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Detection and analysis of three highly excited vibrational bands of 16O3 by CW-CRDS near the dissociation threshold
Journal of Quantitative Spectroscopy & Radiative Transfer 152 (2015) 84–93
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Detection and analysis of three highly excited vibrational bands of 16O3 by CW-CRDS near the dissociation threshold A. Campargue a,b,n, S. Kassi a,b, D. Mondelain a,b, A. Barbe c, E. Starikova d,e, M.-R. De Backer c, Vl.G. Tyuterev c a
Université Grenoble Alpes, LIPhy, F-38000 Grenoble, France CNRS, LIPhy, F-38000 Grenoble, France Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, UFR Sciences Exactes et Naturelles, BP 1039, 51687 Reims Cedex 2, France d Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics SB RAS, 1, Academician Zuev Square, Tomsk 634021, Russia e QUAMER, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russia b c
a r t i c l e in f o
abstract
Article history: Received 3 September 2014 Received in revised form 22 October 2014 Accepted 25 October 2014 Available online 4 November 2014
The present contribution is devoted to the analysis of three extremely weak A-type bands of 16O3 recorded near 7686, 7739 and 7860 cm 1 i.e. only a few % below the dissociation limit, D0, at about 8560 cm 1. They correspond to the most excited vibration–rotation states of ozone observed so far via high-resolution absorption spectroscopy. They were detected by high sensitivity CW-cavity ring down spectroscopy with a typical noise equivalent absorption, αmin, on the order of 2 10 10 cm 1 and modelled using the effective operator approach. The derived band centres and rotational constants show a very good agreement with recent theoretical predictions based on a new ab initio potential energy surface. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Ozone CW-cavity ring down spectroscopy Resonance coupling Effective Hamiltonian model Potential energy surface
1. Introduction During the last years, we have systematically studied highly excited vibration–rotation states of the ozone molecule from the analyses of its very weak absorption spectrum in the 5850–7600 cm 1 range [1–9]. For the main isotopologue, 16O3, 26 A-type bands were detected by highly sensitive CW-cavity ring down spectroscopy (CW-CRDS). This number is to be compared to a total of 41 bands of the same symmetry type predicted in the same range from the potential energy surface (PES) [10] of the molecule. The modelling and analyses of the recorded spectra were carried out using the effective
n
Corresponding author. E-mail address: [email protected] (A. Campargue).
http://dx.doi.org/10.1016/j.jqsrt.2014.10.019 0022-4073/& 2014 Elsevier Ltd. All rights reserved.
operator approach. All the CRDS results below 7600 cm 1 were summarized in a recent review [11]. Several obtained line-lists are available in the SMPO databank devoted to the ozone molecule [12]. A large part of bands has been included in the last edition of the HITRAN database [13]. The present contribution is devoted to three extremely weak A-type bands observed near 7686, 7739 and 7860 cm 1 which correspond to the most excited vibration–rotation states of ozone analysed so far by highresolution absorption spectroscopy. The spectra analyses were particularly challenging at this high excitation level as numerous resonance couplings with “dark” states lead to qualitative changes in the molecular polyad structure. The corresponding perturbations would have been impossible to treat in absence of reliable predictions for the energy levels, vibrational assignments and rotational constants. This applies in particular to the nearby “dark” states
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which could perturb the rotational patterns of the observed bright states. Recent improvements of electronic structure calculations [14–16] enable a considerable progress in this domain. In this work we used the predictions obtained from accurate PESs of Refs. [16,17]. Note that, contrary to the low energy range where spectra simulation close to the experimental accuracy could be achieved, in the case of the presently studied bands, such a spectrum reproduction seems out of reach. Nevertheless, these analyses are expected to provide new valuable information for checking theoretical hypotheses concerning the shape of the ozone PES at high energy range. As the upper studied band is located only 8% below the dissociation threshold of the ground electronic state (D0 8560 cm 1 [14–16]), this new information permits considerably augmenting the knowledge of unusual properties of excited ozone such as the selective enrichment of heavy ozone isotopomers in the atmosphere and in laboratory experiments [18,19]. Note that many features related to the process of ozone formation are still far from being understood [20]. In particular the existence of a reef-like structure [18,21,22] on the minimum energy path towards the dissociation, which should have an impact on the ozone dynamics, is an intricate subject of theoretical discussions [23,24]. Let us mention that, in the considered spectral region, falls the extremely weak 3A2(000)–X(110) hot vibronic band affected by predissociation broadening [25,26]. In spite of the very small population of the (110) level at 1796 cm 1, this band could be identified near 7756.78 cm 1 in the CRDS spectra of Ref. [25] (see Fig. 6 of this reference). Contrary to the 18O3 isotopologue where the corresponding hot band dominates compared to the nearby vibrational bands, in the case of studied 16O3 species, the hot band is significantly weaker than the nearby vibrational band at 7739 cm 1, for instance [25].
2. Experiment The fibre-connected CRDS spectrometer and the ozone synthesis have been described in our preceding papers [1–9]. The spectra were recorded in the 7600–7920 cm 1 interval with an ozone pressure of about 60 Torr. The full spectral range was covered with the help of 11 distributed feed-back (DFB) laser diodes, each of them allowing for a 30 cm 1 coverage by temperature tuning from 10 1C to 60 1C. The spectrometer presents unique performances in terms of sensitivity [27,28] that enable recording ozone spectra with a routine noise equivalent absorption αmin 2 10 10–5 10 11 cm 1, typically two or three orders of magnitude better than that achieved with Fourier Transform Spectrometers coupled to multi-pass cells [29,30]. The calibration of the frequency axis was provided by a wavemeter. We estimate to better than 1.5 10 3 cm 1 the accuracy on the line positions, as confirmed below by ground state combination differences (GCSD). Our estimated value on the error bar on the line intensities is 15– 20% as a result of the extreme weakness of the considered bands (see Fig. 4 of Ref. [13]).
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3. Theory 3.1. Vibrational predictions and assignments Accurate predictions of band centres and rotational constants, particularly for dark perturbing states, are of crucial importance for identifying resonance interactions and for an appropriate set up of the effective Hamiltonian (EH) model. These calculations were performed by the variational method from two recent PESs [16,17] which are considerably more accurate than those used in previous works. The first one is a new ab initio PES which was constructed in Ref. [16] from extended electronic structure calculations. It has a more realistic De limit which differs by only 0.6% from experimental determination. The second PES also based on a fit of ab initio points was empirically optimized in the vicinity of the equilibrium configuration [17]. It is worth noting that the bound ozone states observed via spectral transition recorded in this work would lie in a continuum beyond the dissociation threshold of the PES of Ref. [21]. The quality of new predictions for the rotational constants and band centres has been first tested on the bands previously analyzed up to 7600 cm 1 [8,9] as discussed in our review paper [11]. An overall agreement on the order of 1 cm 1 was obtained for the band centres and better than 1% for the A, B and C rotational constants. In this work we extend these calculations to the higher energy range corresponding to new observed bands. As in all our recent ozone analyses [11], we used the vibrational normal mode assignment obtained as follows. First an EH for overlapping polyads of interacting states was built from a PES using high-order contact transformations and the MOL_CT program suite [31,32]. Then the eigenfunctions of the EH were decomposed in normal mode basis and the contribution corresponding to the major mixing coefficient was used for the assignment. This procedure is referred to as “EH normal mode decomposition” or briefly “%-decomposition” labelling [11]. At low vibrational energy, the ozone molecule is known to behave as a normal mode molecule. Calculations with the PES [10] used in previous analyses [1–9] indicated that normal mode assignments for highly excited vibrations become ambiguous for some states because of the absence of a dominant contribution. Note that a local mode assignment is not universally applicable as well. As recently shown in Ref. [24], the “inflation” of normal modes dramatically increases with energy when approaching the dissociation threshold, though there should exist few “stability islands” of regular normal mode vibrations. This means that for some states at high energy range there is no dominant normal mode contribution and the same normal mode basis function could give major contributions to different vibration states. This occurs when the normal modes are strongly mixed due to anharmonic resonance interactions including interpolyad couplings. For this reason the “%-decomposition” labelling could change with an improvement of the PES, as was already mentioned in Ref. [11]. For example, using a more accurate ab initio PES [16] the vibrational state near
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7452 cm 1 labelled as (243) in Ref. [9] is re-assigned to (045) with a dominant contribution of only 23%. On the contrary, the (243) labelling is attached to the higher state analysed in the present study at 7686 cm 1 with a major contribution of 28%. Consequently, for some states approaching the transition range towards the dissociation threshold a normal mode assignment is not absolute and should be taken with great caution as a “nominative labelling”. In certain cases this could however give useful hints for a choice of appropriate coupling in empirical EH models.
