High resolution investigation of the v3 band of trifluoromethyliodide (CF3I)

Journal of Molecular Spectroscopy xxx (2015) xxx–xxx

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High resolution investigation of the (CF3I)

v3 band of trifluoromethyliodide

F. Willaert a, P. Roy a, L. Manceron a,⇑, A. Perrin b, F. Kwabia-Tchana b, D. Appadoo c, D. McNaughton d, C. Medcraft d, J. Demaison e a

Synchrotron SOLEIL, AILES, L’Orme des Merisiers, BP 48, 91192 Saint-Aubin, France Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA), UMR7583 CNRS/Univ Paris Est Créteil and Université Paris 7 Denis Diderot, Institut Paul Simon Laplace, 61 Av du Général de Gaulle, 94010 Créteil, France c Australian Synchrotron, Blackburn Road, Clayton, Victoria 3168, Australia d School of Chemistry, Monash University, Clayton, Victoria 3800, Australia e Chemical Information Systems, Universität Ulm, D-89069 Ulm, Germany b

a r t i c l e

i n f o

Article history: Received 15 October 2014 In revised form 15 December 2014 Available online xxxx Keywords: Trifluoromethyliodide CF3I Coriolis resonance SOLEIL synchrotron Ab initio

a b s t r a c t The high-resolution absorption spectrum of trifluoromethyliodide (CF3I), an alternative gas to chlorofluorocarbons but with potential greenhouse effects, has been recorded at 0.001 cm1 resolution in the 200–350 cm1 region with the Bruker IFS125HR Fourier transform spectrometer at synchrotron SOLEIL. Due to the spectral congestion and the presence of numerous hot bands, the spectra have been recorded at the AILES Beamline facility at SOLEIL either at room temperature using a 150 m optical path length cell or at 163 K using the new LISA-SOLEIL cryogenic cell and at the Australian synchrotron using a flow cooling cell. This enables a detailed analysis of the v3 band at 286.29712(3) cm1 of CF3I. The results of previous microwave measurements in the v3 = 1 and v6 = 1 vibrational states (Walters and Whiffen, 1983; Wahi, 1987) were combined with those of the present infrared analysis of the v3 band to obtain an improved set of parameters for the v3 = 1 (C–I stretching) and v6 = 1 (I–C–F bending) interacting vibrational states accounting for the Coriolis resonance coupling the v3 = 1 energy levels with those of the dark v6 = 1 state (located at 261.5 or at 267.6 cm1). Finally, a first investigation of the 2v3  v3 hot band is also performed. Ó 2015 Elsevier Inc. All rights reserved.

1. Introduction The trifluoroiodomethane molecule (12CF3I), which belongs to the symmetry group C3v, is a prolate symmetric rotor. It has three symmetric vibrations (type A1) and three degenerate (type E) normal vibrations, which are described shortly in Table 1. This molecule was the subject of numerous spectroscopic studies using microwave [1–4], infrared (Fourier transform or tunable diode laser) [5–13], Infrared-Microwave Double Resonance [14], infrared radio frequency double resonance [15], laser microwave double resonance [16], Lamb dip spectroscopy [17], Raman [18,19], or electron diffraction spectroscopy [20] techniques. This molecule was also the subject of harmonic force field calculations [21]. Indeed, this molecule represents quite a challenge for both theoretical and experimental studies for the following reasons:

⇑ Corresponding author.

It is a heavy molecule, and its spectrum is very dense in the infrared region because of the low values of the rotational constants (A  0.1921 cm1, B = 5.0811241  102 cm1). CF3I has several low frequency vibration modes (v6  261.5 cm1 and v3 = 286.303 cm1, for example). Therefore, the rotational structure arising from the relatively strong hot band absorptions complicates the observed pattern of the main cold bands. To exemplify this fact, Table 2 gives the Boltzmann population at T = 296 K and T = 163 K, together with the predicted relative band intensities for the v3 cold band as compared to its first associated hot bands. Because of the existence of a non-zero nuclear spin for the iodine nucleus (I = 5/2), each rotational level of CF3I is split into six sublevels designated by the F quantum number (F = J ± 1/2, J ± 3/2 or J ± 5/2, with F > 0). This quadrupole hyperfine structure is easily observable by microwave techniques in the ground state [1,2,4], and in the 31 and 61 vibrational states [2,3]. Usually, this hyperfine structure gives rise to an increase of the apparent linewidth in infrared spectra [8]. However, due to the large value of

http://dx.doi.org/10.1016/j.jms.2014.12.021 0022-2852/Ó 2015 Elsevier Inc. All rights reserved.

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Table 1 Vibrational fundamental bands of 12CF3I.

a

Mode

Symmetry

Description

Eva

Reference

v1 v2 v3

A1 A1 A1

CF3 stretch CF3 deformation C–I stretch

v4 v5 v6

E E E

CF3 stretch CF3 deformation Bending of C–I against –CF3

1076.0551(1) 743.36912(12) 286.303(8) 286.29712(3) 1187.62771(5) 539.830(7) 261.5(15) 258 267

[12] [8] [6] This work [10] [7] [7] [19] [2]

Vibrational energies (Ev) and band center (v) in cm1.

