model. Band

RMS,%

Number of data

Jmax /Kmax

2v3 (A1 ) 2v3 (E) v 3 +2 v 4 ( E ) v 1 +v 3 ( E ) 2v1 (A1 ) v 1 +v 2 +v 4 ( E )

5.28 5.68 2.68 3.63 1.14 3.72

2185 4443 1079 2983 648 172

30/30 30/30 30/30 30/30 30/24 30/30

and v1 +v3 (A1 ) we used the experimental transitions from [17]. In [17] the line positions were assigned up to high J∼ 60 and K quantum numbers using the FTIR spectrum at room temperature. Unlike our previous work [25], the experimental energies from [18] were also included in the fit to refine the parameters of the upper states of 2v1 (A1 ) and v1 +v2 +v4 (E). In Table 12, the results of the fit to experimental data in the Tetradecad region are shown. According to our ab initio line list, the v3 +2v4 (E) cold band with the moderate integrated intensity is clearly seen at 1876.58 cm−1 between the 2v3 (E) and v1 +v3 (E) strong bands. Finally, six cold bands were taken into account when determining the effective

dipole moment parameters from the fit to the ab initio line intensities (Table 13). The centers of the 2v3 (A1 ) and 2v3 (E) bands are quite close within 7.5 cm−1 . Due to strong transitions of the 2v3 (E) band, the ro-vibrational patterns of weaker 2v3 (A1 ) band are significantly blended and it could be resolved in the low wavenumber region only. According to [17], the ࢞K = +1 transitions in the R branch of the 2v3 (E) band are the strongest ones and they form the clusters with the (J + K = constant) selection rule. In the case of the ࢞K = –1 transitions, the P branch lines form strong series with pronounced heads at J = K. The v1 +v3 (E) band is slightly stronger than 2v3 (E)

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668

(Table 14). Generally, the ro-vibrational structure of the v1 +v3 (E) band is similar to that of v3 (E) but the lines of the v1 +v3 (E) band are sparser. According to [17], to find the origins of the clusters the J – K = constant rule can be applied as well as for v3 (E). The weakest 2v1 (A1 ) and v1 +v2 +v4 (E) cold bands were analyzed in [18] using room temperature and low temperatures spectra at T = 120 K. These bands were assigned up to Jmax = 36, Kmax = 22 and Jmax = 26, Kmax = 25 respectively. We included some experimental energy levels from [18] to refine the spectroscopic parameters of the upper states of 2v1 (A1 ) and v1 +v2 +v4 (E) (Table 12). Similarly to the other polyads, numerous hot bands accompany the cold transitions in the Tetradecad region. The strongest hot bands correspond to the transitions between the states of the Icosad polyad (that is the highest one accounted in this work)

13

and those of the Dyad (Table 14). To the left of the 2v3 (A1 ) band there is a series of the hot transitions from the v4 (E) and v2 (A1 ) states to 2v3 +v4 (E, A1 ) and v2 +2v3 (E, A1 ) respectively. The hot band transitions 2v3 +v4 (A2 )–v4 (E) are the strongest ones and are located between the cold 2v3 (A1 ) and 2v3 (E) bands. The next cold band v3 +2v4 (E) is surrounded by the hot transitions of v2 +3v4 (A2 , E)–v4 (E). The left wing of the strong v1 +v3 (E) band is again superimposed with hot bands as well as in the case of the v3 (E) band (Table 8). These hot bands are produced particularly by the transitions v1 +v3 +v4 (A1 , E, A2 )–v4 (E). To the right of the v1 +v3 (E) band another series of v2 +2v3 (A1 , E)–v4 (E) are located. Generally, there is a good agreement between the simulated absorption coefficient and PNNL measurements (Fig. 7a). Note

Fig. 7. Simulated absorption coefficient of NF3 in comparison with the measured PNNL spectrum in the Tetradecad region: a – overview region from 1700 to 2200 cm−1 ; b – region of 2v3 (A1 , E); c – v3 +2v4 (E); d – region of v1 +v3 (E); e – 2v1 (A1 ); f – v1 +v2 +v4 (E).

