Vibrational levels and anharmonicity in SF6—I. Vibrational band analysis

Spectrochimica Acro, Vol 42A. No. Z/3, pp. 351-369,

0584&8539/86 $3.00 + 0.00 Pergamon Press Ltd.

1986.

Printed I” Great Bntain.

Vibrational

levels and anharmonicity in SF,analysis * t

I. Vibrational

band

ROBIN S. MCDOWELL, BURTON J. KROHN, HERBERT FLICKER and MARIENA C. VASQUEZ University

of California,

Los Alamos

National

(&&tied

Laboratory,

Los Alamos,

New Mexico 87545, U.S.A.

29 August 1985)

Abstract-The vibrational spectrum of SF, has been recorded with a Fourier-transform i.r. spectrometer at a resolution of 0.05 cm- ’ and pressure-path length products of up to 2 x 10’ Torrxm. Twenty-nine bands were observed. Rotational structure was resolved for 11 of these and polynomials were fitted to the observed frequencies to yield the scalar spectroscopic constants, including the band origins m and derived values of %I?,, and the Coriolis constants 4’.For 12 other unresolved bands accurate estimates of the origins could be made from the frequency of a sharp Q-branch edge. Three more bands (v3, 2v, + vg, and 3v,) were not resolvable at our resolution but have been previously analyzed from Doppler-limited or sub-Doppler spectra. In addition, about IO assignable hot bands were observed whose frequency shifts relative to the principal transitionscould be accurately measured; two of these were sufficiently resolved for full scalar analyses. These frequencies were combined with results of several high-resolution Raman studies by other authors to yield the most complete data set on SF6 vibrational levels yet obtained. Isotopic frequency shifts have also been measured. The effective Coriolis constants for combination and overtone bands of octahedral molecules are discussed.

higher-level detuning from the pump source that occurs for nvJ alone [l l-131. In fact, the interpretation of many vibrational pumping experiments on SFs depends critically upon the anharmonicity constants other than those that simply determine the nvj ladder [14-161. Ultimately, a realistic anharmonic potential is needed to describe the distribution of energy in SF6 molecules pumped by strong i.r. fields, and the dynamic crossover from discretely pumped levels to the “quasicontinuum” [ 171. This interest has led to several recent attempts to model the anharmonicity in In the work of KROHN and SF6 [ 18-201. OVEREND [2Oa], a geometrical intramolecular force field was developed that included a general valence harmonic potential plus anharmonicities due to a Morse bond-stretching potential and Urey-Bradley nearest-neighbor non-bonded F . . . F interactions. Observed anharmonicities are the bench-mark against which such models must be tested, and in fact some spectroscopic results from the early stages of the present study contributed to the input for the Krohn-Overend potential. In addition to the obvious concern with the positions of higher vibrational levels as they affect multiphoton processes, there are experiments in other areas whose interpretation depends to some extent on a knowledge of the anharmonicity in SF6. Among these are the analysis of two-phonon spectra ofcombination bands[21], a quantitative account of the intensities of combinations [22], understanding the relation between temperature and vibrational amplitudes in electron diffraction experiments at high temperatures [23], and the assignment and interpretation of the higher (> 2800 cm- ‘) overtone and combination spectrum [24]. Several systematic attempts to obtain the anharmonicity constants of SF6 have been reported. In 1976,

INTRODUCTION Laser photochemistry, especially laser-induced molecular dissociation and laser isotope separation, has been a burgeoning area of research during the last decade [l-6]. One of the more important molecules thus studied has been SF6. whose strong v3 fundamental absorbs in the region of CO2 laser emission. Since isotopically selective multiphoton dissociation of SF, was reported in 1975[7, 81, the i.r. spectrum of this molecule has been studied in exhaustive detail. Of particular interest is the problem of anharmonicity in SF6, especially as it affects the positions of the higher vibrational states. Here attention has focused on the nv3 ladder, for a single-frequency laser that optically pumps vj will remain in resonance for only the first few levels, after which anharmonicity will detune the pump frequency from any SF, absorption. As a spherical-top molecule, SF, exhibits not only the usual frequency shifts of overtone bands due to anharmonicity, but also anharmonic splitting of the higher levels. The extent to which this splitting, and the influence of rotational structure, can compensate for the anharmonic frequency defect was a matter of some concern. With the analysis of the i.r.-active overtone 3v, [9, lo], the constants that determine the positions of the nvj levels are now known. While the nv3 ladder of SF, is now understood, the other anharmonicity constants, which determine the structure of other highly excited vibrational states, are also important. There is interest, for example, in the connection between the nvg and (n - l)v, + vZ + v6 levels, for the latter may partially compensate for the

*Work performed under the auspices of the United States Department of Energy. tDedicated to Professor RICHARDC. LORDLY theoccasion of his 75th birthday. 351

352

ROBIN S. MCDOWELL et al.

in an earlier festschrift paper dedicated to Professor

RICHARDC. LORD[25], hereinafter cited as “MAH”, the stronger i.r. combination bands of SF6 were remeasured with a grating spectrometer and the band origins estimated. These data were combined with existing Raman frequencies to obtain estimates for the anharmonicity constants and hence for the harmonic frequencies, from which a force field was derived. Many of the anharmonicity constants Xi, involving bending modes did not appear in any observed combination band, so MAH simply assigned to them estimated values of -0.5 f 1.0 cm- ‘. Even for the observed bands, no rotationalanalysis was possible with the OScm-t resolution available then. In addition, it soon became apparent that some of the Raman data on which these anharmonicity constants were based needed revision. RUBIN et al. [26] next reexamined the Raman spectrum with sufficient resolution to observe the shapes of the Q branches and to resolve hot bands. They reported revised values for the band origins of v1 , vz, vs and v6, and for the constants Xt6, X26, X56 and X66. PERSONand KIM [27] studied the v4 region of the i.r. spectrum using a tunable semiconductor diode laser to achieve Doppler-limited resolution. They criticized the conclusions of MAH, and attempted to disentangle the hot bands accompanying v4 by measuring the absorption intensities as a function of temperature. This paper reported fairly precise values for the anharmonicity constants involving v4, and was the first to stress the complications such as anharmonic level splittings that so plague studies of anharmonicity in molecules of this type. Rotational Raman lines in vz of SF6 were first resolved by ABOUMAJDet al. [28] at a resolution of L 0.3 cm-‘. These authors studied vl, vs and 2v6 as well, and synthesized the Q-branch contour of vi to estimate the constants Xti. Combining their data with the i.r. frequencies of MAH[25], they reported new values for many of the anharmonicity constants and summarixed preferred values for the others. Similar results for Xi?, Xi4 and Xrs were obtained in another Raman study that also used contour synthesis methods to fit the hot bands accompanying v, [29]. The above studies were specifically concerned with the anharmonicity problem in SF6, or at least they resulted in the determination of several of the anharmonicity constants. There have also been a number of papers in which precise values of single anharmonicity constants have been reported, generally in the course of studying some other aspect of SF6 spectroscopy. As mentioned previously, interest in the v3 ladder has led to numerous efforts to obtain XjJ and the other anharmonic constants GJS and T~J that determine the energy levels of nvp. After several initial attempts at these constants [30-321, they were determined precisely from the 3vJ spectrum of the vapor [9, lo], and have recently been confirmed by the two-photon spectroscopy of 2vJ [33]. This has enabled multipho-

ton excitation of the vJ ladder to be correctly modeled [3436]. Another well-determined anharmonicity constant is Xt3, from the Raman spectrum of the hot band vt + vj - vs accompanying vi [37,38]. Xi 1 has been obtained from the Doppler-limited spectrum of 2vi + vJ,combined with earlier i.r. and Raman measurements [17]. A different approach was taken by SALVI and SCHET-ITNO[~~], who calculated several of the X,,s from the shapes of combination bands in the two-

phonon spectrum of crystalline SF6; their values, however, do not agree with what we now consider to be the best determinations from vapor-phase spectroscopy. Recently the constants XJ4, Gs, and S,, have been reported from the double-resonance spectrum of the v3 + v4 - v3 hot band [39]. The most recent systematic study of the anharmonicity constants of SF6 was that of ABOUMAJDet cl. [28] in 1979. It would seem to be time to examine this problem once again. There are now the more precise values of X1 I, Xr3, and X3, that have been reported since 1979; and ABOUMAJDet al. [28] included in their summary several of the bending Xi,s estimated by MAH[25], which are, after all, simply guesses. Furthermore, we have found evidence that some of the reported anharmonicity constants may need major revision. The problem of level splitting pointed out by PERSON and KIM [27] also deserves consideration, at least to the extent of recognizing the difference between effective constants obtained from separate bands. To this end we have undertaken a new study of the overtone and combination spectrum of SF6 between 500 and 3000 cm- ‘, at sufficient resolution to resolve the rotational structure in many of the bands. This paper will discuss the analysis of these bands and the assignment of hot-band transitions, and will present a consistent data set for the vibrational levels of SF6. In the paper immediately following, referred to in the text as “Paper II” [40], we will evaluate the anharmonicity constants and harmonic frequencies and will redetermine the general quadratic force field of SF6. EXPERIMENTAL Commercial C.P. grade SF6 was used (minimum purity 99.8%). Infrared survey spectra indicated the presence 6f small amounts of CO, and H20. Since these immkties were useful in establishing-the frequency calibration-as discussed below, no attempt was made to purify the SF, further. The sample also contained about 0.02 % CF.,. Spectra were recorded on a Nicolet Instruments Model 7199 Fourier transform i.r. spectrometer operating at a resolution of usually 0.05 cm- ‘. This instrument is subject to a frequency correction that is always linear in wavenumber throughout the i.r. for a given scan, though the magnitude of the correction varies between spectra recorded at different times. The correction was established by measuring the absorption lines of CO2 and Hz0 that were present as impurities in the SF6 sample. Lines from three bands were used: CO2 between 660 and 68Ocm-’ [41], Hz0 between 1285 and 14OOcm-t [42] and COz between 2235 and 2380 cm- 1[43]. The frequency corrections for individual