3.2. Rotational assignments and spectra modeling The spectra were rotationally assigned by systematically searching lines fulfilling GSCD relations as described in Ref. [12]. The rovibrational energy levels and transitions were calculated with the GIP code [33] using the effective models for interacting bands. Common features of effective Hamiltonian and effective band transition moments approach in the case of the ozone molecule have been described in previous works ([11,12,34–36] and references therein). The spectroscopic and coupling parameters of the sets of states coupled through rovibrational resonance interactions were fitted, the parameters of the vibrational ground state being fixed to literature values [12,34]. The diagonal vibration blocks were chosen in the standard Watson form [37] corresponding to the A-type reduction whereas resonances were taken into account by offdiagonal vibration blocks involving anharmonic and/or Coriolis coupling parameters (Eqs. (2,3) of Ref. [12]). The
ðJ 7 ; J z Þ symmetry adapted representation [38,39] of ladder angular momentum components implemented in the GIP code [33] was used for the computation of line positions and intensities. As a first iteration, for each studied band, a spectrum was calculated using the predicted band centres [16,17] and upper state rotational constants [40]. Then we used the “ASSIGN” code [41] to identify a first Ka series of transitions. Unfortunately, this code is difficult to use for dense spectra involving many weak lines sometimes blended by impurity lines (mainly water in the present case). In that case, line positions fulfilling GSCD relations were searched “by hand”, in particular for J and Ka values corresponding to the predicted band head. In parallel, the “MultiFit” code [42] including line intensity calculations was systematically used to compare the experimental and synthetic spectra at the various steps of the analyses. Selected measured line intensities of non-blended transitions were then fitted using effective dipole transition moment (EDTM) parameters (see Ref. [36] and refs. therein for the definition of the EDTM parameters).
4. Results The spectra analyses become more and more complicated with increasing energy: line intensities become weaker and the spectra are more congested. As a result, the set of assigned transitions per observed band becomes more limited whereas the number of possible resonance interactions of upper states with the dense environment of neighboring “dark” perturbers is larger.
Fig. 1. Perturbations of the (243) state at 7686.08 cm 1 by Coriolis interactions with the (172) and (036) dark states. The upper and lower panels show the resonance perturbations in line position and mixing coefficients for the Ka ¼ 0 and Ka ¼1 series, respectively.
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In addition, the precision of theoretical predictions for band centres [16,24], and rotational constants also decreases. In these conditions we could only include a limited set of couplings in the EH models and had to constrain poorly determinable parameters, particularly for dark states. Due to these approximations and to missing information, the dark state parameters have to be taken with caution, as discussed in Ref. [11]. Because of these model errors a true uncertainty of dark state parameters could be in average by one order of magnitude larger than statistical standard deviations (1σ) of the fitted values, given in parentheses in the corresponding tables. This concerns both dark state vibration levels and rotational constants. On the contrary, the band centres and rotational constants – A, B, C – as well as the energy levels derived from assigned transitions, represent accurately determined information. 4.1. The 2ν1 þ4ν2 þ3ν3 band near 7686 cm 1 The band observed around 7686 cm 1 was assigned as 2ν1 þ4ν2 þ3ν3. Note that the same labelling has been used in our previous analysis [9] for the band centred near 7452 cm 1. However as explained in Section 3, the latter one has been re-assigned to 4ν2 þ 5ν3 [12] using the “%-decomposition” labelling from new ab initio PES [16]. The analysis of the 2ν1 þ4ν2 þ3ν3 was difficult because of several perturbations with dark states affecting its rotational structure. In Fig. 1 (left panels), the shift of the Ka ¼0, 1 line positions from their unperturbed values (calculated using a single state model) with the predicted
Table 1 Spectroscopic parameters and fit statistics for the states.
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values of the rotational constants, are plotted versus the J rotational quantum number. The first strong interaction is a Coriolis type coupling between the Ka ¼1 series with the Ka ¼2 levels of the (172) vibrational state perturbing as well the lower J levels of the Ka ¼0 series. The corresponding mixing coefficients are presented on the right panels. A second strong perturbation of Coriolis type was identified between the Ka ¼0 levels of the (243) state and the Ka ¼ 3 levels of the (036) state. Including relevant terms in the effective Hamiltonian model, it has been possible to reproduce a set of 196 transitions with a root-mean square (rms) deviation of 0.014 cm 1. One transition corresponding to the level {J, Ka, Kc}¼{29,1,28} was excluded from the fit because it could not be reproduced satisfactorily. The obtained fitted values of the effective Hamiltonian parameters are listed in Table 1 and an overview of the set of determined energy levels is given in Fig. 2. Note that limited information on assigned series of resonance perturbations did not allow for a reliable determination of the dark state rotational constants, particularly for the (036) state. As explained in Ref. [11] the true errors of fitted dark state parameter values are much larger than the purely statistical standard deviations quoted in Tables 1–4. (A) To derive the d1 parameter of the effective dipole transition moment operator, presented in Table 1(ii), 36 line intensities were selected. An rms deviation of 19% between observed and calculated line intensities was achieved (Table 1(iv)). Fig. 3 shows an example of agreement between the observed and calculated spectra achieved in the R-branch region.
O3 band centred at 7686 cm 1 with the EH model involving resonance perturbations by two dark
16
(i) Spectroscopic EH parameters (in cm 1)
(iii) Statistics for line positions
Coupled upper states EVV A (B þC)/2 (Bþ C)/2 (B C)/2 ΔK 103 ΔJK 105
(036) 7653.9300 (56) 3.37876 (25) 0.3810 [f] 0.0261 [f] g g
(172) 7683.9486 (53) 3.2933[f] 0.3843196 (96) 0.025872 (32) g g
(243) 7686.08162 (37) 3.059717 (93) 0.3873856 (16) 0.0262483 (33) 0.5995 (53) 3.2040 (93)
Upper vibrational state Jmax Ka max Number of transitions Number of levels rms (10–3 cm 1)
ΔJ 107
g
g
0.677 (18)
(iv) Statistics for line intensities
δJ 106
g
g
0.48217 (23)
Coriolis coupling terms: ð172Þð243Þ C 001 ð036Þð243Þ C 003
10
1
0.25557 (22)
10
4
0.23441 (60)
Jmax Ka max
25 4
Number of transitions
36
rms (%)
19.1
Sv (cm/molecule)a
3.21 10–26 (271 lines)
(ii) Dipole transition moment parameter for the 2ν1 þ 4ν2 þ 3ν3 band d1 105
(243) 30 4 197b 116 13.7
0.48229 (85) Debye
[f] – fixed to the values predicted [40] from the PES [17]. [g] – fixed to their ground state values as well as other higher order centrifugal distortion parameters quoted in [12]. Grey background corresponds to dark perturber states. a Integrated band intensity calculated with a cut off of 1 10–29 cm/molecule at 296 K. b Corresponds to the fit of 196 transitions (see text).
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Fig. 2. Overview of the rovibrational levels of the (243), (271) and (405) states of 16O3 derived from the analysis of the CRDS spectrum between 7600 and 7920 cm 1. The number of assigned lines sharing the same upper energy level is given for each upper J, Ka value. An asterisk (*) has been added to the level of the (243) state excluded from the effective Hamiltonian model (see Text).
