J . Phys. Chem. 1991,95, 3045-3062
3045
Pyrolysis Jet Spectroscopy: The S,-So Band System of Thioformaldehyde and the Excited-State Bending Potential James R. Dunlop, Jerzy Karolczak,t Dennis J. Cloutbier,* Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506-0055 and Stephen C. Ross Department of Physics, University of New Brunswick, Fredericton, NB E3B 5A3 Canada (Received: July 31, 1990)
Rotationally resolved fluorescence excitation spectra of many bands of the A'A2-g1A, system of the transient molecule thioformaldehyde have been recorded by using the pyrolysis jet spectroscopic technique. The rotational constants and precise band origins have been obtained from the rotational assignments. A simultaneous fit of all the available data to a semirigid invertor model has yielded a potential function for the out-of-plane bending coordinate and a planar excited-state equilibrium geometry.
I. Introduction The history of thioformaldehyde spectroscopy is short but eventful. The first conclusive evidence for its existence was the discovery of the microwave spectrum in 1970.' The molecule proved to be a transient species, unstable with respect to polymerization centered on the C-S double bond. It is most conveniently generated by flash vacuum pyrolysis of stable organic precursors, such as thiacyclobutane. Since the initial discovery, the ground-state spectroscopy has been extensively studied by microwave, millimeter wave, laser Stark, FTIR, molecular beam electric resonance, and rotational Zeeman effect techniques.2 In 1975, the SI-Soand TI-So electronic transitions were identified as sharp, rovibronically resolvable band systems in the visible r e g i ~ n . ~In a series of classic papers, Judge et aLH reported vibrational and rotational analyses of both band systems. In sharp contrast to formaldehyde, thioformaldehyde was found to have a near-planar excited-state geometry. A detailed comparison of the spectroscopy of formaldehyde and thioformaldehyde has been published with an extensive review of the literature up to 1982.* The observation that emission could be readily excited from the triplet and singlet states in thioformaldehyde vapor7**catalyzed an avalanche of laser-induced fluorescence (LIF) studies,*2o which examined the excited states in ever increasing detail. Most of this work has focused on the SI-So410 band, due to the fortuitous overlap between it and the rhodamine 6G ring dye laser tuning range. The spectroscopic picture emerging for the SIstate has exciting implications for photophysical studies of the excited-state dynamics. Fully resolved rovibronic eigenstates are accessible with conventional pulsed dye laser sources, without supersonic expansion cooling. Ab initio calculations suggest that photodissociation should not occur in low-lying levels of SIor Tl.2'-zs In the Oo level, extensive perturbations have been thoroughly analyzed and shown to be due to interactions with a triplet level through a vibronic spin-orbit m e c h a n i ~ m . ' ~ -In~ ~the * ~4'~ level, magnetic rotation,14 subDoppler,'2 and microwave optical doubleresonance (MODR)'3*'620 experiments have established that individual rotational states are coupled to triplet levels, while others are perturbed by high levels of the ground state. Thus, in a single molecule, the opportunity exists to study internal conversion and intersystem crossing from single rotational levels in the absence of photochemical complications. We are actively engaged in such measurements at present. Despite the impressive amount of spectroscopic data that has accumulated for the lowest two vibronic levels in SIthioform'Permanent address: Quantum Electronics Laboratory, Institute of Physics, A. Mickiewicz University, Grunwaldzka 6. 60-780 Poznan, Poland. *Towhom correspondence should be addressed.
aldehyde, higher levels have not been examined since the pioneering work of Judge and King.3-5 They assigned 42 H2CS vibronic bands in the 610-440-nm region, of which Ooo, 410, and 310430were thoroughly rotationally analyzed and 420was partially analyzed. The vibrational analysis of the spectrum was complicated by the near coincidence of v i , v i , and 2uql. In anticipation of the need for more extensive data in support of our dynamical studies, we have reexamined the SImanifold of levels. To make rotational analysis more tractable and relieve spectral congestion, we have restored to the pyrolysis jet technique recently reported from our laboratory.28 Although rotational
(1) Johnson, D. R.; Powell, F. X . Science 1970. 169, 679. (2) Clouthier, D. J.; Ramsay, D. A. Annu. Reu. Phys. Chem. 1983,34,31 and references therein. (3) Judge, R. H.; King, G.W. Con. J . Phys. 1975, 53, 1927. (4) Judge, R. H.; King, G.W. J . Mol. Spectrosc. 1979, 74, 175. (5) Judge, R. H.; King, G. W. J. Mol. Spectrosc. 1979, 78, 51. (6) Judge, R. H.; Moule, D. C.; King, G. W. J . Mol. Spectrosc. 1980,81, 31. (7) Clouthier, D. J.; Kerr, C. M.L.; Ramsay, D. A. Chem. Phys. 1981, 56, 73. (8) Clouthier, D. J.; Kerr, C. M.L. Chem. Phys. 1982, 70, 55. (9) Clouthier, D. J.; Kerr, C. M. L. Chem. Phys. 1983, 80, 299. (10) Suzuki, T.; Saito, S.; Hirota, E. J. Chem. Phys. 1983, 79, 1641. (11) Dixon, R. N.; Gunson, M. R. J . Mol. Specrrosc. 1983, 101, 369. (12) Fung, K. H.; Ramsay, D. A. J . Phys. Chem. 1984,88, 395. (13) Petersen, J. C.; Ramsay, D. A.; Amano, T. Chem. Phys. Lett. 1984, 103, 266. (14) Dixon, R. N.; Gunson, M. R. Chem. Phys. Lett. 1984, 104, 418. (15) Suzuki, T.; Saito, S.;Hirota, E. J. Mol. Spectrosc. 1985, I l l , 54. (16) Petersen, J. C.; Ramsay, D. A. Chem. Phys. Lett. 1985, 118, 34. (17) Petersen, J. C.; Ramsay, D. A. Chem. Phys. Lett. 1985, 118, 31. (18) Fung, K. H.; Petersen, J. C.; Ramsay, D. A. Con.J . Phys. 1985.63, 933. (19) Petersen, J. C.; Ramsay, D. A. Chem. Phys. Lett. 1986, 124, 406. (20) Huttner, W.; Petersen, J. C.; Ramsay, D. A. Mol. Phys. 1988, 63, 811. (21) Pope, S. A.; Hillier, I. H.; Guest, M. F.J . Am. Chem. Soc. 1985, 107, 3789. (22) Simard, B.; Bruno, A. E.; Mezey, P. G.; Steer, R. P. Chem. Phys. 1986. 103, 75. (23) Tachibana, A.; Okazaki, I.; Koizumi, M.; Hori, K.; Yamabe, T. J . Am. Chem. SOC.1985, 107, 1190. (24) Goddard, J. D. Con. J . Chem. 1985.63. 1910. (25) Goddard, J. D. J. Mol. Struct. 1987. 149, 39. (26) Clouthier, D. J.; Moule, D. C.; Ramsay, D. A.; Birss, F. W. Can. J . Phys. 1982,60, 1212. (27) Clouthier, D. J.; Ramsay, D. A.; Birss, F. W. J . Chem. Phys. 1983, 79, 5851.
0022-365419 112095-3045%02.50/0 0 1991 American Chemical Society
3046 The Journal of Physical Chemistry, Vol. 95, No. 8, I991
Dunlop et al.
cooling simplifies the spectra, it also drastically reduces the range of J'and K'values, making accurate determinations of many of the rotational constants difficult. However, the data presented here do provide an extensive map of the higher levels in SI,yield accurate vibronic band origins, and have been used to refine the excited-state potential. 11. Experimental Section The pyrolysis jet apparatus has been described in detail elsewhere.28 Briefly, the precursor mixed with argon is continuously flowed through a variable-temperature pyrolysis zone just prior to expansion out of a quartz nozzle. In the thioformaldehyde case, the room-temperature vapor pressure of trimethylene sulfide (Aldrich) was diluted with 150-200 psi of argon and bled into the pyrolysis jet with a backing pressure of 2-3 atm. The pyrolysis temperature, as measured with a thermocouple in the gas flow, was 650-700 OC. The pyrolysis products exited the jet through a 0.15" nozzle and were interrogated with the laser 30 nozzle diameters downstream. The resulting fluorescence was imaged through a short focal length lens to provide a slightly magnified image on a V-shaped mask. The mask was used to spatially discriminate against scattered laser light and emission from warm molecules excited outside the collision-free region of the jet. A second lens then imaged the emission onto the photocathode of a photomultiplier (EMI9816QB), through an appropriate long-pass cutoff filter. Two different excitation sources were used. Medium- and low-resolutionspectra were recorded by use of an excimer-pumped pulsed dye laser (Lambda Physik FL 3002E), with or without an intercavity etalon. Pressure scanning the etalon with propane gas enabled us to perform 0.04-cm-' resolution continuous scans over a range of 30-40 cm-'. Rhodamine 6G and coumarin 540A, 500, and 480 laser dyes (Exciton) were used to cover the 600-460-nm region. Very high resolution spectra were recorded in the 581568-nm region by use of a single-mode scanning ring dye laser (Coherent 699-29 Autoscan) operated with rhodamine 6G. The laser line width was < I MHz at typical powers of 200-400 mW. Sub-Doppler line widths were achieved by narrowing the spatial filter to a 1.5-mm slit parallel to the jet and perpendicular to the laser beam. In the pulsed laser experiments, the photomultiplier signals were sent to a gated integrator and displayed on a strip-chart recorder. A second gated integrator was used to simultaneously record an I2 LIF spectrum for frequency calibration. This was displayed with a second pen on the chart recorder, offset, and synchronized to the first with a digital delay. Etalon scans were monitored by visual examination of fringes from a I-cm-' free spectral range solid etalon. The ring laser data were recorded digitally, using the Apple computer which controls the scanning of the 699-29, and transferred to an IBM PC for analysis. Three channels of data were recorded. The first was the output of the fluorescence detection system, after current-to-voltage conversion and low pass filtering. The second was the LIF spectrum of 12, excited by a small portion of the laser beam. The third was the transmission signal from the vernier etalon in the laser wavemeter, providing a fringe pattern suitable for detecting mode hops or other irregularities in the scan. Absolute line frequencies in the medium- and high-resolution spectra were calibrated with respect to the spectrum of 12,29 including the -0.0056-cm-' correction factor published later.30 In the medium-resolution spectra, H2CS line frequencies were calculated by interpolation between well-resolved I2 lines which bracketed the region of interest. These are thought to have an absolute uncertainty of *0.008 cm-' for unblended lines. The high-resolution data were treated by fitting the calibration lines over a 20-cm-' region to a quadratic equation, which was used (28) Dunlop, J. R.; Karolczak, J.; Clouthier, D. J. Chem. Phys. Lett. 1988, 151, 362. (29) Gerstenkorn, S.; Luc, P. Atlas Du Spectra DAbsorption De Lo
Molecule Dlode; Centre National de la Recherche Scientifique: Paris, France, 1978. (30) Gerstenkorn, S.;Luc, P. Reo. Phys. Appl. 1979, 14, 791.