the quadrupolar constant (eQq = 2147.65 MHz, [2]), this type of structure can also be identified in (v1 = 1; ‘ = 0) energy levels when the spectra are recorded at very high resolution (and/or) for very low temperature, as in a supersonic jet expansion [12,14–17,22]. No significant perturbations were mentioned during the analyses of the v2 [8], and v4 [5,9,10] bands. On the other hand, the (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) energy levels are coupled by a B-type Coriolis resonance [2,6]. In a similar way, the v2 + v3 band has been found to be perturbed by Coriolis resonance coupling (v2 = 1, v3 = 1; ‘ = 0) and (v2 = 1, v6 = 1; ‘ = ±1) [11]. Finally, v5 [7] and v1 [12,15,16] are severely perturbed due to the near proximity of several dark states in the 550 and 1076 cm1 regions, respectively. It is necessary to detail some of the most relevant literature results for the first vibrational states (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1). 1.1. Infrared and Raman studies The vibrational spectrum of CF3I has been investigated at low [23,24] and medium resolution [6,7]. In particular, the band center of the v3 parallel band was estimated at 286.303(5) cm1 and several hot bands were identified [6]. Finally, an estimation of the A3 and B3 rotational constants (v = 3; ‘ = 0) was deduced from band contour investigations of infrared [6] and Raman spectra [19]. For the v6 perpendicular band, which is thought to be about four times weaker than v3 [23] such direct infrared identification was problematic. Person et al. [23] proposed E6  260 cm1 (no quoted uncertainty) for the (v6 = 1; ‘ = ±1) vibrational band center, while the value E6  261.5(15) cm1 was deduced from the identification of several unresolved combination and difference bands [7]. These two values agree rather well with the Raman spectroscopy observations [19] which lead to E6  258 cm1. The Raman spectrum in liquid xenon shows E3  286 cm1 and E6 = 267 cm1 [18]. 1.2. Microwave studies Using radiofrequency–microwave double resonance spectroscopy, the rotational spectrum of CF3I in the v3 = 10 and (v6 = 1; ‘ = ±1) excited vibrational states was investigated by Walters and Whiffen [2] for transitions involving J and F values (F = J ± 1/2, J ± 3/2 J ± 5/2) up to J00 = 40 and 45, for v3 and v6 respectively. This study was complemented by later waveguide Fourier transform microwave measurements [3] of ‘-type doubling transitions in the v6 = 1±1 state. These ‘‘A1 M A2 ‘‘or ‘‘A2 M A1‘‘transitions for (K ‘ = 1) (see the next paragraph) involve J and F values with 40 6 J 6 51 and with DJ = DF = 0 selection rules. Using their v3 and v6 microwave data, two types of calculations were performed by Walters and Whiffen [2]: The first calculation of the rotational transitions within v3 and v6 [2] and of the ‘-type doubling in v6 [3] was performed assuming

that (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) were ‘‘isolated states’’. This means that the Coriolis resonances coupling the energy levels of these two states were not accounted for explicitly. Table 3 describes the theoretical Hamiltonian that they used and for the (v6 = 1; ‘ = ±1) degenerate state this model accounts for the ðD‘ ¼ 1; DK ¼ 1Þ resonances. In addition the quadrupole hyperfine and spin-rotation effects [2,3] were also considered explicitly. The set of rotational, ‘-type doubling and hyperfine parameters obtained in this way for (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) enables satisfactory reproduction of the observed microwave transitions. However the authors had to face two different problems: The values achieved for several centrifugal distortion constants are clearly unreasonable. For example D3JK and D6JK for (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1), respectively differ from the ground state value D0JK , while the of these two parameters is close to the  mean value  v = 0 value D3JK þ D6JK =2  D0JK . Furthermore, it was necessary to include H3JK and H6JK sextic constants in the list of retrieved parameters. These facts indicate the existence of a Coriolis resonance coupling of the (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) energy levels. Assuming that (v6 = 1; ‘ = ±1) is an isolated state, the absolute sign of the Isol q622 parameter involved in the description of the ðD‘ ¼ 1; DK ¼ 1Þ resonance cannot be obtained from the measured v6 M v6 microwave data [2,3]. For rovibrational levels with (K  ‘) = 0, this resonance induces an ‘‘A1 M A2 ‘‘‘-type splitting [25], which can be written as:

Tðv 6 ¼ 1; ‘ ¼ 1; J; K ¼ 1; A1 Þ  Tðv 6 ¼ 1; ‘ ¼ 1; J; K   ¼ 1; J; A2 Þ  ð1ÞJ JðJ þ 1Þ  4 Isol q622 þ ::::

ð1Þ

In Eq. (1), T(v6 = 1; ‘ = ±1; J, K = ±1, A1) and T(v6 = 1; ‘ = ±1); J, K = ±1, A2) denote the term values of the two split sub-components. Since the microwave measurements do not give information on the A1 or A2 (resp. A2 or A1) assignment of the upper (resp. lower) level of the transition, the Isol q622 sign cannot be determined. Using the convention adopted in this work (see Table 3) and in Refs. [26,27] for this operator, the (absolute) value of Isol q622 proposed by Walters and Whiffen [2] is1:

Isol 6   q  ¼ 0:7340ð1Þ MHz 22

ð2Þ

In their second energy levels calculation, Walters and Whiffen [2] accounted for the (v3 = 1; ‘ = 0) M (v6 = 1; ‘ = ±1) Coriolis resonance, using the Hamiltonian matrix described in Table 3. For simplicity, the quadrupole coupling was not considered explicitly during this new calculation, and the observed rotational transitions within (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) were corrected for the hyperfine structure, before their introduction into the least squares fit. The goal of this new calculation [2], which enables the satisfactory reproduction of the measured transitions within the v = 3 and v = 6 states, was to fulfil several conditions: (1) The values of the centrifugal distortion constants for the (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) must not differ significantly from those of the ground state (more explicitly, D3JK  D6JK  D0JK , etc..). In addition, the vibrational dependences of the Av and Bv rotational constants in the (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) vibrational states should remain weak (i.e A6  A3  A0, etc. . .). (2) Walters and Whiffen presumed that the observed ‘-type doubling in the (v6 = 1; ‘ = ±1) state is due (at least partly) to the existence of the Coriolis resonance coupling (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1). More explicitly, for each even 1 Because Walters and Whiffen [2] are using a different convention, their value for  q622 has to be divided by a factor of 4 (q622 (in Ref. [2]), ? q622 4 (in the present convention)).