Table 2 Spectroscopic parameters and fit statistics for the 16O3 band centredb at 7739.62 cm 1 with the EH model involving resonance perturbations by three dark states. (i) Spectroscopic EH parameters (in cm 1)
(iii) Statistics for line positions
Coupled upper states
(008)
(450)
(0 10 1)
(271)
EVV A (B þ C)/2 (Bþ C)/2 (B C)/2 ΔJ 106
7715.124 (53) 2.9454 (18) 0.389301 (45) 0.0250 [f] g
7718.563 (16) 3.2006 (11) 0.399336 (38) 0.0247 [f] g
7726.8856 (96)b 3.6739 [f] 0.380699 (89) 0.0272 [f] g
7739.60600 (65)b 3.179264 (69) 0.3785876 (21) 0.0272023 (11) 0.8226 (38)
Resonance coupling terms:
Upper vibration state Jmax Ka max Number of transitions Number of levels rms (10–3 cm 1)
(271) 26 5 135 83 8.0
(iv) Statistics for line intensities
F ð0101Þð271Þ 000
0.4758 (85)
Jmax
C ð450Þð271Þ 001
0.015450 (37)
Ka max
3
C ð008Þð271Þ 011
0.013051 (40)
Number of transitions rms (%) Sv (cm/molecule)a
45 31.6 4.56 10–26 (213 lines)
(ii) Dipole transition moment parameter of the 2ν1 þ 7ν2 þ ν3 band d1 105
20
0.6675 (12) Debye
[f] – fixed to the values predicted [40] from the PES [17]. [g] – fixed to their ground state values as well as other higher order centrifugal distortion parameters quoted in [12]. Grey background corresponds to dark perturber states. a Integrated band intensity calculated with a cut off of 1 10–29 cm/molecule at 296 K. b Because of the Fermi coupling, the centres of the 2ν1 þ7ν2 þ ν3 band (7739.6237 cm 1) and of the 10ν2 þν3 band (7726.87 cm 1 ) differ from the diagonal EH matrix elements EVV listed in the table.
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4.2. The 2ν1 þ7ν2 þν3 band near 7739 cm 1
Fig. 3. Comparison of the experimental and calculated spectra of 16O3 in the R-branch region of the 2ν1 þ 4ν2 þ3ν3 band near 7690 cm 1. Upper panel: Simulated spectrum. The line positions were corrected by replacing calculated upper state energies by their experimentally determined values while the line intensities were calculated using the fitted value of the transition moment parameter. The assignment of the most excited transition is given as example. Lower panel: CRDS spectrum.
Table 3 Comparison between predictions for the rotational constants of the upper states near 7740 cm 1 and results of experimental spectra analyses. Vib. states
A
B
C
(107) pred. [40] (271) pred. [40] EH fit
3.3938 3.5591 3.5578
0.4134 0.4042 0.4058
0.3610 0.3514 0.3514
This band extends from 7680 up to 7750 cm 1 and exhibits a compressed R-branch near 7740 cm 1, where several absorption lines of H2O are superimposed. The ab initio calculations of Ref. [16] predict two bands with appropriate symmetry in the region: the 2ν1 þ7ν2 þν3 and ν1 þ7ν3 bands at 7741 and 7758 cm 1, respectively. Previous analysis at lower energies [12] has shown that the most intense bands up to 7000 cm 1 correspond to high values of antisymmetric stretch quantum number (v3) and low values of the bending quantum number (v2). Following these intensity considerations, an assignment to the ν1 þ7ν3 band seems reasonable. It has nevertheless to be excluded considering the large shift of about 18 cm 1 between the calculated and experimental vibrational energies, much larger than observed for nearby bands. Consequently, the band observed near 7739.6 cm 1 was assigned to 2ν1 þ7ν2 þν3 in spite of the unusually high value of the bending quantum number of the upper vibrational state. This situation may result from the considerable mixing of the vibrational levels in the region, the dominant vibrational state giving a very partial picture of the real vibrational wavefunction, but could also reflect a significant change of the shapes of potential and dipole moment surfaces in this range. From a synthetic spectrum calculated with the Multifit code [42], and using the “Assign” code [41] the Ka ¼0–2 series could be assigned for intermediate values of J ¼10– 16. Based on the theoretical predictions of Refs. [16,17], three dark states were included in the EH model in order to reproduce the observed perturbations: (i) the (008) state whose Ka ¼5 series interacts with the Ka ¼4 series of (271) through a Coriolis perturbation, (ii) the (450) state responsible of the perturbation of the Ka ¼2 levels
Table 4 Spectroscopic parameters and fit statistics for the 16O3 band centred at 7860 cm 1 with the EH model involving resonance perturbations by one dark state. (i) Spectroscopic parameters (in cm 1)
(iii) Statistics for line positions
Coupled upper states EVV A (B þC)/2 (Bþ C)/2 (B C)/2 ΔK 103 ΔJK 104
(405) 7860.07730 (33) 3.07687 (47) 0.3835226 (22) 0.0252447 (11) 0.2559 (15) 0.23585 (97)
(234) 7889.4678 (39) 3.1128 [f] 0.3851 [f] 0.0258 [f] g g
ΔJ 106
0.3735 (34)
g
HKJ 105
0.13693 (23)
g
Upper vibrational state Band centre (cm 1) Jmax Ka max Number of transitions Number of levels rms (10–3 cm 1)
(405) 7860.077 26 6 199 121 13.6
(iv) Statistics for line intensities Jmax
Coriolis coupling term: ð234Þð405Þ 104 C 003
0.2676 (14)
5
Number of transitions
40
rms (%) Sv ¼3.72 10–26 cm/molecule at 296 K
(ii) Dipole transition moment parameter the 4ν1 þ5ν3 band ðAÞ
d1 105
23
Ka max
0.49592 (52) Debye
[f] – fixed to the values predicted in Ref. [40] from the PES of Ref. [17] (see text). [g] – fixed to their ground state values as well as other higher order centrifugal distortion parameters quoted in [12]. Grey background corresponds to the “dark” perturber state. a Integrated band intensity calculated with a cut off of 1 10–29 cm/molecule.
19.4 a
(298 lines)
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Fig. 5. Comparison of the experimental and calculated spectra of 16O3 in the R-branch region of the 2ν1 þ7ν2 þ ν3 band near 7740 cm 1. Upper panel: Simulated spectrum. The line positions were corrected by replacing calculated upper state energies by their experimentally determined values while the line intensities were calculated using the fitted value of the transition moment parameter. One assignment is given as example. Lower panel: CRDS spectrum.
4.3. The 4ν1 þ5ν3 band near 7860 cm 1
Fig. 4. Mixing coefficients (%) into the (271) state induced by various resonance interactions with the (450), (008) and (0 10 1) dark states.
through a Coriolis interaction (C001 coupling term), (iii) the (0 10 1) state interacting with (271) through a Fermitype coupling (F0 0 coupling term). The mixing coefficients corresponding to these three resonances are illustrated in Fig. 4. The statistics of the final fit on 135 transitions (Jmax ¼26, Ka max ¼5-see Fig. 2) is reported in Table 2(iii). A set of 45 selected line intensities allowed to derive a value of d1 ¼ 0.67 10–5 Debye (Table 2(ii)). An example of agreement between observed and calculated spectra is given in Fig. 5. The comparison of the fitted values of the A, B, C rotational constants with the predicted values [40] of the (271) and (107) states confirms that the observed band should be labeled as 2ν1 þ7ν2 þν3 rather than ν1 þ7ν3 (Table 3) though the comments of Section 3 for the “nominative assignment” apply also to this case.
