Unexpectedly rich vibronic structure in supersonic jet spectra of sulfur dioxide between 360 and 308 nm

Chemical Physics ELSEVIER

Chemical Physics 200 (1995) 181-199

Unexpectedly rich vibronic structure in supersonic jet spectra of sulfur dioxide between 360 and 308 nm J.S. Baskin *, F. A1-Adel, A. Hamdan Laser Research Laboratory, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 6 October, 1994; in final form 11 July 1995

Abstract An extensive vibrational resolution study of SO 2 between 27780 and 32500 cm-l, spanning absorption to the 3B 1, ZA2, and JBj electronic states, has been carded out via fluorescence excitation in a molecular beam, achieving substantial improvements in sensitivity and rotational cooling over previous studies. Characterization of the dependence of transition intensities on molecular beam conditions has been used to identify and separate the contributions of cold and hot transitions in the spectra. Vibrational-mode-selective, carder-gas-dependent cooling is observed and is instrumental in the identification of a group of vibrational levels exhibiting novel Franck-Condon patterns and little or no cold absorption. At least 135 vibronic levels are identified in the energy range studied, adding 71 to the previous total reported from our own and other laboratories. Eight levels below 29000 cm-1 are assigned to the 3B l electronic state, supported by a set of anharmonic constants to approximate the observed vibrational structure. In the higher energy region, the accepted two-singlet-electronicstate model is compared to the experimental results and shown to be inadequate to account for the large number of observed levels.

1. Introduction The complexities o f the near-ultraviolet absorption spectrum of sulphur dioxide have attracted continuing interest over the last sixty years [1-13]. The lowest observed transition is the 3B~ ~ X ~A l transition which has been well characterized from bulb [4,5] and crystal [6] spectra between 390 and 345 nm. At higher energy this transition is supplanted by a series of gradually intensifying vibronic bands which have been attributed to the mixing of two singlet electronic states [8,9,11,14]. These are an electronically forbidden ~A2 state, for which the

* Corresponding author.

analyses of Brand and Nanes [7] and of Hamada and Merer [8] have placed the origin near 28000 cm - I , and an allowed 1B~ state at higher energy, from which the lower energy state gains its absorption strength via vibronic cOupling. The ~B 1 state is not directly observed, but proposed positions for its (000) level start above 31000 cm-1 [9,14]. Extensive perturbations of rotational structure, the absence of transitions with attributes expected of the t B I state, anomalously long lifetimes, and the observation of magnetic field effects indicate involvement of Renner-Teller coupling to the dense ground state vibrational manifold as well as singlet-triplet interactions via spin-orbit coupling [ 11,14-19] The peak intensity of the first singlet absorption band is not reached until ~ 35000 cm -1 [14], some

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7000 c m - l above the presumed 1A2 origin, and the sharp decline in intensity toward the red has hampered investigation of the low energy region of the manifold. The scheme of two mixed singlet states with origins near 28000 and 31000 cm -~ outlined above was advanced when only about one dozen cold singlet-singlet vibrational transitions below 31000 cm -~ and a further 14 or so between 31000 and 32000 c m - i had been correctly identified. Based on this limited direct data and application of a variety of arguments involving measured isotope shifts and Franck-Condon patterns in absorption and emission [7-9], approximate vibrational frequencies for both singlet states were proposed which have since constituted the standard working model for vibrational structure in this region. During the last decade, a number of molecular beam studies have added substantially to the list of bands between 31000 and 32000 cm-1 [10-12]. Nevertheless, as we began the current experiments, with the intention of studying the ultraviolet spectroscopy of SO 2 van der Waals complexes, it became evident that the majority of SO 2 vibrational levels between 28000 and 32000 cm -~ had still not been identified in the literature. We made it our goal then to fill this gap, because a complete and accurate tabulation of SO 2 bands is essential both as a practical tool for more complex spectroscopic studies and as a test of any theoretical model of SO 2 vibronic structure. In a preliminary report on our work [13], we identified four further singlet vibrational levels below 30000 c m - l , which were found to be consistent with the ~A2 vibrational assignment of Hamada and Merer [8]. In this paper, we report the full results of our investigation of SO 2 vibrational bands between 27780 and 32500 c m - i ( ~ 360 to 308 nm), in which variation of molecular beam parameters (e.g., SO 2 concentration, carrier gas species, total pressure, and laser-to-nozzle distance) has been used extensively to identify the nature of observed transitions. The presentation is organized as follows. After a description of the experimental apparatus in Section 2, results are presented in Section 3. In Section 4, we discuss several topics related to these results: the dependence of vibrational cooling on carrier gas and vibrational mode (Section 4.1), identification of transitions due to minor isotopic species (Section 4.2), a group of levels exhibiting novel Franck-Condon

patterns (Section 4.3), and the evaluation of theoretical models of excited state vibronic structure in light of the many newly reported cold bands (Section 4.4). We conclude with a summary of findings in Section 5.

2. Experimental The experimental apparatus and procedures employed in this work have been described in detail elsewhere [13]. Briefly, nanosecond UV laser pulses were generated by frequency doubling the output of a Q-switched N d - Y A G pumped dye laser. The wavelength range 360 to 307.5 nm was covered using the dyes LDS 698 and DCM. The bandwidth of the UV output beam was typically ~ 0.5 cm -I . The laser beam crossed a pulsed molecular beam of room temperature SO 2 entrained in He, Ar, or N 2. High purity SO 2 (Air Products, UK 99.97%) was used both without further purification and after vacuum distillation, with no differences observed in the resulting spectra. The sample and carrier gas were either premixed or mixed on-line using an adjustable needle valve to select the desired SO 2 concentration. Nozzle diameters of 300 and 100 Ixm were employed, with stagnation pressures of from 3 to 7 atm absolute. For fluorescence excitation spectra, fluorescence was collected by an f / 1 quartz lens and directed through a Melles Griot GG395 filter onto a UV sensitive photomultiplier tube. The fluorescence signal and the measured excitation power were averaged by a boxcar integrator, the latter for use in subsequent signal normalization. For dispersed fluorescence, the filter was replaced by a 0.5 m spectrometer which was scanned with the excitation wavelength held fixed. Band intensities as given in Table 1 have been determined by integrating over rotational contours and subtracting the contribution of the estimated local background intensity due to scattered light and a quasi-continuum of absorption which increases with energy and SO 2 concentration. To establish a true relative intensity scale spanning the entire range of these experiments, intensities of bands in regions common to successive scans have been matched as

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

accurately as possible. For all spectra utilized in the determination of relative intensities, multiple scans were run to verify the stable operation of the pulsed molecular beam valve. Reproducibility of intensities in such series of scans was usually better than 5%. In conjunction with selected scans, wavelength calibrations were performed by comparing the laser wavelength to those of spectral lines from neon and argon discharge lamps by means of a 0.85 m double spectrometer. Clearly identified SO 2 hot bands and the accurately known ground state vibrational frequencies [20,21] made it possible to extend the calibration into regions where neon and argon lines were sparse. An accuracy of ~ 1 cm-~ in the frequency scale was thereby achieved throughout the region of study. Band centers which are given in Table 1 only to the nearest 1 cm-~ are recognized to have higher than normal total uncertainty, estimated at + 2 cm - t , due either to unusual band contour shape or low intensity. Wavelengths are given as values in air and wavenumbers are corrected to vacuum.

3. R e s u l t s

The principal results of this paper are contained in Table 1, in which are listed and identified all vibronic transitions observed in fluorescence excitation spectra of jet-cooled SO 2 between 27780 and 32500 cm -1 . In this section, we describe the format in which this information is presented and the experiments and procedures involved in its derivation. The band centers (~) of all cold bands (i.e. transitions originating in the vibrationless level of the electronic ground state) identified in this study are listed in the first column of Table 1, with relative intensities given in column 3. All other bands observed in the course of our experiments, most of which are identified as hot bands, are listed in column 2. The relative intensities with which these latter bands appear in a given spectrum depend on the molecular beam conditions. The intensities given in column 3 are the maximum values measured. Entries in Table 1 that are uncertain have been placed in braces. These include weak bands that have not been observed consistently under a variety of conditions, and poorly resolved structure which can-