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Table 2 Positions of the various cold and hot bands in the 34 lm region. Boltzmann population of the lower vibrational state and estimation of their relative intensity for two temperatures (T = 296 K and T = 163 K). Cold band or hot bands

Position

v3 2v3  v3 3v3  2v3 4v3  3v3 v3 + v6  v6 2v3 + v6  (v3 + v6) 3v3 + v6  (2v3 + v6)

286.303 284.55 282.82 281.09 285.80 284.08 282.41

Ref

[6] [6] [6] [6] [6] [6] [6]

f(v3)a

1 2 3 4 1 2 3

T = 296 K

T = 163 K

Pop in%

Rel. Int.a

Pop in%

Rel. Int.a

0.322 0.080 0.020 0.005 0.181 0.046 0.011

1. 0.497 0.186 0.062 0.561 0.284 0.071

0.732 0.059 0.005 – 0.146 0.012 –

1 0.160 0.033 – 0.199 0.033 –

   þ1jq3 jv 3 i2 The relative band intensity depends also of the ratio f ðv 3 Þ ¼ hv 3h1jq  of the square of the element of matrix q3 on the upper and lower state 3 j0i functions. a

J-value (resp. odd J-value), the T(v6 = 1; ‘ = ±1; J, K = ±1, C = A1 (resp. C = A2) is resonating with T(v3 = 1; ‘ = 0; J, K = 0, C = A1 (resp. C = A2). In such conditions, the perturbed sub-component of the v = 6 ‘-type doublet is shifted below the other one, because v3 is located above v6 (E3 > E6).

ðTðv 6 ¼ 1; ‘ ¼ 1; J; K ¼ 1; A1 Þ  Tðv 6 ¼ 1; ‘ ¼ 1; J; K ¼ 1; J; A2 ÞÞ  ð1ÞJ 6 0

ð3Þ

Isol 6 q22

Under this assumption, is negative, and the absolute value of the Cor q622 parameter achieved when accounting for this Coriolis resonance has to be significantly weaker than when this resonance is explicitly considered. Therefore: Isol 6 q22

    6 0 and Isol q622  P Cor q622 

ð4Þ

The energy of the E6 state (v6 = 1; ‘ = ±1) is not known very accurately. To fulfil conditions (1) and (2), Walters and Whiffen did several least squares fit calculations of the v3 and v6 microwave data for different values of the (E3–E6) band center separation. As (E3–E6) is strongly correlated with the values of the Av rotational constants in the (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) states, the calculations were performed for A3 = A6 = A0 fixed values (with v = 3, 6 and v = 0). In such conditions, the value of (E3–E6) which leads to the best fit within the constraints D3J  D6J  D0J and D3JK  D6JK  D0JK ; is WW (E3–E6) = 19 cm1. With E3 = 286.2969 cm1, this is equivalent to: WW

E6 ¼ 267:297 cm1 Cor 6 q22

ð5Þ

and the value of the ¼ 0:031725 MHz. Gerke and Harder [3] performed ‘-type doubling measurements for Ka = 1 rotational transitions in the v6 = 1 vibrational state. In this way the hyperfine structure of CF3I for v6 = 1 was determined. On the other hand, the Coriolis resonance coupling (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) was not considered and the ‘-type doubling effects were explained only through the operator described in Eq. (1), and Gerke and Harder confirmed the Isol q622 value achieved by Walters and Whiffen [2]. The purpose of the present study is to investigate in more detail the rotational structure of the (v3 = 1; ‘ = 0) state. For this purpose, Fourier transform spectra were recorded at high resolution (HR) on the BRUKER 125HR of the synchrotron SOLEIL (Saint Aubin, France) and Australian Synchrotron Source facilities (Clayton, Victoria). In order to separate the contribution of the hot bands the spectra were recorded at room and low temperature. This paper describes first the experimental details for the recorded spectra together with the first HR analysis of the v3 band. Then the results of three energy levels calculations which account for, or ignore the (v3 = 1; ‘ = 0) M (v6 = 1; ‘ = ±1) Coriolis resonance, are compared. For this task, we combine the results of the present infrared analysis on the v3 band with the existing microwave data on the v3 = 1 and