Vibrational levels and anharmonicity in SF,-1 runs ranged from (1.5 x lo-‘)v to (7.6 x 10e6)v, and these reproduced the calibration frequencies with r.m.s. deviations of 0.003 cm- ’ or better. This is therefore the estimated absolute accuracy of all the FTIR line positions. Details of the pressures and pathlengths at which individual bands were recorded are given in the discussion of each band.

353

To extract the molecular rotational constants for SF6 from the spectroscopic parameters of Eqn. (l), we begin with equations which are used for i.r.-active fundamental bands: B’ - BfJ = )(2p + I$ Bc = B, -:n < = B[/B’=

@a)

+ $(3p -t.),

(W

Bc/[B,+(B’-B,)].

BAND ANALYSESAND ORIGINS

(24

Our objective here is the analysis of combination, overtone and difference bands of SF6, especially the determination of accurate band origins. At the outset we must clarify that usually a band origin does not coincide with the vibrational manifold origin. For example, the Ye+ vg combination state is split into a manifold having symmetry components A,, + E, + F,, + FZu and the band origin derived for this case (as discussed in the next section) represents only the dipole-allowed transition to the Fr, component of the manifold. The anharmonicity coefficient Xs6 refers to the manifold origin, and the symbol X;, as reported from the present observations is an effective coefficient derived from the origin of the Fi, band. Determination of X56 itself would require more highly resolved data than our instrument provided, as well as a far more complicated analysis. In our present work we give values for Xii (i = 1,2 . . , 6); X,, was determined earlier[lO]. All of the other Xijs reported here are effective coefficients indicated with one or more primes. Some details concerning particular vibrational shifts and splittings are discussed in Paper II [40]. The present band analyses are limited to a scalar treatment because the tensor splittings of individual rotational transitions into their octahedral symmetry components generally cannot be observed at FTIR resolution. Many of the SF6 combination band spectra studied here have simple P, Q and R branches with resolved rotational structure consisting of evenly spaced J-multiplets in the P and R branches. Since the basic examples are the vj and vq fundamentals, we refer to these bands as “fundamental-type”. For such bands the scalar analysis of the P- and R-branch line positions employs a simple polynomial fit to the J quantum number [44,45], as is also done in the case of diatomic molecules: v~,~(M) = m+nM+pM2+qM3+sM4+

..., (1)

where M = -J and J + 1 for P and R branches, respectively, and J refers to the lower state. The symbols m, n, . . . come from the notation of BOBIN and Fox[45]. At higher resolution the J-multiplets may or may not reveal the F4-type structure characteristic of fundamentals, but this is not an issue here. Whenever it was possible, we fitted the observed frequencies in the fundamental-type bands to Eqn. (1). The results of these fits, and for all other SF6 bands for which analyses have been carried out to date, are summarized in Table 1.

Here B. and B’ are the rotational constants for the ground and upper vibrational states, respectively, and B, is fixed at the value 0.091084200 cm-‘, as recently determined from analysis of saturated absorption spectra of v3 [46]. This high-precision determination of the ground-state rotational constant is in excellent agreement with an earlier determination of B. = 0.091084(2) cm-’ from the analysis of 3v, [lo]; the value obtained from two-photon spectroscopy of 2v3 [33] is slightly different. In Eqns (2a) and (2b) p and v are the effective values of B’ -B, for the (P, R) and Q branches, respectively [p is the same constant as in Eqn. (l)], and l is the Coriolis constant expressing the amount of vibrational angular momentum in the upper state. These formulas are approximations in that high-order contributions in Eqns (2a) and (2b) have been neglected. In principle Eqns (2) apply not only to fundamental bands, but also to the more general “fundamentaltype” bands discussed above. The only difficulty is that v can be derived only from a Q-branch analysis, and this would require greater resolution than was available for our work. Laser spectroscopy has yielded v for the v3 [46], v4 [47], 2vi + v3 [17], and 3v, [lo] bands (see Table 1). At the present resolution, however, one must either neglect the small terms &(3p -v) in Eqn. (2b) and (B’ -B,) in Eqn. (2~) or use an approximation. One convenient approximation is simply to assume that v = p so that Eqns (2) become, respectively, B’ -B.

z p,

(34

BI x Bo-in+ip,

(W

i = BU(B, + P).

(3c)

As an illustration of the errors involved here, we consider the vj band, using the values [46] of n, p and v listed in our Table 1.

Source Ref. [46] Eons (2) Eons (3) p=v=o

(B’-B,) x lo4 (cm- ‘)

B[ (cm-‘)

ia

-1.310555 -1.310023 - 1.61557 0.0

0.06307086 0.06307089 0.063094 0.063175

0.69344341 0.69344335 0.69393 0.69358

The small differences between the results from [46] and from our Eqns (2) are due to omission of higherorder terms from the right sides of Eqns (2a) and (2b). This band may provide a more stringent test of the

0.09442(S)

0.30822(4)

991.0773(24)*

1076.3540(13)*

0.055617(8)h

0.056430(6)

2489.4682(l)V

2828.33949(lO)lk’

2v,+v39

0.187(6)

-2.907(14)

-1.73(3)

-1.615569(11)

-1.6123(S)

-4.099(2)h

-2.530(13)

-2.938(17)

-0.6838(7)

-3.033(Z)

.

.

c

[Ol IO1

[OF -3.7(3)

-3.744(Z) -1.3028(4)

LOI

c

c

c

c

c

c

101

-86(3)

101

LOI

co1

LOI LOI

c

c

LOI

-4.3(S)

c c

lOI

IO1

9.1(B)

x

-1.310555(7)

c

c

-1.1038(4)

-1.1127(S)

0.397(14)

-0.1941(16)

c

(B’-BO)

-ll.hZO(b)

LOI

CO1

.

-3.54(20)

LOI

5 x 1010

lOI

-23.7(16) . .

-0.883(6) -1.454(4)

LOI

LOI

-6.91(25)

-7.7(4)

-24.7(15)

LOI

-92(3)

0.960(4)

-h.b(R)

LOI

.

0.146(8)

-1.450(21

-1.294(4)

-0.3363(11)

.

-0,6989320(b)

“’

.t.

-5.37(12)

-14.0(12)

q x 108

IO” BC

0.062804(Z)

0.063089(4)

-0.020216(13)

-0.020018(20)

-0.019099(15)

0.018505(20)

-0.018448(11)

-0.057488(20)

-0.019834(6)

-0.019943(15~

0.018309(20)

-0.063171(20)

0.043788(25)

0.06307086(Z)

-0.044074(15)

0.019744(7)

0

‘..

0

-0.019745(4)

-0.019567(11)

0.6905

0.6955

-0.2226

-0.2205

-0.2100

0.2034

-0.2025

-0.6322

-0.2181

-0.2190

0.2010

-0.6958

0.4817

0.69344

-0.4849

0.2169

0

0

-0.2168

-0.2149

5

= l.00C3

= l.OOtj

= 1.03&

= l.OZr,,,

= o.97t,1,

= -0.94gr

= 0.93c1,

= -0.91r,7

= l.Olr,,,

= l.OICll

= -0.9351,

= -1.00<3

= -0.96C6

= 0.48(55+56)

= -l.OOr,,,

= 0.995,

-..Y-YL.YC-

-.._.