183

not be reliably classified based on the effects of varying beam conditions (vide infra). Band assignments for 3B 1 levels, minor isotopic species, and hot transitions are given in column 4 of Table 1. The first two are discussed in Sections 4.4 and 4.2, respectively. In the hot band assignments, the upper vibronic level is identified by its energy above the (000) level of the ground state, and the lower level by its vibrational quantum numbers. Hot band assignments based solely on the ground state interval are placed in square brackets unless the lower level is a member of (nOOY', lbr which a favorable Franck-Condon overlap is generally expected [9,12]. To resolve individual vibronic bands and establish whether observed transitions are hot or cold, control over vibrational and rotational cooling in the molecular beam is of primary importance. As has been previously reported [15,13], the rotational temperature (T~ot) of SO 2 is strongly influenced by the concentration of SO 2 in the expansion, with the lowest Trot achieved at low concentration. We have further found, however, that vibrational cooling improves with increasing SO 2 concentration [13]. While the consequent inverse relationship between Tvib and Trot with respect to concentration may appear surprising at first glance, it simply provides evidence that the vibrations of SO 2 are more effectively relaxed by collisions with other SO 2 molecules than with molecules of the carrier gases used, while the converse is true of its rotations. Other factors known to influence molecular beam temperatures, such as the ratio of laser-to-nozzle distance to nozzle diameter ( X / D ) , stagnation pressure, and carrier gas, were also varied in this work, but their influence was only able to modify within a limited range the scale of temperatures determined by the choice of concentration. In light of this fact and the inverse cooling effect described in the preceding paragraph, no single set of experimental conditions allowed both optimum resolution of closely spaced bands and elimination of hot bands. For example, Fig. 1 shows a fluorescence excitation spectrum of SO 2 in which data from a number of separate scans have been joined together to cover most of the spectral range studied. Moderate to high (>/6%) SO 2 concentrations were selected for these scans in order to strictly limit observable hot band

J.S. Basldn, et al. / Chemical Physics 200 (1995) 181-199

184

x 50 (--x 5000

o1

o

b.

IJ .

360

350

340

.

.5

i.i_ .

,

.

.

.

.

.

.

330

.

,

320

-

,

310

Wovelength (mm) 30000

30200

Fig. I. Normalized fluorescence excitation spectrum of SO 2 in a molecular beam. Conditions were chosen for effective elimination of hot band activity. The data above 333.5 nm and in the box are magnified by factors of 50 and 5000, respectively, as shown. Sample mixtures and beam conditions for each wavelength range (in this and the following captions, concentrations are estimated except were the use of premixed samples is indicated): 327.5-308 nm, 6% SO 2 in 30 psig He and X / D = 90; 333.3-327.5 nm, 6% SO 2 in 30 psig Ar, X / D = 70; 348-333.6 nm, 10% SO 2 in 30 psig Ar, X / D = 50; 357-348 nm (and 357-346.6 nm in inset), 10% SO 2 in 30 psig He, X / D = 25; 359.7-357 nm (main figure and inset), 10% SO 2 in 30 psig At, X / D = 60.

activity. As a result, rotational temperatures were also moderate to high, on a relative scale ], even for those scans recorded at high values of X/D. To obtain better resolution, at the expense of an accompanying increase in hot band intensity, spectra were also recorded using lower concentration sampies. A detailed view of three such spectra is shown in Fig. 2, above a similarly expanded plot of the data of Fig. 1, covering the high energy range in which spectral congestion is most severe. The specific beam conditions for the upper spectra (which will be pertinent to discussions in Sections 4.1 and 4.3) varied as detailed in the figure caption. The obvious narrowing

J Qualitative assessments made here of rotational temperatures (low, high, etc.) are based on the relative widths of observed contours. For contours characterized as "moderate", such as contour (c) in Fig. 2 of Ref. [13], Trot is estimated at roughly 10 K by comparison with published spectra for which rotational temperatures have been calculated [9-11]. In our " l o w " Trot spectra, as, for example, Fig. 2e of Ref. [13] and the lower scan of Fig. 3 in this paper, rotational contours of 2.7 to 3.7 cm -1 fwhm are measured, with intensities of isolated bands dropping to less than 1% of the peak value at + 5 c m - i.

30400

30600

Wovenumber

31200

31400

31600

30800 (cm'9

31800

3|000

32000

31200

32200

Wovenumber (cm") Fig. 2. SO 2 fluorescence excitation spectra recorded with variation of vibrational and rotational temperature. The bottom spectra are those of Fig. 1. Above these are shown three spectra obtained for the following sample mixtures and beam conditions: lower, 3% distilled SO 2 in 90 psig Ar (premixed) and X/D=80; middle, 1% SO 2 in 30 psig Ar, X / D = 50; top, 3% SO 2 in 30 psig He, X / D = 25.

of the band contours in these spectra permits many hitherto unresolved bands to appear distinctly. Relative intensity variations in spectra such as these also provide the principal tool for determining the provenance of observed bands. An ideal case is offered by bands that appear only under certain beam conditions (e.g. those at 30116, 30133, and 30147 cm- ] ) which can be placed immediately in column 2 of Table 1. The assignment of many of these as ~,'( hot bands is obvious, as also noted in Ref. [12], based on intensity patterns and the measured ground state interval of 1151.7 cm -l [20]. Several other strong hot bands are readily assigned to transitions from v~ (517.9 cm -I [21]) consistent with favorable

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

Franck-Condon factors exhibited in dispersed fluorescence [ 12]. The cleanest of these are the bands at 30656 and 31201 cm -1. Observation of bands such as these makes it possible to assess changes in v]' and v~ populations between any two measured spectra. When, in contrast, the intensity at a given energy varies but does not vanish under any beam conditions, identification of the number and nature of transitions involved is based on the following considerations: (1) how the variation in intensity compares to variations of the isolated v'~ and v~ hot bands; (2) whether hot bands are expected at the energy in question, based on observed cold bands and measured Franck-Condon factors; and (3) the observation of associated hot bands, for example, 518 or 1152 c m - ~ below the energy in question. The last point will be discussed in relation to the identification of isotopic species in Section 4.2. When a hot and cold band are found to overlap, if the hot band achieves sufficient strength, then both band centers and their associated intensities can be measured, and the two bands are listed separately in Table 1. Otherwise, two intensities are given next to the entry for the cold band, one measured under conditions of minimum hot band activity and a second (in parentheses) under conditions of maximum hot band activity, with the hot band assignment also in parentheses. From comparisons with the rotationally resolved spectrum of the 29459 c m - i band [8], it appears that the three peaks in the typical rotational contour observed at our low temperature and low instrumental resolution [13] correspond, in order of increasing energy, to (in the prolate symmetric top approximation) (1) a °Q I band head, (2) rQ transitions for low J" and K", and (3) overlap of rR transitions for J " = 0 to 4. For bands displaying this structure, the term value, v0, lies ~ 1 c m - l lower in energy than ~, the band center. Comparisons of the values quoted in Table 1 with the results of rotational analyses carried out on a number of bands throughout this region [8,11,14] show fairly consistent agreement with this expectation. Exceptions involve cases of highly perturbed rotational structure where the rotational analyses are uncertain. Of course, these same bands are likely to have unusual contours as well, leading to some ambiguity in the determination of ~.

185

Several points regarding interpretation of the relative intensities given in Table 1 should be borne in mind. Firstly, use of a high pass filter favors some bands over others both because the separation of the bands from the cutoff wavelength changes significantly over the range of the experiments and because the intrinsic emission patterns of different bands vary widely [9,12]. Secondly, the fluorescence lifetimes of bands in this region also vary widely [16,19], often greatly exceeding the limited temporal viewing window ( < 10/xs) afforded by the passage of molecules excited in the molecular beam across the field of view of the collection optics. Our detection efficiency therefore changes from band to band, depending on its lifetime and on the optical alignment. The latter dependence may explain why reproducible but different results were obtained on different days for certain relative intensities, such as those referred to in footnote f of Table 1. Both of the above factors, spectral distribution and lifetime of fluorescence, are also sensitive to collisional relaxation in the excited state, as observed in SO 2 molecular beam studies at higher energies [22]. A change in the collision rate in the jet may then also affect measured intensities. A third variable having an influence on measured intensities is saturation. In some of our experiments the relative intensities of a few strongly absorbing transitions changed by as much as 50% when the excitation power was halved. While efforts have been made to minimize the effect of saturation on the values reported, they have not been exhaustive or uniform across all spectral regions. The first two points above should not effect the vibrational temperatures calculated in Section 4.1. for the molecular beam, but the third may certainly do so, since the difference in Franck-Condon factors typically enhances the susceptibility of hot bands to saturation. The pair of bands at 30057 and 30086 c m - I warrants a special note. The latter is listed as the more intense in Table 1, as we found to be the case at moderate to low Trot (see Fig. 2), but 30057 c m - l had equal or slightly greater intensity at high Tot in our beam. No hot band involvement seems capable of accounting for this observation, and extrapolation of this trend to the much higher rotational temperatures of bulb measurements might explain why the 30057 c m - i band but not the 30086 cm-1 band was

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J.S. Baskin, et al. / Chemical Physics 200 (1995) 1 8 1 - 1 9 9

observed in previous studies [7,3]. Rotational perturbations of the type observed [11] in the Clements' A band provide a possible explanation for such behavior. (The A band is comprised of the four vibrational levels from 31918 to 31950 cm-1,) A final point concerns the listing of bands that occur at high concentration only. Due to the large decrease in the A rotational constant from the ground to the ~A2 electronic states, the normal band contour in the spectral range studied, resulting as it does from a c-axis polarized singlet-singlet transition in a prolate top, shows a severe red shading of K subband structure. These subbands can extend up to 30 cm-1 below the band center in experiments at high SO 2 concentration, for which T~ot is high. Most peaks that grow with concentration are attributed to such subbands and are not listed in Table 1. However, some high concentration peaks which appear to fit least well into a "typical" pattern of rotational subbands are reported as separate bands. Some or all of these may also be subbands which are distorted by large perturbations known to affect the bands throughout the region studied [8,11,14]. Even in this case, their inclusion in Table 1 is of practical utility since they may easily be mistaken for separate bands. Such peaks could also be due to forbidden vibronic bands which appear at higher rotational temperature via Coriolis coupling, or to SO 2 dimers, which are known to form with relatively high efficiency in supersonic expansions [23,24], although there is no obvious relationship between bands of this group and the cold bands of SO z, as would be expected of dimer bands.