19830
19700
FREQUENCY (cm-') Figure 1. A portion of the low-resolution pyrolysis jet spectrum of HzCS in the high-frequency region of the band system. The 410510band shows the typical compact parallel band structure, whereas that of the 2'0320410 band is characteristic of the more extensive rotational structure of the
perpendicular bands. TABLE I: Vibrational Frequencies of Thioformaldehyde (in cm-')
vibration
frequency SIexcited ground state state
description 297 1 .P 3033.4b ul(a,) sym C-H stretch 1334.5b CH2 bend 1457.3 vz(al) 1059.2 8 1 9.7E uj(al) C=S stretch 371.Ic out-of-plane bend 990.2 v4(bl) 3024.6 3054.9b uS(b2) antisym C-H stretch 991.0 785.2c u6(bz) CH2 rock Reference 2. bThis work; fundamental frequency derived from fitting combination bands. 'This work; experimental value obtained by subtracting transition frequency from Tw = 16 394.628 cm-I. to calculate the frequencies of the H2CS lines. The estimated absolute uncertainty is f0.003 cm-I. The low-resolution spectra were calibrated with neon and argon optogalvanic lines recorded simultaneously. 111. Results and Analysis A . Low-Resolution Vibrationally Resolved Spectra. A portion of a 0.1-cm-' resolution scan of the pyrolysis jet spectrum of H2CS in the coumarin 480 dye laser region is shown in Figure 1. The bands are labeled according to the convention originally proposed by W a t ~ o n , ~for ' . ~example, ~ 220411. Mab denotes a vibronic transition involving u quanta in the upper state and b quanta in the lower state, while an upper state level is denoted Ma. Thus, in this example, the transition is a hot band involving one quantum of v4 in So and terminating on the excited state level 2v; vq/. All other vibrational quantum numbers in the two states are understood to be zero. The vibrational numbering, symmetries, and frequencies are shown in Table I. Bands of different polarizations are readily discernible in the low-resolution spectrum. For the formally forbidden n,r* electron promotion in molecules such as H2CS, the transition strength comes from magnetic dipole transitions and Herzberg-Teller coupling. Consideration of the vibronic symmetries leads to the following conclusions concerning band types. If the direct product of the vibrational symmetry species in the upper and lower states is AI, type A (parallel) magnetic dipole allowed bands are expected. If the direct product is A2, type A (parallel) vibronically allowed bands result. Similarly, B, and B2 direct products lead to type B and C (perpendicular) vibronically allowed bands. As first discovered by Judge et al.,3*4all three band types are prom-
+
(3 1) Watson, J. K.G. Ph.D. Thesis, University of Glasgow, Scotland, 1962. (32) Brand, J. C. D.; Callomon, J. H.; Innes, K. K.; Jortner, J.; Leach, S.; Levy, D. H.; Merer, A. J.; Mills, I. M.;Moore, C. B.; Parmenter, C. S.; Ramsay, D. A.; Rao, K. N.; Schlag, E. W.; Watson, J. K.G.; Zare, R. N. J . Mol. Spectrosc. 1903, 99, 482.
The Journal of Physical Chemistry, Vol. 95, No. 8,1991 3047
Pyrolysis Jet Spectroscopy of Thioformaldehyde TABLE 11: Band Origins (in em-') and Assignments of H,CS Bands in the 500-460-nm Region Observed at Low Resolutiona
band origin 20263.5 20 299.8 20 548.4 20637.3 20 749.7 20 784.8
assignment
band origin
3'05'0 420510 2'03304I o 3'04'05~0 1 102'0 2'05'0
21 078.4 21 114.4 21 353.8 21 448.0 21 565.7
3;
assignment 3'05~0 310420510 5 '04'0 3'04'05~0 11 1 I 02 03 o
"Band origins accurate to k 2 cm-I. 17220
'
17205
FREQUENCY (cm- ) Figure 3. A high-resolution spectrum of the 310 band of H2CS. The band
is partially overlapped by lines of the 6'0 band on the low-frequency side. signed as hot bands, originating from the levels 41, 3,, or 61 which form a Coriolis coupled triad in the ground states3' These were not rotationally analyzed. The perpendicular bands consist of well-separated subbands involving K,' K / values of 2 1, 1 0, and 0 1, spread over about 45 cm-'. Each subband has 10-25 lines distributed over P, Q, and R branches. The B- and C-type bands look identical, but the subbands contain transitions from different asymmetry components resulting in different ground-state combination differences, so that the band type can be determined unambiguously. Progressions in the subbands were readily followed out to J = 5-7 and confirmed by ground-state combination differences, using the constants of Clouthier et a1.26 The A-type parallel bands consist of two overlapping subbands with K,' = 1 K/ = 1 and K,' = 0 K/ = 0. These bands were more difficult to assign, especially in congested spectra. Combination differences were used to resolve any questionable assignments. Table XI shows the rotational subband tables of transition frequencies and assignments for the 25 bands which were rotationally analyzed. The data for the bands 610, 310,420,and 4l06lO come from high-resolution spectra. D. Determination of Excited-State Rotational Constants. Rotational constants were obtained from a least-squares fit of the observed transition frequencies to Watson's A reduction of the rotational Hamiltonian in the P repre~entation,~~ using a locally modified version of the program by Birss and R a m ~ a y . The ~~ ground-state constants were fixed at the values given by Clouthier et a1.,26 and A , B, C, and Towere varied for each excited-state level. The centrifugal distortion constants were found to be indeterminate, due to the small range of J and K, values observed in the jet spectra. Although the B and C values are generally reliable, the A inertial constant is less precise, due to the limited range of data. This is particularly true for the A-type bands, where the A& = 0 selection rule limits our observations to K,' = 0 and 1. The band origins are less likely to be affected by the range of data. Rotational constants and band origins are reported in Table 111. The differences between the observed transition frequencies and those calculated from these constants are given as numbers in parentheses in the tables in Appendix I. Comparisons with previous analyses of extensive room-temperature data are shown in Table 111 for the Ooo and 410 bands. The accepted values of the rotational constants are within 3a of the values obtained from the jet data by using data sets with far fewer transitions. This agreement suggests that the constants obtained for those bands which are free of substantial perturbations are reliable within the error limits quoted in Table 111. E. Discussion of Individual Bands and Perturbations. I. Cold Bands. Many of the bands are observed to be perturbed in one
-
30 FREQUENCY (cm-')
Figure 2. A medium-resolution spectrum of the 2l04lOband of H2CS.
inent in the spectrum of thioformaldehyde. Survey 0.1-cm-l resolution spectra were recorded at wavelengths down to 460 nm. In the 500-460-nm region, these low-resolution spectra were used to estimate band origins for the various vibronic transitions, by extrapolation of the observed rotational structure to the region of the hypothetical J' = 0-J" = 0 transition. The assigned low-resolution bands and their observed polarization and estimated band origins are given in Table 11. The band origins are estimated to be accurate to f 2 cm-I. B. Rotationally Resolved Spectra. Medium-resolution spectra were recorded out to 500 nm, at which point the I, reference atlas terminate^.^^ A typical medium-resolution, rotationally resolved spectrum is shown in Figure 2. This particular band, which we assign as 2l04IO,was not observed in the photographic absorption work of Judge and King4 but is very evident in the pyrolysis jet spectra. Individual rotational transitions within a vibronic band are labeled by the notation AKaAJKc(J'?,,,. For example, the transition J' = 2, K,' = 1, K,' = 2 J" = 3, K/ = 2, KF = 1 would be labeled PP2(3),. The e (even) and o (odd) notation describes the parity of the sum of the quantum numbers J"+ K/ K / . Individual branches are simply labeled hKAIK2 The 2l04lO band shows classic low-temperature type B subband structure, which can be approximately simulated with a rotational temperature of 8 K, as long as the appropriate Boltzmann factors are applied to each of the noninterconverting nuclear spin isomers of H2CS.'* High-resolution spectra of four bands in the 581-568-nm region were recorded with the ring laser. A typical example is the 310 A-type band shown in Figure 3. The observed line widths (fwhm) in these spectra are 0.012-0.01 3 cm-', providing a substantial improvement in resolution over room-temperature Doppler-limited line widths, which are typically 3 times broader. This allows most of the observed transitions in the high-resolution bands to be resolved, including the low-J asymmetry splittings. C. Rotational Assignments. Forty-four &-So vibronic bands were observed in the 1540(t20000-~m-~ region. Of these, 25 were shown to originate from the vibrationless level in So, and rotational assignments were attempted for each. Nineteen bands were as-
-
+
-
- - -
(33) Turner, P. H.; Halonen, L.; Mills, 1. M. J . Mol. Spectrosc. 1981,88, 402.