“All constants are in cm-‘, except c (dimensionless). Standard deviations, in units of the last decimal place given, are in parentheses. Brackets indicate constrained values. bQuoted uncertaintiesin m are the standard deviations determined in the least-squares fit. The calibration uncertainties are, in addition:*(FTIR), 0.003 cm- r; t(Raman), O.OlOcn-‘; #(high-resolution stimulated Raman), O.OOlOcm-‘;l/(difference-frequency spectroscopy), c 10m4cm-‘. CB’-go assumed to be equal to p. “KIMet al., Ref. [47]. ‘ESHERICK and OWYOUNG, Ref. [49]. ‘BOBIN et al., Ref. [46]. @PINE and PATTERSON, Ref. [ 173. ‘Constants are for the R branch. The perturbed P branch can be fitted with slightly different values of n and p plus the addition of a q term. ‘PATTERSON et al., Ref. [lo]. ‘All ms are band origins in cases where these and the manifold origins differ, except for 3vs, for which the origin of the 3v3 manifold is given. See the text for discussion.

3

0.222347(25)

2160.0257(12)*

2v1+v4

2

0.22191(4)

{ ::::::::43:

0.219079(22)

0.29700(4)

1587.723(6)

1X98.2889(17)*

0.221707(11)

1388.4204(S)*

*

0.05581924(4)

947.9763358(4)

-1.855(4)

1::::::::::

0.27013(3)

870.4821(11)*

1257.0849(12)*

0.142635(13)

800.5027(11)*

2159.196(3)*

3”

-0.448(6)

-0.191(2)~

.

.

643.350(4)t

-0.1957(22)

...

774.5445(1)§

0.221639(B)

615.0195(4)*

-0.283(6)

Y x 104

. ..

0.221275(21)

614.9107(7)*

p x IO”

774.1820(1)5

”

mb

2Vl+V4+v6-V6

vl+“3-v2

‘2+‘6

us

‘5+‘6

vl+v2-“4

“le

VI+Y6-V6e

“2

u4

v4*v6-v6

Band

Table 1. Analyzed bands of ?jF,: scalar constants’

Vibrational levels and anharmonicity in SF,-1 approximations than do other bands because p and u have markedly different values in vj. In contrast, for v4pand u differ by only 2.4 “,‘,(see Table 1); Eqns (2) and (3) then give results that are in much closer agreement, while the neglect of p and u leads to greater discrepancies. For these reasons we have chosen Eqns (3) to calculate the rotational parameters for the fundamental-type bands. The results are given in the last three columns of Table 1. For the difference bands listed in Table 1, of course., the rotational constant in the lower state is B”, not Bo. Finally, the bands v2 + vq and v1 + v2 + vq exhibit two series of branches, which have been analyzed separately. The nature of this structure will be discussed below when we consider the Coriolis constants in more detail. Many of the bands for which rotational lines in the P and R branches were not resolved, or assignments and analyses were not possible, nevertheless have welldefined Q branches. Most of these have sharp highfrequency branch edges. In the case of a fundamental band such a Q branch belongs to the “very asymmetric” type [48], with v = ABo < 0, so that all Q-branch transitions are at lower frequency than the band origin. We have assumed that this interpretation extends more generally to the other observed bands and have assigned the band origins in these cases as follows: the frequency at which the Q-branch absorption begins to rise above the background was measured, and the origin estimated by subtracting from this frequency the instrumental resolution (usually 0.05 cm-‘) and the full width at half maximum of a single transition, taken to be the convolution of the Doppler width and the pressure broadening of 6.5 MHz/Torr [49]. Comparison of band origins obtained by this method with those from full analyses of fundamental-type bands indicated that the differences did not exceed 0.03 cm- I. Although the above procedure was not needed when a fit could be made to the P- and Rbranch lines, it became the only available method of estimating the band origins in the absence of such a fit. These band origins, together with those obtained from scalar analyses (Table 1), are summarized in Table 2. The Q-branches of many SF6 bands are accompanied by hot bands, and if these can be identified, their displacements from the frequency of the transition out of the vibrational ground state can yield accurate values for the anharmonicity constants. Observed hotband frequency shifts for which theassignment seemed unambiguous are listed in Table 3.

INDIVIDUAL

BANDS

Details of the assignment and analysis of individual bands are discussed here, in order of increasing band frequency. To avoid repetition, the details of the leastsquares fits are given in abbreviated form, where appropriate, by listing the pressure-path product at which the spectra were recorded; the number of lines fitted; the extent of the P- and R-branch coverage and

355

the frequency range of these lines; and the standard deviation of the fit (a). vg (348 cm- ‘) This fundamental is i.r.- and Raman-inactive, and its frequency has been estimated from the position of the Raman-active overtone 2v, to be 347.0[28] and 347.8 [26] cm -I. A prediction that vg may be weakly activated in i.r. absorption by Coriolis interaction with the i.r.-active fundamentals [SO] has recently been confirmed in spectra of the gas and liquid[Sl]. The gas-phase band is centered at 351 cm-’ and exhibits accompanying hot-band absorption. This fundamental also appears in the collision-induced Raman spectrum at 336 cm- ’ (!) and in the liquid at 350 cm- 1[52]. Given the uncertainty in this frequency and the lack of any rotational analysis, the origin of v6 is here treated as an unknown and its value determined from an analysis of combination bands. v5 (524 cm-‘) Raman spectra of this band have been reported by et al.[26] and ABOUMAJD et al. [28], who estimated band origins of 524.0 and 523.5 f 0.1 cm- I, respectively, from the shape of the Q branch. No rotational structure has been resolved. As for vg, the v5 origin was here treated as an unknown to be obtained from combination bands. RUBIN

vq (615 cm-‘) Both FTIR and tunable diode laser spectra of v, were previously analyzed by KIM et al. [47]. The assignments are straightforward, for the Q branch has a sharp high-frequency edge which yields a good approximation to the band origin [47,48]. Our analysis is based on a 12 Torr x 10 cm sample; 200 lines; P(lS-102) and R(2-113), 592.2&639.9cm-‘; u = 0.0030 cm- ‘. The resulting constants (Table 1) are in reasonable agreement with those reported by KIM et nl.[47]; the slight differences between the two sets reflect the inclusion of higher-J transitions and improved calibration techniques in the present work. Several hot-band Q branches accompany the main transition at lower frequencies. The strongest of these, assignable to vq + vg - vg [47], is shifted by 0.11 cm- ‘, and corresponds to a series of lines in the P and R branches that fall between the stronger transitions out of the vibrational ground state, and that have about the expected intensity relative to the latter (0.57 at 300 K). The analysis included 85 lines; P(1746) and R(6-43), In higher600.2-624.6 cm- ‘; u = 0.0031 cm-‘. resolution diode spectra, several other hot-band Q branches are seen (Table 3). These have been assigned by PERSON and KIM[~~] and will be considered further in Paper II with a discussion of the anharmonicity constants. The sharp edge of the 34SF6 Q branch yields an estimated band origin of 612.25 F 0.03 cm- ‘, giving a 32S-34S isotope shift of 2.77 +0.03 cm-’ for ~4, in FTIR values of agreement with previous

356

ROBINS. MCDOWELLet al. Table 2.Band origins of principal absorptions in 3zFe Band

Speciesa

in ohs

(u&p

” ca,c

(cm-‘)

MethodC

((~.O.O,O*l)R

523.5(l)=

(0,0,0,1,0)11

615.020(3)

(O,O,l,O,~J)R

643.350(10)

(1,1,2,.3,4)u

679.91(S)

679.93

Qh

(l.O.l,O,l)p

693.8(l)=

693.79

Qh

(1,0,1,2,3)u

700.74(3)

700.74

Qh

“1 “,+v2-v4

(l.O.O.O.O)g

774.5445(lO)f

(O,O,O,l,l)u

800.503(3)

800.517

A

v2+“5‘v6

(1.1.2,2,2)11

818.21(2)

81R.21

9s

‘5+“6

(l,O,l,l,~)u

870.482(3)

870.49

A

(0,0*0*1,O)l~

947.9763358(4)9

~O,O,O,l,l)u

991.077(4)

% “4 v2 “3+“6-v4 “6 2vS-v6

“3 “2+“6 .iv 6 vl+v3-v2 “4+“5 “3+v4-“6 “2+“4 V412V6 VI+“4 v3+v5 v2+v5+v6 ‘2+‘3 vlw5+v6 vl+v3 “l+v2+v6 3”4 2v2+v4

(0,1,0,1,2)u

-1U45

523.56

Qh A A

A

A 991.08

A

Intensityd

(RI 150 CR) 0.005 CR) 0.02 (R) 0.03 0.15 10 6000 20

1041.47

0.09 0.15

(O,O,O,l,l)u

1076.354(3)

1076.2h9

(0,1,1,l,I)~~

1138.71(3)

1138.71

0.3

1213.40(4)

1213.40

0.1

(O,O,O,l,I)u

1257.085(3)

1257.099

(O,l.l,3,2)u

1310.65(5)

(I,1

,7,3,4)u

(0,0,0,1*0)u (0,1,1.1,1)11

1388.420(3) -1456

5.5 0.06

1388.421

1.6

1470

0.1s

(1,1,2,2,2)u

1511.9(l)