v3-vibrational wave

v6 = 1 states [2,3]. Finally a new investigation of the 2v3  v3 hot band has been performed. 2. Experimental details Owing to their very weak intensities (0.15 and less than 0.05 km/mole, respectively, from Ref. [23]) the t3 and t6 far infrared bands are experimentally challenging, thus no broad band high resolution studies had been undertaken before the advent of synchrotron-based IR facilities. Synchrotron radiation (SR) provides intrinsic advantages (brightness, stability, small beam divergence) which give an important signal-to-noise ratio gain allowing the observation of weak ro-vibrational bands at high resolution in the FIR region [28–31]. In order to update the information on these two weak bands of CF3I, we have recorded the gas phase infrared spectra of CF3I up to 380 cm1 at two temperatures (161 K and 300 K) and different pressures. 2.1. Room temperature data The absorption spectrum of CF3I has been recorded in the 200– 300 cm1 spectral range on the far-infrared beamline AILES at SOLEIL [28]. The average electron beam current for the present results was 400 mA. The spectra were recorded using the AILES Bruker IFS 125HR Fourier transform spectrometer (FTS), fitted with a 6 lm composite silicon-Mylar multilayer beamsplitter and a liquidhelium cooled Si bolometer detector with a 380 cm1 cold cut-off filter and operated without entrance aperture, at the full spectral resolution (0.00102 cm1) given by the 882 cm maximum optical path difference (MOPD) with the Res = 0.9/MOPD Bruker criterion and Boxcar apodization. Averages of 630 interferograms were recorded. The FTS was evacuated down to 0.01 Pa pressure. A White-type multipass absorption cell, made of stainless steel and equipped with polypropylene windows, was connected to the FTS and, for the experiments described here, an optical path of 151.78 m was used [30]. The spectrum was calibrated against known water lines. The CF3I sample was obtained from Sigma Aldrich with purity better than 99%. The absorption cell was evacuated and filled at different pressures, 0.5, 3 and 6 mbar of pure gas at room temperature (at the higher pressure, resolution was limited by collisional broadening). Sample pressure in the cell was measured using a calibrated Pfeiffer capacitive gauge (accuracy of 0.25%) with a full scale reading of 11 mbar. 2.2. Low temperature data Low temperature spectra have also been recorded in the 200–300 cm1 spectral range on the far-infrared beamline located at the Australian synchrotron facility in Clayton, Victoria. A flow

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Table 3 Hamiltonian matrix used to describe the {(v6 = 1; ‘ = ±1), (v3 = 1; ‘ = 0)} resonating states of CF3I. (v6 = 1; ‘ = ±1)

(v3 = 1; ‘ = 0)

(v6 = 1; ‘ = ±1) W(v; ‘ = ±1) c.c. (v3 = 1; ‘ = 0) C(±1; ±1) W(v; ‘ = 0) The W(v; ±‘) are rotational diagonal in v-operators, including both diagonal and non diagonal in ‘ terms. The (D‘; DK) = (0; 0) z-type Coriolis and Anharmonic rotational operator. (1) W(v; ±‘) v-diagonal operators hv ; ‘; JKjHjv ; ‘; JKi ¼ Ev þ Bv JðJ þ 1Þ þ ðAv  Bv ÞK 2  DvJ J 2 ðJ þ 1Þ2  DvJK K 2 JðJ þ 1Þ  DvK K 4 þ HvJ J3 ðJ þ 1Þ3 þ HvJK J2 ðJ þ 1Þ2 K 2 þ HvKJ JðJ þ 1ÞK 4 þ HvK K 6 þLKJ K 4 J2 ðJ þ 1Þ2 þ ½2A1v þ gvJ JðJ þ 1Þ þ gvK K 2 K‘ The diagonal z-Coriolis terms (A1v ) and its expansion (gvJ , etc.) vanish for all ‘ = 0 vibrational states For the (v6 = 1; ‘ = ±1) vibrational state the (D‘; DK) = (±2; ±2) – type operator was taken into account [26,27].a v ;J hv ; ‘ ¼ 1; JKjHjv ; ‘ ¼ 1; JK  2i ¼ 2ðqv22 þ q22 JðJ þ 1Þ þ 12 qv22;K ðK 2 þ ðK  2Þ2 ÞÞ  F 2 ðJ; K; K  2Þ (2) C(±1; ±1) Coriolis off diagonal in v operator:b

hv 6 ¼ 1; ‘ ¼ 1; JKjHjv 3 ¼ 1; ‘ ¼ 0; JK  1i ¼ ðC 0x þ C Jx JðJ þ 1Þ þ C Kx ðK 2 þ ðK  1Þ2 ÞÞF 1 ðJ; K; K  1Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F 2 ðJ; K; K  2Þ ¼ ðJðJ þ 1Þ  KðK  1ÞÞðJðJ þ 1Þ  ðK  1ÞðK  2ÞÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F 1 ðJ; K; K  2Þ ¼ ðJðJ þ 1Þ  KðK  1ÞÞ    1=2

pffiffiffi 1=2 E3 C 0x ¼ 2B1x36 X36 , with X36 ¼ þ EE63 E6 a

Note the different convention used in Ref. [2] for the (D‘; DK) = (±2; ±2) off diagonal operator, and as a consequence for the qWW 22 parameter.

  hv ; ‘ ¼ 1; JKjHjv ; ‘ ¼ 1; JK  2i ¼ 1=2F 2 ðJ; K; K  2Þ  qWW 22 þ ::: : b

The Coriolis operator is set at zero when the Coriolis resonances are not considered explicitly.

cooling cell coupled to the Bruker IFS 125HR high resolution Fourier transform spectrometer was used to record a colder absorption spectrum. The HR125 was fitted with a 6 lm composite siliconMylar multilayer beamsplitter and a liquid-helium cooled Si bolometer detector with a 650 cm1 cold cut-off filter and operated with a 4 mm entrance aperture and 0.002 cm1 spectral resolution The cell was operated in the static mode with nitrogen gas as the coolant and regulated to 161 ± 8 K, for an average pressure of about 2 mbar with a maximum absorption path length of about 30 m. To improve detectivity and resolution, a second spectrum has been recorded at Soleil with a cryostatic cell with longer path length (here 93.17 m) [32] and 0.001 cm1 resolution. The cell temperature was 163 ± 2 K and the gas pressure 1.3 mb. 144 scans were averaged for a measurement time of 9 h.

