Diode laser spectroscopy of the ν8 band of the SF5Cl molecule

Spectrochimica Acta Part A 60 (2004) 3403–3412

Diode laser spectroscopy of the ν8 band of the SF5Cl molecule W. Raballand, N. Benoit, M. Rotger∗ , V. Boudon Laboratoire de Physique de l’Université de Bourgogne, UMR CNRS 5027, 9 av. Alain Savary, B.P. 47870, F-21078 Dijon Cedex, France Received 30 September 2003; accepted 10 November 2003

Abstract Diode laser spectra of SF5 Cl have been recorded in the ν8 band region at a temperature of ca. 240 K, a pressure of 0.25 mbar and an instrumental bandwidth of ca. 0.001 cm−1 . Four regions have been studied: a first one in the P-branch (906.849–907.687 cm−1 ), a second one in the Q-branch (910.407–910.944 cm−1 ), and two other ones in the R-branch (913.957–914.556 and 917.853–918.705 cm−1 ). The whole ν1 /ν8 dyad of SF5 35 Cl has been previously recorded in the group of Professor H. Bürger in Wuppertal, thanks to a Fourier transform infrared spectrometer [J. Mol. Spectrosc. 208 (2001) 169]. These data have thus been combined with our diode laser ones in the aim of refining the analysis. We used an effective Hamiltonian developed up to the fourth order and a set of programs called C4v TDS. One thousand three hundred and forty-six transitions for ν1 , 495 (FTIR: 351; diode laser: 144) transitions for ν8 , and 406 ground state combination differences have been assigned and fitted. A global fit has been obtained with a rms of 0.00081 cm−1 for the ν1 band, 0.0012 cm−1 for the FTIR data of the ν8 band, 0.00055 cm−1 for the diode laser data of this same band, and 0.00064 cm−1 for the ground state. It appears that more data (for instance, using a supersonic jet) are still necessary to obtain a completely satisfactory analysis of the ν8 region. © 2004 Elsevier B.V. All rights reserved. Keywords: Symmetric top molecules; Tensorial formalism; Vibrational extrapolation; SF5 Cl

1. Introduction The photodissociation of a SF5 Z (Z = Cl, Br, etc.) molecule leads to the SF5 radical. This one is also a decomposition product of sulphur hexafluoride and is therefore involved in various industrial processes in electronics [1] and chemistry [2]. Moreover, a derivated molecule, namely SF5 CF3 , has been recently identified in the atmosphere as a potent greenhouse gas [3]. In order to better understand and to model photodissociative processes, the knowledge of the infrared spectra of SF5 Z molecules is needed. However, high-resolution spectroscopy of XY5 Z molecules with C4v symmetry is quite unexplored both in infrared absorption and in Raman scattering. In the case of SF5 Cl, microwave rotational spectra have been obtained many years ago by Jurek and co-workers [4–11] and, in the literature, one only finds low-resolution infrared and Raman spectra [12–15]. To achieve the analysis of rovibrational spectra of these molecules, we have proposed a new tensorial formalism [16,17] and developed a software called C4v TDS [18] adapted to the case of C4v symmetric tops. ∗

Corresponding author. Fax: +33-3-80-39-59-71. E-mail address: [email protected] (M. Rotger).