(34) Watson, J. K. G. J . Chem. Phys. 1967, 46, 1935. (35) Birss, F. W.; Ramsay, D. A. Comput. Phys. Commun. 1984,38,83.
3048 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991
Dunlop et al.
TABLE III: Rotational Constants and Band Origins (in cm-') for Bands That Were Partially or Completely Rotationdly A ~ l y z e d
excited-state rotational constants band tvDe
band
band origin
A
9.43389 (86) 9.44011 9.05712(33) 9.05715 9.86666 (27) 9.40209 (1 30) 8.75989(257) 9.4669,(98) 9.03394 (58) 8.32858 (50) 9.8754,(192) 9.24152 (564) 8.65034(260) 9.12541(18) 9.32463(450) 9.03268 (33) 9.5499, (74)
B 0.53820 (6) 0.538603 0.53707 (9) 0.537785 0.54162 (4) 0.53486 (9) 0.54070 (44) 0.54026(9) 0.53743 (26) 0.53577(20) 0.53936 (21) 0.51231 (96) 0.52891 (20) 0.53828(8) 0.54449(81) 0.52594(1 1) 0.5378, (9)
C 0.50890 (6) 0.508960 0.50972(9) 0.510176 0.50798 (8) 0.50744 (9) 0.5075,(32) 0.50510 (9) 0.5049,(22) 0.51276 (12) 0.50011 (26) 0.4932, (100) 0.50846 (20) 0.5009, (4) 0.48487 (90) 0.50530 (9) 0.5049, (14)
std dev
16 394.633 ( 8 ) O 16 394.628b 16765.747 (1 1) 16 765.737c I7 179.830(8) 17214.263 (12) 17 229.339 (1 5) 17 563.386 (4) 17 582.011 (7) 17736.301 (15) 17997.671 (9) I8 025.290 (52) 18043.648 (21) 18 107.546 (6) 18 377.591 (60) 18389.164(7) 18 544.594 (6) 18548.1 (5) 18548.300( 1 1 ) I8 806.773 (14) 18827.4 (5) 18 920.793 (9) 19 187.928 (7) 19 350.027 (6) 19474.9 (5) 19730.862(13) 19818.8 (5)
0.006
no. of linesd 24
0.011
41
0.006
44 23 16 27 42 39 26
8.29124 (77) 9.74542 (348)
0.53754(25) 0.56931 (47)
0.50719 (26) 0.4680,(34)
0.017 0.009
24 16
9.10096 (155) 9.09317 (56) 8.34635 (30)
0.54696 (46) 0.51445(31) 0.56244(9)
0.49429 (39) 0.51556 (16) 0.46833 (I I)
0.018 0.011 0.010
39 28 30
8.98052(22)
0.53980 (26)
0.50398 (24)
0.014
46
0.008
0.009 0.007 0.014 0.016 0.014 0.023 0.010 0.007 0.022 0.009 0.004
11
14 51 12 38 17
"The numbers in parentheses are 3u error limits and are right justified to the last digit on the line; sufficient additional digits are quoted to reproduce the original data to full accuracy. bRotational constants from an analysis of the absorption spectrum, ref 26. cRotational constants from an analysis of the absorption spectrum, ref 27. dDenotes the number of rotational lines used in the least-squares fitting of the band.
or more subbands. The unperturbed bands are, of course, only stipulated to be free of perturbations in the small range of J'and K,' observed in the jet spectra. It is likely that more extensive perturbations exist in the higher rotational levels of many of the bands. OOo and 410. These two bands have been thoroughly analyzed from room-temperature absorption ~ p e c t r a ~and ~ + were ~ ' recorded only to check the precision of our measurements and the fitting procedure. No perturbations were detected in the jet spectra for these bands. 6'0. This is the lowest energy C-type band in the spectrum. The high-resolution data show that it is unperturbed. Although the K,' = 2 K / = 1 subband is badly overlapped by the 310 band, the lines could be assigned with confidence from the high-resolution spectra. The ug/ frequency obtained from this band is 785.20cm-I, compared to the earlier estimate of 799 cm-l by Judge and King.4 The A constant for bands involving ugl is substantially higher than similar combinations with zero quanta of vgl. This is readily understandable on consideration of the type of deformation involved. The CH2 rocking motion has the effect of making the structure look more like an HCS linear fragment with one hydrogen off-axis, reducing the moment of inertia and increasing A. The value of the A constant provides a useful diagnostic method for distinguishing between alternate vibronic assignments involving the nearly degenerate vibrations ugl and ugl. 3l0. This band is also unperturbed, despite the proximity of 6I. This can be rationalized by comparing the relative energies of the levels, as shown in Figure 4. The K, = 2 levels of 6' lie approximately 9 cm-' below the K , = 1 levels of 3', so that substantial perturbations are not expected for reasonable values of the coupling constant. The value of u,' = 820 cm-l estimated by Judge and King from the absorption spectrum is in good agreement with our more precise value of 819.64 cm-'. 4*0. Although the band has a regular A-type structure, the J' = 1, 2 levels of K,' = 1 are slightly perturbed. It is unlikely that the perturbation is due to a Fermi interaction with 3l or Coriolis coupling with 6l,due to the large energy separations between the bands (Figure 4) and the absence of abnormal shifts in the frequencies of 3' or 42. The perturbations may be attributable to mixing with a nearby TI level.
-
G'+-Corio1is4
3' + Fermi
4
4'
Coriolis
-i l
-4.
-
820
Figure 4. Energy level diagram showing the possible Coriolis and Fermi interactions which could perturb the lower rotational levels of the 3' vibrational state of H2CS.
4I06IO.This band fits very well, with no obvious perturbations. The vibrational interval (798 cm-I) derived for ugl from this combination, using the known 4'-0° interval, is 13 cm-' higher than the 61-0° interval, showing the effect of the large-amplitude motion on the small-amplitude vibrational frequency, as will be discussed in detail later. 3'04'0. All three subbands are assignable, although several of the levels appear to have small perturbations. In particular, the 'Q0 branch has high residuals, indicating that the even parity (e) asymmetry component of K,' = 1 is perturbed. The K,' = 2 stack of the 4'6l level lies about 9 cm-' above the perturbed stack of levels in 3'4l, too far to selectively interact with only one asymmetry component. Magnetic rotation spectra show strong activity in the region of this band26, so T,-S, interactions may be responsible for the perturbations.
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3049
Pyrolysis Jet Spectroscopy of Thioformaldehyde
more promising candidate is the 4)6’ level which is observed with origin at 18 548 cm-l, so that the K, = 1 stack is above the K, = 0 stack of the 3143level. We were unable to fit the 430610band, suggesting that it is strongly perturbed. 210310.This transition was identified as a weak set of lines buried in the 3’04’0 band. Both subbands fit very well, suggesting that the lower rotational levels are unperturbed. 320610. This band is extensively perturbed. The P and R branches of the K,’ = 1 K / = 0 subband are pushed down, while the K,’ = 2 levels are strongly displaced upward. There are a number of possible perturbing states, and no definite identification can be made. The rotational constants are not reliable, although the band origin is probably accurate to fO. 1 cm-’. 330. The A-type structure of this band was found within the 320610band. Few lines could be assigned, but the band origin was determinable. 21$0#1, Perturbations are evident in all the observed K stacks, with the upper asymmetry component of K , = 1 strongly displaced to lower energy. 330#10. The K , = 0 levels are strongly displaced to lower energies in a systematic fashion. The other subbands fit well, but the derived B and C values are inverted, with C slightly larger than E . The band origin is reliable, although the rotational constants are only effective values. 320430.The K, = 0 and 2 levels are unperturbed, and they were used to obtain the rotational constants. The lower asymmetry component in K , = 1 is displaced downward, while the upper is pushed up. 210320410. This band fits well, except that the ‘Q0branch is perturbed, with the levels displaced to lower energy. 510,43,$10, 4’,,.510,and 330.These bands were observed and some of the branches could be assigned, but there were insufficient data to fit them to the standard Hamiltonian. The band origins were determined by extrapolating the assigned progressions back to low J and then using approximate rotational constants to estimate the energy of the rotationless level. It is unfortunate that the Solevel shows extensive perturbations in all subbands, because the perpendicular band structure was easily recognized and assignments were straightforward. The other bands were weak, often overlapped, and show extensive perturbations, making them difficult to assign with confidence. 2. Hot Bands. A number of medium-weak bands were discovered in the spectrum that did not fit into the vibrational pattern of the assigned cold bands and did not have ground-state combination differences consistent with the vibrationless level. The bands did not have regular rotational structure, suggesting that either the upper or lower state, or both, are perturbed. Consideration of the ground-state frequencies suggests that the only vibrationally excited levels likely to be appreciably populated in the ground state are 41, 31, and 61. These levels form a group about lo00 cm-I above the vibrationless level and have been shown to be Coriolis coupled.33 The major interaction is a near 50/50 mixing between 4, and 61,with u4 carrying most of the transition moment in the infrared fundamental at 990.18 cm-I. Fortunately, the K , = 0 states of 41 and 61 are not Coriolis coupled, so that ground-state combination differences could be readily determined from the published infrared data.33 The bands in the jet spectra exhibit combination differences that are not consistent with the vibrationless level but match those in 41, 61, or 31. Band origins for the hot bands were obtained by tracking the K,’ = 1 K,” = 0 or K,’ = 0 K,” = 0 subbands to their first members and then subtracting reasonable intervals to arrive a t the energy of the rotationless level. Subbands involving K,” > 0 were usually not assignable, due to the substantial Coriolis effect in the lower levels. Vibronic assignments were made on the basis of the agreement between calculated and observed band origins, using the upper state vibrational frequencies and anharmonicities obtained from the cold bands (vide supra). The results are shown in Table IV. It is not possible to use vibrational frequencies to distinguish between bands originating from 4, and 6,, since the two levels are almost degenerate. However, the K,” = 0 com-
-
30 20
lo
00
Figure 5. Energy level diagram showing the near resonance between the 3* and 3’6’ levels in the excited state of H2CS.