(O,O,O,l*l)u

1587.723(7)

1587.723

A

(1*0,1,~,l)u

1643.56(3)

1643.55

Qh

(O,O,O;l,O)u

1719.618(2)

1719.619

Qh

1763.0(l)

1762.90

Qh

0.1

Q

0.002

(O.O,O,~,l)u (0,1,0,2,l)u

Qh

-1844.5

0.007 30 0.07 15

(0,0,0,2,l)u

1898.2&39(3)

1898.3

A

0.02

Vl+v2+v4

(0,0,0.1,1)u

2028.155(3)

2028.142

A

0.015

Z”, +v4

(0,0,0,1,0)u

2160.026(3)

2160.029

A

0.015

(O.O,0,2,l)u

2226.6(l)

2226.6

QS

0.5

(0.0,0,1.1)”

2357.1(l)

2357.008

Qh

0.05

(0,0,0,1,0)1~

2489.J6R2(l)h

7389.169

A

0.04

(0,1,0,2,l)u

282R..ii949(10)~

A

0.04

2v2+v3 Vl+“2+V3 2”l+v3 3v3

“The five figures are the number of Al, Al, E, Fl and Fs sublevels in the product of the initial and final states, with the parity (B or u) also indicated. “Band origins listed in Table 1 are here assigned uncertainties that are the root-sumsquares of the standard deviations (Table 1, column 2) and the calibration uncertainty (Table I, note b). ‘Method of determining band origin: A = analysis of rotational structure (Table 1); Qh = position of high-frequency edge of Q branch, corrected for effects of resolution and linewidth; Qs = estimated from the peak of a symmetric Q branch. “Relative intensity = 10’ log,,,(le/l)/l(cm) x p(Torr), where I is measured at the position of maximum absorbance as recorded at 300 K with 0.05-cm-’ resolution. These figures are intended for comparison of relative strengths, and are only approximately accurate. (R) indicates Raman bands. ‘ABOUMAIDet al., Ref. [28]. f ESHERICKand OWYOUNG,Ref. [49]. ~BOBINet al., Ref. [46]. *PINE and PATTERSON, Ref. [ 171. 'PAITERSON et al.,Ref.[lO]. Corrigendum, noted in proof: In this table, the species designation for 3vg should read (t,O,O,t,2)u.

2.80cm-' [47,53]. Diode spectra [47] give a perhaps more accurate value of 2.802 cm-'. v2 (643 cm- ‘) Raman spectra of this band have been reported by a group at Dijon[28, 541, and analyzed to obtain the ground-state [54] and excited-state [28] constants B

and D. To obtain m and B’ -E,, directly, in analogy with the i.r. results, we have reanalyzed their data using a slightly different approach. For rotational levels given by E,=BJ(J+1)-DJ2(J+l)2, line frequencies in the 0 and S branches can be shown

Vibrational levels and anharmonicity in SFs--I Table 3. Assigned Principal

LOWeI

Transitiona

Stilt@

“1

“2

3 “6 “6 2”s ‘“6 “2+“6 “4+V6

cn1c (cm-l)

Pnrnmetersb

-2.44(.3)

RJman

[LR]@

Xl?

-2.358

-2.9.3(i)

Yamnn

[2RlC

X1.3

-2

-?.91O(?)

Ran1nn [ 5x1

X -

-2.90'

-1.08(3)

Raman

[2UJc

Yll

-1.144

-1.15(i)

Raman

[7Xlc

X 15

-1.12

X 16

-0.3625

I .>

907

-0.38(3)

Rnman [281c

-0.3625(2)

Ramnn

(anal.)

-2.30(3)

Raman

[2U]@

2X 1s

-2.24

-0.76(3)

Raman

[281c

2X16

-0.725

-2.82(3)

Reman

[?Xlc

X lZ+Xlh

-2.721

-1.46(i)

Raman

[ 2R Ic

Xl4+Xlh

-1.50:

[-19]

lx16

-0.3625

Rnmnn 12RlC

X 1.5+‘16

-1 .48

-1.84(3)

Raman

[28jc

Xl4 +2X,6

-1.869

V5f2L6

-1.91(3)

Raman

[28]=

X 15 +2x 16

-1.85

-1.09(4)

Raman

[2Rlc

X’24

-1.2’1

vs

-0.62(J)

Raman

[ZU]C

‘Y

-0.31(4)

Rnman

[2Xlc

*X’26

-1.11(2)

FTIR

“6

-1.03(2]

“1

“3 “qd d “5 “6 “6 V6?

“1+“3

“6

“I+“4

“6

“4’“s “51”6

‘6

‘“6 2v,tv4

‘6

v6

“6 \‘,+”

6

2”h

-0.62 -0.348

lx 36

’

-1.102

IR

X 13

-1.144

Diode

1R [2:]

X’24

-1.271

-1.53(2)

Diode

IR

[2;]

X.i4

-1.52

-0.3?(2)

Diode

IR

[2:]

‘2X’ 44

+0.12(z)

Diode

IR

[27]

-0.11(2)

Diode

IR

[2?]

-0.1088(R)

FTIR

(anal.)

-1. 2:

1271

’ 25

Diode

-1.17,

“2

“2+“5-“6

Source

-1.53(3)

“6

vl+“3-“2

(cm-‘)

“Sf”6 v4+2L6

“2

“5

hot bands in 32SF, AV

‘“ohs

“i

“3

351

[2RlC

-0.38 +0.13

X45 ‘A6 ‘X

-0.1086

f

-O.lOBh

46

-1.4(l)

Kaman

-1.5(l)

FTIR

-0.51(J)

FTIR

-0.8(l)

FTIR

-1 .67(10)

FTIR

-0.38(4)

Ram:,”

-0.X30(3)

FTIR

-1.06(3)

FTIK

*s,( 'x;(,-q6

-1.Jq(31

rTIR

‘X~;-X;s+~;;;+X”

X’ 56 ‘X

-1.15

’

~I.465

16+‘36

X

lbfX;6 X”“_X

-0.4’11 +yl~l+X””

35 35 46 'X;;-k;6+'X;;;

[?R]C (anal.)

5h

'h"(,;,-2"~6

-0.30

*2Y,~f\;6

-Il.8336

-1.17

’ S6-2Xh6

-1.2:

“The entries are to be read as follows: principal transition v , , lower state vs indicates the hot band vi + Y, -v, that accompanies vi; principal transition vi + vg -v r, lower state v2 + v6 is vi + vj + v6 - (v2 +v6) accompanying vi + v3 - v2, etc. *Asterisks indicate transitions used in the fit of the anharmonicity constants. ‘The Avs listed here for hot bands accompanying vi are differences between estimated band origins (vO) as fitted by contour synthesis; for those accompanying v 2, vs and 2vs, they are differences between Q-branch maxima. ABOUMAJD et al. [28] appear to have obtained X 24. Xz5 and X,, as the differences between the Qbranch ttmkua ofthe hot bands and the band origin of ~2, which we feel increases the uncertainty. We have followed their assignments here, but as pointed out in Paper II [40], much better agreement with our calculated values is obtained if vq and vs are interchanged, so that vi + Y.,- v,, is reassigned to v, + v5 - vs, etc. dWe have interchanged the assignments of the hot bands originating in Y.,and vs from that of PEasoN and KIM [27]; see Paper II [40] for a discussion. where M = - (25 - 1) and (25 + 3) for 0 and S lines, respectively. The values of v0 (= m) and B’ -B,, given in Table 1 were obtained by fitting the expression for the combination O(J) + S( J - 2):

to be

v = v, +:(B’ +[B’+B”

-B”)

-&(D’-D”)

-+(D’+D”)]M

+:[(I?‘--B”)-y(D’-D”)] -$(D’+D”)M3

M*

-&D’-D”)M4,

2[O(J)+S(J-2)]

= [4v,+3(8’-B”)] + (B’ -B”)(25

- 1)2,

ROBINS. MCDOWELL et al.

358

with D’-D” = 0. We used the transitions 0(22-72) and S(20-70)(617.5-669.6 cm-‘) but omitting 0(37) and 0(39) because of large residuals; u = 0.028 cm-‘. The standard deviation of ve was 0.004 cm- ’ (Table l), but its absolute accuracy was taken to be f 0.010 cm- 1 (Table 2), as given by the original authors [28]. Several hot-band lines accompanying v2 have been reported by ABOUMAJDet al. [28] and are listed in Table 3. V3+V6 -v4 (680cm-‘) A very weak Q branch with a sharp high-frequency edge, recorded at 100 Torr x 20.25 m. 2V6 (694 cm- ‘)

1 for the fundamental and for the accompanying hotband transition originating in V6.Another recent highresolution study, using CARS, has confirmed these values of m and Bi -I&, for v1 [55]. The band origin had previously been estimated from the unresolved Q branch to be at 774.4[26] and 774.53 kO.02 [28] cm-‘; the agreement with 774.545 cm-’ as obtained from high-resolution spectra [49,55] shows that with proper care reasonably accurate band origins can be obtained at lower resolution. In the CARS work[55] the 32SF6-34SF6 isotope shift was measured to be - 0.0574 + 0.0005 cm- ‘, i.e. the Q branch of the heavier molecule lies at higher frequency. This is a consequence of the vibrational anharmonicity, and will be discussed in Paper II.