3. Results of the analysis

positions to obtain a preliminary set of experimental upper state rotational energy levels. These upper state levels were then introduced in a least squares fit to get refined values for the upper states parameters. In this way, an improved synthetic spectrum of the v3 band was generated, which allowed for new assignments, and consequently improved upper state parameters. At a given stage of the assignment procedure, it proved necessary to account also for the (v3 = 1; ‘ = 0) M (v6 = 1; ‘ = ±1) B-type Coriolis resonance as it is described in Table 3. This iterative process was carried out up to a complete assignment of the v3 band. Table 4 describes the results of the present analysis of the v3 band which was clearly pursued in more detail than in Ref. [6]. This is because the spectrum used for the present study was recorded at a higher resolution than in Ref. [6], benefiting from the advantage of synchrotron sources. The Table 4 Statistical analysis of the energy level calculations.

v3 During the whole study, the ground state energy levels were calculated using the ground state parameters resulting from microwave and electron diffraction studies [2,20]. Although it is not possible to determine the quartic centrifugal distortion DK from the present investigation, it has an important effect on the fitted constants. It has already been determined several times from experimental force fields but the obtained values are not consistent as they vary from 0.171 kHz [6] to 0.484 kHz [33]. For this reason, the DK constant has been calculated from an ab initio harmonic force field. The Becke’s three-parameter hybrid exchange functional [34] and the Lee–Yang–Parr correlation functional [35], together denoted as B3LYP was used together with the 6-311G⁄⁄ basis set [36] As a check, the second-order Møller-Plesset perturbation theory (MP2) method [37] was also used. For all calculations, the gaussian03 program was used [38]. Both methods give compatible results, the determined value being: DK = 0.294 kHz. The analysis of the v3 band was initiated by using a predicted line list (positions and relative intensities). For this computation, the (v3 = 1; ‘ = 0) upper state energy levels were generated using the parameters (band centers, rotational constants) quoted in Ref. [2]. In addition, the relative line intensities were computed using standard methods described in Ref. [27]. This predicted line list helped us to perform the first assignments. The calculated ground state energy levels were added to the observed line

2 v3  v3

(A) Range of observed energy levels during the analysis of the 35 lm band of CF3I Number of lines 3073 118 Max J, |K| J 6 115, |K| 6 33 J 6 70, K = 0 Number of levels 1738 58

(B) Statistical analysis of the results of the energy level calculation 1 – The (v3 = 1; ‘ = 0) infrared energy levels Number of levels 1738 Number of levels Cal n°1 Cal n° 2 50.5% 53.7% 0:0 6 d 6 1  104 cm1

Cal n° 3 54.1%

1  104 6 d 6 2  104 cm1

25.0%

21.8%

21.7%

2  104 6 d 6 4  104 cm1

17.1%

17.4%

17.4%

4:104 6 d 6 1:3104 cm1 Standard deviation (in cm1) d ¼ jEobs  Ecalc j

7.4%

7.1%

6.8%

0.21  103

2 – Microwave rotational transitions within the (v6 = 1; ‘ = ±1) and/or (v3 = 1; ‘ = 0) vibrational states Cal n°1 Cal n°2 Cal n°3 Vibration Number of rotational transitions 0:0 6 d 6 0:1 MHz 0:1 6 d 6 0:2 MHz 0:2 6 d 6 0:4 MHz 0:4 6 d 6 1:0 MHz Mean deviation (in MHz)

v3

v3

v6

v3

v6

57 71.9% 22.8% 5.3% 0 0.104

57 77.2% 19.3% 3.5% 0 0.134

93 68.8% 19.4% 8.6% 3.2%

57 79.0% 17.5% 3.5% 0 0.140

93 71.0% 12.9% 12.9% 3.2%

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accuracy associated to a given infrared v3 = 1 energy level ranges from 0.0002 to 0.0005 cm1, depending if the involved infrared transitions are isolated or blended lines, respectively. On the other hand, it was unfortunately not possible to assign any lines from the dark v6 band. In spite of relatively high pressures (up to 6 mbars) we failed to detect the v6 band. Considering the experimental conditions of the recording of the spectrum used for the present study (see the previous paragraph), we presume that the intensity of the v6 band is significantly weaker than one should expect from the conclusions of Person et al [23] which stated the v6 and v3 bands are in the intensity ratio of about R(v6/ v3)  1=4 . A rough estimate from our data suggests that the v6 band intensity should be at least 20 times smaller than that of v3, already very small (0.15 km/mole).