430. The only perturbations evident are in transitions terminating on J’> 4 of K,’ = 0. These lines are weaker than expected for standard B-type band structure, due to mixing with another level. The 210 band is expected to occur in the same region of the spectrum, but there is no evidence of it in the jet spectra. 3’06’0. The K , 2 1 subband was not assignable due to congestion and overlap with the nearby 320band. The K,’ = 2 stack of 3’6I and the K,’ = 1 stack of 32 are separated by 1.3 cm-l, so that Coriolis coupling between them is the likely cause of the perturbation. An energy level diagram showing the near resonance is given in Figure 5. A detailed analysis of the perturbation was not possible, due to our inability to assign the region of overlap between the two bands. jz0. The analysis of this band is not very satisfactory. Few lines could be definitely assigned, and there are many weak extra lines. The band origin is a reasonable value for 2u3’ (2 X 8 15 cm-l), but the other constants are unlikely to be very accurate. 310420. The rotational structure in this band is surprisingly complex, since it is not overlapped by other transitions. A large number of weak lines that do not form well-defined progressions were recorded, interspersed among the strong assignable lines. The rotational constants are close to those of 420,suggesting that they are valid despite the small number of fitted lines. 2104’0.The structure of this band is shown in Figure 2. It is considered to be a model B-type band with very regular rotational structure, even though it has 1713 cm-l of excess energy above the Oo level of SI. The strength of this band in the pyrolysis jet spectrum is surprising, since it was not observed in ab~orption.~ 310410610. The band is heavily overlapped by the K, = 0 1 subband of 320410,making assignments difficult. The K, = 1 stack of levels are in close proximity (1-3 cm-I) to the K , = 0 stack of 3241,so that the two are probably Coriolis coupled. 320410.As discussed above, the K , = 0 levels appear perturbed and no definite assignments could be made. The K, = 1 and 2 stacks are unperturbed and give a good fit. 310430.This band was partially analyzed by Judge5 from extensive absorption data. We agree with him that the K, = 0 levels are extensively and regularly perturbed. Our constants come from a fit of a limited number of K, = 1 and 2 levels and do not agree particularly well with the published values? which were obtained from a fit of only the lines involving K , = 2-6. The absorption analysis constants are undoubtedly superior, since our K, = 1 lines show unacceptably large deviations. Judge5 ascribed the perturbation in K , = 0 to an interaction with the K , = 1 levels of the 2,3’ vibronic state. We find the lowest two K, stacks of this level to be unperturbed, from our analysis of the 2lo3l0 band. A
-
-
-
-
3050 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991
Dunlop et ai.
TABLE I V Hot Bands Observed in the Pyrolysis Jet Spectrum of Thiofornuldebvde freauencv. cm-' band type obsd' caIcdb 15 404.4 B 15 404.4
C
I5 775.0 16 123.3 16 167.0 16 189.6 16 228.8 17 387.6 17 815.8 17816.6 I7 837.7 18 179.8 18 192.2 18618.4 I8 631.3 18 990.6
B
19 257.6
A
19309.5 19 647.3 19 759.4
A
C A A
B
C A
A
B A
C A
B
C B
15 774.7 16 121.9 16 173.9 16 190.9 16223.0 17385.1 17816.2 17817.0 I7 838.3 18 180.0 18 191.0 18 619.0 18 634.9 18 989.5 19 237.6 19 252.9 19 309.2 I9 645.9 19 760.0
Band origins calculated from extrapolations of the observed rotational structure; estimated error f2 em-'. bCalculated from the ground- and excited-state fundamentals and anharmonicities derived from this work. bination differences are sufficiently disparate to allow a definite assignment if the appropriate rotational assignments could be made. On Franck-Condon grounds, we expect v4 to be more prominent in the spectrum, so the lower level was assigned as 41 where other information was unavailable.
IV. Determination of the Excited-State Rovibronic Inversion Potential A. The Hamiltonian. The semirigid bender model is a Hamiltonian that was developed to account for the effects of the interaction between the rotational motion of a molecule and a large-amplitude vibration. It is distinguished from the rigid bender model in that it also takes into account the effects of structural relaxation of the molecule as it undergoes the large-amplitude vibration. That is, it accounts for changes in bond lengths and bond angles as the molecule vibrates. The semirigid bender model was developed by Bunker and L a n d ~ b e r gas~ an ~ approximation to the nonrigid bender model of Hoy and Bunker.37 This approximation was designed to allow the model to be used for more complicated systems than those for which the nonrigid bender is practicable. These models are all based on the original paper by Hougen, Bunker, and Johns?8 now often referred to as HBJ. They were reviewed by Bunker39 and JensemM. Although referred to as "bender" models, these Hamiltonians are equally appropriate for other large-amplitude vibrations, such as the inversional motion in H2CS. The semirigid bender or semirigid invertor models view the large-amplitude motion as taking place by the molecule following the valley in the potential energy function. The molecular geometry adapts itself for each value of the large-amplitude coordinate in such a way as to minimize the potential energy. The purpose of the least-squares fittings to the experimental data is to determine the potential energy function for the large-amplitude motion and, if possible, the geometric relaxation. It should be noted that the significant changes in the effective rotational constants that are often seen in different levels of a large-amplitude vibration arise from the fact that, in the course of such a vibration, (36) Bunker, P. R.;Landsberg, B. M.J. Mol. Specrrosc. 1977,67, 374. (37)Hoy. A. R.;Bunker, P. R.J. Mol. Specrrosc. 1974,52, 439. (38)Hougen, J. T.;Bunker, P. R.;Johns, J. W. C. J . Mol. Specrrosc. 1970, 34, 1362. (39)Bunker, P. R. Annu. Rev. Phys. Chem. 1983,34, 59. (40)Jensen, P. Compur. Phys. Rep. 1983, I , 1.
Figure 6. Coordinates used in the semirigid invertor Hamiltonian for
H2CS. The large-amplitude coordinate is p, and the C-H and C-S bond lengths and the HCH bond angle CY are considered as functions of p.
the molecule is, in effect, averaging over a wide range of geometries. The various bender models take this explicitly into account. The coordinate p, shown in Figure 6, is used to study the large-amplitude motion involved in the inversion.41 It is defined as the angle between the instantaneous H C H plane and the projection of the C-S bond. The geometric parameters are the H C H bond angle, a,the C-H (or C-D) bond length, rCH, and the C-S bond length, rcs, also shown in Figure 6. Each of these three geometric parameters depends on the inversional coordinate p in a specific way. The parameters defining this dependence are referred to as the "semirigidity parameters". Typically, these geometric parameters are written as a quadratic function of p, as, for example, eq 4 of ref 41: rCH(P)
= &I + @Ib2
(1)
The parameters determined in the least-squares fitting would then be the constants r&, which gives the value of the C-H bond len th when the molecule is in the planar ( p = 0) configuration, and which describes how the C-H bond length changes as the molecule undergoes the inversional motion. With such a parametrization of the semirigidity, Jensen and Bunker42have previously used the semirigid invertor model to study excited electronic states of H2CS. However, in the case of the A1A2state, which is considered in the present paper, they were unable to determine any of the semirigidity parameters. They were therefore restricted to modeling this state by a rigid invertor model, in which the bond lengths and H C H bond angle were frozen during the inversional motion. Additionally, although they expanded the potential function as an even degree power series in the inversional coordinate, including terms up to order p 8 , they were only able to determine the coefficient of the quadratic terms in their least-squares fittings. The coefficients of the three higher degree terms were fixed at some convenient values. Initially, the same difficulties were encountered in the present study. It seemed impossible to determine the semirigidity parameters or more than one of the potential constants. Eventually, however, it was realized that there was a systematic variation in the difference between observed and calculated values. It was relatively easy to fit the rotational structure of the lowest lying inversional levels very well, as was indeed done by Jensen and Bunker using a rigid invertor model, but the higher inversional levels created problems. This was particularly evident in D2CS. Jensen and Bunker included only J = 0, 1, and 2 terms for the u4 = 5 inversional level of D2CS. Although their fitted constants give rotational terms for u4 = 0 and 1 that are within 0.1 1 cm-' of the experimental results for the levels that they fitted, for J = 2 in the u4 = 5 state the calculated rotational terms disagree with experiment by more than 0.8 cm-I. If their constants are used to predict rotational terms for higher J values than those included in their fitting, this disagreement increases to 4.9 cm-' for the level SS0 in u4 = 5 . However, if their constants are used to extrapolate up to J = 7 for the u4 = 0 and 1 levels, the agreement is better than 0.2 cm-'. This contrast between the quality of extrapolation based on rigid invertor predictions for low-lying inversional states where things work well and the higher u4 = 5 state where they do not indicates that the "average" geometry of the molecule in u4 = 5 is significantly different from that in u4 = 0 or 1. This observation suggests that it is essential to use a semirigid invertor model and that it is appropriate to use
&,
(41)Jensen, P.;Bunker, P. R.J . Mol. Specrrosc. 1982, 94, 114. (42) Jensen, P.; Bunker, P. R. J . Mol. Specrrosc. 1982,95, 92.
