Assignment of far infrared laser lines in silyl fluoride

Spccrrochimica Printed

in Great

Arm,

Vol. 4lA.

No.

l/Z, pp. 367-370.

058.-8539/85

1985 Q

Britain.

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1985 Pcrgamon

+ 0.00

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of far infrared laser lines in silyl fluoride

P. B. DAVIES,* D. P. STERN*$ and H. JoNEst *Department of Physical Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 lEP, U.K. and TDepartment of Physical Chemistry, University of Ulm, D-7900 Ulm, F.R.G. (Received 15 June 1984) Abstract-Eleven far i.r. laser lines, generated by optical pumping with a CO1 laser, have been assigned with the aid of available spectroscopic data and an accurate calculation of the vibration-rotation spectrum around 10 pm. The absorbing i.r. transitions coincident with the laser are in the vI and v5 bands of %iHsF which are strongly perturbed by Coriolis and l-type doubling effects. Predicted far i.r. transition wavenumbers are in close agreement with experiment and with predictions derived from a recent extensive FTIR and laser study in the i0 pm region.

absorption spectrum in the region of the pump line, identify the SiH3F absorption coincident with it and hence the FIR transition itself. Several of the FIR laser lines were readily identified and then incorporated in a fit and prediction program until 11 of the laser transitions had been assigned. All the corresponding i.r. absorptions were then used in a final fit to derive parameters for u2 = 1 and u5 = 1 in SiH3F. Shortly after this was completed an analysis of a very extensive FTIR and laser Stark study of SiHJF in this region was published [9]. The results are generally in good agreement with this work, as described later, and confirm the correctness of the FIR laser assignments.

INTRODUCTION

Many of the far i.r. molecular lasers are small organic molecules often containing fluorine [ 11. A number of their silicon analogues also absorb in the 9-10 pm

emission region of the CO1 lasers, which are used for optical pumping of far i.r. lasers. However, it has only recently been shown that some of these silicon compounds, namely SiHJF [2], SiH,F, [3], SiFJH [3] and SiHsCN [3], will act as FIR lasers. It might appear that among this group the symmetric top silyl fluoride would be the easiest in which an assignment of the new emissions could be made (by analogy with CH3F [4]). However, the vibration-rotation spectrum of SiH,F between 9-10pm is complicated. The two strong absorption bands due to the v2 and v5 modes, centred at 991 and 962 cm-’ respectively, interact through Coriolis effects and are further complicated by I-type doubling [5]. Nevertheless, provided sufficiently accurate spectroscopic data are available, it should be possible to identify the vibration-rotation transition coincident with the pumping CO2 laser line from a calculated spectrum, and hence the FIR lasing transition for comparison with experiment. Even a relatively low precision measurement of the FIR laser wavelength provides a quite rigorous test of the correct assignment of both the emission line and the absorbing i.r. transition. In the absence of a precision frequency measurement of the laser, this calculated FIR frequency should be sufficiently accurate for further experiments, e.g. when the laser is the source oscillator in Laser Magnetic Resonance spectroscopy [6]. A similar approach has already proved successful in identifying some of the laser transitions in DCOF [7] and CH3F [8]. Conversely accurate frequency measurements would test the validity of the calculations and lead to improved spectroscopic parameters. In this work spectroscopic parameters for SiH3F from a number of sources were used to calculate the

EXPERIMENAL

In addition to the laser lines reported earlier [2] five new lines were detected using a waveguide structure [lo] instead of an open resonator. Four of these were obtained using isotopic “CL602 lasers. All the FIR laser lines are listed in Table 1. VIBRATION-ROTATION

ENERGY LEVELS

The vibrational modes which absorb strongly in the region 01 interest are the SiHB deformations v,(A,) andv,(E).Thev, mode (A,)at 875 cm-’ hasalso to be considered. Coriolis coupling and I-type doubling lead to modification of the rotational levels and both effects must be incorporated in an exact calculation of the vibration-rotation spectrum. However, for the ground, u2 = 1 and u3 = 1 states the rotational energies are given by the usual expression for unperturbed rotational levels: E,,,=BJ(J+1)+(A-B)K2-D,JZ(J+1)2 -D,,J(J+1)K2-D,K4. (a) Coriolis coupling

*Present address: McKinsey & Company Inc. (U.K.), 74, St. James Street, London SWlA IPS, U.K.