4. Energy levels calculations 4.1. The v3 cold band and the rotational transitions within (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) The energy levels calculation of the (v3 = 1; ‘ = 0) state was performed combining the infrared data achieved during the present study (experimental energy levels) with the microwave data existing in the literature for the rotational transitions within (v3 = 1; ‘ = 0) [2] and (v6 = 1; ‘ = ±1) [2,3] (see Table 4A). As was the case during previous investigations [2,3], the quadrupole coupling was not considered explicitly, and the observed rotational transitions within (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) were corrected for the hyperfine structure, before their introduction in the least squares fit. For this preliminary task, we used the method described in Ref. [39] and the (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) quadrupole hyperfine and spin-rotation constants quoted in Refs. [2,3], respectively. The uncertainty associated to these corrected microwave data is estimated to be between 10 and 300 kHz depending on the recommendation of the authors, and of the complexity of the hyperfine structure. Then, the v3 = 1 infrared energy levels resulting from this analysis together with the (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) ‘‘corrected’’ microwave data [2,3] were introduced in a least squares fit calculation at their estimated uncertainty (see the text above) in order to determine the upper set parameters for the (v3 = 1; ‘ = 0) and (v6 = 1; ‘ = ±1) interacting states. Three types of calculations, here referred as ‘‘Calc n°1’’, ‘‘Calc n°3’’, and ‘‘Calc n°2’’ were performed. The first calculation was performed for (v3 = 1; ‘ = 0) considered as an ‘‘isolated state’’, while the two others accounted explicitly for the (v3 = 1; ‘ = 0) M (v6 = 1; ‘ = ±1) resonance. As demonstrated in Table 4, these three calculations lead to rather similar results in terms of the ‘‘observed- calculated’’ differences both for the (v3 = 1; ‘ = 0) infrared energy levels and for the microwave transitions within (v3 = 1; ‘ = 0) (Table 4A and B). This is also the case for the microwave data within (v6 = 1; ‘ = ±1) for ‘‘Calc n°3’’ and ‘‘Calc n°2’’. The parameters resulting from these calculations (E3 vibrational energy, v = 3 and v = 6 rotational and centrifugal distortion constants, and parameters involved in the Coriolis resonance) are quoted together with their associated uncertainties in Table 5A–C. It is interesting to compare the values delivered for the parameters during these three calculations, which may differ significantly depending on the calculation. The values delivered by the three calculations for the A3 rotational constant are very similar (A3 = 5758.580 to 5758.634 MHz, corresponding to aA3 ¼ A0  A3 ¼ 1:418ð3Þ MHz) proving that A3 is only weakly affected by the v = 3 M v = 6 Coriolis resonance. This aA3 differs from the rough estimation provided by a band contour study (aA3 ¼ 0:60ð30Þ MHz in Ref. [6]).

5

4.1.1. Calculation n°1: (v3 = 1; ‘ = 0) considered as an ‘‘isolated state’’ As was the case in Ref. [2] it was necessary to adjust a large number of constants (nine in our case) to reproduce the v3 = 1 experimental data (Table 5A). This set of parameters include high order centrifugal distortion constants (up to the LKJ constant), and this is because the Coriolis resonances perturbing (v3 = 1; ‘ = 0) were not accounted for explicitly. Therefore, as compared to Calc. 2 and 3, the price to pay for not considering explicitly this resonance is that nine additional v6 = 1 parameters (see Table 2 of Ref. [2]) are required to reproduce the microwave data within (v6 = 1; ‘ = ±1). 4.1.2. Calculation n°2 and n°3 These two calculations, ‘‘Calc. n°2’’ and ‘‘Calc. n°3’’ during which the (v3 = 1; ‘ = 0) M (v6 = 1; ‘ = ±1) Coriolis resonance was accounted for, differ mainly by the (v6 = 1; ‘ = ±1) band center which was fixed to the values E6 = 267.65 cm1 (Calc. n°2) and E6 = 261.5 cm1 (Calc. n°3) proposed by Walters and Whiffen [2] and Bürger et al. [7], respectively (Table 5B). As in Ref. [2] we had to face the problem of the existence of large correlations between the adjustable parameters. For example the (Af)6 parameter, which clearly cannot be determined confidently, was constrained to the value ((Af)6 = 787.5 MHz) achieved in Ref. [2]. We initiated ‘‘Calc. n°2’’ by setting the parameters to the values proposed by Walters and Whiffen [2], and refining only the v3 = 1 vibrational energy and the A and B rotational constant (E3 and A3 and B3). As expected, the v3 = 1 infrared energy levels involving high values of the J and K quantum numbers could not be reproduced satisfactorily. This is also the case for the microwave data on ‘-doubling splittings in v6 = 1 [3] for which the calculation was unsatisfactory for transitions involving high J values. Therefore, it was clear that the Coriolis resonance was not modelled correctly. For this reason, we considered higher order terms in the expansion of the Coriolis operator (see Table 3), and 11 constants, listed in Table 5 were determined. It appeared that the zero order term q622 involved in the description of the (D‘; DK) = (±2; ±2) – type resonance could not be determined and only higher order terms were considered in the calculation. Finally, the A6 rotational constant for (v6 = 1; ‘ = ±1) state, which could not be determined was maintained fixed at the (v3 = 1; ‘ = 0) value (i.e. A3 = A6). The calculation ‘‘Calc. n°3’’ was performed in order to test the reliability of the v6 = 1 band center set at E6 = 261.5 cm1 in Ref. [7]. Table 5 lists the 11 parameters which had to be considered during the least squares fit calculation. During this calculation, the A6 rotational constant and the q622 parameter had to be refined during the least squares fit calculation. It is necessary to compare the values achieved for some parameters during ‘‘Calc n°2’’ and ‘‘Calc n°3’’. 4.1.3. Coriolis resonance Because the v6 band center was set at two different values, for the first parameters involved in the description of the Coriolis operator (see Table 3) different values were obtained for C 0x (see Table 5C) and, consequently also for the 1x36 unitless parameter:

1x36 ¼ 0:405627ð15Þ ðCalc: n 2Þ and 1x36 ¼ 0:539087ð42Þ ðCalc: n 3Þ

ð6Þ

4.1.4. The v6 = 1 A6 rotational constant In ‘‘Calc. 3’’, A6 differs from its v3 = 1 counterpart (A3), while during ‘‘Calc. 2’’ calculation, A6 had to maintained at the A3 value. Let

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Table 5 Vibrational energies, rotational and interaction constants for the ground state and for the {(v3 = 1; ‘ = 0)}, and {(v3 = 1; ‘ = 0), (v6 = 1; ‘ = ±1)}, and {(v3 = 2; ‘ = 0)}, vibrational states of CF3I.j

|0> (A) Vibrational band centers, rotational constants for isolated states Ev 0 A 5759.01a B 1523.28267b DK  103 0.294c 0.9925b DJK  103 DJ  103 0.16462b HK  109 HKJ  107 HJK  108 LKJ  1011

Calc n° 1 (v3 = 1 ; ‘ = 0)

Calc n°4 (v3 = 2 ; ‘ = 0)

286.29694(6) 5758.6354(140) 1522.31695(62) 0.8557(180) 0.57112(490) 0.1705495(510)

570.8429(2) 5758.25 1521.499(2) i i i

0.9981(670) 0.1707(420) 0.2539(640)

i i i

Calc n° 2 (v3 = 1 ; ‘ = 0)

Calc n° 3 (v3 = 1 ; ‘ = 0)

(B) Vibrational band centers, rotational constantsj for the {(v = 3; ‘ = 0), (v = 6; ‘ = ±1)} interacting states Ev 286.29712(3) 267.65f (Af) 787.5h 0 q622 0.3237(200) q6;J  106

(v3 = 1 ; ‘ = 0)

(v6 = 1; ‘ = ±1)

286.29713(5)

261.5e 787.5h 0.23992(150) 0.3079(140)

22

3 q6;K 22  10 A B DK  103 DJK  103 DJ  103

Constants

0.1069(140) 5758.58175(320) 1519.3811454(290) 0.294d 0.94497(420) 0.16462d

5758. 58175g 1522.077878(100) 0.294d 1.02069(330) 0.16462d

5758.57992(480) 1518.42181(610) 0.294d 0.94198(260) 0.16462d

Calc. n°2 Values

5782.48471(240) 1522.55761(310) 0.294d 1.02228(150) 0.16462d Calc. n°3 Values

(C) Interaction parametersj for CF3I (v6 = 1; ‘ = ±1) M (v3 = 1 ; ‘ = 0) with ðD‘; DKÞ ¼ ð1; 1Þ selection rule 903.7567(340) C0

1201.113(940)

C Jx  10þ3

0.79255(410)

1.55868(720)

C Kx  10þ2

0.4767(350)

0.5831(180)

x

i

Constants fixed to the (v3 = 1; ‘ = 0) values. a Ref. [20]. b Ref. [2]. c Ab initio (This work). d Fixed to the ground state value. e E6 fixed to Ref. [7]. f E6 fixed to Ref. [2]. g The A6 rotational constant is held fixed to the A3 value. h (Af) fixed to the Ref. [2]. j The four calculations (‘‘Calc n°1 to n°4) are described in the text. The vibrational band centers are in cm1. All other constants are in MHz. The quoted errors are one standard deviation.

us recall, however, that the v6 infrared band could not be observed during this work. Therefore the values quoted for A6 in Table 5 are not fully reliable. 4.1.5. Centrifugal distortion constants Among the centrifugal distortion parameters, only the DJK were adjusted, and the values obtained for the D3JK and D6JK do not differ significantly when comparing ‘‘Calc. n°2’’ and ‘‘Calc. n°3’’. As a matter of conclusion, two reasons prompt us to prefer ‘‘Calc. n°2’’ to ‘‘Calc. n°3’’: (1) ‘‘Calc. n°2’’ necessitates only 11 flexible parameters instead of 12 for ‘‘Calc. n°3’’. (2) The q622 parameter could not be determined during ‘‘Calc. n° 6;J 3’’, and the higher order q6;K 22 and q22 parameters are rather small. This means that most of the ‘ doubling effects observed for v6 = 1 energy levels with K = 1 find their existence through a Coriolis resonance coupling for J = even and C = A1 (resp. J = odd, C = A2) the [J, K = 1, C] (v6 = 1;

‘ = ±1) energy levels with those of [J, K = 0, C] (v3 = 1; ‘ = 0). To give an order of magnitude, the (%(J)) percentage of mixing of these resonating wave functions grows with J from %(J) = 1.3% for J = 50 up to %(J) = 4.5 for J = 95. However, we can state that only the observation at high resolution of the v6 band in infrared spectra will allow the final choice between ‘‘Calc. n°2’’ and ‘‘Calc. n°3’’. 4.2. The 2v3  v3 first hot band Among the various hot bands observable in the spectrum, the structure of the 2v3  v3 was easily observable. We therefore performed the assignment of the QP(J, K) and QR(J, K) peak series for K = 0. The calculated (v3 = 1; ‘ = 0) energy levels were added to the observed line positions to obtain the upper state rotational energy levels (v3 = 2; ‘ = 0) for K = 0. For this excited state, we use the notation ‘‘v = 33’’ for simplicity. The calculation of the E33 band center and of B33 rotational constants for (v3 = 2; ‘ = 0) state