The Journal of Physical Chemistry, Vol. 95, NO. 8, 1991 3051
Pyrolysis Jet Spectroscopy of Thioformaldehyde a functional form for the potential and semirigidity that, after an interval of slow change with inversional coordinate around the planar configuration ( p = 0), starts to change more dramatically than the p2 dependence Jensen and Bunker attempted to use. These considerations led to our eventual use of a p4 dependence for the bond length semirigidity. Indeed, using a p4 type variation for the bond length semirigidity allowed the determination of all of the semirigidity parameters for both H2CS and D2CS. In addition, by modeling the potential energy as a quadratic plus quartic function of p, it was possible in the least-squares fitting to determine all of the parameters used in the model. The HCH bond angle was modeled as a quadratic function of p . In summary, the geometric constants of the molecule were modeled as
(3) a(p)
=do)
+ ff(2)p2
(4)
Due to the effects of averaging over the small-amplitude vibrations of the molecule, the geometric parameters depend on the isotopic species being considered. In principle, therefore, each of the six parameters in the expressions above has to be determined for both H2CS and D2CS. The pure inversional potential function Vo(p)was modeled as a quadratic plus quartic function of the inversional coordinate: Other than the large-amplitude vibration v4, there are five small-amplitude vibrations in the molecule. These can be treated in the semirigid invertor model by an adiabatic approximation. This was done by assuming that the small-amplitude vibrations are "fast" enough that they adapt to the instantaneous inversional configuration. During the course of the inversional motion, the harmonic frequencies of these small-amplitude vibrations will change. This results in the inversional motion in any particular small-amplitude state seeing an "effective" potential consisting of the pure inversional potential plus the energy of the smallamplitude state, which is now a p-dependent quantity. In addition, the present model makes allowance for anharmonicity of the small-amplitude vibrations but not for any p dependence of this anharmonicity. The resulting effective inversional potential function for a particular small-amplitude state is then given by a slightly extended version of eq 20 of ref 43 which derives from eq A4 of ref 31:
(6) Bunker, Landsberg, and Winnewi~ser~~ used this formula without the anharmonicity terms in their study of the HCNO molecule. However, it was only after fitting individual effective inversional potential functions for each of the small-amplitude states that they used this formula in a subsequent least-squares fitting to the fitted potentials to determine the various coefficients involved in it. J e n s p and Bunker4' mention this formula in their discussion of the A1A2and @A2states of formaldehyde but make no use of it. Previous direct use of the formula in least-squares fittings of semirigid or rigid bender Hamiltonians was made in studies in HCN44*45and HCP.& The dependence of the harmonic frequencies on the inversional coordinate was taken as a simple power series in p q(p)
=up
+ 0 p p 2 + wj4)p4
(7)
(43) Bunker, P. R.;Landsberg, B. M.;Winnewisser, B. P. J . Mol. Spectrosc. 1979, 74, 9. (44) Ross,S.C.; Bunker, P. R. J . Mol. Spectrosc. 1983, 101, 199. (45) Ross. S.C.; Bunker, P. R.J . Mol. Spectrosc. 1984, 105, 369. (46) Lehmann, K. K.; Ross, S.C.; Lohr, L. L. J . Chem. Phys. 1985,82,
4460.
with the series termination depending on the available data and the results of the least-squares fittings. While Vo(p)is, in principle, independent of isotope, Ve&) will be dependent on both the isotope and the particular excitation of the small-amplitude vibrations. This is because the five harmonic frequencies for the small-amplitude vibrations will depend in different ways on the inversional coordinate p and will also be different for each isotopic species. Therefore, accounting for the variation with p of each of the harmonic frequencies of the small-amplitude vibrations for both isotopic species allows the cleanest determination of the pure (i.e., isotope independent) inversional potential function Vo(p). In the present work, the dependence of the harmonic frequencies for all but one of the small-amplitude vibrations in H2CS, and all but two in D2CS, was determined. Partly as a result of this, the pure inversional potential Vo(p)determined in this work was "pure" enough that it could be used simultaneously for both H2CS and D2CS. Each of the parameters p(")( r t i , a("),V"),to(")), specifying the variation of some property with respect to the inversional coordinate p , is defined in terms of radians. This is particularly convenient in the present case, because the classically allowed region for the states studied here extends out to approximately 1 rad. Thus, p(")approximates the maximum contribution of this term in the classically allowed region. The angle t3* between the molecular framework and the molecule-fixed axes was chosen in the standard way:' so that the pJp) element of the inverse moment of inertia matrix becomes zero for all values of the inversional coordinate p. In the present least-squares fitting, the pseudo potential energy term V(p)as given by eqs 23-24 of Sarka and Bunker4' was used, instead of the less complete pseudo potential energy term V,(p) that has usually been used in semirigid bender/invertor fittings. (Vl(p)is directly related to thef,(p) function of Hougen, Bunker, and Johns.3s) These terms result from the noncommutation of various parts of the Hamiltonian operator. For the set of parameters for H2CS determined in the present work, the difference between U(p) and Vl(p) ranges from about 0 to about 25 cm-l. This difference adds directly to the effective potential used in the numerical integration that determines the inversional basis set. However, this difference is not very important on the scale of the potential for the A1A2state. It did, however, result in improvement of about 1 cm-' in the fitting of some of the pure inversional levels. In the case of the H3A2triplet state, however, there is some question as to whether there is a potential barrier to The presence or size of such a barrier could be masked by the use of U,(p) instead of V(p). Or, indeed, the neglect of this term could lead, in the course of a least-squares fitting, to the finding of a barrier to planarity in the inversional potential that was merely the unaccounted for effect of U(p). It will therefore be crucial to include this term in the study of the triplet state of H2CS. The final set of parameters used to specify the model was obtained by initially fitting with all parameters that could possibly be determined by the data and by then removing from the model, one at a time, those parameters that were undetermined. This was continued until the quality of the fitting started to degrade. In this way it was discovered that fitted values of the C-H and C-S bond lengths in the planar configuration, were the same for H2CS and D2CS. That is, the difference between the fitted values for these quantities in H2CSand D2CS was smaller than the error of this difference. As a result, the C-H and C-S bond lengths at planarity were considered as isotopically independent in the final fitting. The semirigidity of these bond lengths, however, was different for H2CS and D2CS. The isotopic independence of the planar values of the bond lengths may be considered a sign of the success of the semirigid invertor in accounting for the effects of the large-amplitude displacements involved in the inversional motion. The rapid variation of the quartic dependence of these bond lengths on p explains why Jensen and Bunker42 were unsuccessful in fitting with a model involving (47) Sarka, K.; Bunker, P. R. J . Mol. Spectrosc. 1987, 122, 259. (48) Goddard, J. D.; Clouthier, D. J. J . Chem. Phys. 1982, 76, 5039.
3052 The Journal of Physical Chemistry, Vol. 95, No. 8,1991 TABLE V Fitted Inversion-Rotation Constants HZCS H2CS and D2CS DZCS 4% A 1.7014 (12)" r&, A/rad4 0.0142 (38) 0.0546 (23) A 1.0818 (20) A/rad4 0.2079 (69) 0.1130 (33) do),deg 118.28 (34) a#= + 1.17 (13)* a(2), deg/rad2 -7.38 (82) -7.60 ( 1 9) P4),cm-'/rad4 2288 (60)
$A, $A,
"The value quoted in parentheses is one standard error in units of the last digit quoted for the parameter. bThe bond angle for D2CS was fitted as a correction to the H2CS value aRics. Thus a&s = 119.45'. quadratic dependence of the bond lengths on p. This probably also explains why they had to restrict the fitted data set to values of J no greater than 2 for the data from the highest observed inversional level, u4 = 5 of D2CS, where the effects of semirigidity are greatest. In the present work, levels up to J = 7 were included with no special difficulty. Along with the completely undetermined parameters, there were two that were only very poorly determined in initial fittings. These were wb4) for H2CS and x36 for D2CS, whose fitted values were less than I .4 times their respective standard errors. Removing them from the fitting did not result in any significant change. They were therefore removed from the model for the final fitting, by being fixed to zero. The HCH bond angle was not the same for both isotopic species, and a separate value for each species was used in the model. As a curiosity, it may be noted that semiridigity of this bond angle does seem to be the same for both isotopic species. In the final fitting, however, the semirigidity of the HCH bond angle was allowed to be different for H,CS and D2CS. To test numerical convergence, the program was rerun with the final set of parameters but with the following extensions: (i) A total of 500 points were used in the numerical integration, instead of 100. (ii) The inversional basis set was extended to u,,, 4, instead of u, + 2, where u,,, is the highest inversional level involved in the fitted data. (iii) The range of integration was extended out to p = 1.75 rad, instead of only out to p = 1 S O rad. These extensions resulted in only insignificant changes to the calculated term values. No calculated rotational term shifted by more than 0.001 cm-I, while the largest change in any vibrational term was 0.036 cm-', which was for a term involving the highest inversional excitation, u4 = 5, for D2CS. These deviations are more than an order of magnitude smaller than the final observed minus calculated residuals from the least-squares fitting. The limits used in the least-squares fitting (100 points, u4 basis up to umax+ 2, and p out to 1.50 rad) are therefore clearly satisfactory. The program used in this work is an extended version of the program used in ref 49. B. Vibrational and Rotational Data Used in the Least-Squares Fitting. Vibrational and rotational data for both H2CS and D2CS were included in the fitting. Only rotational terms for the pure bending states (i.e., those not involving excitation of any of the small amplitude states) and involving J I7 were included. All available vibrational terms for both isotopes were considered for the fittings. However, there always remains the possibility of vibrational perturbation or misassignment in the vibrational data. Because the model does not account for either of these factors, it was essential to eliminate at the outset any of the assigned levels that could be in either of these categories. This was done by performing a careful inspection of all of the observed vibrational series and by considering term difference sequences between inversional series built on different small-amplitude states. Also, in the initial runs, all levels involving excitation of more than two of the small-amplitude vibrations were excluded. Only when a satisfactory fitting of all of the most clearly correct and not strongly perturbed levels was obtained were the initially excluded terms
Dunlop et al.