4. Discussion

conditions producing v'~ hot bands about equal to those in the scan beneath, the v~ hot bands are about a factor of 4 lower in intensity. Hot bands of 2 v~ are also reduced in the top scan. (Because the concentrations as well as the carder gas species differ between the scans, these results reflect only a relative and not an absolute improvement in v~ cooling from Ar to He.) The comparative effect of nitrogen on v~ and v'~' hot bands appears to be intermediate to that of Ar and He, although the absolute cooling efficiency of N 2 was lower than for either of the other gases. At higher concentrations of SO 2, the differential effect of the gases is difficult to ascertain, because all hot bands become much weaker. One may quantify the above observations by calculating for each hot vibration a Boltzmann temperature which yields the same ratio of hot band to cold band intensity as that measured in a given excitation spectrum. (Since different vibrational modes are not generally equilibrated, the "temperatures" found for different vibrations are not expected to be equal.) We use as the basis of these calculations the relation [25] Ii

.

lj

.

A significant feature of the spectra in Fig. 2 is the different effect or argon and helium on the cooling of the v'( and v~ populations in the low concentration scans. From the second to the third scans in the figure, numbering from the bottom, all hot bands increase fairly uniformly. Both were measured in argon, at different SO 2 concentrations and pressures. However, in the top scan, recorded in helium under

.

l,j

(F-C) i . . exp ( E j - e ' i ' ) / k T ] [ "

(F-C)j

(1)

for the ratio of fluorescence excitation intensities I i and lj of two transitions at frequencies v i and vi which terminate on a common upper vibrational level and originate in thermally equilibrated levels at energies ~ ' and Ej' in the ground state. ( F - C ) i / (F-C)j, the ratio of squared vibrational overlap integrals (Franck-Condon factors) for the two transitions, may be derived from dispersed fluorescence measurements and the following equation for the ratio of emission intensities [25] I?m

4.1. Mode selectivity and carrier gas dependence of vibrational cooling

l-'i

Ifm

.~_ ( 1)/]4 (F-C)i ~ vj] ( F - C ) j "

(2)

We have measured dispersed fluorescence for a number of single vibronic bands, for the more intense of which we have corrected the resonance fluorescence for scattered laser light. These are generally in reasonable agreement with the data of Metha et al. [12] for major bands in the spectrum, allowing for the fact that our spectra have not been corrected for the slight wavelength dependence of detection efficiency. There are, however, some significant dif-

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

ferences. Fo~ tmple, we find emission to v~ to be 2.5%, 2%, ano ~< 1.5% of that to v]' for the 30553, 31037, and 32042 cm -I bands, respectively, while these ratios from Ref. [12] are 12%, 0%, and 6%. The cause of these differences is uncertain, but one possibility is collisional relaxation, as mentioned earlier [22]. If this occurs, the Franck-Condon factors obtained from the dispersed fluorescence are not purely those of the optically active excited state vibration. In making the following calculations, we assume that the majority of emission observed in molecular beam experiments is that of the initially excited level, and thus that F - C factors determined from strong emission lines are reliable. We note also that calculated temperatures, due to their logarithmic dependence on F - C factors and intensities, will be reasonably accurate even when errors in these measurements are rather large. We first make two independent calculations of the single v]' temperature which characterizes the top two spectra of Fig. 2. From our dispersed fluorescence, the ratio of emission intensity to (100Y' to that to (000)" was tbund to be 8.2 for excitation to 31795 c m - i and 5.6 for excitation to 32042 cm - I . The v]' hot bands to these two levels have intensities of about 4 and 1.6 in the spectra of interest. (Since a v~ hot band to the 31409 cm-1 level coincides with the u'~' hot band to 32042 cm -1 (at about 30891 cm-~), the latter intensity was derived from measured intensities of 2 and 3.3, respectively, in the helium spectrum and upper argon spectrum of Fig. 2.) One finds good agreement between the two sets of values, both yielding a v'~/(OOOY' population ratio with an equivalent temperature of about 235 K. Similarly, considering the transitions 31718 cm -1 ~(010Y' (which occurs at 31201 cm - I ) and 31718 cm -1 ~ (000)", and using an emission intensity ratio of 1.4 derived from the dispersed fluorescence spectra shown in Fig. 2 of Ref. [12], v~ temperatures of 140 and 190 K are found for the helium and upper argon spectra, respectively. The difference in these values represents the difference in relative cooling capacity between He and Ar, while the large difference between the v'j' temperature and both v~ temperatures leads us to conclude that jet cooling is more effective for v.~ than for v'~ in all carrier gases used. For hot bands at wavelengths above 334 nm, we find that the intensities given in Table 1 and F - C

187

factors from dispersed fluorescence yield v'~ and 2v]' temperatures in the range of 280 to 310 K. These intensities were derived from experiments in which small X / D and excitation in the edges of the molecular beam pulse were used to intentionally maximize vibrational temperatures.

4.2. Assignment of transitions by isotopic species There are three naturally occurring minor isotopic variants of SO 2 of sufficient abundance to merit consideration here: 34SO2 (4%), 33SO 2 (0.8%), and SJ8OI60 (0.4%). A significant criterion for the identification of bands due to these species are their shifts from the corresponding bands of 32SO2. For S18ot60, a rough guide to the shifts is given by taking half the measured S1802 values [7]. For 3450.~ and 33SO2, estimates of band shifts were calculatec] in harmonic approximation, based initially on the proposed vibrational assignment of Hamada and Merer (which itself was derived in part from the isotope shifts of St80/) [8]. These calculations require a complete set of normal mode frequencies for the ground and excited states of each species. The only precisely measured fundamentals available for these two species are v I and v 3 of the 34502 ground state [21]. Remaining frequencies were derived from those of the normal species using Teller-Redlich relations for symmetric triatomics [26], combined with the IA l a n d IA 2 bond angles of 119.3 ° and 99.6 °, respectively [8]. Since only u 3 and the product u l . u 2 are given by these relations, estimates of ul and u z were made by assuming that the fractional change upon isotopic substitution calculated for their product is shared equally between them. In the case of 34SO 2, calculations were also made applying the experimentally derived ground state isotope ratios to the IA 2 state 2. Using these values, one finds shifts to lower energy of 34SO2 bands relative to those of the normal species increasing from under 10 to about 50

z In principle, the valence force model for symmetric triatomics [27] permits calculation of all three individual frequencies, but, in practice, valence force calculations of individual v~ and v 2 values were not found to be accurate even for the 32 SO 2 ground state, nor are the vibrational frequencies for the ~A2 state from Ref. [8] compatible with a valence force description.

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J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

cm -1 over the range of observed singlet bands. Shifts at a given excess energy depend substantially on the mode character of the vibration, particularly its v 3 content, since v 3 is most sensitive to sulphur substitution. The predicted shifts of 33SO2 bands are slightly more than half those of 34SO2. Bands whose positions and intensities relative to a stronger band are consistent with the predicted range of shifts and the natural abundance of one of the minor species are identified in column 4 of Table 1 by the pertinent substituent atom. Most isotope assignments are based only on this circumstantial evidence and are indicated as questionable. When possible, supporting evidence for the species assignment was sought in the ground state vibrational frequencies of the molecule, which can be determined from hot transitions and dispersed fluorescence. For example, observation of a hot band I 152 cm-1 below a transition of interest is conclusive evidence that it is a cold band of 32SO 2 (assuming that no alternate assignment exists for the hot band). Unfortunately, however, the comparable test for assignment as a cold transition of the most abundant minor species is not as definitive, since the values of v'~ of 34802 and 2v'(-v~ of 32SO2 are almost equal (1144.5 and 1144.1 c m - 1, respectively [20,21]). This has the interesting consequence that a hot band at ~ - 1144 c m - 1 can be associated with either a cold band of the 34SO2 isotope or a v'~ hot band of 32SO2. As an illustration of these points, two scans of the band cluster between 31100 and 31200 cm-1 (around 321 nm), are compared in Fig. 3 with a scan of the spectral range 1151.7 cm -~ lower in energy. The scale on the x-axis applies to the bottom and middle traces, at low and moderate Trot , respectively. There are three prominent cold vibrational bands listed in this region, at 31130, 31149, and 31174 cm -1. (The second of these consists of the two distinct peaks seen at 31146 and 31151 cm - l . It and similar related bands will be discussed further in Section 4.4.) The 31130 c m - I band, marked by a dashed line in the figure, is clearly resolved from 31149 cm - I only at low Trot , but it can also be seen in Fig. 2, where it appears with comparable intensity in each of the three upper scans. It has been assigned as a cold band on the basis of this behavior, among other considerations.