The major Coriolis interactions are those within the degenerate v5 mode and between v2 and v5. Due to the band centre separation, that between vg and vg is much smaller [ 1l] and its effect on the accuracy of calculation required here is negligible. The appropriate

367

368

P. B. DAVIESet al. Table

%HIF

Wavelength brn)

Laser pump

1. Far i.r. laser lines in

line

Observed*

lOP18$ lOR10$ lOR26$ lOR22 lOR14 lOR16 lOR20 lOR22 lOR30 lOR32 lOR38 lOP14$ lOR6 lORl0 lOR26 lOR36

622 1056 1058 330 343.5 369 516 341 1014 1286 280.5 689 236 187 264.5 221

Assignmentt Upper(vi,

Predictedt 617 1050 1052 329 343 366 512 340 1013 1270 278

J, K)

Lower(vi,

“5 17,ll “5 10.5 “5 IO,3 vs 32,4 “2 30,2 Yg 29,2 y2 20,o vs 13,5 “2 10,2 vz 8,O v2 38,11

J, K)

vs 16, 11 YS935 v5 9,3 Ys 31,4 Yt 29, 2 vs 28,2 “* 19,0 vs 30,5 y2 932 vz 7,O vq 37, 11

*Experimental errors are estimated in [2]. tBased on the final parameters in Table 3. $r3C’60Z laser

matrix element for the degenerate us = 1 level is given by, (~g,l5,J,kl~~]t)5,1s,J,k). = -2kI,(A&

+ 15k(q,J( J + l)+qKk2)

where q, and qK are centrifugal distortion coefficients. The Coriolis interaction between v2 and vg connects levels of A, and E symmetry with the same J and differing in K (= 1k I) by one and is given by the matrix element,

into sub-matrices for diagonalization. Two of these are identical, of the order (25 + l), and represent the levels of E symmetry. There are also two smaller matrices of the order (J + 1) and J for the Al and A2 levels. A program was written to diagonalize these matrices up to J = 42 and produce energy levels and transition wavenumbers. The appropriate vibration-rotation selection rules are: v2 band: AK = 0, AJ = 0, + 1 v,band:AK=

(us,ls

= fl,J,kfl)~corlu2,J,k) = fD[J(J+l)-k(k+l)]“’

and for the rotational

fl,AJ=O,

&-1

relaxations:

AK=O,AJ=&l,Au=O where D = (@I),, 5 i,c(~y”+(~)“‘].

with the added symmetry selection rule

The ‘giant’ I-type doubling

in us = 1 is largest for low K levels where the energies are closest. This (2, 2) interaction is given by [12] =0.5[Q5+q5J(J+1)][{J(J+1)-k(k+l)} x (J(J+l)-(k+l)(k+2)}]“2. A second I-doubling effect, the (2, - 1) interaction, has also been considered. It links I, = + 1, k levels with I, = - 1, k + 1 levels [13] and is strongest between K = 2 and 1. Although in methyl fluoride it is so large that a non-crossing effect is observed it was calculated to be much smaller in SiH3F and the uncertainty resulting from its omission was less than the error inherent in the constants used. (c) Transition predictions The matrix derived from the above interactions is of the order 3(2J + 1) for each J but it can be factorized

A, ++ Al.

E +-+E,

(b) l-Type doubling

A second program was written to perform a least squares fitting procedure on the assigned transitions and derive the molecular constants. This least squares fitting routine followed the procedure of CASTELLANO and BOTHNER-BY [ 141 and the calculation of individual energy levels used the matrix elements given above. To test the program data of BENTRENCOURT and MORILLON-CHAPEY [ 131 on used and molecular constants

methyl

fluoride

were

in good agreement with

their results were obtained. ASSIGNMENT The

ground

GEORGHIOU

et

state

al. [lS]

microwave

constants

of

were used throughout. Vibration-rotation parameters from several sources [S, 11, 151 were used to start the calculation of the i.r. spectra. The possible contribution of the essentially unperturbed v3 band was also investigated by calculating its spectrum from the constants of ESCRIBANO et al. [l 11.No coincidences were found with CO2 laser

Assignment

Table 2. Infrared

of laser lines in SiHxF

transitions

coincident

369

with COa laser lines

Assignment Ground

(J,K) 17, 12 11, 6 11,4 33, 3 31, 2 28, 3 21.0 31, 4 11, 2 9, 0 31.11

Upper

(v, J, K)

Calculated Derived from[9]

v,17, 11 v,lO, 5 v,lO, 3 v,32,4 v,30,2 v,29,2 v*20,0 v,31,5 v,10,2 v,8,0 ~~38, 11

*Calculated from parameters tData taken from [16]. $i3Ci602 laser.

wavenumber This work*

898.6761 921.6884 932.6118 942.3283 971.8915 973.3151 975.8723 977.1354 982.0882 983.2455 986.5977

898.6488 921.6727 932.6083 942.3837 971.9317 973.2884 975.9276 977.2120 982.0953 983.2550 986.5672

CO2 lasert 898.6488 921.6753 932.6051 942.3833 971.9303 973.2885 975.9304 977.2139 982.0955 983.2523 986.5674

lOP18$ lORlO$ 1OR26$ lOP22 lORl4 10Rl6 lOR20 lOR22 lOR30 lOR32 lOR38

in Table 3.

lines and only the v2 and v5 bands were investigated further.

and led eventually to assignment of the 11 lines given in Table 1.