1386-1425/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2003.11.042

The ν1 /ν8 dyad of SF5 Cl has been chosen as a first test to validate our theoretical model. A preliminary analysis in the region of the ν1 /ν8 dyad of SF5 35 Cl has been previously performed in [19], thanks to the data obtained in the group of Professor H. Bürger. The Fourier transform spectra were recorded in Wuppertal, in the 650–960 cm−1 region at a temperature of 203 K, a pressure of 0.2 mbar and an instrumental bandwidth of 0.002 cm−1 . One thousand three hundred and forty-six transitions for ν1 , 351 transitions for ν8 , and 406 ground state combination differences were assigned and fitted. A global fit was obtained with a rms of 0.00082 cm−1 for the ν1 (a1 ) band, of 0.0011 cm−1 for the ν8 (e) band, and of 0.00064 cm−1 for the ground state. However, the analysis of the very dense ν8 region was still very unsatisfactory. Diode laser spectra of natural abundance SF5 Cl in several regions between 910 and 920 cm−1 have been recorded in Dijon. Using the tensorial formalism and the C4v TDS software developed in Dijon for XY5 Z molecules, we were able to re-analyse the ν1 /ν8 dyad of SF5 35 Cl by combining the previous data to our diode laser ones. We have determined again several parameters up to the fourth order that, in particular, enable a slightly better reproduction of the ν8 (e) perpendicular band than the one obtained in [19] even if, as

3404

W. Raballand et al. / Spectrochimica Acta Part A 60 (2004) 3403–3412

we will see, further experiments will be necessary to obtain fully satisfactory simulations. The experimental details concerning the recording of absorption spectra are given in Section 2. The theoretical model based on the tensorial formalism is recalled in Section 3 and the results concerning the ν1 /ν8 dyad analysis are given in Section 4.

Table 1 Experimental conditions FTIR [19]

Diode laser (this work)

203 0.2 20 650–960 0.002 277 CO2 lines

241 0.15 50 900–920 0.001 Average over 30 SiH4 lines

2. Experiment

Temperature (K) Pressure (mbar) Absorption length (cm) Recorded domain (cm−1 ) Resolution (cm−1 ) Number of scans Calibration

The ν8 band has been recorded in two different ways: (i) a Fourier transform infrared spectrum [19] has been obtained previously for SF5 35 Cl in the 650–960 cm−1 region in Wuppertal with an instrumental bandwidth of 0.002 cm−1 and with the experimental conditions listed in Table 1; (ii) diode laser spectra of natural abundance SF5 Cl have been recorded with an instrumental bandwidth of ca. 0.001 cm−1 . The gas cell has been cooled thanks to the circulation of a cryogenic fluid and the lowest temperature obtained with this set-up was about 240 K (see Fig. 1). Fig. 2 describes schematically the diode laser experiment. We use a LN2 -cooled lead salt diode laser and HgCdTe detectors. The diode laser frequency has been scanned by modulating its current with a triangle signal for different

fixed temperatures. Table 1 summarises the experimental conditions. The frequency calibration of the diode laser absorption spectra has been realised as follows. First, the absorption spectrum has been recorded simultaneously with the transmission fringes of a Fabry–Perot etalon consisting of two germanium windows separated by a 42 cm distance. Then the spectrum of a reference gas (SiH4 ) in a 20 cm long cell has been recorded, again together with etalon fringes. Etalon fringes have been used to linearise the frequency scale, while the SiH4 lines gave the absolute calibration. We have chosen natural abundance SiH4 as a reference gas for two reasons. First, this gas presents absorption lines in the 920 cm−1 re1 External jacket

7

2 Internal jacket

6 6

3 Cryogenic oil 4 Primary vacuum

7

5 Gas cell 6 KBr windows

1

2

3

4

7 ZnSe windows

5

Fig. 1. The gas cell.

HgCdTe

DATA ACQUISTION HARDWARE

COMPUTER

FABRY-PEROT CAVITY

GAS CELL

HgCdTe

MEASUREMENTS AND ABSOLUTE FREQUENCY CALIBRATION

RELATIVE FREQUENCY CALIBRATION

MONOCHROMATOR

DIODE LASER

Fig. 2. The experimental set-up.

W. Raballand et al. / Spectrochimica Acta Part A 60 (2004) 3403–3412

gion, and secondly the frequencies of these lines are well known from the STDS database [20].