I Wovenumber

(cm-D

Fig. 3. Comparison of two scans of the 31100 to 31200 cm -I region of the SO 2 spectrum with the corresponding hot transitions 1152 cm - l lower in energy (top). Wavenumber values are approximate. Sample mixtures and beam conditions for the three scans: lower, 1% SO 2 in 30 psig Ar, X / D = 50; middle, 6% SO 2 in 30 psig He, X / D = 90; top, 6% SO 2 in 30 psig He, X / D = 25.

The rotational temperature for the top scan of Fig. 3 was similar to that of the middle scan, while the spectral range covered is shifted down by an interval equal to v~' of 32SO2. The 29942 and 30057 c m bands, which are the strong bands exceeding the scale of the plot, are the only cold bands in this range. The intervening hot structure, listed in four entries in column 2 of Table 1, shows peaks clearly matching those at 31146, 31151, and 31174 c m - ~ in the scan immediately beneath it, confirming their assignment to transitions from v'( in 32SO2. There is no equivalent match, however, for the lowest energy hot band at 29986 c m - l , marked by the second dashed line in Fig. 3. While there is some intensity in the middle scan at the corresponding energy, it is clear from the bottom scan, in which the rotational contour of the 31149 cm-J band is greatly reduced, that there is no distinct cold band at that position. Nor has any other likely hot assignment involving 32SO2 been found for the 29986 cm -1 band. Similarly, the 31130 cm -1 band, which is 1144 cm -1 higher in energy, has no apparent 32SO2 hot band counterpart in the upper plot. These circumstances are consistent with the two bands either

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199 being a hot and cold band pair of the 34SOz molecule, or being 2 v l' and v'~ hot bands of 31SO2. Comparison of intervals in the dispersed fluorescence of the 31130 cm -1 band with vibrational data for the ground states of 32SO2 and 34SO 2 [20,21,28] confirms this conclusion. The indications that 31130 cm-~ is a cold band, as well as the shift of the 31130 cm -1 band from the 31149 cm -t band and the intensity ratio of the two bands of about 1:20, strongly suggest that the 34502 assignment is the correct one. A noteworthy feature of the list of transitions of minor isotopic species is the absence of any 34SO2 analog for the very intense 30995 c m - l band. The expected intensity of about 19 would make this band easily detectable in the predicted spectral range (20 to 30 c m - J red of 30995 c m - 1). The obvious candidate, the 30967 cm-1 band, is marked as a transition of the normal isotope by a hot band 1152 cm -~ lower in energy. There is potentially an alternate assignment for the 29815 cm -~ band as 30851 cm -~ (020)", but the dispersed fluorescence of Ref. [12] shows that no intensity is expected for this transition. There is also evidence to suggest that 30851 and 30857 cm-~ are not independent vibronic levels (as discussed in Section 4.4), making the appearance of an isolated hot band of 30851 cm -1 impossible. Moreover, there is clearly no hot band at ( 3 0 9 6 7 1144) = 29823 cm -~ of the intensity expected if 30967 cm -t were a 34502 band. The weak band at 30981 cm-~ is also believed to be a 32802 band on the basis of the hot band at 29828 cm -1. We therefore conclude that the 34SO2 band in question is unusually weak or displaced a minimum of 10 c m - ~ out of its predicted energy range, assuming the displacement is such as to leave it unresolved from the normal isotope peak. A possible explanation for an anomalous intensity a n d / o r position is a severe vibronic interaction caused by a close resonance with a perturbing vibrational level in one of the isotopic species and not the other. This could occur since the isotope shift would differ for the two interacting levels. No previously available data 3 or The much larger shifts reported to above 33000 cm- t for the 32S 1sO2 isotope [7], including that of the 30995 cm- l band, show no deviations outside experimental uncertainty and the + 10 cm- i variation expected from differences in mode character.

189

analyses would suggest such an explanation at this energy, at least 250 c m - i below the accepted origin of the ~B~ state, but it is consistent with evidence to be presented in Section 4.4 of complications in vibronic structure exceeding and at lower energy than any recognized prior to this study. 4.3. Evidence f o r levels with novel Franck-Condon patterns and weak cold absorption Bands identified by footnote c in Table 1 display a very similar intensity dependence on beam conditions to those bands which are readily assignable as v~ hot bands, including a marked intensity increase relative to v'[ hot bands in Ar compared to He, but are not shifted from any prominent cold band by a low ground state interval involving v~. A common explanation for this group is favored not only by the shared intensity variation of its members, but also by the fact that many of them seem to join into progressions with intervals close to the 300 c m - l interval of the cold band progressions. However, since assignment of these bands as transitions from v~ implies drastic deviation from known Franck-Condon patterns and the existence of a number of vibrational levels not otherwise observed, careful consideration was given to possible alternative assignments. Evidence gathered in the investigation of two of these bands is presented in this section. First is the 32019 cm-1 band. Since the energy of this band is approaching the upper limit of our detailed studies, we can only say that there is no obvious hot band assignment from any ground state vibration below ~,.~. There is a weak band at ~ (32019 + 518) = 32537 cm - I , with an estimated relative intensity (from a scan using an expansion of 6% SO 2 in argon) of 20, roughly half the maximum intensity of the 32019 cm-1 band itself. Similarly, a weak shoulder to the red of the Clements' F band is near (32019 + 1035) cm - t . No associated hot bands are identifiable in the congested spectral region ~ 1152 cm - t below 32019 cm -1. The dispersed fluorescence of the 32019 cm -J band at 80 c m - l resolution is shown in Fig. 4. The displacements of the emission bands from the excitation energy (calibrated relative to a high resolution scan of 32042 cm -1 dispersed fluorescence) are shown in the figure and listed in Table 2. Included in

190

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

Table I Vibrational bands in the fluorescence excitation spectrum of SO 2 between 27780 and 32500 c m Band center (cm- i) cold

Relative intensity a

Band assignment

other

27837 27934 27978 27989 28257.7 28275 28307.4 28323 28366 28394 28457 {28492 28497 28523 28560.3 28574.9 28621.4 28626 28668 28700.6 28790.0 28829.6 28855.3 28906.4 28934.4 28940.8 29036.3 29048.4

cold 0.21 0.16 0.03 0.04 0.04 0.01 0.11 0.16 ~ 0.02 ~ 0.02 ~ 0.02 0.04 0.02 0.02 0.04 0.20 0.06 0.03 0.06 0.25 0.15 (0.20) 0.03 0.24 0.42 0.24sh ~ 0.03 ~ 0.04

{ ~ 29070 29092.8

29163.0

0.51 0.04 1.2 0.04

29182.4 29208.2 29218.3 29227.4 29885.5 29915.5

0.O5 0.16 sh 0.3 0.26 7.2 1.1

{29128 29142.1

29941.7 29985.7 29992.4 29998.3 30021.0 30057.4 30085.5 30115.9 30133.2 30147.4

Band center (cm- l)

15 0.4 sh 0.4 sh 3.2 0.5 12 15 2.0 1.5 2.5

3B l (210) 3B I (012) [29644-(110)] 29142-(100) 30553-(200) [29942-( 110)] 29459-(100) 3B I (300) 31795-(300)? 30691-(200) 30753 -(200) 29644-(100)} 3Bj (230) 3B l (102) 30857-(200) 29727-(100) 29774-(100) 3B i (310) 3B I (160) 30995-(200) 29942-(100) 3B I (I 12), ([30379-(030)]) (31151)-(200) 30057-(100) 30086-(100) [29459-(010) 30186-(100) [30714-(I 10)], 31342-(200) 3B i?} 30244-(100) 34S or [29644-(010)]?} 31457-(200), [30714-(030)] 31478-(200) [29727-(010)] 30370-(100) 30379-(100) 31037-(100) 31581 -(110) (and 31 063 -(100))

l

Relative intensity a other 29247-58

29278 29286 29301 29314.4 29332 29336 {29344

0.34

~ ~ ~

29352.6 29358.2 29377.9 29401.3 29423.8 29429 29458.8 29473.3 29485 29500 29507 29525.3 29539.7 29562.7 {29572 29589 29602.0 29621 29636.5 29644. I 29668.9 29700 29705.2 29726.9 29773.6 29815 29828 29844.1 29873 30538.2 30552.6 30567.1 30579