(a) Long wavelength FIR laser lines

MOLECULAR

The long wavelength lines at 1014, 1056, 1058 and 1286 pm could be assigned without difficulty (Table 1). The small discrepancy between predicted and measured FIR wavelengths falls within experimental error [2]. The predicted wavenumber of the absorbing i.r. transition and the frequency of the CO2 laser pump line [ 161 are given in Table 2. These predicted frequencies are based on the least squares fit to all the assigned i.r. absorption lines coincident with CO1 laser lines as described later. However, even with the initial parameters derived from other studies the calculated line positions were within 0.2 cm-’ of the pump laser frequency for these long wavelength lines. (b) Short wavelength FIR laser lines These proved more troublesome to assign. The first step in eventually extending the assignment was to determine vibration-rotation parameters from a fit to the frequencies of the i.r. transitions leading to the long wavelength lines (Table 2), assuming these to be coincident with the pump laser frequency [16]. With so few data points the constants were varied singly so that the problem of too few degrees of freedom was essentially eliminated. Calculations with this new set of parameters then enabled two more transitions to be assigned with reasonable confidence. However, the next longest wavelength line from the group in (a) at 516 pm could not be assigned with certainty to either of the two possibilities: v,,J=20,K=O+v,,J=19,K=O v5, J = 19, K = 5 -,v2, J = 18, K = 6

(i) (ii)

((ii) arises from the second order Coriolis mixing of the two vibrational states). Provisionally the latter assignment was selected and on including its pumping transition in the fit the parameters converged rapidly

PARAMETERS

The rms error between the observed pump laser frequencies (assuming they are exactly coincident with the laser) and predicted vibration-rotation lines derived from a final fit of the 11 lines was 0.0020 cm-r, about the Doppler width of the i.r. transitions. (This final fit indicated that in fact assignment (i) was the correct choice for the 516 pm line.) The final fit constants are given in Table 3 and the associated transitions in Tables 1 and 2. DISCUSSION

Five of the observed laser lines cannot be assigned to any of the pumping transitions with certainty. These laser lines may be associated either with hot band transitions or with very high J states. Although the latter fall outside the prediction capability of the Table

3. Molecular parameters (cm-‘) of ‘sSiHJF certainties are 3a in the last quoted digit(s))

A B

D, x 10’ D,, x lo6 D, x IO5

Ground State*

v2 = 1

vj = 1

2.8407 0.478583 5.163 7.062 1.771

2.85009(60) 0.47743(6) 5.749(51) 4.52(147) 1.796(42)

2.82936(48) 0.47967(6) 5.068(36) 8.24(84) 1.562(51) 0.316712(78) - 0.36296( 156)

(B 02. 5 (A Ch

ot ot

‘IJ

VK q5 x 106 Qs x lo3 v0 *From[l5]. tConstrained

(un-

990.8569(27)

to zero in the tit.

1.9(6) - 2.5(3) 962.2308(33)

370

P. B. DAVIESet

computer program tentative J (but not K) assignments to lines at 1 = 236, 221 and 187 pm could be made. The parameters well determined in the present study are the v2 and v5 band centres, the two Coriolis coupling constants, q5, Q5, and the rotational constants for u2 = 1 and for v5 = 1. Although’only 11 i.r. transitions were used in the fit to derive the upper state parameters if any assignment was changed by one unit in J or K the fit was much worse with an increase in rms error of three- or four-fold. Of the centrifugal distortion constants, D,, in the two vibrational states was found to have a small effect on the fit and is therefore poorly determined. Similarly D, has a relatively large uncertainty because the laser transitions involve only low K levels. In contrast much larger values of J are involved and D, itself is better determined. The ‘I, and qK distortion terms in the Coriolis interaction were also poorly determined and set to zero in the final fit. Since the calculation of the i.r. spectrum and assignment was completed ESCRIBANOand BUTCHER[~] have published an analysis of the vz/vs band system based on laser Stark and Fourier transform spectroscopy. Their molecular constants are similar to those determined here but outside the combined 3a error limits which might suggest that the errors in the parameters of Table 3 are over optimistic. The rms error quoted by ESCRIBANO and BUTCHER[~] is ti.006 cm - ’ which, considering the resolution of their _ 0.06 cm-’ and the very large FTIR instrument number of lines fitted, is very satisfactory. However, this rms is based on a non-uniform weighting of the lines, seven of which have been given a relative weight of 1000. Five of these are coincident with CO2 laser lines and it is assumed (though not specifically stated) that the increased measurement precision of these lines is the reason for this large weighting. We have used the parameters of ESCRIBANOand BUTCHER[9] to predict the i.r. spectrum and FIR laser wavenumbers; the results are given in Tables 2 and 4. Table 4. Measured COZ pump line 1OP 10R 10R IOP 10R 10R 10R 10R 10R 10R 10R