3. Theory The theoretical model described further to develop the Hamiltonian operator is based on the tensorial formalism and vibrational extrapolation methods used in Dijon. These methods have already been explained, for example, in [20–23]. We only recall here the basic principles and their applications to the case of XY5 Z molecules [16,17] belonging to the C4v group. The model is based on the idea of considering XY5 Z molecules as distorted XY6 molecules, by substitution of one ligand. Practically, this means that we start from the O(3) ⊃ Oh formalism used for octahedral species [21] and make a symmetry reduction (or reorientation) into the C4v group. This procedure has been detailed in [16]. In the following, all the C4v oriented tensor operators will be denoted in the form: (... ,Γ,Γ˜ )

Tσ˜

,

3405

Ω(K ,nΓg ,Γ˜ )Γ1µ Γ2µ Γvg

g In this equation, the t{ns }{m s}

˜ RΩ(Kg ,nΓg ,Γ )

are the parame-

˜ % V Γ1µ Γ2µ (Γvg ,Γ ) {ns }{ms }

and are ters to be determined. rotational and vibrational operators of respective degree Ω (maximum degree in the rotational angular momentum components Jx , Jy and Jz ) and Ωv (degree in creation and annihilation operators). Their construction is described in [23]. The order of each individual √ term√is Ω + Ωv − 2. β is a numerical factor equal to [Γ1 ](− 3/4)Ω/2 if (Kg , nΓg ) = (0, 0A1g ) and equal to 1 otherwise. Such an Hamiltonian development scheme enables the treatment of any polyad system. In this work, we will use only the two following effective Hamiltonians: • The ground state effective Hamiltonian:

GS

H GS = H{GS} .

(4)

• The ν1 /ν8 stretching dyad effective Hamiltonian:

ν /ν 

ν /ν 

1 8 H ν1 /ν8  = H{GS} + H{ν11/ν88} .

(5)

Recalling that the ν1 /ν8 dyad comes from the splitting of the ν3 band of the XY6 “parent” molecule; thus, H{ν1 /ν8 } Γ

Γ

1µ 2µ is constructed using % V{3}{3}

+(F ) a3 1u

(Γvg ,Γ˜ )

vibrational operators

(F ) a3 1u

Γ (=A1τ , A2τ , Eτ , F1τ , F2τ ; τ = g or u) and Γ˜ (=a1 , a2 , b1 , b2 , e) denoting Oh and C4v irreducible representations (irreps), respectively. This way of handling XY5 Z molecules has some consequences on the labelling of Hamiltonian and transition moment parameters. The energy level labels are also different from the “usual” ones used in the standard treatment of symmetric tops, as it will be detailed further. If we consider a XY5 Z molecule for which the vibrational levels are grouped in a series of polyads designed by Pk (k = 0, . . . , n), P0 being the ground state (GS), the Hamiltonian operator can be put in the following form (after performing some contact transformations):

with

H = H{P0 ≡GS} + H{P1 } + · · · + H{Pk } + · · ·

v1 , . . . , v6 are vibration quantum numbers for the XY6 “parent” molecule. C˜ v is the vibrational symmetry in C4v :

+ H{Pn−1 } + H{Pn } .

(1)

Terms like H{Pk } contain rovibrational operators which have no matrix elements within the Pk
P 

P 

P 

n H Pn  = P Pn  HP Pn  = H{GS} + H{P1n} + · · · + H{Pkn}

P 

P 

n n + · · · + H{Pn−1 } + H{Pn } .

(2)

The different terms are written in the form: H{Pk } =




Ω(K ,nΓg ,Γ˜ )Γ1µ Γ2µ Γvg

g t{ns }{m s}

all indices

(a1 )  Γ Γ2µ (Γvg ,Γ˜ ) ˜ × β RΩ(Kg ,nΓg ,Γ ) ⊗% V{n1µ . s }{ms }

(3)

which involve and creation and annihilation operators. The matrix elements are calculated in the coupled basis: ˜

˜

˜ (C)

|[Ψr(J,nCr ,Cr ) ⊗ Ψv(Cv ,Cv ) ]σ˜ , ˜

(6)

(A )

|Ψv(Cv ,Cv )  = |[[[[Ψv1 1g ⊗ Ψv(l22 ,C2 ) ⊗ Ψv(l33 ,n3 C3 ) ](C23 ) ⊗ Ψv(l44 ,n4 C4 ) ](C234 ) ⊗ Ψv(l55 ,n5 C5 ) ](C2345 ) ˜

⊗ Ψv(l66 ,n6 C6 ) ](Cv ,Cv ) .