31130-(100) 34S (31146)-(1 00)

30617.1 30627.2

~

~

0.04 0.04 0.04 0.23 0.04 0.03 0.02 0.08 0.1 0.07 3.4 0.4 0.1 sh 7.0 0.1 0.06 0.08 0.08 0.3 sh 2.0 0.8 0. I 0.15 sh 1.4 0.1 0.2 sh 0.8 (1.0) 0.3

0.6 sh 1.6 2.2 (2.7) 11 0.43 0.3 13 2.5 sh 4 100 5 3 6 1.2 sh

(31151)-(100) 30633.3 30642.4 30655.7

31174-(100)

31267-(100) 31285-(100) 31301-(100)

30675.8 30691.0 3~13.8

Band assignment

1.4 4 3.2 14 52 18 (25)

30399-(100), 30405-( 100), [29774-(010)] 30430-(100)

31581-(200) 30445-(100) 34S 30466-(100) 30998-(110)? h [30370-(020)] [30379-(020)]} 31024-(110) 31674-(200) 30553-(100) [29942-(010)] 30579-(1 00) 31769-(200) (31151)-(110) 31795-(200) 31174-(I 10) 30676-(1 00) 30691 -( 100) 30714-(100) 30723-(100)} 31769-(120) 3O753-( 100) 31918 -(2OO) ?b (? h) 30821-(100) (or [30186-(010)]?) 30851 -(100) 30857-( 100) (30878-(100)) 30967-( 100) 30981 -( 100) 30995-(100) 31024-( 100) ~4S 31718-(100) 31769-( 100) 31780-(100). (31146)-(010)

(31151)-(OLO) 31795-(100) 31174-(010)

(31861 -(100))

J.S. Baskin, e t al. / Chemical Physics 200 (1995) 181-199

191

Table 1 (continued) Band center (cm- ') cold

Relative intensity a

Band assignment

cold

other

{30169 30180-90 30186.5 30195.5 30244.3 30283.4 30286 30288.8 30305.3 30326.2 30328 30339 30357 30369.8 30379.2 30398.6 30405.0 30429.5 30430.5 {30442 30444 (30445 30465.6 30480.0 30501 30505.9

0.1 3 1.8 3 18 3.0 0.4 2.5 1.0 3.0 0.1 0.16 1.0(2.4) 13(16) 8.0 1.6/(3.4) 1.2J 3.0 0.6 0.5 0.7 0.3 7.0 2.2 0.6 5

30520.5

4

31062.8

480 ~ ~5sh 41 150 4 19

30995.4 31013.5 31024.5 31036.8 31045.5

31063.4

34S? }

[30714-(010)]

31440-(100) 31342-(020), 31456-(100) 31478-(100)

31119.9 31129.8 31148.8 31156.2 31160.4 31165 31174.4

1

4 5 7 3 13 sh 260 14 sh ~3

(31548-(100), 31558-(100))

{30838 30851.0 30856.7

3158141O0)

30877.7

31186 31191.6 31201.0 31209.0

1.2 2.0 2.7

30767.0 30777.9 30789.2 30789.9 30811-26

58 5 3 sh 13 3 ~8

30838.4

6

1

30998-(010) ? c in helium only 31024-(010), 31659-(100) 31674-(100), 31037-(010) ~S?

31581-(010) (and 32220-(I 00)) 32236-(100) 32244-(100) 32142-(020) ?c

31674-(010) high conc. a

31718-(010) 32244-(020)

30945.0

4 4 1

30960.5 30966.8 {30973.5 30977 30981 31409.0 31419.2 31435.1 31440 31448.8 31456.9 31477.9 31497.6

5 sh 13 3 sh ~2 3 56 I0 (26)

31507.6 31523.1 31534 31547.7 31558 31566 31581 31591.5 {31598.7 31604.0 31612.4 31621.1 31631.8 31646.5

23 3.3 ~ 1 (2 sh)

30918 30922

31607 32338-(100)

31918-(100) 31929-(100) 9¢ 31950-(100) 31333-(010), 31968-(100), 32485-(1 I0), 31974-(100) 31989-(100), 32507-(110) 34S?}

15 sh

30914.5

~4S = (31146) + (31151)

high conc. d 31769-(02O) ~4S?}

42 30891.0

1

50 3 3 19 1.7

30728 30733.6

30821

3457 (?) (31523-(100))

high conc. a} 31478-(020) 34S ?}

Band assignment

other

{30734 30753.3

31435-(100)

18 o? 18 o?

Relative intensity a

30723.4

31342-(100), 31333-(100)

6 31086 31092.9 31106 31115

Band center (cm- l )

250 150 3 40 f 270 18 15 330 8 sh 20 (33) 65 ~10 280 2 2 2 sh ~5 10 sh 37 (55) ~3 5O

32042-(100), 31409-(01 O) (32066-(100)) 31435-(010) 31440-(010) I~0 ,? 31478-(0 I0) 32125-(I 00)/ [(32011)-(020)]?

~4s?(? ,~)

34s?

partially ~4S,, [32027-(010)? c ?~ (32066-(010)) = (31556.7) + (31561.7) high conc. 'j 32627-(020) 34S?) 32125-(010) (32142-(010)) high conc. a

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

192 Table 1 (continued) Band center (cm-J) cold

Relative intensity a

Band assignment

other

31223.2 31235.1 31241.5 31252.4 31258.8 31266.9 31277.3 31285.1 31292.7 31300.8 31309.2 31325.4 31333.1 31341.7 31354 31366.1 31380.8 31392.1 {31400.2 31843.3 31844.8 31860.7 31886 31896 31900 31917.9 31929.0 31942.5 31949.6 31968.2 31973.7 31988.9 32008 32019.3 {32026.6 32041.7 32054.2 32065.6 32076.8 32084.0 32094.2 32107.1

Band center ( c m - t) cold

6 (8.5) 4 7 5 6 sh 140 5 90 5 sh 140 6 sh (16) 13 sh 45 65 (90) 4 ~ 1 4 8 6 sh} 12 ~ 30 320 14 sh 30 14 700 190 250 sh 560 50 sh (85) 190 (220?) 220 r 50 35 10 300 20 250 25 40 15 15

(32376-(100)) ~S? 32287-(020) (and 32399-(100)) 32411-(100)

Relative intensity a other

31659.2 31674.3 31683 31695.2 31702.0 31718.4 31727.5 31742.4

~ S or 32430~100)?

30 (50) 370 ~ 2 sh 20 30 e 640 ~ 15sh 5 sh

or 32449(100)? 31746 ([31828-(010)]? c)

31861-(010) 32506-(100) high conc. a

31749.0 31768.6 31780.3 31794.7 {31808 31819.9

high cone. a

~S ? ? c

(32485-(010)) (?)

31827.8 31838.4 {32116 32125.0 32142.1 32158.4 32168.7 {32175.6 32185.2 32199.7 {32207.8 32219.7 {32229 32236 32244.2 32259.3

30 20 780 45 sh 500 e

([32176-(010)1? c) ? 34S?

[32220-(010)1 [32244-(010)1 32895-(100) or [32259-(010)] 34S? [ ~ 32786-(020)]

2} 31820

? c

Band assignment

~

11 11 16 16 30 sh 300 820 80 70 25 sh} 1000 g

32338-(010) 34S? 34s?}

partially 34S? ?c

250 10} 400 25} 70 sh

32267.6

380 60 120

partially 34S ? [ ~ 32786-(010)]

= (32005.1) + (32011.3) Major bands only from 309.5 to 307.5 nm 32537-(010) c ~ S ?}

? c ? c

32287.3 32338.3 32375.9 32399.2 32411.4 32430.2 32448.7 32485.1

900 290 200 450 sh 750 180 600 ~ 600

a s h denotes shoulder. For bands other than cold bands, maximum observed relative intensity is given. h Assignment is discussed in Section 4.8. c These bands behave like v~ hot bands bat are not shifted 517.9 c m - i from strong cold bands. See Section 4.3 for discussion. a These features appear or grow stronger at high SO z concentration. See text for discussion. e These relative intensities varied greatly ( > 20%) with laser power and SO 2 concentration, in a manner consistant with saturation. ~ For these bands, relative intensities measured under the conditions of the upper scan of Fig. 2 were 50% higher than the values given. g Includes the peak at 32191.1 which becomes dominant at high concentration.