As for the two previous bands, the upper vibration state near 7860 cm 1 results from a strong mixing of various normal mode states. We formally label this band as 4ν1 þ5ν3 according to a slightly leading term in the %-decomposition. The corresponding analysis was made difficult by the superposition with some absorption lines of water, HF and O2 (a1Δg–X3Σg band) present in the ozone sample as impurities. Despite the weakness of this band (maximum line intensity on the order of 2 10–28 cm/molecule at 296 K), the rotational assignment was relatively easy, thanks to the good quality of the predictions and to the low values (J¼11, Ka ¼1) of the quantum number corresponding to the band head. The usual procedure of successive fits and assignments was repeated providing a total of 199 assigned transitions with Jmax ¼26 and Ka max ¼6 (see Fig. 2). Only one small perturbation of the Ka ¼3, J even series could be evidenced from the (Obs. – Calc.) deviations obtained using a single state Hamiltonian. From the energy crossing illustrated in Fig. 6, the perturbation was identified as a Coriolis interaction with the Ka ¼0 series of the (234) dark state. Using the suitable interacting term, C003, and the Hamiltonian parameters given in Table 4(i), an rms value of 13.6 10–3 cm 1 was achieved for the fit of the line positions. The principal term of the dipole transition moment parameter was derived from the fit of 40 selected line intensities (Table 4 (ii) and (iv)). The comparison presented in Fig. 7 shows the quality of agreement achieved between the CRDS and simulated spectra. Taking into account the weakness of the considered band, such an agreement is considered satisfactory. 5. Summary and conclusion The derived values of the energy levels of the three bright upper states under consideration – (243), (271) and
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Fig. 7. Comparison of the experimental and calculated spectra of 16O3 in the R-branch region of the 4ν1 þ 5ν3 band near 7860 cm 1. Upper panel: simulated spectrum. The line positions were corrected by replacing calculated upper state energies by their experimentally determined values while the line intensities were calculated using the fitted value of the transition moment parameter. The assignment of the highest energy transition is indicated. Lower panel: CRDS spectrum.
Fig. 6. Coriolis interaction of the (405) vibrational state near 7889 cm 1 with the (234) dark state. Upper panel: shifts of the line position of the Ka ¼ 3 series (J even) Lower panel: corresponding mixing coefficients (%) of the dark state into the (405) bright state.
(405) – are provided as Supplementary materials together with the corresponding line-lists calculated using the Hamiltonian and transition moment parameters given in Tables 1, 2 and 4, respectively. As the developed EH models do not allow reproducing the measured spectra within the experimental frequency accuracy (1.5 10–3 cm 1), the calculated line positions have been adjusted according to the experimental values of the energy levels. The line lists are then limited to the experimentally determined upper levels (Fig. 2). In addition, an intensity cut off of 1 10– 29 cm/molecule was applied. A total of 271 transitions are calculated for the 2ν1 þ4ν2 þ3ν3 band leading to a band intensity of Sv ¼3.21 10–26 cm/molecule at 296 K. The corresponding line number and band intensity for the 2ν1 þ7ν2 þν3 and 4ν1 þ5ν3 bands are 4.56 10–26 and 3.72 10–26 cm/molecule for 213 and 298 transitions, respectively. The presently calculated line-lists are displayed in Fig. 8, together with those obtained in our previous CRDS analysis of the of 16O3 spectrum (29 bands in total). This plot illustrates the steep decrease of the band intensities approaching the dissociation limit. The “inflation” of normal modes [24] quickly increases with energy when approaching the dissociation threshold. Neither normal nor local mode assignments are fully satisfactory for some series of strongly coupled states. The (v1v2v3) labelling has to be taken with caution as “nominative assignment”. This applies in particular to dark state parameters for which true uncertainties are larger than statistical fit standard deviations [11].
Fig. 8. Overview of the line-lists of 16O3 constructed on the basis of the modelling of CRDS spectra between 5850 and 7920 cm 1 [1–9]. The three most excited bands above 7600 cm 1 are the 2ν1 þ4ν2 þ 3ν3, 2ν1 þ7ν2 þ ν3 and 4ν1 þ 5ν3 bands studied in this work. The dissociation energy around 8560 cm 1 is indicated.
On the contrary, the centres and rotational constants A, B, C of observed bands and the energy levels derived from assigned transitions, represent accurately determined dataset which can be used for the validation of theoretical PESs [24]. The achieved satisfactory modelling of the spectrum indicates that resonance interactions are still tractable in the vicinity of the dissociation limit. This achievement would have not been possible without the accurate predictions provided by variational calculations [16,17,40]. As a further illustration of the quality of these predictions, we compare in Table 5 the band centres and rotational constants for the three studied bands. Note that the experimental data obtained in this contribution have been found of crucial importance for checking theoretical hypotheses related to the shape of the ozone PES in the high energy transition state range,
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Table 5 Comparison between observations (O) and calculations (C) for the centres and rotational constants of the three 16O3 bands analyzed in this work. All values are given in cm 1. (a) Band centers State
Obs.
Emp.a
(v1v2v3) (243) (271) (405)
7686.0816 7739.6060 7860.0773
Calc. 7684.85 7737.56 7857.86
Ab initiob O–C 1.23 2.05 2.21
Pred. 7687.22 7741.15 7863.32
O–C 1.14 1.54 3.24
(b) Rotational constants State (v1v2v3) (243) (271) (405)
A Obs. 3.4471 3.5579 3.4603
a
Calc. 3.4507 3.5591 3.4365
B O–C 0.0036 0.0012 0.0238
Obs. 0.4136 0.4058 0.4088
C a
Calc. 0.4111 0.4042 0.4076
O–C 0.0025 0.0016 0.0012
Obs. 0.3611 0.3514 0.3583
Calc.a 0.3593 0.3514 0.3580
O–C 0.0018 0.0000 0.0003
a Calculated values from the PES of Ref. [17] empirically optimized from experimental levels below 5000 cm 1, this PES is also used for the prediction of A, B, C constants [40]. b From the ab initio PES of Ref. [16].
particularly for the intricate question concerning the existence of the “reef-type” structure along the minimum energy path towards the dissociation [24].
[5]
[6]
Acknowledgments This work is jointly supported by the ANR project IDEO (Isotopic and Dynamic effects in Excited Ozone, ref. FI071215-01-01), LEFE ChAt CNRS program, and the Laboratoire International Associé SAMIA (Spectroscopie d'Absorption des Molécules d'Intérêt Atmosphérique) between CNRS (France) and RFBR (Russia) as well as by Tomsk State University Competitiveness Improvement Program. Vl.T. is indebted to IDRIS/CINES computer centres of France and of the ROMEO computer centre ReimsChampagne-Ardenne.
[7]
[8]
[9]
[10]
[11]
Appendix A. Supplementary materials Supplementary materials associated with this article can be found in the online version at http://dx.doi.org/10. 1016/j.jqsrt.2014.10.019.