˜

˜ (Cv ) . D(Cv ) ↓ C4v ⊃ D

(7)

(8)

Expressions of the matrix elements are given in [17]. All ˜ labels the rovibrational levels are described by (J, α, ˜ C) where α˜ is a numbering index for levels that have the same C4v symmetry within a J block. This labelling is related to our group chain choice which considers XY5 Z molecules like near-spherical tops. In this way, the usual K quantum number is hidden and related to the C˜ symmetry. So, the K values do not appear explicitly in our labels, and the 0K nomenclature does not occur in our transition labels. The strength of a transition between the molecular rovi˜ i (with energy Ei ) and Φ ˜ f (with energy brational states Φ Ef ) is calculated using:
˜ i |µ ˜ f |2 , | Φ ˜ Z |Φ (9) Sif = Kif gi e−hcEi /kT Mi ,Mf

3406

W. Raballand et al. / Spectrochimica Acta Part A 60 (2004) 3403–3412

where Kif is a numerical coefficient and gi the spin statisti˜ i . The values of spin statistical weights cal weight of state Φ in XY5 Z (C4v ) molecules, with Y ligands having spin 21 , are listed in Table 2. The sum is realised over the spherical components Mi and Mf of the two states in the laboratory-fixed frame (LFF). In order to calculate transition intensities, we

Table 2 Spin statistics weights C˜ gi

a1 12

Fig. 3. The ν1 parallel band: experiment and simulation.

Fig. 4. The ν8 perpendicular band: experiment and simulation.

a2 12

b1 8

b2 8

e 12

W. Raballand et al. / Spectrochimica Acta Part A 60 (2004) 3403–3412

developed the dipole moment operator through the zeroth order only using the methods explained in [17]. In the present study, we only consider relative intensities.

4. Analysis As explained earlier, we use a dyad model in which the ν1 and ν8 bands are strongly linked to each other. A first analysis of this dyad in the ν1 region (840–870 cm−1 ) and in the ν8 region (900–920 cm−1 ) has been performed thanks to

3407

the data obtained by FTIR spectroscopy (see [19] and Figs. 3 and 4). This work has led to a global fit of the dyad and of the ground state by determining many effective rovibrational parameters of our model. So in the aim of improving the simulations, we have combined the diode laser data to the FTIR ones in a new global fit. For this, H{GS} has been developed to the second order and H{ν1 /ν8 } to the fourth order. In preceding works, we have already determined which parameters could be fitted with only the ν1 band data. These parameters have A1g vibrational symmetry and are marked

Table 3 Effective Hamiltonian parameters for the global fit of the ν1 /ν8 dyad Level