14

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668

Fig. 7. Continued

particularly an agreement in the wings of the 2v3 (A1 , E) and v1 +v3 (E) bands where the results of empirically corrected line positions are clearly seen (Fig. 7b and d). The Q branch of the v3 +2v4 (E) band has a shift of ∼ 0.5 cm−1 in the pure ab initio line list (Fig. 7c). This shift was corrected in our global combined line list by fitting the vibrational parameter of the upper state of v3 +2v4 (E) using the PNNL data. The absorption coefficient in the regions of the weak 2v1 (A1 ) and v1 +v2 +v4 (E) cold bands is shown in Fig. 7e and f. These regions also include the hot transitions but they are weaker than those presented in Table 14. Particularly, the hot bands produce two peaks at 2155 cm−1 . The total list of the integrated intensities is given as the supplementary material 2 to this paper. Finally, our global combined line list correctly describes the absorption in the P and Q branch of the 2v1 (A1 ) band in comparison with the PNNL experimental spectra.

8. Conclusion In this work, ab initio line intensities were calculated for the first time for more than 40 cold and 680 hot sub-bands of NF3 in the 0–2200 cm−1 region. Combining the ab initio calculations for line intensities with the effective operator approach for line positions, the first global combined line list was produced for NF3 . This list is quite similar in terms of absorption to our theoretical complete ab initio line list at low and medium resolution, but is more accurate for rotationally resolved line positions. The line positions of the refined bands correspond to the high-resolution measurements (see, for example, Rodina et al. [25]). The overall absorption is validated by the comparison with the PNNL measurements recorded under resolution of 0.1 cm−1 and the absorption of hot bands are analyzed at T = 298 K.

O. Egorov, A. Nikitin and M. Rey et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 239 (2019) 106668

15

Table 14 Integrated intensities (in cm−1 /(molecule × cm−2 )) of the strongest bands of NF3 in the Tetradecad region at T = 296 K∗ . Center

Band

Transition

Integrated intensity

1792.0371298 1798.4105418 1799.9568691 1799.9587741 1803.12990301803.130213(57)1 1803.7181391 1810.42581101810.423993(21)1 1865.3593641 1876.5765520 1883.5023671 1900.1061548 1920.9407591 1922.3080328 1923.6832461 1927.5191621 1931.56497701931.577516(19)1 1945.7487871 1952.1221991 2013.7107420 2058.30297902058.3038392 2163.8766530 2163.8748442

v2 +2v3 (A1 )–v2 (A1 ) v2 +2v3 (E)–v2 (A1 ) 2v3 +v4 (A1 )–v4 (E) 2v3 +v4 (E)–v4 (E) 2v3 (A1 ) 2v3 +v4 (A2 )–v4 (E) 2v3 (E) v3 +3v4 (A2 )–v4 (E) v 3 +2 v 4 ( E ) v3 +3v4 (E)–v4 (E) 2v1 +v4 (E)–v2 (A1 ) v1 +v3 +v4 (A2 )–v4 (E) v1 +v2 +v3 (E)–v2 (A1 ) v1 +v3 +v4 (E)–v4 (E) v1 +v3 +v4 (A1 )–v4 (E) v 1 +v 3 ( E ) v2 +2v3 (A1 )–v4 (E) v2 +2v3 (E)–v4 (E) v 1 +2 v 4 ( E ) 2v1 (A1 ) v 1 +v 2 +v 4 ( E )

Dyad–Icosad Dyad–Icosad Dyad–Icosad Dyad–Icosad Ground–Tetradecad Dyad–Icosad Ground–Tetradecad Dyad–Icosad Ground–Tetradecad Dyad–Icosad Dyad–Icosad Dyad–Icosad Dyad–Icosad Dyad–Icosad Dyad–Icosad Ground-Tetradecad Dyad–Icosad Dyad–Icosad Ground-Tetradecad Ground–Tetradecad Ground–Tetradecad

2.15809E-021 1.84921E-020 3.75687E-020 2.48815E-021 6.47749E-020 5.51360E-020 4.67844E-019 1.16998E-021 1.43896E-020 2.49409E-021 2.06206E-021 2.13525E-020 1.90968E-020 4.23037E-020 1.70893E-020 5.08122E-019 4.65950E-021 2.76660E-021 1.48120E-021 5.16909E-021 1.86499E-021

∗ integrated intensities were calculated with an intensity cutoff value of 10− 25 cm−1 /(molecule × cm−2 ); 1 and 2 – experimental band center values from Najib et al. [17] and Bolotova et al. [18].