TABLE VI: Fitted Smrll-Amplitude Vibration Constants ($) in cm-llnd"; x,, in em-')
HXS 3041.7 (52)" b 831.5 (28) up' -25.6 (46) wi4' b wio) 802.1 (41) w i 2 ) 78 ( 1 1 ) wi0) wI2) wi0'
xi2
-12.3 (50)
~ 1 3 -4.4 (25) X33 -3.67 (53) X36 -2.0 (12)
D,CS 1021.7 (27) b 2352.7 (45) -144 (15) b
b -17.2 (27) -2.32 (47) b
-17.3 (27) b -16.4 (36)
x25
x26 X56
-43.2 (33) b
*The number quoted in parentheses is one standard error quoted in units of the last digit quoted for the parameter. bConstantsso denoted were not included in the model. reexamined in terms of the predictions of the model. This reconsideration led to the final data set that was used in the fitting reported in this paper. For H,CS, the rotational terms used in the least-squares fitting of the semirigid invertor model were all taken from the present work. The vibrational terms were taken from both the present work and that of Judge and King,' with the value of Tootaken from ref 27. For D,CS, the rotational terms used are those calculated from the rotational constants of Judge and King.5 In the case of the u4 = 5 state of D,CS, the data are not as complete as in the lower u4 = 0 and 1 states. In particular, the transitions seen by Judge and King involve several 'R progressions. The u4 = 5 rotational levels that they actually observed areSo Ka=4;J=12
K, = 5; J = 1 1 , 12, ..., 19, 20 K, = 6; J = 1 1 , 12,
+
(49) Ross, S. C. J . Mol. Spectrosc. 1988, 132, 48.
D,CS HXS 2139.7 (42) who) 1356.9 (50) b to$') 59 (18) 774.5 (27) wio) 3058.1 (36) 168 (17) ~5') -94 (32) -234 (27) US" 248 (47) 609.3 (41) 21 (12)
..., 19
K, = 7; J = 1 1 , 12, ..., 19 K, = 8; J = 12 Ka=9;J=12 K, = 1 1 ; J = 12 From these transitions, JudgeMobtained rotational constants for a symmetric top approximation with observed minus calculated residuals all less than 0.012 cm-]. It is clear that these data cover a wide enough range of J and K, to allow us to use all of the terms calculated from their constants for J = 0-7 and for K, = 0, 3-7. Terms with K, = 1 and 2 are not included in our fitting, as the asymmetry is not seen in the experimental data and is therefore not reflected in the rotational constants. For the u4 = 5 level of D2CS,Jensen and Bunkef12restricted their data set to J I2. This is probably an indication of the difficulties that they experienced in trying to fit D2CS as a rigid, rather than a semirigid, bender. The vibrational terms for D2CS are taken from Judge and King4 using their value for Too. In the least-squares fitting, the inversional and vibrational data were given weight 1.0. Because the rotational data are more precise and are better modeled by the Hamiltonian, they were weighted 10000. These weights were chosen to correspond to errors of 1.0 and 0.01 cm-l, respectively. C. Results of Least-Squares Fitting to the Semirigid Invertor Model. The semirigid invertor model described above was used in a least-squares fitting to the experimental data. A single simultaneous fitting to all of the rotational, inversional, and vibrational data for both isotopic species, H2CS and D2CS, was made. The final standard deviation of the 31 1 fitted terms (226 rotational, 7 inversional, and 78 vibrational) was 3.4 cm-'. In this (SO) Judge,
R. H. Personal communication.
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3053
Pyrolysis Jet Spectroscopy of Thioformaldehyde
TABLE VII: Comparison of the Observed a d Clleulrted Rotationrl Energy Levels of H2CS and D2CS in the SIState (in em-') H2CS D2CS 04 = 0 u4 = 1 u4 = 2 u4 = 3 v4 = 0 v4 = 1 v, = 5 Juu. obs 0 - C 4 obs 0 - C obs 0 - C obs 0 - C J u r obs 0-C obs 0-C obs 0-C ~
1.048 9.949 9.979
I -24 -22
1.048 9.567 9.594
-1
3.144 12.015 12.104
4 -23 -17
15.715 24.410 24.854 51.458 5 1.460
17 -23 8
21.999 30.607 3 1.229 29.329 37.836 38.665
0
-1
5 6
1.049 9.202 9.229
3.144 I 1.635 11.718
-4 1 3
3.146 1 1.274 11.355
-3
15.716 24.044 24.457 49.843 49.845
-23 -2 1 -1 1 2 2
15.727 23.731 24.108 48.401 48.404
-13 23
23 -23 21
22.001 30.247 30.826
-32 -33 -1 9
22.035 29.925 30.485
22.024 29.581 30.1 14
26
30 -23 35
29.375 37.531 38.284
29.378 37.177 37.924
29.363 36.840 37.549
36
1.049 8.841 8.864
-I -5 -1
3.146 10.915 10.984
2 -9
15.732 23.359 23.704 46.945 46.947
18 -36 -1 1 -1 1
4
2 3
0.876 4.655 4.691
56.038 56.038 85.290 85.290 122.882 122.882
-4 -4 1 1 -6 -6
52.459 52.459 79.061 79.061 113.404 113.404
-6 1 -6 1 -54 -54 101 101
24.507 28.169 29.262 41.263 41.297 62.174 62. I74 9 1.423 91.423 129.014 129.014
-33 -40 -18 -22 -21 -14 -14 -10 -10 -18 -18
24.482 27.700 28.720 39.616 39.649 58.592 58.592 85.193 85.193 119.535 119.535
98
0.875 5.153 5.193
0 5 7
0.877 5.039 5.078
57.033 57.033 87.062 87.062 125.627 125.627
31 31 19 19 -39 -39 1
24.462 28.220 29.355 41.680 41.716 63.159 63.159 93.186 93.186 131.750 I3 1.750
-1 3
29 21 23 30 30 18 18 -42 -42
-1
-34 -34 -28 -28 128 128
"Observed minus calculated values in units of 0.001 cm-I. bRotational terms without 0 - C values are calculated values only. fitting, all of the 39 parameters used in the model were determined. Table V reports the fitted values for the inversion-rotational constants in the model. These are the parameters specifying the planar geometry, the semirigidity, and the potential function. Note that the HCH bond angle in D2CS was fitted as a correction to the value of this angle in H2CS and that the pure inversional potential function was fitted as a purely quartic function of p. Table VI reports all of the final fitted values for those parameters describing the small-amplitude vibrations. These are the parameters specifying the harmonic frequencies, the dependence of the harmonic frequencies on the inversional coordinate, and the anharmonicity constants. (The latter were modeled as independent of p.) Any parameters not presented in either Table V or VI were not included in the model, either because they were not supported by the data or because they had a standard error nearly equal to or greater than their value. Parameters falling in either of these categories were fixed at zero. The quality of the final fitting can be seen by examining Tables VI1 and VITI, which report the observed minus calculated residuals for all of the rotational and vibrational terms, respectively, used in the least-squares fitting. To illustrate the improvement obtained by using the semirigid invertor rather than the rigid invertor, Table IX compares the root-mean-square (rms) differences between observed and calculated term values using the rigid invertor constants of Jensen and Bunker42and the present semirigid invertor results. For this comparison to be clear, these errors must be calculated on the same data sets. To this end, the rms errors for the inversional and rotational term values were calculated on two data sets. The first of these was designed to be similar to the one that Jensen and Bunker used in their work; the second was the relevant portion of the data set actually used in the present work. Because Jensen and Bunker did not consider vibrations other than inversion, this comparison can only be made with inversional and rotational terms. First to consider are the rms errors for the pure inversional levels. From either the left or right-hand portions of Table IX (for H2CS the two data sets have the same inversional levels), it can be seen that Jensen and Bunker do manage to fit the H2CS inversional levels about 3 times better than is done in the present work. This is not particularly significant, because the model is unlikely to be significantly more accurate than 1-2 cm-I in terms of inversional energies. Also, they had four potential constants at their disposal for each isotopic species, were only fitting with pure inversional levels, and gave the inversional levels the same
weight as the rotational levels. Each of these factors allowed them to obtain a better fitting of the inversional data than was obtained here. For the D2CS inversional levels, the comparison of rmserrors between their work and ours is in their favor if the u4 = 4 level is not included, as in their data set (left-hand portion of Table IX), or in our favor if it is included, as in our data set (right-hand portion of Table IX). In conclusion, the fact that Jensen and Bunker obtained a better fitting of the inversional levels when using a total of seven different potential constants to describe the six term values to which they fit, than we do with one potential constant to describe the seven term values to which we fit, cannot in any way be considered a failing of the present work. The data set designed to be similar to the one used by Jensen and Bunker in their least-squares fitting was obtained by restricting the data set used in this work to those J values fitted by Jensen and Bunker (u4 = 0-3; J = 0-5; u4 = 5 ; J = 0-2). If we use this data set, the effect of determining the semirigidity is clearly evident. For H,CS, the semirigid invertor model that was used in the present work fits the rotational data more than 50 times better than the fitting obtained by Jensen and Bunker. For D2CS, the improvement is smaller, but is still a factor of 8. (Note: The standard deviation of 0.44cm-l reported by Jensen and Bunker for their fitting of D2CS seems to be rather high. Using their constants, we obtain a standard deviation of only 0.19 cm-I.) Making the same comparison based on the data set used in the present work also shows the significant improvement obtained when the semirigid invertor is used. For H2CS, the improvement over the results obtained by using the constants of Jensen and Bunker is approximately a factor of 50 and, for D2CS, the improvement is now a factor of over 35. Of particular note is the significant degradation of the quality of the earlier results when applied to higher J levels in D2CS. This is due to the rather significant change in the vibrationally averaged geometry for the u4 = 5 level from the next lowest level for which rotational data are available, u4 = 2. The rigid bender model used in the previous work could not account for this. In conclusion, the semirigid invertor model would appear to be near its limits in terms of fitting the inversional levels of both isotopic species with a single parameter inversional potential and to have enormously improved agreement with regard to the rotational levels built on the inversional structure, when compared to the previous rigid bender results obtained by Jensen and Bunker.42 Perhaps the most interesting results of the least-squares fitting concern the potential energy function obtained for the inversional
Dunlop et al.