Order

Ω(Kg ,nΓg ,Γ˜ )Γ1µ Γ2µ Γvg

Ω(Kg , nΓg , Γ˜ ) v=0

v=1 c

c c

c c

c c

0 0 2 2 2 2 0 0 1 1 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

Value (cm−1 )a

Parameter t{ns }{ms } 2(0, 0A1g , a1 ) 2(2, 0Eg , a1 ) 4(0, 0A1g , a1 ) 4(2, 0Eg , a1 ) 4(4, 0A1g , a1 ) 4(4, 0Eg , a1 ) 0(0, 0A1g , a1 ) 0(0, 0A1g , a1 ) 1(1, 0F1g , a2 ) 1(1, 0F1g , e) 2(0, 0A1g , a1 ) 2(0, 0A1g , a1 ) 2(2, 0Eg , a1 ) 2(2, 0Eg , a1 ) 2(2, 0Eg , b1 ) 2(2, 0F2g , b2 ) 2(2, 0F2g , e) 3(1, 0F1g , a2 ) 3(1, 0F1g , e) 3(3, 0F1g , a2 ) 3(3, 0F1g , e) 3(3, 0F2g , e) 4(0, 0A1g , a1 ) 4(0, 0A1g , a1 ) 4(2, 0Eg , a1 ) 4(2, 0Eg , a1 ) 4(2, 0Eg , b1 ) 4(2, 0F2g , b2 ) 4(2, 0F2g , e) 4(4, 0A1g , a1 ) 4(4, 0A1g , a1 ) 4(4, 0Eg , a1 ) 4(4, 0Eg , a1 ) 4(4, 0Eg , b1 ) 4(4, 0F1g , e) 4(4, 0F2g , b2 ) 4(4, 0F2g , e)

{ns } 000000 000000 000000 000000 000000 000000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000

Γ1µ A1g A1g A1g A1g A1g A1g F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u

{ms } 000000 000000 000000 000000 000000 000000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000 001000

GSCD: 406 assigned lines, Jmax =79, σ = 0.64 × 10−3 cm−1d ν1 : 1346 assigned lines, Jmax =79, σ = 0.81 × 10−3 cm−1d ν8 by FTIR: 351 assigned lines, Jmax =79, σ = 1.20 × 10−3 cm−1d ν8 by diode laser: 144 assigned lines, Jmax =79, σ = 0.55 × 10−3 cm−1d a b c d

One standard deviation in parentheses. Fixed. “ν1 ” parameters. Root mean square.

Γ2µ A1g A1g A1g A1g A1g A1g F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u F1u

Γvg A1g A1g A1g A1g A1g A1g Eg A1g F1g F1g A1g Eg A1g Eg Eg F2g F2g F1g F1g F1g F1g F2g A1g Eg A1g Eg Eg F2g F2g A1g Eg A1g Eg Eg F2g F2g F2g

“Usual” notation [24]

0.7074100(96) × 10−1 0.605373(36) × 10−2 0.1607(18) × 10−7 −0.5780(43) × 10−8 0.854(28) × 10−9 0.0b 0.3678797(14) × 102 0.89229893(13) × 103 0.148420(10) −0.18256(27) −0.11760(14) × 10−3 −0.8352(45) × 10−4 −0.77957(92) × 10−4 −0.7877(20) × 10−4 −0.8305(44) × 10−4 0.0b −0.357(31) × 10−4 0.2775(26) × 10−6 0.0b 0.0b −0.309(14) × 10−6 0.1097(25) × 10−5 0.38018(28) × 10−7 −0.2493(33) × 10−8 −0.26989(12) × 10−7 0.0b 0.0b 0.0b 0.0b 0.8284(15) × 10−8 0.0b −0.7493(19) × 10−8 −0.2193(30) × 10−8 0.0b 0.0b 0.0b 0.0b

(C0 + 2B0 )/3 √ (C0 − B0 )/2 6

2(ν8 − ν1 )/3 (ν1 + 2ν8 )/3 ν8 Coriolis (ν1 , ν8 ) Coriolis

3408

W. Raballand et al. / Spectrochimica Acta Part A 60 (2004) 3403–3412 10

-3

( vobs - vcalc ) / 10 cm

-1

5

0

-5

-10 0

20

40 J

60

80

Fig. 5. The “observed–calculated” frequency differences for the ν8 band.

Experiment ( FTIR ) T=203 K

Intensity

Simulation

Experiment ( Diode laser ) T=241 K

910.45

910.50

910.55 -1 Wavenumber / cm

910.60

910.65

0.5 Simulation

Absorption / a.u.

0.4

0.3

0.2 Experiment

0.1

0.0

910.65

910.70

910.75

910.80 -1 Wavenumber / cm

910.85

910.90

Fig. 6. Part of the ν8 Q-branch: experiment and simulation.