The Q branch of this overtone is seen in Raman spectra, with the band origin estimated to be v1 +vz -v4 (801 cm-‘) 693.8 cm-’ by both RUBIN et al. [26] and ABOUMAJD This difference band is illustrated in Fig. 1: 100 Torr et al. [28] (Table 2). The latter authors also report a hot x 20.25 m; 52 lines; P(24-60) and R(19-54), band that they aSSign as 3V6-V6 (Table 3). 791.8-808.2 cm- ‘; u = 0.0034 cm- ‘. 2V, - V6 (701 cm- ‘) A weak Q branch with a sharp high-frequency edge, Vz+V,-V, (818cm-‘) recorded at 100 Torr x 20.25 m. v1 (775 cm- ‘) The Q branch of the totally symmetric fundamental has been resolved by ESHERICKand OWYOUNG[49], using stimulated Raman spectroscopy with a resolution of 0.002 cm- ‘. Their constants are given in Table

785

790

795

100 Torr x (0.75-9.75 m). The Q branch of this transition (Fig. 1) appears symmetric and narrow (fwhm ca 0.3 cm- ‘); the band origin was taken to be at the center of the Q branch. The rotational structure is irregular and could not be assigned. A similarly shaped Q branch at 8 16.94 f 0.02 cm- ’ presumably belongs to V2+Vs+V6_2V&

800 805 810 815 WAVE NUMBER (cm-‘)

820

825

830

Fig. 1. The difference bands v1 +v, -v, (801 cm-‘) and v2+ vs -v, (818 cm-‘) as recorded with p = 100 TOK and I= 20.25m. Vertical scale approximately O-100 % transmittance. At lower absorption the principal Q branches of both bands have about the same width.

Vibrational

vs + v6 (870

levels and anharmonicity

cm- ‘)

MARCHE~I[~~] has recorded portions of the R branch of this band using a tunable diode laser. This branch resembles that of a fundamental band, and yields approximate values of the spectroscopic constants m, n and p. Our more extensive FTIR analysis was performed on samples of 12 Torr x 10 cm and 1OOTorr x 0.75 m; 123 lines; P(lS-80) and R(6-75), 847.7-889.9 cm- r; ~7= 0.007 cm- r. The origin of 870.482 cm- ’ agrees well with 870.6 f 0.3 cm- ’ estimated from grating spectra [25] and 870.3 + 0.1 cm-’ from diode spectra [56]. One hot band is evident; like the main transition, this has a sharp high-frequency edge, and we assign it as v5 t 2v, -vs (Table 3). MARCHETTI[~~] has noted that the rotational manifolds in this band are distorted from those usually seen, being somewhat compressed on the eight-fold side. Such behavior has been observed in other bands in which perturbations can occur; the vr/vJ diad of SiH.+ is an example [57, 581. v3 (948 cm- ‘) The transition from the vibrational ground state to t+ = 1 has been analyzed in exhaustive detail for 32SF6 using Doppler-limited spectra obtained with tunable diode lasers [59962] and sub-Doppler saturation spectra [46, 63, 641. The scalar constants given in Table 1 for this band were taken from the results of BOBIN et al. [46-j. The ground-state v3 transition is accompanied by numerous hot bands [65567]. This complex structure

I

980

982

I

904

I

I

359

in SF,-1

can be modeled with reasonable success by assuming that the anharmonic shift for a given hot band is proportional to the amount of energy in the lower state [66,67]. While this furnishes a qualitative match to the observed spectrum, it is obviously an oversimplification and neglects any splitting that may occur in the upper states. The strongest hot band, assignable with some confidence to v,+vs -vg, is shifted - 1.11 fO.O2cm-’ to the red from the Q branch of v3 itself. Assignments of the other features are much less certain. In particular, because of the anomalous contour of the combination band vj + vg at 1456 cm- ’ (see below), it is doubtful whether a sharp transition due to vj + v5 - vs is even to be expected near vj. We have chosen to report only the vj + vg - vg hot band in Table 3, and not to use any other features in the vj region in the determination of the Xij s. Spectroscopic constants have also been reported for the v3 fundamentals of 33SF6 [61] and 34SF,s[68], so the isotope shifts are known. From the present FTIR spectra, measuring from corresponding points on the ?SF6 and isotopic Q branches, we obtain frequency shifts of 8.97 f 0.02 cm -’ and 17.43 + 0.01 cm- ’ for 33SF6 and 34SFs, respectively, which are in close agreement with the diode results [61, 681. v2 +

v6

(991 cm-‘)

This band (Fig. 2) and the following one present certain difficulties, and they are probably both perturbed by v3. In fact, Fermi resonance between nv3 and (n - l)v, + v2 + vg has been shown to provide a resonant

I

I

986 988 990 992 WL$fE NUMBER (cm-l)

I

I

994

996

998

CHM-“G-7555 Fig. 2. The combination ~2+ YSas recorded at p = 12 Torr and I = 10 cm. Vertical scale approximately 50-90 “i, transmittance.

ROBINS. MCDOWELLet d.

360

pathway for i.r. multiphoton absorption in SF6, thus compensating for the detuning of the v3 ladder from the pump frequency due to anharmonicity[ll-131. One Q branch, without a sharp branch edge, peaks at 991.36 cm-‘; another one with about half its intensity is at 989.66 cm- I. The second of these is situated more nearly between the P and R branches, but the stronger Q branch, despite its apparently asymmetric location, agrees with the position calculated for this band from the most probable values of v6 and X26 (991.08cm-‘) [4O]. RUBIN et al. [26] have also observed this combination in the i.r. and feel that the 991cm-’ Q branch varies in intensity in different gas samples and may be an impurity; they place the origin with the Q branch at 990 cm- ‘. We have not observed such an intensity variation, but we cannot deny that it may occur. On balance, we prefer to place the origin near 991 cm-‘, admitting that this assignment is tentative. As recorded with a 12 Torr x 10 cm sample, there is a long series of well-resolved P lines, but only a few lines with a corresponding spacing can be identified in the more compact and weaker R branch. Assignments were attempted based on a simple PQR structure and were made to minimize the uncertainties in the parameters and to place the origin near the position calculated above; 55 lines; P(24 - 85) and R( l&23), 982.4993.2 cm- ‘; c = 0.005 cm-‘. Based on the observed v2 + v6 band alone, this assignment would have to be regarded as uncertain by a few units in J; but the

I

I

I

I

excellent agreement of the origin with that obtained from an analysis of other bands involving v6 and xi6 (see Paper II) increases our confidence that it is correct. 3v,j (1045 cm- ‘) This band lies between the stronger v2 + v6 and vl bands and may be perturbed. It appears + v3 -v2 somewhat similar to v2 + v6, having a P branch with a broad maximum at 1031 cm-‘, a weaker and more compact R branch at 1051 cm-‘, and two narrow Q branches at 1045.2 and 1047.2 cm- ’ that, like those of v2 + v6, are nearer the R branch than the band “center”. Here the lower-frequency Q branch is slightly more intense than the higher-frequency one (which, incidentally, corresponds to the expected position of the inactive overtone 2~~). Rotational structure is mostly irregular, but in the P branch between 1010 and 1030 cm- ’ there is a series of weak features with spacing 0.30 cm- ‘. This spacing appears to decrease with increasing frequency, and at the center of 3v6 it could easily be the 0.273 cm- ’ required for [ = - l/2, but we cannot discount the possibility that these lines belong instead to v2 + vs. This band will require much higher resolution for a proper interpretation. We find no evidence for a reported [69] band near 1056 cm- ’ assignable to v2 + v3 - vs; from our constants, this transition would have its origin at 1064.2cm-1. vl +v3 -v2 (1076cm-‘) 1OOTorr x 20.25 m;

I

I

r

I

(Fig. 3) 40

lines;

P(20-35)

I

R(i5)

1

1060

1064

1068

I

1072 1076 1080 1084 WAVE NUMBER (cm”)

I

I

1088

1092

1096

CHM-VG-7554

Fig. 3. The difference band v, + v, - v2 as recorded with p = 100 Torr and I = 20.25 m. Vertical scale approximately O-lOO”~ transmittance.

and

Vibrational

levels and anharmonicity

R(1049), 1065.2-1091.0cm-‘; u = O.O05cm-‘. A strong hot-band Q branch is assigned as v, +v3 +vg - (v2 + vg ) (Table 3). vq+v5

(1139cm-‘)