[12]
[13]
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[30] Mikhailenko S, Barbe A, Tyuterev VlG, Regalia L, Plateaux JJ. Line positions and intensities of the ν1 þ ν2 þ 3ν3, ν2 þ 4ν3, and 3ν1 þ 2ν2 bands of ozone. J Mol Spectrosc 1996;180:227–35. [31] Tyuterev VlG, Tashkun SA, Seghir H. High-order contact transformations: general algorithm, computer implementation and triatomic tests. SPIE 2004;5311:167–75. [32] Tyuterev VlG, Tashkun SA, Kochanov RV, Rey M, 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. [33] Tashkun SA, Tyuterev VlG. GIP: a program for experimental data reduction in molecular spectroscopy. SPIE 1994;2205:188–91. [34] Flaud JM, Camy-Peyret C, Rinsland CP, Smith MA, Malathy Devi V. Atlas of ozone spectral parameters from microwave to medium infrared. Boston: Academic Press; 1990(600 p.). [35] Flaud JM, Bacis R. The ozone molecule: infrared and microwave spectroscopy. Spectrochim Acta Part A 1998;54:3–16. [36] Mondelain D, Campargue A, Kassi S, Barbe A, Starikova E, De BackerBarilly MR, et al. The CW-CRDS spectra of the 16O/18O isopotologues of ozone between 5930 and 6340 cm 1. Part 1: 16O16O18O. J Quant Spectrosc Radiat Transf 2013;116:49–66. [37] Watson JKG. Determination of centrifugal distortion coefficients of asymmetric-top molecules. J Chem Phys 1967;46:4189–96. [38] Perevalov VI, Tyuterev VlG. Effective centrifugal Hamiltonian with empirically determinable parameters in case of Coriolis resonances in symmetric-top molecules. Opt Spectrosc 1982;52:644–50. [39] Mikhailenko SN, Tyuterev VlG, Starikov VI, Albert KK, Winnewisser BP, Winnewisser M, et al. Water spectra in the 4200–6250 cm 1 region: extended analysis of ν1 þν2, ν2 þ ν3, and 3ν2 bands and confirmation of highly excited states from flame spectra and from atmospheric long-path observations. J Mol Spectrosc 2002;213: 91–121. [40] Tyuterev VlG, Kochanov RV, Tashkun SA, Starikova EN, Barbe A, et al. (in preparation). [41] Chichery A. (thesis) Univ. Reims, 09/20/2000. [42] Plateaux JJ, Régalia L, Boussin C, Barbe A. Multispectrum fitting technique for data recorded by Fourier transform spectrometer: application to N2O and CH3D. J Quant Spectrosc Radiat Transf 2001;68:507–20.
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Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt
Detection and analysis of three highly excited vibrational bands of 16O3 by CW-CRDS near the dissociation threshold A. Campargue a,b,n, S. Kassi a,b, D. Mondelain a,b, A. Barbe c, E. Starikova d,e, M.-R. De Backer c, Vl.G. Tyuterev c a
Université Grenoble Alpes, LIPhy, F-38000 Grenoble, France CNRS, LIPhy, F-38000 Grenoble, France Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, UFR Sciences Exactes et Naturelles, BP 1039, 51687 Reims Cedex 2, France d Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics SB RAS, 1, Academician Zuev Square, Tomsk 634021, Russia e QUAMER, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russia b c
a r t i c l e in f o
abstract
Article history: Received 3 September 2014 Received in revised form 22 October 2014 Accepted 25 October 2014 Available online 4 November 2014
The present contribution is devoted to the analysis of three extremely weak A-type bands of 16O3 recorded near 7686, 7739 and 7860 cm 1 i.e. only a few % below the dissociation limit, D0, at about 8560 cm 1. They correspond to the most excited vibration–rotation states of ozone observed so far via high-resolution absorption spectroscopy. They were detected by high sensitivity CW-cavity ring down spectroscopy with a typical noise equivalent absorption, αmin, on the order of 2 10 10 cm 1 and modelled using the effective operator approach. The derived band centres and rotational constants show a very good agreement with recent theoretical predictions based on a new ab initio potential energy surface. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Ozone CW-cavity ring down spectroscopy Resonance coupling Effective Hamiltonian model Potential energy surface
1. Introduction During the last years, we have systematically studied highly excited vibration–rotation states of the ozone molecule from the analyses of its very weak absorption spectrum in the 5850–7600 cm 1 range [1–9]. For the main isotopologue, 16O3, 26 A-type bands were detected by highly sensitive CW-cavity ring down spectroscopy (CW-CRDS). This number is to be compared to a total of 41 bands of the same symmetry type predicted in the same range from the potential energy surface (PES) [10] of the molecule. The modelling and analyses of the recorded spectra were carried out using the effective
n
Corresponding author. E-mail address: [email protected] (A. Campargue).
http://dx.doi.org/10.1016/j.jqsrt.2014.10.019 0022-4073/& 2014 Elsevier Ltd. All rights reserved.
operator approach. All the CRDS results below 7600 cm 1 were summarized in a recent review [11]. Several obtained line-lists are available in the SMPO databank devoted to the ozone molecule [12]. A large part of bands has been included in the last edition of the HITRAN database [13]. The present contribution is devoted to three extremely weak A-type bands observed near 7686, 7739 and 7860 cm 1 which correspond to the most excited vibration–rotation states of ozone analysed so far by highresolution absorption spectroscopy. The spectra analyses were particularly challenging at this high excitation level as numerous resonance couplings with “dark” states lead to qualitative changes in the molecular polyad structure. The corresponding perturbations would have been impossible to treat in absence of reliable predictions for the energy levels, vibrational assignments and rotational constants. This applies in particular to the nearby “dark” states
A. Campargue et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 152 (2015) 84–93
which could perturb the rotational patterns of the observed bright states. Recent improvements of electronic structure calculations [14–16] enable a considerable progress in this domain. In this work we used the predictions obtained from accurate PESs of Refs. [16,17]. Note that, contrary to the low energy range where spectra simulation close to the experimental accuracy could be achieved, in the case of the presently studied bands, such a spectrum reproduction seems out of reach. Nevertheless, these analyses are expected to provide new valuable information for checking theoretical hypotheses concerning the shape of the ozone PES at high energy range. As the upper studied band is located only 8% below the dissociation threshold of the ground electronic state (D0 8560 cm 1 [14–16]), this new information permits considerably augmenting the knowledge of unusual properties of excited ozone such as the selective enrichment of heavy ozone isotopomers in the atmosphere and in laboratory experiments [18,19]. Note that many features related to the process of ozone formation are still far from being understood [20]. In particular the existence of a reef-like structure [18,21,22] on the minimum energy path towards the dissociation, which should have an impact on the ozone dynamics, is an intricate subject of theoretical discussions [23,24]. Let us mention that, in the considered spectral region, falls the extremely weak 3A2(000)–X(110) hot vibronic band affected by predissociation broadening [25,26]. In spite of the very small population of the (110) level at 1796 cm 1, this band could be identified near 7756.78 cm 1 in the CRDS spectra of Ref. [25] (see Fig. 6 of this reference). Contrary to the 18O3 isotopologue where the corresponding hot band dominates compared to the nearby vibrational bands, in the case of studied 16O3 species, the hot band is significantly weaker than the nearby vibrational band at 7739 cm 1, for instance [25].
2. Experiment The fibre-connected CRDS spectrometer and the ozone synthesis have been described in our preceding papers [1–9]. The spectra were recorded in the 7600–7920 cm 1 interval with an ozone pressure of about 60 Torr. The full spectral range was covered with the help of 11 distributed feed-back (DFB) laser diodes, each of them allowing for a 30 cm 1 coverage by temperature tuning from 10 1C to 60 1C. The spectrometer presents unique performances in terms of sensitivity [27,28] that enable recording ozone spectra with a routine noise equivalent absorption αmin 2 10 10–5 10 11 cm 1, typically two or three orders of magnitude better than that achieved with Fourier Transform Spectrometers coupled to multi-pass cells [29,30]. The calibration of the frequency axis was provided by a wavemeter. We estimate to better than 1.5 10 3 cm 1 the accuracy on the line positions, as confirmed below by ground state combination differences (GCSD). Our estimated value on the error bar on the line intensities is 15– 20% as a result of the extreme weakness of the considered bands (see Fig. 4 of Ref. [13]).