910.95

W. Raballand et al. / Spectrochimica Acta Part A 60 (2004) 3403–3412

by a footnote “c” in Table 3. The other v = 1 parameters will be considered either as “ν8 ” parameters or as ν1 /ν8 interaction parameters. The correspondence between some of our parameters and the “usual” ones is given in [17] and in the last column of Table 3. Let us first summarise the analysis of the FTIR data performed in [19]. In a first step, “ν8 ” parameters were fixed to zero and 1347 assignments were made in the ν1 band region. This partial fit led to determine ten “ν1 ” and ground state parameters. In a second step, the “ν1 ” parameters have been fixed to their values. Compared to the ν1 band, only a few assignments (270) have been performed in the very crowded ν8 region. Finally, both bands were fitted simulta-

3409

neously together with a third set of assignments consisting of 406 ground state combination differences (GSCD). In this way, 24 parameters values were obtained and the root mean square for the ground state is equal to 0.64 × 10−3 cm−1 . It is 0.82 × 10−3 cm−1 for the ν1 parallel band and 1.10 × 10−3 cm−1 for the ν8 perpendicular band. The fits were realised using a new set of programs called C4v TDS derived from STDS [20] and HTDS [22] softwares. The resulting parameters are listed in Table 6 of [19]. Fig. 3 shows the experimental and calculated overview spectra of the ν1 (a1 ) band. We can notice the presence of other Q branches due to hot bands. Having no data on the vibrational levels involved, they have neither been analysed

0.5 Experimental scan #1

Absorption / a.u.

0.4

0.3

Experimental scan #2 0.2

0.1

0.0 907.00

907.05

907.10 -1 Wavenumber / cm

907.15

907.20

907.30 -1 Wavenumber / cm

907.35

907.40

0.5 Experimental scan #1

Absorption / a.u.

0.4

0.3

Experimental scan #2 0.2

0.1

0.0 907.20

907.25

Fig. 7. Parts of the ν8 P-branch: experiment.

3410

W. Raballand et al. / Spectrochimica Acta Part A 60 (2004) 3403–3412

nor simulated. Fig. 4 is an overview of the ν8 band. The ν8 lines appear to be superimposed on a broad unresolved structure. As for the ν1 band, the spectrum is perturbed by overlap with hot bands but here the P-Q-R branches are much denser. The ν8 band data recorded by diode laser spectroscopy consists in four regions: a first one in the P-branch (906.849–907.687 cm−1 ), a second one in the Q-branch (910.407–910.944 cm−1 ), and two other ones in the R-branch (913.957–914.556 cm−1 and 917.853–918.705 cm−1 ). One hundred forty-four new assignments have been combined to the 351 previous ones to perform the new global fit. The parameter fit has re-adjusted the 24 already

determined parameters to new values that are listed in Table 3. The present analysis has given a more satisfactory rms standard deviation for diode laser data than the one obtained with only FTIR data. Fig. 5 shows the difference between the experimental frequency and the calculated one for each transition observed in our diode laser ν8 band data. The transitions are regularly distributed in the J range which implies a correct sampling of the whole band. The (νobs − νcalc ) differences do not exceed 0.003 cm−1 for all J values. Fig. 6 shows two parts of the Q-branch region (910.407–910.944 cm−1 ) together with the calculated spectrum. We can notice two points in this part of the spectrum: (i) there are some (yet unexplained)

0.4 Simulation

Absorption / a.u.

0.3

0.2

Experiment

0.1

0.0 914.05

914.10

914.15 -1 Wavenumber / cm

914.20

914.25

914.50 -1 Wavenumber / cm

914.55

914.60

0.4 Experimental scan #1

Absorption / a.u.

0.3

0.2 Experimental scan #2

0.1

0.0 914.40

914.45

Fig. 8. Parts of the ν8 R-branch (region I): experiment and simulation (top).