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

0 D ta_

31 O0

3200

3400

3300

3500

3600

WovQIQngth (~) Fig. 4. Dispersed f l u o r e s c e n c e o f the 3 2 0 1 9 c m - I absorption. Measured displacements f r o m the excitation are given in c m - j for m a j o r emission peaks. The p e a k at the laser w a v e l e n g t h ( m a r k e d b y an asterisk) is mostly scattered laser light, v~ progressions are indicated. S p e c t r o m e t e r resolution (R): 80 c m -~ . S a m ple mixture a n d b e a m conditions: 3 % S O 2 in 3 0 psig At, X / D = 25.

the latter is the band at - 4 4 3 3 cm-1 measured in a lower resolution scan since it is, with the - 3 3 1 5 cm-~ band, one of the two strongest lines in the spectrum. No emission was detected in scans extending up to 1300 cm -1 to the blue of the laser, v~'

Table 2 Emission b a n d s o b s e r v e d in dispersed fluorescence exciting at 3 2 0 1 9 c m - I in S O 2 Shift a f r o m excitation (cm- i )

Shift f r o m 32537 cm- i ( c m - l)

Terminal g r o u n d state assignment

Expected b _ m e a s u r e d shift (cm- i)

~-621 c -1148 ~ -1358 c ~ - 1542 c - 1788

-1140 -1666 -1876 - 2060 -2306

(100) (110) (011) (040) (200)

-12

-2188

-2706

(002)

- 2282 ' - 2699 -2915 -3192 c -3315 - 3431 -3817 - 4042 - 4433 a

- 2800 - 3217 -3433 -3710 -3833 - 3949 -4335 - 4560 - 4951

(210) (012) or (140) (300) (150) (102) (310) (112) or (240) (400) (202)

+ 2 0 c m -K . b F r o m Refs. [19,20,26]. c A p p r o x i m a t e positions for very w e a k lines. a L o w e r resolution m e a s u r e m e n t ( + 4 0 c m - l ).

0 0 -7 +10 -8 -7 -6or +11 +1 -7 -5 +9 - 9 or - 2 -1 -3

193

progressions accounting for all the major bands are also represented in Fig. 4. The emission peaks at - 1 7 8 8 , - 2 9 1 5 cm - l , etc., unambiguously signal involvement of v~ in the initial state. Analysis based on both the vibrational intervals and the intensity pattern uniquely favors the hypothesis of absorption from v~ to a level at 32537 cm -~. Shifts from this energy and the associated ground state assignments are given in Table 2. For these assignments, the strongest progressions become (n02)" and (nOOY'. Both are common in SO 2 dispersed fluorescence, with members of the (nOOY' progression among the most intense emission peaks in all reported spectra [9,12]. This evidence, in corroboration of the observed excitation intensity dependence, leads us to conclude that the 32019 c m - J band is a v~ hot band. While the above conclusion is based in part on compatibility with known emission spectra, it should be emphasized that certain characteristics of the Franck-Condon pattern implied for the 32537 c m level are quite unique among spectra measured either in this laboratory or elsewhere [9,12] for any band in the near ultraviolet absorption. Although differences which reflect the fact that 32537 cm -J is weak in cold absorption and the data available for comparison are subject to a sampling bias toward levels with strong overlaps to (000)" are expected, the degree of divergence is nonetheless striking. Most notable in this regard is that aspect which prevented immediate assignment of the 32019 cm -t band: the 32537 c m - ~ level displays a ratio of absorption from v~ to absorption from (000)" that is at least an order of magnitude greater than any previously recognized. Another distinguishing trait evident from Fig. 4 is the very slow buildup in (n00)" progression intensity. In no other known case is the intensity of the n = 1 member of this progression more than a factor of 2 or 3 smaller than the maximum, with n = 1 itself the maximum for all previously reported spectra recorded from 32100 to 34000 cm -1 . We next consider the 30789 cm -1 band. This time there is only weak absorption and no distinct band at the position 518 cm -~ higher in energy. The dispersed fluorescence measured while exciting at 30789 cm-~ in a beam of SO 2 at low concentration in Ar is shown in Fig. 5. Although some fluorescence intensity appears approximately 1750 cm -~

194

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

~>" i a~

£

(~ 1 ( 2 0 0 (300) ) "~10"~7 cm-'

30789 cm"~ ta_ 2000

1000

0

-1000 -2000 -3000 -4000 loser (cm-O Fig. 5. Dispersed fluorescence of the 30789 cm- t absorption in a molecular beam (R: 240 cm- i ). The dispersed fluorescenceof the 31037 cm-i band is shown for comparison (R: 160 cm-l), with the peaks of the (n00)" progression labeled. The peaks at 0 shift are predominantly laser light. Sample mixture and beam conditions for both spectra: 3% SO2 in 30 psig Ar, X / D = 25. 5 h i £ t £rom

below the excitation frequency, by scanning the laser while detecting at - 1 7 8 0 cm -1 , it could be clearly shown that the hot absorption responsible for this emission was centered at 30782.6 c m - l , corresponding to excitation from v~ to the 31301 cm -1 vibrational level. The remainder of the spectrum appears indistinguishable from those of many cold bands in this spectral region. As an illustration of this fact, we also show in Fig. 5 dispersed fluorescence of the cold band at 31037 cm - l , at slightly higher resolution, with the excitation energies of the two spectra aligned. At the low resolution of the 30789 cm-~ data in Fig. 5, it is impossible to conclusively assign the emission peaks. Some underlying hot absorption from v'( to the levels of the Clements' A band is certainly present, but under the given beam conditions, the contribution from the 30789 cm-1 band dominates this background, as seen in Fig. 2. If this band is a v~ hot band as its excitation intensity variation suggests, then the excited state level which is reached has a F r a n c k - C o n d o n pattern totally unlike that of any other known level, for its (nOOY' progression would show almost no intensity up to at least n = 4. The resemblance of this dispersed fluorescence to that of a cold band, and the unassigned hot band at 29636 cm -1, raise the possibility that the 30789 c m - J band is due to an SO 2 complex whose formation in the molecular beam is favored by low rotational temperature. Since the band is seen in all

carrier gases, the only candidate complex is the SO 2 dimer. For the relative concentration of dimers in the beam to rise as SO 2 concentration decreases would imply an extraordinary sensitivity to rotation. Moreover, substantial increases in stagnation pressure, such as for the second scan in Fig. 2, produced no enhancement of the band. These facts clearly favor attribution of the 30789 cm -t band to the SO 2 monomer, leaving the peak at 29636 cm-1 to be explained either as part of an unusual rotational contour for the 29644 cm-1 band or as a v'~ + v~ hot band of 31301 c m - i. We also considered assignment of 30789 c m - ~ as a v~ hot band. In the IA 2 state, only vibrations of species b 2 (eA2×Vb2=eVB 1 vibronic symmetry), which include an odd number of quanta of v 3, may be reached in vibronically allowed transitions from (000)" [8]. Conversely, from v~, transitions are vibronically allowed only to the totally symmetric vibrations of the ~A2 state, which in turn can fluoresce only to b z vibrational levels of the 1A 1 ground state. The dispersed fluorescence of Fig. 5 is consistent with this pattern, although the resolution is insufficient to allow any firm conclusions to be drawn from that data alone. However, it is clear from the figure that a strong transition is centered near ( 3 0 7 8 9 - 1150) cm -1, which must therefore leave the molecule with a net increment of one vibrational quantum in the v I mode after absorption and emission. This transition is predicted at 29641 cm -1 if the 30789 cm-1 transition originates in v~, or 29651 cm-1 if it originates in v~. An accurate calculation of hot band intensity expected from this transition in our excitation spectra is prevented by laser light contamination of the dispersed fluorescence and uncertainty about the relevant ground state vibrational populations in the molecular beam. However, under reasonable assumptions, the intensity calculated for a v~' + v~ hot band at 29641 cm -I is perfectly consistent with the observed increase in intensity of the 29644 cm-~ band in a vibrationally hot beam. If, on the other hand, 30789 cm -1 were a v~ hot band, neither the increase of the 29644 c m - 1 band nor the absence of a detectable hot band at 29651 cm-1 could be as readily understood. The evidence of the above examples leaves little grounds to doubt that there exist levels with an unprecedented bias toward absorption from v~ over

195

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

absorption from (000)", and therefore that assignIt ment of bands as 1:1, or possibly 2 v~, hot bands may generally be made on the basis of intensity variations alone. Specific assignments are given in Table 1, however, only when the existence of the upper level is confirmed by an observed cold band. (An exception is the assignment of the 30480 cm-~ band as a u ¢t2 hot band of an unobserved level at 30998 cm -L, whose cold transition is hidden within the contour of the 30995 c m - t band. Ample evidence, including contour widths, dispersed fluorescence of the 30995 cm-~ band, and the hot band at 29332 cm -1, supports this assignment.) From each band labeled by footnote c remaining without assignment, a vibrational level which is not represented in the cold band list of Table 1 can be inferred. It is important to recognize that for any description of SO 2 vibronic structure in this spectral range to be complete, it must account for these indirectly observed bands and their Franck-Condon patterns. 4.4. Assignment o f SO 2 vibronic structure

As described in the introduction, all singlet levels recently reported below 30000 cm - l [13] fit well into the assignment scheme established by Hamada and Merer for the JA 2 state [8]. With those levels firmly documented, there remained below 30000 cm -~ only two predicted vibrational levels of B 1 vibronic symmetry which had not been observed: (011)' and (001)'. From the regular and slowly decreasing intervals of the presumed (0nl), progression above 29142 cm - l , these levels are to be expected near 28825 and 28505 cm -~, respectively. The presence of a relatively strong absorption of the 3Bj ~ JA 1 electronic transition at 28830 c m - t (347 nm) precludes a definitive statement about a possible singlet-singlet transition at the first of these energies, although the intensity of such a band can be concluded to be at most a few percent of that of the 29142 cm -1 band [13]. The (001)' band is predicted near 350.7 nm. As one may see in the inset of Fig. 1, some very weak cold intensity does appear near this wavelength. Since observing a singlet level here would give a much firmer basis for the proposed assignment, we undertook a careful investigation of this region. The results are illustrated by the comparisons of vibra-

M

2

11.