The global combined line list covers the important spectral regions. For atmospheric applications, particularly, it perfectly describes the region of the strongest v3 (E) band (at 907 cm−1 ) where more than 30 hot sub-bands are located. This line list with the different cutoff values in line intensities is now available on the website of the information system TheoReTS (http: //theorets.univ-reims.fr). We also give the “light version” with the 10−25 cm−1 /(molecule × cm−2 ) cutoff as supplementary material 1. We believe that our line list will be helpful for experimental investigation of hot bands of NF3 and particularly their line intensities, which were lacking in previously published spectra analyses. Declaration of Competing Interest All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version. This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue. The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript. Acknowledgements The research at the V.E. Zuev Institute of Atmospheric Optics was performed under contract № 17–17–01170 with the Russian Science Foundation. V.T. acknowledges the support from Academic D. Mendeleev program of Tomsk State University. The support of the ROMEO computer center Reims-Champagne-Ardenne is acknowledged. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jqsrt.2019.106668.

References [1] Robson JI, Gohar LK, Hurley MD, Shine KP, Wallington TJ. Revised IR spectrum, radiative efficiency and global warming potential of nitrogen trifluoride. Geophys Res Lett 2006;33(10):L10817. [2] Prather MJ, Hsu J. NF3 , the greenhouse gas missing from Kyoto. Geophys Res Lett 2008;35:L12810. [3] Prather MJ, Hsu J. Correction to “NF3 the greenhouse gas missing from Kyoto”. Geophys Res Lett 2010;37:L11807. [4] Dillon TJ, Vereecken L, Horowitz A, Khamaganov V, Crowleya JN, Lelieveld J. Removal of the potent greenhouse gas NF3 by reactions with theatmospheric oxidants O(1 D), OH and O3 . Phys Chem Chem Phys 2011;13:18600–8. [5] Arnold T, Mühle J, Salameh PK, Harth CM, Ivy DJ, Weiss RF. Automated measurement of nitrogen trifluoride in ambient air. Anal Chem 2012;84:4798–804. [6] Weiss RF, Mühle J, Salameh PK, Harth CM. Nitrogen trifluoride in the global atmosphere. Geophys. Res. Lett. 2008;35:L20821. [7] Gordon IE, Rothman LS, Hill C, Kochanov RV, Tan Y, Bernath PF, et al. The HITRAN2016 molecular spectroscopic database. J Quant Spectrosc Radiat Transfer 2017;203:3–69. [8] Jacquinet-Husson N, Armante R, Scott NA, Chédin A, Crépeau L, Boutammine C, et al. The 2015 edition of the GEISA spectroscopic database. J Mol Spectrosc 2016;327:31–72. [9] Dubernet ML, Antony BK, Ba YA, Babikov Yu L, Bartschat K, Boudon V, et al. The virtual atomic and molecular data centre (VAMDC) consortium. J Phys B: At Mol Opt Phys 2016;49:074003. [10] Dubernet ML, Boudon V, Culhane JL, Dimitrijevic MS, Fazliev AZ, Joblin C, et al. Virtual atomic and molecular data centre. J Quant Spectrosc Radiat Transfer 2010;111:2151–9. [11] Boulaftali N, Ben Sari-Zizi N, Wötzel U, Demaison J, Margulès L, Harder H, Mäder H, Mkadmi EB, Bürger H. The v4 = 1 state of 14 NF3 at 493 cm−1 studied by high-resolution FTIR, centimeter-wave, and millimeter-wave spectroscopy. J Mol Spectrosc 2002;212:41–52. [12] Akkad K, Ben Sari-Zizi N, Bakri B, Demaison J, Bürger H, Mkadmi EB. Fourier transform infrared and millimeter-wave study of the v2 = 1, 2 and the v2 = v4 = 1 rovibrational states of 14 NF3. J Mol Spectrosc 2003;218(1):36–47. [13] Ben Sari-Zizi N, Najib H, Demaison J, Bakri B, Colmont JM, Bürger H. Highresolution FTIR and MMW study of the v4 = 2(A1 , E) excited state of 14 NF3 near 985 cm−1 : the axial ground state rotational constants derived by the "loopmethod". J Mol Spectrosc 2004;228:511–27. [14] Najib H, Ben Sari-Zizi N, Demaison J, Bakri B, Colmont J-M, MKadmi EB. High-resolution infrared and millimeterwave spectra of the v3 = 1 vibrational state of 14 NF3 at 907 cm−1 . J Mol Spectrosc 2003;220:214–22. [15] Hmimou S, Msahal H, Najib H. First high-resolution FTIR study of the v1 = v4 = 1 rovibrational state of 14 NF3 near 1523 cm−1 . Mol Phys 2010;108(6):787–94. [16] Najib H, Hmimou S, Msahal H. High-resolution infrared spectroscopy of the ν 1 + ν 4 band of 14 NF3: reductions of the rovibrational hamiltonian. E-J Chem 2012;9(1):253–9. [17] Ben Sari-Zizi N, Najib H. High-resolution infrared study of the 2 v3 ( a1 , E) and ν 1 + ν 3 ( E) bands of 14 NF3. J Mol Spectrosc 2006;240(2):210–26.