The grating spectrum of this band was reported [25] to exhibit a strong, narrow peak at 1140.4 cm- ’ and an adjoining “P branch” at ca 1134 cm-r. FTIR spectra, recorded at 100 Torr x 0.75 m, reveal that the former is a compact R branch (maximum at 1140.3 cm- ‘), and the latter a broad, extended P branch (Fig. 4). The Q branch, which appears only very weakly in grating scans, is clear in the FTIR spectrum which a maximum and a sharp high-frequency edge from at 1138.5cm-’ which the band origin can be estimated. No certain rotational structure was evident. There is a single resolved hot-band Q branch, presumably of v4 + v5 with a high-frequency edge at 1137.9 +v6 -v6, fO.l cm-‘. v-, +v4 -vg

(1213 cm-i)

This band (Fig. 5) has weak, complex Q-branch structure; one of its features has a sharp highfrequency edge at 1213.40 cm- ‘. v2+v4

(1257cm-‘)

This band has resolved P and R structure and an unusually narrow Q branch (fwhm ca 0.2 cm- ‘). The Q branch is somewhat sharper on the high-frequency side, but careful examination suggests that this is not a branch edge; instead, it appears that the band origin

1130

I

I

1132

1134

Fig. 4. The combination

SA(A)42:2/3-T

361

should be placed near the Q-branch maximum at 1257.07 f 0.03 cm- ‘. The analysis was made of spectra recorded at 12 Torr x 10 cm and 100 Torr x 0.75 m, and the lines were assigned to yield a band origin near the Q-branch maximum. The fit included 71 lines; P(3064) and R(9-60), 1247.9-1266.0cm-‘; Q = 0.005 cm-‘. At higher pressure-path products (100 Torr x 0.75 m) it is evident that outside this region there are approximately 5-cm-’ intervals in both branches in which the structure is confused due to the beating of two series of lines. At still higher J, the second series appears clearly, and requiring these lines to have nearly the same origin as the inner series results in a unique assignment. Sixtyfive of these lines were fitted; P(61-107) and R(61-90), 1233.0-1243.4 and 1270.7-1276.9 cm- ‘; c = 0.005 cm-‘. Since m is determined with a rather large uncertainty (0.01 cm-‘) in this fit, its value was constrained to that determined from the analysis of the first series. To anticipate the discussion of the anharmonicity constants in Paper II, we note that the above assignment, with m = 1257.085 cm-‘, yields Xi, = (v2 + v4) - v2 - v4 = - 1.285 f 0.011 cm- ‘. If this assignment is changed by one unit in J, to bring the band origin nearer the high-frequency side of the Q branch, m becomes 1257.230cm-’ and Xi, = -l.l4cm-‘. We prefer the assignment given in Table 1, for the alternative band origin seems too far to the blue to match the observed Q branch, though it cannot be rejected with certainty. (If the va +v4 Q branch is

I

WAVE

in SF,-1

1136

NUMBER

I

1138 (cm-l)

vq + v5 as recorded with p = 100 Torr, 50-100% transmittance.

I

I

1140

1142

1144

CHM-“G-7556

I = 0.75 m. Vertical scale approximately

ROBINS. MCDOWELLet al.

362

I

1200

1203

I

1206

I

II

Y

1

I

1209 1212 1215 1218 WAVE NUMBER (cm-‘)

I

I

1221

1224

1227

CHM-VG-7557

as recorded with p = iOOTorr, I= 20.25m. Vertical scale approximately 0-100’~ transmittance.

Fig. 5. The difference band vj +v, -v,

assumed to have a sharp leading edge that begins at the band origin, one obtains m = 1257.14cm-i, but the higher-frequency hot band mentioned below makes this figure somewhat uncertain.) From a diode study of the hot bands accompanying v.,, PERSON and KIM [27] reportx;, = -1.22cm-‘;thisisanaverageof -1.17 and - 1.27 cm- ’ from two Q branches, both of which they assign to v2 + vq - ~2. Our preferred analysis, with m at 1257.085cm-’ and Xi, = -1.28cm-‘, evidently corresponds to the second of PERSON and KIM’S hot band assignments. Whether their hot band is indeed split, or the other Q branch belongs to a different transition, is uncertain at present. There are several weak hot-band Q branches accompanying v2 + v4, but their assignment is not obvious. The strongest isO. f 0.02 cm- 1to higher frequencies from the main Q branch, but several others nearly as strong are present on the low-frequency side. v4+2vs (1311 cm-‘) The structure of this band is unclear. At 1OOTorr x (9.75 or 20.25 cm), it appears to have PQR structure. The sharp edge of the apparent Q branch falls at 1310.65 f 0.05 cm- ‘, and there is a strong, relatively narrow P branch at 1308.2 cm- ‘. vl +v4 (1388 cm-‘) (Fig. 6). Recorded with 1OOTorr x 0.75 m; 149 lines; P(ll-81) and R(8-95), 1369.6-1408.4cm-1; u = 0.0028 cm- ‘. Several hot-band Q branches appear, of which the strongest, displaced by 0.51 f 0.04 cm- ‘,

is assignable to vl + v4 + r6 - v6 (Table 3). At least two series of weak P- and R-branch lines belonging to these hot bands are also evident, but they could not be assigned unambiguously. vJ + vg (1456 cm-‘) At grating resolution, this band appears as a broad, nearly symmetric absorption centered at 1456 cm- ’ with a total width of ca 50cm-’ and no apparent rotational structure [70]. An FTIR spectrum (100 Torr x 9.75 m) presented a similar overall shape, on which were superimposed numerous weak and irregularly spaced rotational lines. No Q branch is evident near the band’s calculated center of 1470 cm- ‘, or elsewhere, and no analysis was possible. This fuzzball of a band remains the most puzzling of all SF6 i.r. absorptions. V2+Vs+V6

(1512cm-‘)

This band is a very weak Q branch with a sharp highfrequency edge, partly obscured by water vapor; it was recorded at 100 Torr x 20.25 m.

v2+v3 (1588cm-‘)

(Fig. 7)

This band exhibits several poorly-developed series of lines with different spacings. The Q branch has a sharp low-frequency edge at 1587.7 cm- ’ and degrades to higher frequencies. One series of P and R lines could be identified with a spacing of ca 0.30 cm- ’ (i.e. R +, P- branches with [,s = -&), and only one assignment of this series yielded a band origin that fell at a

Vibrational

1365

levels and anharmonicity

I

I

I

I

1370

1375

1380

1385

in SFs-I

I

I

1390

363

I

1395

1400

I

1405

1410

WAVE NUMBER (cm-‘) Fig. 6. The combination v, + v, as recorded with p = 100 Torr and I = 0.75 m. Vertical scale approximately O-l 00 “” transmittance. Strong, narrow absorptions due to water vapor are visible in the P and R branches of SF6.

1565

I

I

1570

1575

I

1580

I

1585

I

I

1590

1595

I

1600

I

1605

1610

WAVE NUMBER (cm-‘) Fig. 7. The combination v2 + vg as recorded with p = 5.47 Torr and I = 2.25 m. Vertical scale approximately O-70?,, transmittance. Some water vapor lines are present. Identifications are made for the Pm, R + branches (spacing ca 0.30 cm- ‘). Other series of lines have spacings of (A) 0.145 cm- I and (B) 0.167 cm ‘.

364

ROBIN S. MCDOWELL et al.

reasonable point in the Q branch. These branches were recorded at 5.5 Torr x 2.25 m; 30 lines; P(36-55) and R(51-67), 1571.0-1576.8 and 1602.8-1607.3cm-1; c = 0.007 cm-‘. Other branches are present in this band but are difficult to identify. A series of lines between 1578.5 and 1581.6 cm-’ (A in Fig. 7) has a spacing of 0.145 cm- 1and may correspond to Q * branches (Jdf = 1 -cs, calculated spacing O.l26cm- ‘), but no corresponding series is obvious in the R branch. There isa short progression in the R branch near 1601 cm- ’ (B in Fig. 7) with a spacing of O.l67cm-‘, possibly = 0, calculated spacing belonging to R" (cef 0.182 cm- ‘). These multiple branches result in a dense and confused rotational structure, and we were unable to make firm assignments except in the R+, Pbranches. v1 +vs +vg (1644cm-‘) This band has a narrow Q branch with a sharp highfrequency edge. vl +v3 (1720cm-‘) An FTIR spectrum of this band exhibits P,Q and R branches with only partially resolved rotational structure. Unlike vs itself, the Q branch has a sharp highfrequency edge, from which the origin can be estimated to be 1719.60 f 0.03 cm- ‘. To fix this more accurately, the band was reexamined with a 9 Torr x 1.25 m sample using a tunable semiconductor diode laser. The Q branch was calibrated against an OCS transition at 1719.63079 cm- ’ [71], with the tuning rate determined from interference fringes produced by a 7.5cm germanium etalon. The beginning of the Q branch was corrected for the estimated line fwhm of 0.0027 cm-’ (convolution of the Doppler width of 0.0018 cm- ’ and pressure broadening of 0.0020 cm- ‘) to yield a band origin of 1719.618fO.O02cm-‘. Several Q branches appear on the low-frequency side, of which the strongest, presumably originating in v6, is 1.5 cm- ’ from the main transition.