W. Raballand et al. / Spectrochimica Acta Part A 60 (2004) 3403–3412

3411

0.20 Experimental scan #1

Absorption / a.u.

0.15

0.10 Experimental scan #2

0.05

0.00 918.30

918.35

918.40 -1 Wavenumber / cm

918.45

918.50

918.60 -1 Wavenumber / cm

918.65

918.70

0.20 Experimental scan #1

Absorption / a.u.

0.15

0.10 Experimental scan #2

0.05

0.00 918.50

918.55

Fig. 9. Parts of the ν8 R-branch (region II): experiment.

discrepancies between the FTIR and diode laser spectra; and (ii) the prominent features are sub-band heads consisting in the accumulation of hundreds of lines, thus almost impossible to assign. Fig. 7 shows the reproducibility of two different diode laser scans in the 907–907.40 cm−1 region (P-branch). Figs. 8 and 9 do the same for the two regions of the R-branch. However, it appears that the spectra in the various regions of ν8 (see Fig. 6–9) are extremely dense and consist in clusters of superimposed lines (particularly in the Q-branch) together with a large number of hot bands. The analysis that we are able to perform with the present data is still not sat-

isfactory, as we can see in the figures. Further investigations would require simplified spectra, for example, cold spectra recorded thanks to a supersonic expansion jet experiment.

5. Discussion We can notice that our tensorial constants could be written as infinite developments of the “usual” ones. As an example, we have compared our zeroth-order parameters and the “usual” ones as given in [17]. The approximate correspondence is recalled here:

3412

W. Raballand et al. / Spectrochimica Acta Part A 60 (2004) 3403–3412

Table 4 Effective harmonic wavenumbers in cm−1

ν1 ν8 a

[13] (1967)

[19] (2001)a

This worka

854.6(2) 909.0(2)

855.51103(35) 910.69364(26)

855.510 96(27) 910.69292(20)

One standard deviation in parentheses.

Table 5 Ground state rotational constants in cm−1

C0 B0 a b

satisfactory thanks to these new recorded data. In order to improve this agreement, we could record more regions of this band with other diode lasers. One other solution would also be to obtain cold spectra thanks to a supersonic expansion jet experiment with the aim of reducing hot bands.

Acknowledgements

[4] (1991)

[19] (2001)a

This worka

0.090203503b 0.060861854(3)

0.0905136(30) 0.0608548(30)

0.0905124(15) 0.0608553(21)

Support from the Région Bourgogne for the computer equipment of the Laboratoire de Physique de l’Université de Bourgogne is gratefully acknowledged.

One standard deviation in parentheses. Calculated value.

2(0,0A ,a )A A A t{0}{0} 1g 1 1g 1g 1g 2(2,0Eg ,a1 )A1g A1g A1g

t{0}{0}

0(0,0A1g ,a1 )F1u F1u Eg

t{3}{3}

0(0,0A1g ,a1 )F1u F1u A1g

t{3}{3}

References

2B0 + C0 = + ··· 3 C0 − B0 = + ··· √ 2 6

(10)

2(ν8 − ν1 ) + ··· 3 2ν8 + ν1 + ··· = 3

(11)

=

High-order terms can be neglected in a first approximation. The correspondence is much more difficult to perform for higher-order tensorial parameters. This comes from the different construction of the rotational operators between the Dijon group [25] and the “usual” method [24]. Provided the preceding restrictions, we can deduce approximate values for the effective harmonic frequencies of the ν1 and ν8 modes given in Table 4. We can also recalculate approximate values of the ground state rotational constants (see Table 5). Harmonic frequencies and rotational constants are compared to previous values. Our constants are in reasonable agreement with what was obtained in other works [4,13,19]. 6. Conclusion In the aim of improving the previous analysis [19], we have used the same effective Hamiltonian developed through the fourth order. The ν1 /ν8 dyad of SF5 Cl was analysed again using the C4v TDS software. We have re-estimated the values of the effective harmonic frequencies and also those of ground state rotational constants of zeroth order. Moreover, some other rovibrational parameters have been determined. For the analysis of the ν8 (e) band, the addition of 144 diode laser data up to Jmax = 79 has produced a global root mean square for all ν8 data of 0.00105 cm−1 , slightly lower than in [19]. However, the agreement between calculated and experimental spectra is still quite bad for the very dense ν8 perpendicular band but is a little bit more