28500

28600

28700

Wovenumber (cm'1)

Fig. 6. Unnormalized fluorescence excitation scans at high and low Tvjb in the vicinity of the proposed (001) band of the 1A2 electronic state of SO~. Sample mixture and beam conditions: upper, 6% SO2 in 30 psig Ar, X / D = 25; lower, 10% SO2 in 30 psig Ar, X / D = 60.

tionally hot and vibrationally cold scans shown in Fig. 6. The lower plot is a detailed scan of the wavelength range of approximately 351 to 348 nm under conditions similar to those of Fig. 1. The upper plot shows the same region at much higher vibrational temperature. From the large change in intensity of the 28621 cm -t u'~ hot band, one may be confident that all other hot bands have been effectively eliminated from the lower scan. Likewise, from observations of the changes in stronger hot bands outside the region shown, it can be concluded that any hot absorption remaining at 28621 cm -~ is a minor contributor to the intensity in the lower plot. From a study of Fig. 6, we are readily able to identify four weak cold bands. Of these, the two lower energy bands, at 28497 and 28523 c m - ~ , are poorly resolved in the lower spectrum due to the higher rotational temperatures of the jet. These bands were also observed in spectra recorded using distilled SO 2. We assign all four bands as 3B~ state absorptions on the basis of their characteristically broad rotational contours [5,13,29]. Although only the strongest of these bands is listed by Brand et al. from their bulb absorption study [5], the measurements shown in Fig. 1 of that reference, except for the rising background of con-

J.S. Bask, in, et al. / Chemical Physics 200 (1995) 181-199

196

gestion, agree very well with our data. On the other hand, a comparison of the 343 nm singlet and 347 nm triplet bands in our Fig. 1 with the same wavelengths in the absorption data shows that our relative sensitivity to singlet transitions is apparently an order of magnitude or more greater than theirs. Thus the close correlation of the two sets of data near 28500 cm -~ further supports the assignment of all observed structure to the triplet state. In identifying the three newly observed bands as 3B! vibrational levels, we are compelled also to consider how these bands fit into the vibrational structure of t h e 3B I state. The (000)' *- (000)" band of this system is at 25765.7 cm -] [29], and levels beginning with (100)' show perturbations in rotational structure attributed to interaction with other triplet electronic states [5]. Assignment of the bands below (000)' + 1800 c m - ] is straightforward [4-6], entailing only combinations of v'l and v[. Starting with these assignments, we were able to fit the excess energies of the eight bands we have observed and those of the nine lower energy levels as given in Ref. [5] to a simple anharmonic model. In light of the perturbations and uncertainties in the

Table 3 Vibrational constants ( c m -~ ) for the 3B~ electronic state o f S O 2 % = 1016 to 2 = 381 to3 = 1 1 1 4 x H = -62 x22 = - 3.5 x33 = - 6 0 Xl2 = - - 3 XI3

0

=

xz3 = - 2 0 YlN = 6.6 Yll2

=

--4

vibrational energies, the inclusion of higher order anharmonic terms was limited to only those needed to reduce the difference between calculated and observed term values to under 10 cm -1 for all lines. The resulting vibrational constants are given in Table 3, and vibrational assignments corresponding to this analysis are given in column 4 of Table 1. By assigning bands absent in the crystal spectrum [6] to combinations involving 2v~, all assignments could be made to totally symmetric vibrations.

%,

,,)-

o ql

I

q

"

II

1

a a a

.,

a a

q q

I,

~) : I

~. 1 ~ " ,

I

L" b

.", 1[

,,t, , ~I , . q

,

29000

....

,

....

s,

o, q

,,,

,

t,

.

L

.

! ~

.J,I

30000 Wovenumber

Fig. 7. Stick s p e c t r u m o f o b s e r v e d cold transitions a b o v e 2 9 0 0 0 c m - i transitions into p r o g r e s s i o n s with intervals n e a t 3 0 0 c m - : .

t

,,

Q1 "

. !',.•,

I

,

"

il

"

z

i

t

II~ I II!l

L~ II ~ " :11I

al 1 a l ( I

li Ih

:~/

II I kI1, II11

I

(1111 i H

Iz

II II

I / I

III I II

illl,ll Jlhl lib

LIIJIIII J Llll

IJlllldIIIIILLIII

•i,.!I. L.W!.l!l! li! JIJli,!ll 31000

32000

(cm-:) assigned to 32 SO2. Also s h o w n is one possible a r r a n g e m e n t o f

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

While providing a plausible description of observed triplet levels, this model is not without weaknesses. For example, rather poor agreement is found between measured slSo2 isotope band shifts [5] and those calculated in harmonic approximation using o~j, to2, and to3 from Table 3, measured 81802 ground state vibrational frequencies [30], and other frequencies derived as described in Section 4.2. Also, the model fails to extrapolate well to the triplet levels reported above 29000 cm -l in Ref. [5], although there is at most very slight triplet intensity above 28830 c m - i in our own spectra. These difficulties may indicate that the vibrational structure is too severely perturbed to be well represented by any simple model, or that all observed transitions cannot be ascribed to a single triplet state. We return now to consideration of the tA2 state. With no evidence of the predicted singlet levels below 29142 cm -1, our analysis of singlet vibronic structure must rest upon the expanded list of levels at higher energy. Assuming that the first dozen or so of these belong to the IA2 state, their spacing leaves no reasonable alternative to the long recognized [3,7,9] value of about 300 c m - l for the lowest frequency upon which regular progressions are built. We have therefore organized all the observed 32802 levels into progressions with intervals near this value. If the two-singlet-state description were essentially valid, correlation of these progressions with expected IA 2 progressions would allow at least a gross determination of IA 2 vibrational frequencies and possibly reveal the approximate position of the I B 1 state by the appearance of additional, unassignable bands. Known perturbations (vide infra) and mixing of the IA 2 and ~Bt states do not alter this result, even when irregularity in intervals and intensities renders individual mode assignments questionable, because the number of distinct vibrational levels is conserved. One such organization of bands is presented in Fig. 7. Only levels listed in Table 1 were considered, although it was shown in Section 4.3 that there are a number of other vibronically allowed levels in this region which must be accounted for in a rigorous treatment. The numbering given for the first four progressions is in accord with the number of v~ quanta in the assignment of Ref. [8]. The only cold singlet bands from Table 1 not included in progressions, besides 17 bands assignable to transitions of

197

minor isotopic species (which are not plotted), are three uncertain bands: 31293 cm -1, which may be hot, 32176 and 32208 cm -1. Nine bands are included which are indicated in Table 1 as possibly due in whole or in part to minor isotopic species, and three bands have been treated as consisting of two overlapping bands and assigned to two different progressions. The second progression in Fig. 7 (starting at 29353 cm- 1) deserves special comment. If the bands numbered 3, 5, 6, and 7 in this progression (at 30244, 30854, 31149, and 31438 cm -1) are in fact single bands, they have very unusual rotational contours, not only in shape but also in rotational temperature dependence. The first of these appears in Fig. 2 and has a unique symmetric contour; the third was described in connection with Fig. 3. When considered in isolation, each of the other two appears to consist of two separate, closely spaced bands, with band centers as listed in Table 1. While two progressions could be formed from a reasonable alternative interpretation of these bands, in anticipation of the finding below of an inexplicable excess of vibrational levels, only one progression is indicated in Fig. 7, under the assumption that some related form of perturbation produces the apparent splittings. If that is the case, however, it is rather surprising that the very regular 30553 cm-1 band is also a member of this progression. As noted above, the first four progressions of Fig. 7, which include all eleven levels up to 30244 cm- 1, correspond to v~ progressions in the 1A2 model of Hamada and Merer [8]. Specifically, the 29142, 29353, 29727, and 30187 cm -I levels (none of which were known when the model was proposed) can be assigned as (021)', (101)', (003)', and (201)', respectively, yielding values of v'1 = 850 cm -I, v~ =611 cm -1, and a (O00)'*--(O00Y' energy of ~ 27894 cm - t , compared to the earlier values of 790, 607, and 27930 cm -I [8]. 34SO2 band shifts calculated from these values are also in reasonable accord with those observed for the 34SO2 counterpart to the second progression, although such agreement is not unique to this assignment. The success of this model in accounting for observed levels breaks down completely, however, above 30250 cm - l . For example, only four additional v~ progressions of B 1 symmetry with 9 bands