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[18] Bolotova IB, Ulenikov ON, Bekhtereva ES, Albert S, Bauerecker S, Hollenstrein H, et al. High resolution analysis of the FTIR spectra of trifluoroamine NF3 . J Mol Spectrosc 2018;348:87–102. [19] Cazzoli G, Cludi L, Degli Esposti C, Dore L. Microwave and far infrared spectrum of nitrogen trifluoride. J Mol Spectrosc 1992;152(1):185–91. [20] Höhe W, Häring U, Kreiner WA, Essig H, Ruoff A. Analysis of the v1 fundamental of NF3 combining FT and laser side-band saturation spectroscopy. A secondary standard for the 10 0 0–1060 cm−1 region. Can J Phys 1994;72:1051–9. [21] Breidung J, Constantin L, Demaison J, Margulés L, Thiel W. Ground state rotational spectrum, k = 3 splittings, ab initio anharmonic force field and equilibrium structure of trifluoroamine. Mol Phys 2003;101(8):1113–22. [22] Cazzoli G, Puzzarini C. Ground state rotational spectrum of nitrogen trifluoride: the k = 3 splittings of 14 (NF3 ) and 15 (NF3 ). J Mol Spectrosc 2006;239:59–63. [23] Novick SE, Chen W, Munrow MR, Grant KJ. Hyperfine structure in the microwave spectrum of NF3 . J Mol Spectrosc 1996;179(2):219–22. [24] Molina LT, Wooldridge PJ, Molina MJ. Atmospheric reactions and ultraviolet and infrared absorptivities of nitrogen trifluoride. Geophys Res Lett 1995;22(14):1873–6. [25] Rodina A, Egorov O, Nikitin A, Rey M, Serdyukov V, Sinitsa L, Tashkun S. Line list for NF3 molecule in the 1750–1950 cm−1 region. J Quant Spectrosc Radiat Transfer 2019;232:10–19. [26] Sharpe SW, Johnson TJ, Sams RL, Chu PM, Rhoderick GC, Johnson PA. Gas-phase databases for quantitative infrared spectroscopy. Appl Spectrosc 2004;58(12):1452–61. [27] Rey M, Nikitin AV, Babikov Y, Tyuterev VLG. TheoReTS–An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces. J Mol Spectrosc 2016;327:138–58. [28] Nikitin A, Champion JP, Tyuterev VLG. The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules. J Quant Spectrosc Radiat Transfer 2003;82:239–49. [29] Nikitin AV, Rey M, Champion JP, Tyuterev VLG. Extension of the MIRS computer package for modeling of molecular spectra: from effective to full ab initio ro-vibrational Hamiltonians in irreducible tensor form. J Quant Spectrosc Radiat Transfer 2012;113:1034–42. [30] Rey M, Nikitin AV, Tyuterev VLG. Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing energy levels from potential energy surfaces for symmetric-top molecules. Mol Phys 2010;108(16):2121–35. [31] Nikitin AV, Champion JP, Tyuterev VLG, Brown LR. The high resolution infrared spectrum of CH3 D in the region 90 0–170 0 cm−1 . J Mol Spectrosc 1997;184:120–8. [32] Nikitin A, Champion JP, Tyuterev VLG, Brown LR, Mellau G, Lock M. The infrared spectrum of CH3 D between 900 and 3200 cm−1 : extended assignment and modeling. J Mol Struct 20 0 0;517-518:1–24. [33] Nikitin A, Brown LR, Féjard L, Champion JP, Tyuterev VLG. Analysis of the CH3 D Nonad from 20 0 0 to 3300 cm−1 . J Mol Spectrosc 2002;216:225–51.