85
3. Theory 3.1. Vibrational predictions and assignments Accurate predictions of band centres and rotational constants, particularly for dark perturbing states, are of crucial importance for identifying resonance interactions and for an appropriate set up of the effective Hamiltonian (EH) model. These calculations were performed by the variational method from two recent PESs [16,17] which are considerably more accurate than those used in previous works. The first one is a new ab initio PES which was constructed in Ref. [16] from extended electronic structure calculations. It has a more realistic De limit which differs by only 0.6% from experimental determination. The second PES also based on a fit of ab initio points was empirically optimized in the vicinity of the equilibrium configuration [17]. It is worth noting that the bound ozone states observed via spectral transition recorded in this work would lie in a continuum beyond the dissociation threshold of the PES of Ref. [21]. The quality of new predictions for the rotational constants and band centres has been first tested on the bands previously analyzed up to 7600 cm 1 [8,9] as discussed in our review paper [11]. An overall agreement on the order of 1 cm 1 was obtained for the band centres and better than 1% for the A, B and C rotational constants. In this work we extend these calculations to the higher energy range corresponding to new observed bands. As in all our recent ozone analyses [11], we used the vibrational normal mode assignment obtained as follows. First an EH for overlapping polyads of interacting states was built from a PES using high-order contact transformations and the MOL_CT program suite [31,32]. Then the eigenfunctions of the EH were decomposed in normal mode basis and the contribution corresponding to the major mixing coefficient was used for the assignment. This procedure is referred to as “EH normal mode decomposition” or briefly “%-decomposition” labelling [11]. At low vibrational energy, the ozone molecule is known to behave as a normal mode molecule. Calculations with the PES [10] used in previous analyses [1–9] indicated that normal mode assignments for highly excited vibrations become ambiguous for some states because of the absence of a dominant contribution. Note that a local mode assignment is not universally applicable as well. As recently shown in Ref. [24], the “inflation” of normal modes dramatically increases with energy when approaching the dissociation threshold, though there should exist few “stability islands” of regular normal mode vibrations. This means that for some states at high energy range there is no dominant normal mode contribution and the same normal mode basis function could give major contributions to different vibration states. This occurs when the normal modes are strongly mixed due to anharmonic resonance interactions including interpolyad couplings. For this reason the “%-decomposition” labelling could change with an improvement of the PES, as was already mentioned in Ref. [11]. For example, using a more accurate ab initio PES [16] the vibrational state near
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7452 cm 1 labelled as (243) in Ref. [9] is re-assigned to (045) with a dominant contribution of only 23%. On the contrary, the (243) labelling is attached to the higher state analysed in the present study at 7686 cm 1 with a major contribution of 28%. Consequently, for some states approaching the transition range towards the dissociation threshold a normal mode assignment is not absolute and should be taken with great caution as a “nominative labelling”. In certain cases this could however give useful hints for a choice of appropriate coupling in empirical EH models.
3.2. Rotational assignments and spectra modeling The spectra were rotationally assigned by systematically searching lines fulfilling GSCD relations as described in Ref. [12]. The rovibrational energy levels and transitions were calculated with the GIP code [33] using the effective models for interacting bands. Common features of effective Hamiltonian and effective band transition moments approach in the case of the ozone molecule have been described in previous works ([11,12,34–36] and references therein). The spectroscopic and coupling parameters of the sets of states coupled through rovibrational resonance interactions were fitted, the parameters of the vibrational ground state being fixed to literature values [12,34]. The diagonal vibration blocks were chosen in the standard Watson form [37] corresponding to the A-type reduction whereas resonances were taken into account by offdiagonal vibration blocks involving anharmonic and/or Coriolis coupling parameters (Eqs. (2,3) of Ref. [12]). The
ðJ 7 ; J z Þ symmetry adapted representation [38,39] of ladder angular momentum components implemented in the GIP code [33] was used for the computation of line positions and intensities. As a first iteration, for each studied band, a spectrum was calculated using the predicted band centres [16,17] and upper state rotational constants [40]. Then we used the “ASSIGN” code [41] to identify a first Ka series of transitions. Unfortunately, this code is difficult to use for dense spectra involving many weak lines sometimes blended by impurity lines (mainly water in the present case). In that case, line positions fulfilling GSCD relations were searched “by hand”, in particular for J and Ka values corresponding to the predicted band head. In parallel, the “MultiFit” code [42] including line intensity calculations was systematically used to compare the experimental and synthetic spectra at the various steps of the analyses. Selected measured line intensities of non-blended transitions were then fitted using effective dipole transition moment (EDTM) parameters (see Ref. [36] and refs. therein for the definition of the EDTM parameters).
4. Results The spectra analyses become more and more complicated with increasing energy: line intensities become weaker and the spectra are more congested. As a result, the set of assigned transitions per observed band becomes more limited whereas the number of possible resonance interactions of upper states with the dense environment of neighboring “dark” perturbers is larger.
Fig. 1. Perturbations of the (243) state at 7686.08 cm 1 by Coriolis interactions with the (172) and (036) dark states. The upper and lower panels show the resonance perturbations in line position and mixing coefficients for the Ka ¼ 0 and Ka ¼1 series, respectively.
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In addition, the precision of theoretical predictions for band centres [16,24], and rotational constants also decreases. In these conditions we could only include a limited set of couplings in the EH models and had to constrain poorly determinable parameters, particularly for dark states. Due to these approximations and to missing information, the dark state parameters have to be taken with caution, as discussed in Ref. [11]. Because of these model errors a true uncertainty of dark state parameters could be in average by one order of magnitude larger than statistical standard deviations (1σ) of the fitted values, given in parentheses in the corresponding tables. This concerns both dark state vibration levels and rotational constants. On the contrary, the band centres and rotational constants – A, B, C – as well as the energy levels derived from assigned transitions, represent accurately determined information. 4.1. The 2ν1 þ4ν2 þ3ν3 band near 7686 cm 1 The band observed around 7686 cm 1 was assigned as 2ν1 þ4ν2 þ3ν3. Note that the same labelling has been used in our previous analysis [9] for the band centred near 7452 cm 1. However as explained in Section 3, the latter one has been re-assigned to 4ν2 þ 5ν3 [12] using the “%-decomposition” labelling from new ab initio PES [16]. The analysis of the 2ν1 þ4ν2 þ3ν3 was difficult because of several perturbations with dark states affecting its rotational structure. In Fig. 1 (left panels), the shift of the Ka ¼0, 1 line positions from their unperturbed values (calculated using a single state model) with the predicted
Table 1 Spectroscopic parameters and fit statistics for the states.
87
values of the rotational constants, are plotted versus the J rotational quantum number. The first strong interaction is a Coriolis type coupling between the Ka ¼1 series with the Ka ¼2 levels of the (172) vibrational state perturbing as well the lower J levels of the Ka ¼0 series. The corresponding mixing coefficients are presented on the right panels. A second strong perturbation of Coriolis type was identified between the Ka ¼0 levels of the (243) state and the Ka ¼ 3 levels of the (036) state. Including relevant terms in the effective Hamiltonian model, it has been possible to reproduce a set of 196 transitions with a root-mean square (rms) deviation of 0.014 cm 1. One transition corresponding to the level {J, Ka, Kc}¼{29,1,28} was excluded from the fit because it could not be reproduced satisfactorily. The obtained fitted values of the effective Hamiltonian parameters are listed in Table 1 and an overview of the set of determined energy levels is given in Fig. 2. Note that limited information on assigned series of resonance perturbations did not allow for a reliable determination of the dark state rotational constants, particularly for the (036) state. As explained in Ref. [11] the true errors of fitted dark state parameter values are much larger than the purely statistical standard deviations quoted in Tables 1–4. (A) To derive the d1 parameter of the effective dipole transition moment operator, presented in Table 1(ii), 36 line intensities were selected. An rms deviation of 19% between observed and calculated line intensities was achieved (Table 1(iv)). Fig. 3 shows an example of agreement between the observed and calculated spectra achieved in the R-branch region.