[1] D.M. Manos, D.L. Flamm, Plasma Etching: An Introduction, Academic Press, Boston, 1989. [2] M.E. Sitzmann, W.H. Gilligan, D.L. Ornellas, J.S. Trasher, J. Energ. Mater. 8 (1990) 352–374. [3] W.T. Sturges, T.J. Wallington, M.D. Hurley, K.P. Shine, K. Sihra, A. Engel, D.E. Oram, S.A. Penkett, R. Mulvaney, C.A.M. Brenninkmeijer, Science 289 (2000) 611–613. [4] P. Goulet, R. Jurek, Europhys. Lett. 15 (1991) 485–490. [5] P. Goulet, R. Jurek, Europhys. Lett. 22 (1993) 425–431. [6] R. Jurek, A. Poinsot, P. Goulet, J. Phys. 47 (1986) 645–648. [7] J. Bellet, R. Jurek, J. Chanussot, J. Mol. Spectrosc. 78 (1979) 16–30. [8] R. Jurek, J. Chanussot, J. Bellet, J. Phys. 37 (1976) 1129–1134. [9] J. Bellet, R. Jurek, J. Chanussot, C. R. Acad. Sci. Paris 277 (1973) 53–56. [10] P. Suzeau, R. Jurek, J. Chanussot, C. R. Acad. Sci. Paris 276 (1973) 729–732. [11] R. Jurek, J. Chanussot, C. R. Acad. Sci. Paris 272 (1971) 941–944. [12] R.E. Noftle, R.R. Smardzewski, W.B. Fox, Inorg. Chem. 16 (1977) 3380–3381. [13] J.E. Griffiths, Spectrochim. Acta A 23 (1967) 2145–2157. [14] L.H. Cross, H.L. Roberts, P. Goggin, L.A. Woodward, Trans. Faraday Soc. 56 (1960) 945–951. [15] R.R. Smardzewski, R.E. Noftle, W.B. Fox, J. Mol. Spectrosc. 62 (1976) 449–457. [16] M. Rotger, V. Boudon, M. Loëte, J. Mol. Spectrosc. 200 (2000) 123–130. [17] M. Rotger, V. Boudon, M. Loëte, J. Mol. Spectrosc. 200 (2000) 131–137. [18] Ch. Wenger, M. Rotger, V. Boudon, J. Quant. Spectrosc. Radiat. Transfer 74 (2002) 621–636. [19] M. Rotger, A. Decrette, V. Boudon, M. Loëte, S. Sander, H. Willner, J. Mol. Spectrosc. 208 (2001) 169–179. [20] Ch. Wenger, J.-P. Champion, J. Quant. Spectrosc. Radiat. Transfer 59 (1998) 471–480. [21] N. Cheblal, M. Loëte, V. Boudon, J. Mol. Spectrosc. 197 (1999) 222–231. [22] Ch. Wenger, V. Boudon, J.-P. Champion, G. Pierre, J. Quant. Spectrosc. Radiat. Transfer 66 (2000) 1–16. [23] J.-P. Champion, M. Loëte, G. Pierre, in: K.N. Rao, A. Weber (Eds.), Spectroscopy of the Earth’s Atmosphere and Interstellar Medium, Academic Press, San Diego, 1992, pp. 339–422. [24] D. Papoušek, M.R. Aliev, Molecular Vibrational–Rotational Spectra, Elsevier, New York, 1982. [25] J. Moret-Bailly, Cah. Phys. 15 (1961) 237–316.