and predicted

Measured cm-’ (G l/L) 1I(* lo* 26’ 22 14 16 20 22 30 32 38

16.1 9.47 9.45 30.3 29.1 27.1 19.4 29.3 9.86 7.78 35.7

cm-

’ of SiH3F laser lines

Predicted This work Derived 16.207 9.521 9.506 30.341 29.184 27.475 19.556 29.338 9.878 7.876 35.943

from[9]

16.198 9.520 9.506 30.346 29.176 27.471 19.551 29.331 9.876 7.875 35.963

al.

The agreement with our predictions is very satisfactory although the predictions based on ESCRIBANOand BUTCHER’Sparameters are slightly further from the CO, laser frequencies (Table 2). This perhaps is not surprising since our parameters are derived exclusively from the 11 transitions assumed to be coincident with CO, lines. In addition we have used our formulation of the Hamiltonian which differs in small respects from that in [9], e.g. our neglect of the vs(A,+, interaction. It should be noted that ESCRIBANO and BUTCHER’S own listing of the lines coincident with CO2 laser lines (weight 1000) are calculated to be in excellent agreement with experiment (Table IX in Ref. [9]). The satisfactory agreement between our parameters and those of the much more extensive study of ESCRIBANO and BUTCHER[~] shows that the approach is valid for assigning the i.r. and FIR transitions from a relatively small data set. Clearly state-of-the-art parameters can only be derived from a much enlarged data set. It remains to test the accuracy of the predictions further by exact frequency measurement of the FIR lasers[17] and these experiments are now being planned. Acknowledgements-We thank NATO for a collaborative award and the Science and Engineering Research Council for a studentship for D.P.S.

REFERENCES

Cl1D. J. E. KNIGHT, NPL Report QU45 (1982). PI P. B. DAVIES and D. P. STERN, Int. J. IR mm W3, 909 iI

(1982). P. B. DAVIES, A.

[lj

H. E. RADFORD, IEEE .f. Q. Electr. QE-11,213 (1975). R. ESCRIBANO, M. G. HERNANDEZ and R. J. BUTCHER, J. molec. Spectrosc. 95, 334 (1982).

OLSEN, A. G. MAKIand R. C. SAMS,J. molec. Spectrosc. 55, 252 (1975). Cl33 M. BENTRENCOURT and M. MORILLON-CHAPEY, Molec. Phys. 33, 83 (1977). [I41 S. CASTELLANOand A. A. BOTHNER-BY, J. them. Phys. 41, 3863 (1964). Cl51C. GEORGHIOU, J. G. BAKERand S. R. JONES, J. molec. Spectrosc. 63, 89 (1976). Cl61C. FREED, L. C. BRADLEYand R. G. O’DONNELL, 1EEE J. Q. Eleczr. QE-16, 1195 (1980).

1121W. B.

Cl71 H. *‘3C’602.

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published. II41T. Y. GHANG and T. J. BRIDGES, Opt. Commun. 1, 423 (1970). l-51A. G. ROBIETTE, G. J. CARTWRIGHT,A. R. HOY and I. M. MILLS, Molec. Phys. 20, 541 (1971). P. B. DAVIES, J. phys. Chem. 85, 2599 (1981). I!] H. JONES,P. B. DAVIES and W. LEWIS-BEVAN, Appl. Phys. B30, 1 (1983). PI P. B. DAVIES, A. H. FERGUSON, P. A. HAMILTON, T. L. AWYES and I. M. R. VAN LAERE, Int. J. IR mm W4,1029 (1983). PI R. ESCRIBANOand R. J. BUTCHER, J. molec. Spectrosc. 99, 450 (1983).

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