O3 band centred at 7686 cm 1 with the EH model involving resonance perturbations by two dark
16
(i) Spectroscopic EH parameters (in cm 1)
(iii) Statistics for line positions
Coupled upper states EVV A (B þC)/2 (Bþ C)/2 (B C)/2 ΔK 103 ΔJK 105
(036) 7653.9300 (56) 3.37876 (25) 0.3810 [f] 0.0261 [f] g g
(172) 7683.9486 (53) 3.2933[f] 0.3843196 (96) 0.025872 (32) g g
(243) 7686.08162 (37) 3.059717 (93) 0.3873856 (16) 0.0262483 (33) 0.5995 (53) 3.2040 (93)
Upper vibrational state Jmax Ka max Number of transitions Number of levels rms (10–3 cm 1)
ΔJ 107
g
g
0.677 (18)
(iv) Statistics for line intensities
δJ 106
g
g
0.48217 (23)
Coriolis coupling terms: ð172Þð243Þ C 001 ð036Þð243Þ C 003
10
1
0.25557 (22)
10
4
0.23441 (60)
Jmax Ka max
25 4
Number of transitions
36
rms (%)
19.1
Sv (cm/molecule)a
3.21 10–26 (271 lines)
(ii) Dipole transition moment parameter for the 2ν1 þ 4ν2 þ 3ν3 band d1 105
(243) 30 4 197b 116 13.7
0.48229 (85) Debye
[f] – fixed to the values predicted [40] from the PES [17]. [g] – fixed to their ground state values as well as other higher order centrifugal distortion parameters quoted in [12]. Grey background corresponds to dark perturber states. a Integrated band intensity calculated with a cut off of 1 10–29 cm/molecule at 296 K. b Corresponds to the fit of 196 transitions (see text).
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Fig. 2. Overview of the rovibrational levels of the (243), (271) and (405) states of 16O3 derived from the analysis of the CRDS spectrum between 7600 and 7920 cm 1. The number of assigned lines sharing the same upper energy level is given for each upper J, Ka value. An asterisk (*) has been added to the level of the (243) state excluded from the effective Hamiltonian model (see Text).
Table 2 Spectroscopic parameters and fit statistics for the 16O3 band centredb at 7739.62 cm 1 with the EH model involving resonance perturbations by three dark states. (i) Spectroscopic EH parameters (in cm 1)
(iii) Statistics for line positions
Coupled upper states
(008)
(450)
(0 10 1)
(271)
EVV A (B þ C)/2 (Bþ C)/2 (B C)/2 ΔJ 106
7715.124 (53) 2.9454 (18) 0.389301 (45) 0.0250 [f] g
7718.563 (16) 3.2006 (11) 0.399336 (38) 0.0247 [f] g
7726.8856 (96)b 3.6739 [f] 0.380699 (89) 0.0272 [f] g
7739.60600 (65)b 3.179264 (69) 0.3785876 (21) 0.0272023 (11) 0.8226 (38)
Resonance coupling terms:
Upper vibration state Jmax Ka max Number of transitions Number of levels rms (10–3 cm 1)
(271) 26 5 135 83 8.0
(iv) Statistics for line intensities
F ð0101Þð271Þ 000
0.4758 (85)
Jmax
C ð450Þð271Þ 001
0.015450 (37)
Ka max
3
C ð008Þð271Þ 011
0.013051 (40)
Number of transitions rms (%) Sv (cm/molecule)a
45 31.6 4.56 10–26 (213 lines)
(ii) Dipole transition moment parameter of the 2ν1 þ 7ν2 þ ν3 band d1 105
20
0.6675 (12) Debye
[f] – fixed to the values predicted [40] from the PES [17]. [g] – fixed to their ground state values as well as other higher order centrifugal distortion parameters quoted in [12]. Grey background corresponds to dark perturber states. a Integrated band intensity calculated with a cut off of 1 10–29 cm/molecule at 296 K. b Because of the Fermi coupling, the centres of the 2ν1 þ7ν2 þ ν3 band (7739.6237 cm 1) and of the 10ν2 þν3 band (7726.87 cm 1 ) differ from the diagonal EH matrix elements EVV listed in the table.
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4.2. The 2ν1 þ7ν2 þν3 band near 7739 cm 1
Fig. 3. Comparison of the experimental and calculated spectra of 16O3 in the R-branch region of the 2ν1 þ 4ν2 þ3ν3 band near 7690 cm 1. Upper panel: Simulated spectrum. The line positions were corrected by replacing calculated upper state energies by their experimentally determined values while the line intensities were calculated using the fitted value of the transition moment parameter. The assignment of the most excited transition is given as example. Lower panel: CRDS spectrum.
Table 3 Comparison between predictions for the rotational constants of the upper states near 7740 cm 1 and results of experimental spectra analyses. Vib. states
A
B
C
(107) pred. [40] (271) pred. [40] EH fit
3.3938 3.5591 3.5578
0.4134 0.4042 0.4058
0.3610 0.3514 0.3514
This band extends from 7680 up to 7750 cm 1 and exhibits a compressed R-branch near 7740 cm 1, where several absorption lines of H2O are superimposed. The ab initio calculations of Ref. [16] predict two bands with appropriate symmetry in the region: the 2ν1 þ7ν2 þν3 and ν1 þ7ν3 bands at 7741 and 7758 cm 1, respectively. Previous analysis at lower energies [12] has shown that the most intense bands up to 7000 cm 1 correspond to high values of antisymmetric stretch quantum number (v3) and low values of the bending quantum number (v2). Following these intensity considerations, an assignment to the ν1 þ7ν3 band seems reasonable. It has nevertheless to be excluded considering the large shift of about 18 cm 1 between the calculated and experimental vibrational energies, much larger than observed for nearby bands. Consequently, the band observed near 7739.6 cm 1 was assigned to 2ν1 þ7ν2 þν3 in spite of the unusually high value of the bending quantum number of the upper vibrational state. This situation may result from the considerable mixing of the vibrational levels in the region, the dominant vibrational state giving a very partial picture of the real vibrational wavefunction, but could also reflect a significant change of the shapes of potential and dipole moment surfaces in this range. From a synthetic spectrum calculated with the Multifit code [42], and using the “Assign” code [41] the Ka ¼0–2 series could be assigned for intermediate values of J ¼10– 16. Based on the theoretical predictions of Refs. [16,17], three dark states were included in the EH model in order to reproduce the observed perturbations: (i) the (008) state whose Ka ¼5 series interacts with the Ka ¼4 series of (271) through a Coriolis perturbation, (ii) the (450) state responsible of the perturbation of the Ka ¼2 levels
Table 4 Spectroscopic parameters and fit statistics for the 16O3 band centred at 7860 cm 1 with the EH model involving resonance perturbations by one dark state. (i) Spectroscopic parameters (in cm 1)
(iii) Statistics for line positions
Coupled upper states EVV A (B þC)/2 (Bþ C)/2 (B C)/2 ΔK 103 ΔJK 104
(405) 7860.07730 (33) 3.07687 (47) 0.3835226 (22) 0.0252447 (11) 0.2559 (15) 0.23585 (97)
(234) 7889.4678 (39) 3.1128 [f] 0.3851 [f] 0.0258 [f] g g
ΔJ 106
0.3735 (34)
g
HKJ 105
0.13693 (23)
g
Upper vibrational state Band centre (cm 1) Jmax Ka max Number of transitions Number of levels rms (10–3 cm 1)
(405) 7860.077 26 6 199 121 13.6
(iv) Statistics for line intensities Jmax
Coriolis coupling term: ð234Þð405Þ 104 C 003
0.2676 (14)
5
Number of transitions
40
rms (%) Sv ¼3.72 10–26 cm/molecule at 296 K
(ii) Dipole transition moment parameter the 4ν1 þ5ν3 band ðAÞ
d1 105
23
Ka max
0.49592 (52) Debye
[f] – fixed to the values predicted in Ref. [40] from the PES of Ref. [17] (see text). [g] – fixed to their ground state values as well as other higher order centrifugal distortion parameters quoted in [12]. Grey background corresponds to the “dark” perturber state. a Integrated band intensity calculated with a cut off of 1 10–29 cm/molecule.
19.4 a
(298 lines)
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Fig. 5. Comparison of the experimental and calculated spectra of 16O3 in the R-branch region of the 2ν1 þ7ν2 þ ν3 band near 7740 cm 1. Upper panel: Simulated spectrum. The line positions were corrected by replacing calculated upper state energies by their experimentally determined values while the line intensities were calculated using the fitted value of the transition moment parameter. One assignment is given as example. Lower panel: CRDS spectrum.