3054 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 TABLE VIII: Comparison of Observed and Calculated Vibrational Energies of H3CS and D2CS in the S1 State (in cm-') vibrational level v , v2 v, v5 v6 v, 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 5 0 0 0 0 0 6
H2CS term* 0 - Cb 0 371.1 0.8 834.7 -3.9 1341.7 0.4 1856.1 2371.8 2883.9
DZCS term 0-C 0 275.3 2.0 618.5 -7.3 1016.5 1430.5 -0.8 1861.2 1.1 2296.5 598.5 878.5 1232.8 1625.1 2041.3 2471.5 2909.4
-4.3 -0.2
2324.8 2581.5 2917.5 3301.3 3706.1 4125.3
0.8 1.5 -3.8
2912.5 3169.1 3512.0
2.0
771.3 1056.5 1405.8 1792.5 2200.4 2620.5 3045.2
0.7 2.6
0 0 0 0 0 0 0
0 0 0 0 0 0 0
1 1 1 1 1 1 1
0 1 2 3 4 5 6
785.2 1168.8 1642.9 2153.5 2673.6 3195.3 3712.9
0
0 0 0 0 0 0
1 1 1 1 1 1
0 0 0 0 0 0
0 1 2 3 4 5
3054.9 3424.2 3905.2 4416.4 4959.2 5487.7
0 0 0
0 0 0
0 0 0
1 1 1
1 1
1
0 I 2
3841.4 4223.2 4708.6
0 0 0 0 0 0 0
0 0 0 0
1 1 1 1 1 1 1
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 1 2 3 4 5 6
819.7 1187.4 1649.1 2153.7 2664.6 3178.3 3688.5
1.0 1.9 -2.4 1.8
0 0 0 0
0 0 0 0
1 1 1
1 1 1 1
0 1 2 3
1603.0 1983.0 2453.8 2961.0
-0.2 2.2
1376.5 1660.5 2012.8 2401.2
3.2 1.3
1
0 0 0 0
0 0 0 0 0
0 0 0 0 0
1 1 1 1 1
1 1 1 1 1
0 0 0 0 0
0 1 2 3 4
3868.9 4242.7 4719.8 5232.1 5761.8
-4.7 1.1 2.0
3095.5 3360.5 3700.8 4076.6 4474.0
0.4 -0.3
0 0 0 0 0
0 0 0 0
1 1 1 1 1
1 1 1
1 1
0 1 2 3 4
4658.1 5036.6 5519.6 6036.0 6576.4
3679.5 3949.8 4291.6 4669.0 5068.0
-2.0
0 0 0 0
0
0 0 0 0 0
0 0
0
0 0 0 0 0 0
0 0 0 0
0
0
0 0 0
0
1 1
1 1 1
-1.3 1.3 1.1
(25.4) -2.1 0.4 -4.9 (JK) 6.2
-4.6 (new)
-0.1
0.6
vibrational level HZCS u , v2 u, v5 v6 v4 term 0-C 0 0 3 0 0 0 2432.8 -1.1 0 0 3 0 0 1 2793.3 -0.4 0 0 3 0 0 2 3254.9 0 0 3 0 0 3 3750.9
2 2 2 2 2
0 0 0 0 0
0 0 0 0 0
0 1 2 3 4
1630.7 1994.5 2457.4 2955.4 3465.6
0.7 1.2 0.6 (JK) 0.4
0 0 0
1 1 I
0
1
0 1 2 3
2414.1 2486.4 3257.3 3762.3
1.5 -0.3 (JK)
0 0
2 2 2 2
0 0 0 0 0
0 0 0 0 0
2 2 2 2 2
1 1
0 1
2 3 4
4683.8 5053.4 5523.0 6035.6 6563.2
-1.1
1
0 0 0 0 0
0 0 0
0 0 0
2
1 1 1
1 1 1
0 1 2
5467.5 5842.5 6323.3
0 0 0
0 0
0 0
0
0
0 0
2 2
1 1
4.0 -0.4 (new)
1536.5 1829.6 2181.2 2563.7 2964.1
0.2
21 39.0 2434.8 2788.3 3172.5 0.4 4.6
4447.5 4725.8 5066.7
(-17.0)
0-C -0.6
0
0 0 0 0
1 1 1 1
0 1 2 3
3214.7 3587.4 4053.5 4556.3
0 0 0 0 0
0 0 0 0 0
3 3 3 3 3
1 1 1 1 1
0 0 0 0 0
0 1 2 3 4
5488.9 5852.4 6317.4 6831.7 7357.2
0 0 0
0 0 0
4 4 4
0 0 0
0 0 0
0 2
3230.5 3586.7 4045.6
3053.1 3366.7 3718.3
0 0 0
0 0 0
4 4 4
1 1
0 1 2
6285.5 6643.0 7112.6
5381.5 5674.6 6012.2
2.8
I
0 0 0
0 0 0 0
1 1
0 0 0 0
0 0 0 0
0 1 2 3
1334.5 1712.9 2186.7 2694.7
1012.5 1287.8 1638.8 2029.6
-0.6 1.4
1
0 0 0 0
0 0 0 0
1 1 1 1
0 0 0 0
0 0 0 0
1
1 1 1
0 1 2 3
2077.7 2469.4 2947.6 3462.3
0 0 0 0
1 1 1 1
0 0 0 0
1
0 0 0 0
0 1 2 3
4390.2 4768.8 5252.5 5774.1
0.8
1 1 1
0 0 0 0 0
1
1 1
0 0 0 0 0
2 3 4
2150.0 2526.2 2999.6 3505.3 4022.9
-3.3 -2.1
1 1 1
0 0 0 0 0
0
1 1 1 1
0 0 0 0
1 1 1 1
1 1 1 1
0 0 0 0
1 1
1
0 1 2 3
2894.5 3277.4 3758.6 4271.1
0 0 0
1 1 1 1
1 1 1 1
1 1 1 1
0 0 0 0
0 1 2 3
5213.4 5584.2 6065.6 6585.0
0 0 0 0
1 1 1 1
2 2 2 2
0 0 0 0
0 0 0 0
0 1 2 3
2964.1 3336.2 3805.1 4308.5
0
1 1
6019.5 6392.1 6871.3
0 0
0
I
I
1
1
2
1
1 1
0 0 0
0 1
1
2 2
0 0 0
1 1 1
3 3 3
0 0 0
0 0 0
0 1
2
3768.6 4136.6 4603.3
1 1 1 1 1
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 1 2 3 4
3033.4 3403.8 3872.0 4374.7 4889.5
0 0
3861.5 4141.5 4475.9 4846.9 5236.5
term 2296.5 2600.6 2952.0 3330.0
3 3 3 3
0 0 0 0
0 0 0 0 0 0
DZCS
2
2.2 (JK)
2.5 (JK) -4.3 (new)
-0.1
2.7 (JK)
-2.7 (JK)
5.2 (JK)
-0.5 0.1
2899.8 3205.8 3559.2 3938.9 4620.5 4903.5 5246.3 5612.3 5993.3
-1.8 -4.6
1615.9 1891.7 2245.9 2638.2 3319.8 3580.5 3917.0 4297.1 1782.5 2068.5 2417.5 2805.6 3213.4 2386.4 2672.2 3025.9 3414.3 4086.5 4357.5 4696.6 5072.3 2549.3 2842.7 3194.2 3576.8 4855.5
4.8
-1.1 1.6 -1.3 (new)
(-17.7)
-4.3 0.9
(-20.2)
-1.4
5 132.6 5471.6
(17.2) 0 (JK)
3310.2 3613.6 3965.1 2131.1 2404.4 2757.5 3147.6 3562.4
0.6
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3055
Pyrolysis Jet Spectroscopy of Thioformaldehyde TABLE VI11 (Continued) vibrational level v i vz v, us ug u, 1 0 I 0 0 0 I I 1 1
1 I
I I I
0 0 0 0 0 0 0 0 0
1 1 1 I
2 2 2 2 2
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1
2 3 4
0 1
2 3 4
~~~
HZCS terma 0 - Cb 3847.7 4214.5 4680.4 5180.9 5693.6
2884.5 3167.8 3518.5 3906.5 4314.3
4654.6 5017.9 5481.5 5979.7 6490.2
~
DZCS term 0 - C
3633.0 3926.3 4278.5 4660.4 5060.9
-1.2
0.6
vibrational level
HzCS 0- C
DZCS term 0 - C
uI
uz
u3
u5
ug
u4
term
1 1 1
1
0 0 0
0 0 0
0 0 0
0
4355.1 4734.2 5207.8
-0.6
1 1
3144.2 3417.5 3770.0
1 1 1
1 1 1
1 1 1
0 0 0
0 0 0
0
1.1
2
5171.1 5545.0 6016.3
3897.6 4180.8 4532.7
1 1 1
1 1 1
2 2 2
0 0 0
0 0 0
0 1 2
5976.4 6348.5 6817.4
1
2 1
-0.6 (JK)
4646.1 4939.4 5291.0
OH2CSterms are from the present work unless denoted JK (for terms from ref 4) or "new" for terms from ref 4 that we have reassigned. Term values that are reported without observed-calculated values are calculated values and correspond to levels unobserved experimentallyor data which were not included in the least-squares fitting. bobserved minus calculated values. Values in parentheses correspond to terms not included in the least-squares fitting. In this case the reported term value is the calculated value. 'All DzCS terms are from ref 4. Terms labelled "new" have been reassigned in the present work. TABLE IX Comparison of RMS Errors for Rigid Bendep and Semirigid Bender Models (in c d ) data set similar data set used in this work, using to ref 42, using constants from constants from ref 42 present work ref 42 present work 0.7 2.3 H2CS inversion 0.7 2.3 0.752 0.014 0.767 0.016 rotation DzCS inversion 0.5" 4.40 6.6b 3Xb 0.159 0.019 rotation 1.454 0.040 OJensen and Bunker42give the level u4 = 4 zero weight. It is not reflected in the rms errors given above for their constants. Their prediction lies 13 cm-I below the observed level. bThe level u4 = 4 is included in this value. This is the only difference between the two data sets with regard to inversion.