186Ocm-‘, and from their spacing n = 0.2206 +O.O015cm-‘, or C = (-0.211*0.008) * [,. 2vr+v4 (1898cm-‘) 1OOTorr x 20.25 m; 66 lines; P(22-54) and R(22-72), 1886.5-1914.4cm-1; c = 0.007 cm-‘. The P-and R-branch lines persist to very high J values and can be identi8ed to J > 90, but the inclusion of these high-1 data significantly increases the standard deviation of the fit. vl +v1+v4

(2028cm-‘)

100 Torr x 20.25 m. As for vz + v4, two series of lines are apparent in this band. The high-frequency edge of the Q branch, while sharp, has a “shelf n about halfway up that makes the location of the band origin some what uncertain. However, choosing m to be consistent with the v2 + v4 frequency and preliminary values of Xl2 and XI4 as obtained from other bands resulted in an unambiguous assignment. For the inner series we measured 78 lines; P(30-68) and R(7-53), 2018.0-2035.7 cm- ‘; u = 0.005 cm- l. The outer series was weak, and only 27 lines were accurately measured: P(51-78) and R(Sl-71), 2010.1-2016.5 and 2039.2-2043.3 cm- ‘; CT= 0.008 cm- 1 (m constrained to the value determined from the inner series). 2vr +v4 (216Ocm-‘) (Pig. 8) 1OOTorr x 20.25 m; 106 lines; P(15-68) and R(13-65), 2143.5-2173.5cm-1; 0 = O.O04cm-‘. As for v4, weaker transitions in the P and R branches can be assigned to 2vl +v4+vs -v6: 36 lines; P(15-52) and R(37-45), 2146.9-2168.8 cm-‘; u = 0.007 cm-r. 2vl + v3 (2227 cm- ‘) As recorded at 100 Torr x (0.75-9.75 m), this band exhibits poorly-defined PQR structure. The nearly symmetrical Q branch peaks at 2226.6 f 0.1 cm-r. The rotational structure is irregular and no assignments could be made. vl + v2 + v3 (2357 cm- ‘)

Vr+vZ+V6 (1763cm-‘)

This is a weak band partially obscured by absorg tion due to a trace of CO2 in the sample. As recorded with 100 Torr x 20.25 m, only a Q branch is visible with a sharp high-frequency edge.

Recorded at 100 Torr x (0.75-20.25)m. The Q branch is partially obscured by water vapor but appears to have a high-frequency edge at 1763.0 f 0.1 cm- ‘. This band resembles v1 + v6 in that the R branch is weak, compact and poorly developed; it has a maximum at 1765.5 cm- ‘, but no structure could be assigned. The P branch, however, is broader and exhibits a regular series of lines between 1753 and 1760 cm- ‘. The line separations were measured and extrapolated to the band center to obtain an estimate of n = 0.094 &-0.003 cm- ‘, which corresponds to [ = 0.484 *0.016, or about l/2 (i.e. -&).

All three branches of this band are narrow (fwhm ca 0.8011~‘)andpeakat 2487.42489.1 and 2491.1 cm-’ (P,Q and R, respectively). Rotational structure is unresolved at FTIR resolution; Doppler-limited spectra obtained with a difference-frequency spectrometer reveal a wealth of individual rovibrational lines, which have been analyzed by PINEand PATTERSON[ 173.

3v, (1845 cm-t)

3v, (2828 cm- ‘)

The Q branch of this very weak band is obscured by a strong water vapor transition at 1844.2 cm-‘. Pand R-branch lines occur between 1832 and

As the most direct way of obtaining the constants XJJ, GsJ and T,s that determine the nature of the nvg ladder, this band has been the object of much atte-

2vl +vs (2489cm-‘)

365

Vibrational levels and anharmonicity in SF,-1

R(65)

I

2140

2144

I

I

2148

2152

WAVE Fig. 8. The combination

2160

NUMBER

I

2164

2168

I

2172

2176

(cm-‘)

2v, + vq as recorded with p = 100 Torr and I = 20.25 m. Vertical scale approximately 60-lOO’& transmittance.

ntion. Initial studies with grating [30] and FTIR [31] spectrometers did not permit correct assignments of the structure, until finally a Doppler-limited spectrum was analyzed by PINE and ROBIE~E [9] and in detail by PATTERSON et al. [lo]. Here we merely add that the 32SF6-34SF6 isotope shifts as measured at the peaks of the!= lQ~andRbranchesare51.90and51.58cm-’, respectively, each + 0.03 cm- i. HOT BANDS Hot bands can provide an excellent method for determining anharmonicity constants, for the shift of a hot band from its principal transition (e.g. v3 + v6 - v6 from VJ can be accurately measured even on spectra of moderate resolution; and one thus does not have the problem of combining i.r. and Raman spectra, or i.r. spectra obtained in different regions, for which calibration consistency must be assured. There are, however, several potential difficulties with the use of hotband frequencies that can affect their usefulness. The first of these is the problem of identification. At 300 K, the vibrational states of SF, that have at least 1 % of the total population are as follows: Ground state vg = 1 us = 1 V6 = 2 u‘$ = 1 us = vg = 1 D2 = 1

I

I

I

2156

30.37 % 17.16 7.40 6.47 4.77 4.18 2.78

= 1 3 1, us = 2 us = 1 2 v5 = 1 v4 = 1, vg = 2 All others (each < 1 ‘%)

v4

=

vg = v5 = v2 = us = v4 =

vg

2.70 2.03 1.57 1.57 1.20 1.16 1.02 15.63

It follows that the strongest hot band accompanying a given transition is that originating in vs, and this should be more than twice as intense as any other hot band (assuming that the transition moment for the hot band is the same as that for the ground-state transition). One must be careful, however, in automatically assigning an obvious hot band accompanying the transition v, to v, + vg -vs. If the resolution is not adequate to reveal the true nature of the hot-band structure, an accidental coincidence of, say, the transitions out of V~and 2vg could be mistaken for that due to vg itself; or the vg hot band could be lost in the Q branch of the principal transition. Several such assignments made in the grating spectra of SF6 [25] have had to be abandoned for these reasons. With the resolution of 0.05 cm- 1 used in the present study we feel that chances for such errors have been significantly reduced. Ideally, this problem could be resolved by studying the temperature-dependence of the hot-band intensities. The populations in v4 = us = 1 and u2 = 1, for example, have quite different trends as the temperature

366

ROBINS.MCDOWELL~C

is changed despite their similarity at 300K. Such studies require high resolution and a broad range of temperature variation, and it is not clear that the present resolution would be adequate. PERSON and KIM [27] have made such an investigation of the hot bands accompanying v4 using tunable diode lasers, but even here overlapping of different hot bands was the major contribution to the experimental uncertainties in the intensity measurements. Another sign&ant problem is that the hot-band transitions, especially those involving higher states of degenerate fundamentals, may split into several components [31]. The resulting multiplicity of Q branches can make the assignments even less certain, and this uncertainty will render intensity measurements of limited usefulness. Despite these difficulties, it seems probable that at the present time many of the stronger hot bands of SF6 have been correctly assigned and can be useful in determining the anharmonicity constants. These more reliable assignments are summarixed in Table 3. The sources of these data are indicated there: in addition to FTIR frequency shifts obtained in the present work, there exist studies of the hot bands accompanying Raman transitions, and those associated with v4 in the i.r. We will discuss briefly the applicability of these results to the present investigation. Raman studies of vi include accurate determinations of the frequency shifts of vi + vJ - v3 [38] and, of course, the analysis of vi + v6 -v, (Table 1) [49]. There is also work at lower resolution by ABOUMAJDet al. [28], in which the contour of the v1 complex was recorded and then synthesized by adjusting the values of the anharmonicity constants. The difficulty here is that at this level of resolution the assignments are not unambiguous. While we feel that in genera1 their assignments are correct, we will discuss in Paper II reasons for believing that their derived Xi4 and Xi5 constants should be interchanged. Because of the uncertainty in this approach, we have not used any of the vl Raman data of ABOUMAJDet al. [28] in our analysis, although for reference the frequency shifts they measured are summarixed in Table 3. ABOUMAJD et al. [Zs] also assign Raman hot bands accompanying v2 and 2v6. Here the assignments are more straightforward, and we have used some of their data in our fit of the anharmonicity constants (Table 3). The most detailed study of SF6 hot bands is that of PERSONand KIM [27] in the v4 region in the i.r., using tunable diode lasers to provide Doppler-limited spec tra. Their results are summarized in Table 3. We have not used most of their frequency shifts in our analysis, although our results are generally in agreement with theirs. The single exception is in the hot bands originating in v4 and vs, for which we feel the assignments should be interchanged; this point will be discussed further in Paper II. We note in passing that for the 2v4 -v4 hot band, the appropriate anharmonicity constant is

al.