198

J.S. Baskin, et al. /Chemical Physics 200 (1995) 181-199

are predicted to appear below 31500 cm -1, while Fig. 7 shows an additional 15 progressions with 35 bands. Even by liberalizing the criteria for selecting valid progressions and ignoring bands which are not established beyond reasonable doubt as cold 32SO2 transitions, a substantial number of bands cannot be accounted for. The evidence of Section 4.3 that at least seven vibronically allowed bands are missing from Fig. 7 reinforces this discrepancy. The (000) level of the I B l state has been postulated to lie at 31240 cm - l [9] or even higher [14]. The fact that the ~A2 state assignment fails at a far lower energy demonstrates clearly the inadequacy of the commonly accepted description. Even a ~B~ state 1000 cm -~ lower than believed with a v 2 frequency the same as that of the ~A2 state (the v 2 value proposed in Ref. [9] for the 1B 1 state is 460 c m - l ) , would contribute only two v 2 progressions below 31500 cm -1, for v I of 650 cm -I or more. To account directly for the excess levels, the ~B~ state would have to be lowered at least an additional 1000 to 2000 cm -~. The absence of I B 1 bands at lower energy and the dominance of IA 2 rotational constants at all energies do not appear consistent with such a possibility. In order to account for a much larger number of vibrational levels within the IA 2 electronic state, other assignment schemes were considered, including associating the 300 cm - I frequency with v'1 rather than with v~ and relaxing symmetry restrictions to allow assignment of some transitions to totally symmetric vibrations. None of these alternatives were found to fit the data with any degree of consistency. Thus we are unable to ascribe any clear meaning to, or deduce any information on vibrational constants from, the progressions of Fig. 7 above 30250 c m - 1. Rotational line splittings of fractions of 1 c m - i observed at 30995 cm-1 and higher [11,14], ranging up to more than 2 cm-~ for some rotational lines of the Clements' E band (32871 cm - l ) [15] have been attributed to interaction of the ~A2 state with the ground state and lower triplet states. Although perturbations of rotational structure are present in each of the bands of this system that have been studied, down to the 29459 cm - l band [8], they decrease significantly below 31000 c m - l [ 14]. Such perturbations are therefore not considered a plausible source

of the widely separated bands observed in this work, especially in the lower energy region. In light of the present results and the absence of viable alternative explanations, the conclusion appears inescapable that more than the two recognized singlet electronic states, IA2 and ~BI, contribute to the gross vibronic structure of this spectral region. A much stronger interaction with the ground electronic state than deduced from the observations cited in the preceding paragraph is one possibility. In that case, given the high and relatively constant density of vibrational states at this energy ( ~ 1 / c m - l ) , a high degree of selectivity would be required in order to reproduce the well-resolved structure observed. Alternatively, additional excited states might be directly involved. While the Walsh diagram shows that the 1A2 and IB t states are expected to be the lowest excited singlet states of SO 2 [31], ab initio calculations [32] which accurately reproduce characteristics of the observed 3B1, IA2, and ~B2 [33] states show 3A 2 and 3B 2 states lying at much lower energies. These calculations are supported by experimental evidence implicating those two triplet states in perturbations of the 3B 1 state [5]. If the relatively low energies of these triplet states reflect a general trend, then triplet versions of other allowed transitions described by Walsh [31] may also lie below the IB 1 state. Thus, many weak bands above 30250 c m could reasonably be attributed to one or more triplet states, independent of any coupling to IA 2 or tB 1, with, in addition, a IB I state substantially below 31000 cm - I to account for excess bands of higher intensity. Without more information, assignment of levels to specific electronic states within such a model would be highly speculative and has not been attempted. Rotational analyses of some of the unassignable bands, such as those at 30676 and 30714 cm - l , as well as a detailed study of the spectra of isotopically substituted species could help to resolve this issue in a definitive manner.

5. Conclusion The carefully controlled molecular ments reported here provide a wealth the rich and imperfectly understood troscopy of SO 2 in the near-UV. No

beam measureof new data on vibronic specsinglet level is

J.S. Baskin, et al. / Chemical Physics 200 (1995) 181-199

| o u n d b e l o w that p r e v i o u s l y reported [13] at 29142 c m - I , and all l o w e r e n e r g y c o l d bands are incorporated into a vibrational analysis o f the 3B l state. W h i l e the p r o p o s e d ~A 2 vibrational a s s i g n m e n t of H a m a d a and M e r e r [8] p r o v i d e s an adequate description for singlet levels o b s e r v e d b e l o w 30250 c m - I , the vibronic structure at h i g h e r energy d o c u m e n t e d in this w o r k displays far greater c o m p l e x i t y than that predicted on the basis o f this a s s i g n m e n t and the e x p e c t e d location o f the ~B l electronic state. N o m o d i f i c a t i o n o f the 1A 2 vibrational a s s i g n m e n t or simple d i s p l a c e m e n t o f the I B 1 state appears capable o f a c c o u n t i n g for these observations, leading to the c o n c l u s i o n that a m a j o r portion o f o b s e r v e d vibronic structure is contributed by one or m o r e additional electronic states.

Acknowledgement Support from the R e s e a r c h Institute o f the K i n g Fahd U n i v e r s i t y o f P e t r o l e u m and M i n e r a l s is gratefully a c k n o w l e d g e d .

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[10] H. Watanabe, Y. Hyodo, S. Tsuchiya and S. Koda, J. Phys. Chem. 86 (1982) 685. [11] R. Kullmer and W. Demtr'6der, Chem. Phys. 92 (1985) 423. [12] G.F. Metha, D.C. McGilvery, R.J.S. Morrison and M.F. O'Dwyer, J. Phys. Chem. 94 (1990) 67. [13] F. Al-Adel, A. Hamdan, O. Binbrek and LS. Baskin, Chem. Phys. Letters 189 (1992) 23. [14] Y. Hamada and A.J. Merer, Can. J. Phys. 53 (1975) 2555. [15] R. Kullmer and W. Demtr5der, J. Chem. Phys. 81 (1984) 2919. [16] D.L. Holterman, E.K.C. Lee and R. Nanes, J. Phys. Chem. 87 (1983) 3926. [17] R. Kullmer and W. DemtriSder, J. Chem. Phys. 83 (1985) 2712. [18] H. Watanabe, S. Tsuchiya and S. Koda, J. Phys. Chem. 87 (1983) 906. [19] O. Sne and O. Cheshnovsky, Chem. Phys. Letters 130 (1986) 487. [20] G. Guelachvili, O.N. Ulenikov and G.A. Ushakova, J. Mol. Spectry. 108 (1984) 1. [21] G. Guelachvili, O.V. Naumenko, and O.N. Ulenikov, J. Mol. Spectry. 125 (1987) 128; 131 (1988)400. [22] S. Koda, H. Yamada and S. Tsuchiya, J. Phys. Chem. 92 (1988) 383. [23] R.L. DeLeon, A. Yokozeki and J.S. Muenter, J. Chem. Phys. 73 (1980) 2044. [24] D.D. Nelson Jr., G.T. Fraser and W. Klemperer, J. Chem. Phys. 83 (1985) 945. [25] G. Herzberg, Molecular spectra and molecular structure, Vol. 1. Spectra of diatomic molecules, 2nd ed. (Van Nostrand Reinhold, New York, 1950) pp. 200-201. [26] G. Herzberg, Molecular spectra and molecular structure, Vol. 2. Infrared and Raman spectra of polyatomic molecules (Van Nostrand Reinhold, New York, 1945) pp. 228-229. [27] G. Herzberg, Molecular spectra and molecular structure, Vol. 2. Infrared and Raman spectra of polyatomic molecules (Van Nostrand Reinhold, New York. 1945) p. 168. [28] K. Yamanouchi, S. Yakeuehi and S. Tsuchiya, J. Chem. Phys. 92 (1990) 4044. [29] J.C.D. Brand, V.T. Jones and C. di Lauro, J. Mol. Spectry. 40 (1971) 616. [30] A. Barbe and P. Jouve, J. Mol. Spectry. 38 (1971) 273. [31] D.A. Walsh, J. Chem. Soc. (1953) 2266. [32] I.H. Hillier and V.A. Saunders, Mol. Phys. 22 (1971) 193. [33] J.C.D. Brand and K. Srikameswaran, Chem. Phys. Letters 15 (1972) 130.