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were performed on these ‘‘experimental energy levels’’ assuming for the A33 rotational constant an extrapolated value deduced from the ground and the (v3 = 1; ‘ = 0) values:

A33 ¼ 2  A3  A0

ð7Þ

The centrifugal distortion constants were fixed to the values achieved for (v3 = 1; ‘ = 0) during ‘‘calculation n° 1’’. The results of the 2v3  v3 assignment and the values of the E33 and B33 rotational constants (calculation n° 4) achieved in this way are quoted in Tables 4A and 5A, respectively. It is clear that the B33 rotational constant varies only marginally from the value Pred B33  1521.35 MHz which can be calculated from the B0 (ground state) and B3 ((v3 = 1; ‘ = 0) during ‘‘calculation n° 1’’) values using the following expression: Pred

B33  2  B3  B0

ð8Þ

7

5. Modelling of the experimental spectra and conclusions Using the theoretical methods described in this work for the positions and in Ref. [27] for the intensities, several lists of line positions and intensities was generated for the v3 and 2v3  v3 bands. These lists were used to compare the observed and calculated spectra. It is necessary to detail the parameters which were used for the line positions: For the 2v3  v3 band, the parameters used in Table 5A were used for the v3 = 2 and v3 = 1 vibrational states. Two line lists were generated for the v3 band. The first one used, for the computation of the (v3 = 1; ‘ = 0) M (v6 = 1; ‘ = ±1) interacting energy levels, the parameters achieved during this work during the calculation ‘‘Calc. 2’’ and quoted in Table 5B and C. It is clear, however, that any other set of v3 = 1 parameters (‘‘Calc. 1’’, ‘‘Calc. 2’’, or ‘‘Calc. 3’’) will lead to similar results, as far as the infrared energy levels are concerned (see the statistical analysis given in Table 4B). The second one used the parameters quoted for the (v3 = 1; ‘ = 0) M (v6 = 1; ‘ = ±1) interacting energy levels in Table 3 of Ref. [2]. For the purpose of this computation, the value E3 = 286.2974 cm1 was set for the v3 = 1 vibrational energy.

Fig. 1. Overview of the v3 band of CF3I recorded on the synchrotron SOLEIL in the following experimental conditions (T = 163 ± 2 K, path length = 93.17 m, Pressure = 1.3 mb). The line by line calculations are for the v3 and 2v3  v3 cold and first hot bands, respectively. The triangle indicates the position of the v3 + v6  v6 hot band.

Fig. 3. Detailed view of the CF3I spectrum at 163 K in the 286 cm1 spectral region. In this spectral region the Q branches from the v3 and 2v3  v3 bands are indicated. Other hot bands were assigned by Burczyk and Bürger [7] (see Table 2).

Fig. 2. Detailed view of the CF3I spectrum at 163 K in the 278.8 cm1 spectral region giving portions of the P- branches of the v3 and 2v3  v3 bands. From the top to the bottom, the traces give (i) the calculated line list for the 2v3  v3 band (ii) the calculation (‘‘Calc n°2’’) performed for the v3 band using the parameters generated during this study (iii) the observed spectrum (iv) the calculation (W.W.) generated using the parameters from Ref. [2]. The agreement between the observed and calculated spectra is significantly better for ‘‘Calc n°2’’ than when using the parameters from Ref. [2] (WW).

Fig. 4. Detailed view of the CF3I spectrum at 163 K in the 287.8 cm1 spectral region. Contributions from the R- branches of the v3 and 2v3  v3 bands are indicated. The J0 assignments in the upper states are also given.

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References

Fig. 5. Detailed view of the CF3I spectrum at 163 K in the 292 cm1 spectral region which corresponds to the QR(J00 = 56) stack of the R-branch of the v3 band. The contribution due to the 2v3  v3 band is rather weak in this spectral region. The upper and lower traces are calculations performed for the v3 band using the parameters generated during this study (‘‘Calc n°2’’) and in Ref. [2] (W.W.). On each of these traces, the K assignments are given, and the line intensities are twice stronger for K values with |K| = 3n than for K = (3n ± 1). The agreement between the observed and calculated spectra is significantly better for ‘‘Calc n°2’’ than when using the parameters from Ref. [2].

Fig. 1 gives an overview of this comparison in the whole 275– 297 cm1 spectral region, while Figs. 2–5 gives detailed views of the spectrum in the P, Q and R branches. It is clear that an excellent agreement was achieved between the observed and calculated spectra when using the parameters generated during this work for the v3 and 2v3  v3 bands. Figs. 2 and 5 also detail part of the P- and R-branches for transitions involving rather high rotational quantum numbers. It is clear that the parameters achieved by Walters and Whiffen [2] are not able to provide a reliable model of the v3 band in these parts of the spectrum, illustrating the pertinence of the present study. 6. Conclusion Using spectra recorded at SOLEIL and the Australian synchrotron, we performed the first detailed infrared analysis of the v3 and 2v3  v3 bands of the CF3I molecule. These infrared results were combined with those achieved during previous microwave studies involving the (v3 = 1; ‘ = 0) M (v6 = 1; ‘ = ±1) interacting states. In this way it was possible to detail the effect of the Coriolis resonance coupling the v3 = 1 energy levels with those from the v6 = 1 state, depending on the location of this dark state (at  261.5 or at 267.6 cm1). Finally, a first investigation of the 2v3  v3 hot band was also performed.

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