so their value of this constant should be + 0.06 cm-’ rather than + 0.12 cm- 1as they report; but since this is one of the assignments that we propose revising, the point is not important. CORIOLISCONSTANTS

Coriolis constants obtained from band analyses are given in Table 1 to four significant figures. We note immediately that for the i.r.-active fundamentals the zeta-sum is c3 +c4 = 0.4766, which differs from the expected harmonic value [72] of l/2 by 4.7 %. This discrepancy arises from the approximation of Eqn. (2), in which c was determined from (B&,&B’. The actual way in which Centers into the spectroscopic constant n is rather more complex, and has been considered in detail for tetrahedral XY4 molecules by HECHT[~~]. Extending his treatment to the octahedra1 case, we can write for v3 (Bl3)es = BeI; - tM333 - f C diM3ii if3 + tz3, +1F3s,

where the Mi,k are third-order interaction constants that express the change in the effective Coriolis interaction in various vibrational states, and which are complicated functions of the cubic and quartic potential constants. The scalar rovibrational constant ZJ, and the higher-order Coriolis constant F3, are too small to have much effect in this expression [lo], but the MS are not. Unfortunately, the only one of these known is MJJ3 = 1.47 constants that is x 10T4 cm-’ [lo]; its effect on the derived value of C3 will be 5M3,,/2B, = 0.0040. Considering that six such terms enter into the determination of each of (3 and (4 from the effective values of (B[), a correction of this magnitude is obviously adequate to account for the discrepancy of 0.0234 between the observed zeta-sum and its theoretical harmonic value. We cannot at this time, however, report harmonic values of (3 and (4 because most of the necessary correction terms are unknown. For the combination bands, most of the Coriolis constants in Table 1 have been obtained using the approximation that B’ -Be = p, but this will not introduce a significant uncertainty (cf the discussion above on the determination of C3).In considering the effective Is for combination bands, however, we must keep in mind that errors of the order of 5 % can arise due to the neglect of the third-order constants M as discussed in the preceding paragraph for the fundamentals. Another complexity that can arise for combination bands has been discussed in some detail for the case of the va + v4 band of CF4 [74]. The structure of such a band depends upon the splitting, A, between the FI and F2 sublevels. If A is large compared to the Coriolis splitting )2Bc,.lI, then F1 and F2 are approximately good quantum labels, and only Fz is dipole-allowed, giving a band with the usual P +, Q’, R - branches and [es = -& However, if A + 12BC4J 1 the sublevels

Vibrational levels and anharmonicity in SF-1 are mixed and all nine branches become allowed with i,fi= 0 (PO, R”), L (P+> R-), -L (P-9 R+), 1 -L, (Q’, Q- ), and 1 (Q’). The latter case is the actual situation for v2 + v4 of CF4, and the FTIR spectrum exhibited complex rotational structure much like that observed in some bands of SF6. Only with Dopplerlimited resolution as obtained with a tunable diode laser could the analysis be performed [74]. Nevertheless, the SF6 FTIR spectra allow us to draw some general conclusions about the effective is in combination bands involving one triply degenerate fundamental vi. The following statements seem to hold to within the estimated 5 “/,;uncertainty in the derived values of ccrr (note that is = & = -) in the harmonic approximation [72]). (1) The presence of nvl in the combination does not change the Coriolis constant. (2) The presence of v2 leads to either of two results: (a) Bands which may have more than the usual three branches, but whose strongest lines correspond to ceff = -ii, where ii is the Coriolis constant of the triply-degenerate fundamental present in the combination(v~+v~,v~+~~+~g~~~+~~-~Yq,~~+~~-~~). (b) Bands that definitely have a complex multiple-branch structure analogous to that of v2 + v4 of CF4. In v2 + v4 and v1 + v2 + v4 of SF, the strongest lines belong to branches with I& = f 14; in v2 + vj the strongest branch has & = -&, but branches with ceff = 0 and 1 - c3 are probably present also. (3) The presence of 2v, results in [en = ii, at least in the one such band analyzed (2v, + v4). It is perhaps premature to comment on the effective is for bands involving more than one triply degenerate fundamental, for these must have far more complex structures than are revealed by the FTIR spectra. The hot bands accompanying vq and 2v, + v4 (i.e. v4 + v6 - v6 and 2vl + v4 + v6 - v6) can be analyzed assuming that cefl = c4, and the apparent structure in 3v4 also corresponds to ceB = c4. The combination vg + v6 has a simple structure with ien- = -f = i(<=, + c6) [75]. The weak overtone 3v6 seems to have a branch with [,8 = -: = c6. but much of its rotational structure is complex and irregular at FTIR resolution. ISOTOPE SHIFTS

We complete our treatment of the vibrational bands of SF6 with a summary of the isotopic frequency shifts. Table 4 lists those shifts that have been reported with uncertainties of the order of a few tenths of a cm- ’ or better. These are, for v3 and v4, values of Am; the conversion to true Avs will be discussed in Paper II, where these data and the Coriolis constants l3 and c4 will be used to fix the general quadratic force field.

DISCUSSION

The present status of the band origins of vibrational transitions in ?!jF6 is summarized in Tables 1-3. Table 1 gives the origins, scalar constants and derived

361

Table 4. Isotope shifts from “FgLI Natural Isotope 33SF6

Abundance 0.75%

Am(v,)

Am(v3)

bm(v4)

a.& H.YfJY(SjC 8.YTi2)d

“Shifts are m(a) for “SF, minus m(vi) for the heavier isotope, in cn-- I; estimated error limits are in parentheses, in units of the last decimal place given. Natural abundance of 32SF6 is 95.02 %. bB~~~~~~ et al. [76] (in cryogenic solution). ‘MCDOWELL et nl. [61]; the NH3 reference line v2 aQ(9, 3) used to calibrate the 33SFs v3Q branch was corrected by + 0.0007 cm ’ as per URBAN et nl. [77]. “This work. ‘VOLKOV et al. [55]. ‘BRUNET and PEREZ [65]; for error estimates, cf: [25]. gB~~~~~~~~~~ et al. [68]; this is the difference between their value of m and that of BOBIN et al. [46] for 32SFs. *JONES[53].

‘KIM et al. [47].

values of B’ - Bo, B<, and < of all bands that have been analyzed to date. Nineteen bands are included: three from Raman studies (vlr v2 and v1 +v, -v,), three from previous high-resolution analyses (v,, 2v, + v3 and 3v3), and 11 (plus two accompanying hot bands) analyzed here using FTIR spectra. Table 2 presents, in addition, results for 12 bands that are unresolved at a resolution of 0.05 cm- ‘, but whose origins can be estimated with good accuracy from the sharp leading edges of the Q branches. Table 2 also includes some bands for which the branch structure is less clear; of these, 2v2 + v3 and v2 + vg - v6 have narrow symmetric Q branches which probably give a reasonable approximation to the band origins; and vJ + v5, 3v,, and 3v, do not provide useful frequencies, at least at the present FTIR resolution. Finally, Table 3 collects the frequency shifts of hot bands whose assignments are believed to be unambiguous. These include three analyzed hot bands (vl + v6 - v6, v4 + v6 - v6 and 2v, + v4 + v6 - v6) from Table 1, seven more observed in the present FTIR spectra, and some from other Raman and diode laser i.r. studies. From Table 2, we see that the origins of about 30 vibrational transitions of “SF6 (fundamentals, overtones, combination bands, and difference bands) are now known with accuracies of at least 0.1 cm- ‘, and in most cases much better than this. To these can be added the hot-band frequency shifts from Table 3. The resulting data set is by far the most complete yet assembled on the vibrational levels of SF6, and will be used in Paper II to derive the harmonic frequencies and anharmonicity constants of this molecule. The latter parameters can be used to calculate the observed frequencies, and Tables 2 and 3 show the agreement obtained.

368

ROBINS. MCDOWELL et al.

Paper II will also use the harmonic frequencies determined there to obtain the general quadratic force field of SFs, employing as constraints in the F,, block the Coriolis constants J (Table 1) and the isotopic frequency shifts (Table 4). Acknowledgements-We thank NORRIS G. NERE~ON for recording the tunable diode laser spectrum of the v, + vj Q branch, and G. GUELACHV~LI for sending us his measured Hz0 absorption frequencies in advance of publication. This

paper has benetitted from useful discussions with C. W. PA?TERSONand J. K. G. WATSON. REFERENCES [l]

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El

Vibrational

[60]

[61]

[62]

[63]

[64]

[65] [66] [67]

levels and anharmonicity

in SF,-1

369

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