4.3. The 4ν1 þ5ν3 band near 7860 cm 1
Fig. 4. Mixing coefficients (%) into the (271) state induced by various resonance interactions with the (450), (008) and (0 10 1) dark states.
through a Coriolis interaction (C001 coupling term), (iii) the (0 10 1) state interacting with (271) through a Fermitype coupling (F0 0 coupling term). The mixing coefficients corresponding to these three resonances are illustrated in Fig. 4. The statistics of the final fit on 135 transitions (Jmax ¼26, Ka max ¼5-see Fig. 2) is reported in Table 2(iii). A set of 45 selected line intensities allowed to derive a value of d1 ¼ 0.67 10–5 Debye (Table 2(ii)). An example of agreement between observed and calculated spectra is given in Fig. 5. The comparison of the fitted values of the A, B, C rotational constants with the predicted values [40] of the (271) and (107) states confirms that the observed band should be labeled as 2ν1 þ7ν2 þν3 rather than ν1 þ7ν3 (Table 3) though the comments of Section 3 for the “nominative assignment” apply also to this case.
As for the two previous bands, the upper vibration state near 7860 cm 1 results from a strong mixing of various normal mode states. We formally label this band as 4ν1 þ5ν3 according to a slightly leading term in the %-decomposition. The corresponding analysis was made difficult by the superposition with some absorption lines of water, HF and O2 (a1Δg–X3Σg band) present in the ozone sample as impurities. Despite the weakness of this band (maximum line intensity on the order of 2 10–28 cm/molecule at 296 K), the rotational assignment was relatively easy, thanks to the good quality of the predictions and to the low values (J¼11, Ka ¼1) of the quantum number corresponding to the band head. The usual procedure of successive fits and assignments was repeated providing a total of 199 assigned transitions with Jmax ¼26 and Ka max ¼6 (see Fig. 2). Only one small perturbation of the Ka ¼3, J even series could be evidenced from the (Obs. – Calc.) deviations obtained using a single state Hamiltonian. From the energy crossing illustrated in Fig. 6, the perturbation was identified as a Coriolis interaction with the Ka ¼0 series of the (234) dark state. Using the suitable interacting term, C003, and the Hamiltonian parameters given in Table 4(i), an rms value of 13.6 10–3 cm 1 was achieved for the fit of the line positions. The principal term of the dipole transition moment parameter was derived from the fit of 40 selected line intensities (Table 4 (ii) and (iv)). The comparison presented in Fig. 7 shows the quality of agreement achieved between the CRDS and simulated spectra. Taking into account the weakness of the considered band, such an agreement is considered satisfactory. 5. Summary and conclusion The derived values of the energy levels of the three bright upper states under consideration – (243), (271) and
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Fig. 7. Comparison of the experimental and calculated spectra of 16O3 in the R-branch region of the 4ν1 þ 5ν3 band near 7860 cm 1. Upper panel: simulated spectrum. The line positions were corrected by replacing calculated upper state energies by their experimentally determined values while the line intensities were calculated using the fitted value of the transition moment parameter. The assignment of the highest energy transition is indicated. Lower panel: CRDS spectrum.
Fig. 6. Coriolis interaction of the (405) vibrational state near 7889 cm 1 with the (234) dark state. Upper panel: shifts of the line position of the Ka ¼ 3 series (J even) Lower panel: corresponding mixing coefficients (%) of the dark state into the (405) bright state.
(405) – are provided as Supplementary materials together with the corresponding line-lists calculated using the Hamiltonian and transition moment parameters given in Tables 1, 2 and 4, respectively. As the developed EH models do not allow reproducing the measured spectra within the experimental frequency accuracy (1.5 10–3 cm 1), the calculated line positions have been adjusted according to the experimental values of the energy levels. The line lists are then limited to the experimentally determined upper levels (Fig. 2). In addition, an intensity cut off of 1 10– 29 cm/molecule was applied. A total of 271 transitions are calculated for the 2ν1 þ4ν2 þ3ν3 band leading to a band intensity of Sv ¼3.21 10–26 cm/molecule at 296 K. The corresponding line number and band intensity for the 2ν1 þ7ν2 þν3 and 4ν1 þ5ν3 bands are 4.56 10–26 and 3.72 10–26 cm/molecule for 213 and 298 transitions, respectively. The presently calculated line-lists are displayed in Fig. 8, together with those obtained in our previous CRDS analysis of the of 16O3 spectrum (29 bands in total). This plot illustrates the steep decrease of the band intensities approaching the dissociation limit. The “inflation” of normal modes [24] quickly increases with energy when approaching the dissociation threshold. Neither normal nor local mode assignments are fully satisfactory for some series of strongly coupled states. The (v1v2v3) labelling has to be taken with caution as “nominative assignment”. This applies in particular to dark state parameters for which true uncertainties are larger than statistical fit standard deviations [11].
Fig. 8. Overview of the line-lists of 16O3 constructed on the basis of the modelling of CRDS spectra between 5850 and 7920 cm 1 [1–9]. The three most excited bands above 7600 cm 1 are the 2ν1 þ4ν2 þ 3ν3, 2ν1 þ7ν2 þ ν3 and 4ν1 þ 5ν3 bands studied in this work. The dissociation energy around 8560 cm 1 is indicated.
On the contrary, the centres and rotational constants A, B, C of observed bands and the energy levels derived from assigned transitions, represent accurately determined dataset which can be used for the validation of theoretical PESs [24]. The achieved satisfactory modelling of the spectrum indicates that resonance interactions are still tractable in the vicinity of the dissociation limit. This achievement would have not been possible without the accurate predictions provided by variational calculations [16,17,40]. As a further illustration of the quality of these predictions, we compare in Table 5 the band centres and rotational constants for the three studied bands. Note that the experimental data obtained in this contribution have been found of crucial importance for checking theoretical hypotheses related to the shape of the ozone PES in the high energy transition state range,
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Table 5 Comparison between observations (O) and calculations (C) for the centres and rotational constants of the three 16O3 bands analyzed in this work. All values are given in cm 1. (a) Band centers State
Obs.
Emp.a
(v1v2v3) (243) (271) (405)
7686.0816 7739.6060 7860.0773
Calc. 7684.85 7737.56 7857.86
Ab initiob O–C 1.23 2.05 2.21
Pred. 7687.22 7741.15 7863.32
O–C 1.14 1.54 3.24
(b) Rotational constants State (v1v2v3) (243) (271) (405)
A Obs. 3.4471 3.5579 3.4603
a
Calc. 3.4507 3.5591 3.4365
B O–C 0.0036 0.0012 0.0238
Obs. 0.4136 0.4058 0.4088
C a
Calc. 0.4111 0.4042 0.4076
O–C 0.0025 0.0016 0.0012
Obs. 0.3611 0.3514 0.3583
Calc.a 0.3593 0.3514 0.3580
O–C 0.0018 0.0000 0.0003
a Calculated values from the PES of Ref. [17] empirically optimized from experimental levels below 5000 cm 1, this PES is also used for the prediction of A, B, C constants [40]. b From the ab initio PES of Ref. [16].
particularly for the intricate question concerning the existence of the “reef-type” structure along the minimum energy path towards the dissociation [24].
[5]
[6]
Acknowledgments This work is jointly supported by the ANR project IDEO (Isotopic and Dynamic effects in Excited Ozone, ref. FI071215-01-01), LEFE ChAt CNRS program, and the Laboratoire International Associé SAMIA (Spectroscopie d'Absorption des Molécules d'Intérêt Atmosphérique) between CNRS (France) and RFBR (Russia) as well as by Tomsk State University Competitiveness Improvement Program. Vl.T. is indebted to IDRIS/CINES computer centres of France and of the ROMEO computer centre ReimsChampagne-Ardenne.
[7]
[8]
[9]
[10]
[11]
Appendix A. Supplementary materials Supplementary materials associated with this article can be found in the online version at http://dx.doi.org/10. 1016/j.jqsrt.2014.10.019.
[12]
[13]
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