[34] Nikitin AV, Brown LR, Sung K, Rey M, Tyuterev VLG, Smith MAH, Mantz AW. Preliminary modeling of CH3 D from 40 0 0 to 4550 cm−1 . J Quant Spectrosc Radiat Transfer 2013;114:1–12. [35] Nikitin AV, Ivanova YA, Rey M, Tashkun SA, Toon GC, Sung K, Tyuterev VLG. Analysis of PH3 spectra in the Octad range 2733–3660 cm−1 . J Quant Spectrosc Radiat Transfer 2017;203:472–9. [36] Tyuterev VLG, Perevalov VI. Generalized contact transformations of a Hamiltonian with a quasi-degenerate zero-order approximation. Application to accidental vibration-rotation resonances in molecules. Chem Phys Lett 1980;74(3):494–502. [37] Tyuterev VLG, Tashkun SA, Seghir H. High-order contact transformations: general algorithm, computer implementation and triatomic tests. In: Proceedings of SPIE, 5311; 2004. p. 164–75. [38] Tyuterev VLG, Tashkun SA, Rey M, Kochanov RV, Nikitin AV, Delahaye T. Accurate spectroscopic models for methane polyads derived from a potential energy surface using high-order contact transformations. J Phys Chem A 2013;117:13779–805. [39] Nikitin AV, Rey M, Tyuterev VLG. First fully ab initio potential energy surface of methane with a spectroscopic accuracy. J Chem Phys 2016;145:114309. [40] Nikitin AV, Rey M, Tyuterev VLG. Accurate line intensities of methane from first-principles calculations. J Quant Spectrosc Radiat Transfer 2017;200:90–9. [41] Rey M, Nikitin AV, Tyuterev VG. Complete nuclear motion Hamiltonian in the irreducible normal mode tensor operator formalism for the methane molecule. J Chem Phys 2012;136:244106. [42] Rey M, Nikitin AV, Tyuterev VLG. Convergence of normal mode variational calculations of methane spectra: theoretical line list in the icosad range computed from potential energy and dipole moment surfaces. J Quant Spectrosc Radiat Transfer 2015;164:207–20. [43] Nikitin AV, Thomas X, Daumont L, Rey M, Sung K, Toon GC, Smith MAH, Mantz AW, Tashkun SA, Tyuterev VLG. Measurements and modeling of long— path 12 CH4 spectra in the 5300–5550 cm−1 region. J Quant Spectrosc Radiat Transfer 2017;202:255–64. [44] Rey M, Nikitin AV, Tyuterev VG. Theoretical hot methane line lists up to t = 20 0 0 K for astrophysical applications. Astrophys J 2014;789:2. [45] Rey M, Nikitin AV, Tyuterev VG. Accurate theoretical methane line lists in the infrared up to 30 0 0 K and quasi-continuum absorption/emission modeling for astrophysical applications. Astrophys J 2017;847:105. [46] Yurchenko SN, Amundsen DS, Tennyson J, Waldmann IP. A hybrid line list for CH4 and hot methane continuum. Astronom Astrophys 2017;605:A95. [47] Rey M, Chizhmakova IS, Nikitin AV, Tyuterev VLG. Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF4 . Phys Chem Chem Phys 2018;20(32):21008–33. [48] Najib H. Experimental values of the rotational and vibrational constants and equilibrium structure of nitrogen trifluoride. J Mol Spectrosc 2015;312:1–5.