E /cm- 1
H CS
D2CS
TABLE X: Constants Obtained for the Empirical Energy Level Formula (in cm-') H2CS DZCS E(u4=I ) E(u4=2) E(~4=3) E(~4=4) E(u4=5) E(~4=6)
370.3 (1 4)" 835.3 (19) 1339.7 (21) 1856.1 2371.8 2883.9
278.6 (24) 620.4 (41) 1O16Sb 1430.5 (52) 1854.2 (38) 2296.5
WI
3033.4 (35) 1330.9 (28) 824.9 (16) 3045.9 (21) 787.3 (24)
21 36.0 (63) 1010.3 (33) 777.0 (22) 2318.0 (36) 600.9 (32)
WZ
w3
w3 w6
XI2 XI3
Elm-'
x24
2500
XZS
2500 1
xZ6
x33 x34 x35
C
-9.0 (39) 5.0 (31) -20.7 (43) C
-3.78 (79) C
C
4.1 (20) C
XY
-2.5 (13) 11.78 (98) 8.2 (13)
x56
C
-9.7 (31) 3.3 (15) -11.6 (58)
B
3.5
5.2
x36
x45 I500
-8.9 (55) -5.3 (26) 9.6 (35) 14.8 (43) -40.3 (36) -4.49 (56) -3.16 (55)
OThe value quoted in parentheses is one standard error in units of the last digit quoted for the parameter. bMode 4 terms without quoted errors were taken from the semirigid bender predicted energy levels. 'Parameters so indicated were fixed at zero. dStandard deviation of the vibrational fitting.
p2),in the potential energy function to zero and that is why only f14) is reported in Table V. The same pure inversional potential 1.0
0.5
0,O
0.5
I .o
plradians
Figure 7. Excited-state bending potentials and energy levels for HzCS and DzCS. The pure inversional potential function for HzCS/DzCS is shown by the dashed line. The two solid curves represent the effective inversional potential functions for the ground small-amplitudestates of H2CS(left) and DzCS (right). The dotted curves show the same effective potential functions obtained in ref 42 using the rigid bender model. Horizontal lines indicate the pure inversional energy levels, solid lines for levels that have been observed, and dashed lines for levels only calculated. motion. Early on, it was found that this potential function was best modeled as a quartic function of the inversional coordinate p, with no quadratic term. For this reason, the least-squares fitting reported in this work was done by fixing the quadratic coefficient,
function was used for both isotopic species, H2CS and D2CS. The pure inversional potential energy function is shown by the dashed curve in Figure 7. This curve, which is analogous to the result one would obtain from an a b initio calculation of energy versus out-of-plane angle with fully relaxed geometrics, is the same for both H2CS and D2CS. The solid curves shown in Figure 7 are the effective inversional potential functions for H2CS and D2CS for the ground small-amplitude state (ul,uz,u3,u5,u6)= (O,O,O,O,O). The horizontal lines in this figure represent the calculated pure inversional energy levels for this small-amplitude state. For comparison, the ground small-amplitude state effective inversional potential functions obtained by Jensen and Bunker42are shown by the dotted curves. The fact that the potential energy is a quartic function of the inversional coordinate is, at first, rather surprising. To verify this result, an additional least-squares fitting was done, starting with the final parameters determined here. In this additional fitting,
Dunlop et al.
3056 The Journal of Physical Chemistry, Vol. 95, No. 8,1991
TABLE XI: Subband Tables for the RotPtio~llvAnalvzed Bands in the Pyrolysis Jet Spectrum of H2CS 6'r B u d
(Hlgh R d r t l o n )
K ; = Z c K ; ' =I J
Rm
1
I67927lqlo) 16792.716(-24) l6793.s24(S) 16793.WS) 16794.P1(4) 16794*412(-15) 16794.?74(-24) 16795.147(-2)
2
3 4
ocn
K;=2cK;'= I Pm
16790.393(14) 167W.W IO) 167W.049(19) 16790.m)
16786.883(-6)
J I
17210.039(11)
2
l72lomyl I) l72lO.w-I) I72lO.osyo)
3
I72ll54S(-lO)
4
172l1.753(-10) *17212119(-29) *17212.46!5(-29)
16787.096(-1)
16785.#6(-1 I) 16785.721(-5)
RIn
5
Rm
0
16775.321(7) 16776.232(-2) ICV~.W!JO 16777.731(-6) 16778.320(0) 16778.1#n(ll)
I 2
3 4 5 6
an 16774.206(11) 16774.U33(8) l6773.?74(5) 16773.422(-6) 16773.002(-1) 16772496(1)
wn I677 1.tly) 1677M9l(-tS) 16769.9.009(-14) 16767.41%-9)
J
Rfn
0 1
17190.252(7) 1739123s(4) 1714L139(2) 17192.969(5) 17193.712(0) 17194.385(5)
2 3 4 5 6
K;=OcK;'=l
J
R(JI
OU)
I
16758.600(-5) l6759.492(3) 16760.286(-4) 16761.004(-6) 16761.664(17)
1675647q-7) 1675623I (-I 3) 16755.896(2) 16755.438(10)
2
3 4
5
PUI
J
RLn
I 2 3 4 5
1717 2 . w - 2 ) 17173.W-2) 17174.192(-1) *l7l74.8OO(l8) 17175.258(2)
I
2 3 J
17608.897(8) 17609.666(-6) l7609.777(1) 17610.382(30) 17610.594(31) 17610.891(-20) I 761 1.241(-22)
5
17606.554(8) 17606.65W) 17606.186(3) 17606.392(0) 176057ra(52) 17606.IOy60) 17605.062(-36) I76I)5.620(I )
0
I .)
3 J
c
an
RfJ\ I7591.559(10) l7592.453(-3) I7593.244(2) 17593.W-3) 17594.453(-4)
h
K; = 0W(l\
17588.11q4) 17586.727(0) 17585.229(6) 17583.601(I) I7581.853(-(5)
K;' = 1
I
17574.856(0) 17575.727(1) 17576.530(2 1 ) '17S77.244(3R)
1
1 5
O(J)
17572.7264-IO) 17572.484(-10) 17572.1WS) l757l.6(1l(l4) 17571.orn(l9)
o(11 17170.603(-3) 17170.444(-3) 17170206(-2) 17169.88q-3)
PNI
17169.519(-3) 17168.240(-4) 17166850(-2) 17165.341(-5) 17163.723~ 1)
-
an
PfJ)
2
17761.178((12) 17761.m-2) 17761.8Sq-lS) 177Sr076(-5)
I7758.042(21) I7758.139(14) 17757.665(-12) I7757.875(-lI) 17157.180(-39) I7757.536(-3 1)
17754.554(23) 17754.768(213)
4
maws) 17762814(3)
___
_..
K;r I c K ; ' = O
_ .
l
17186791(-16) 171SS.S07(5) 17184.120(2) I7182657(2)
RLn
3 17603.061(5) 17603.2720 I760I.W(-7) 17601.871(-9)
P(1)
17590.424(-12) 17590.233(-29) *17589.943(-57) 17589.571(-81) l7589.l02(-Il6)
17189mq5) 17188.uo(4) 1711.498(4) 1711.038(0) 17187.47244) 17186.791(5)
J
K;= 1 c K ; ' = O J
Pa\
K;=2tK;'=l Pm
WJI
om
Band
K;=2cK;'=l RIJ)
17204.221(9) 17204.410(-1 I ) l72M705(-1) 17203.M9(4)
K;=OtK;'= 1
3'4'aBMd
J
17241.712(10) 17207.817(10) 17#n.351(-7) 17207.!569(1) 17~.690(-11) 17W.U8(- 13) *I7206.w3(-26) 17206.829(-27)
PIJI
Ki= I c K ; ' = O
K;= I - G P O J
an
P(11 I757 I .715(-14) 17570.495(-19) 17%9.215( I ) l7%7.R~9(Il) I7566.362(7)
J
RLn
an
0
l7745.107(-3S) Inraoay-2) 177&9U7(17) 1n47.aoy) 17748.m4)
In44.w8) 17743.852(4) 17743.601(IO) 17743.259(10)
1
2 3 4
PU)
17741.71q3I ) 17740.3490 17736.876W
Pyrolysis Jet Spectroscopy of Thioformaldehyde
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3057
TABLE XI (continued)
2
3 4 5
6
18135.600(3)
18132.458(6)
18135.705(3)
18132.559(2)
18136.308(7) I81 36.5 I @ 7 ) 18136.888(-1) 18137.242(1) 18137.364(1) 18137.888(.4) 18 137.723(0)
18132.111(3) 18132.32q9) 18131.652(3) 18132.006(9) 18131.078(2)
K;= 1 c K ; ’ = O R(J1
O(J)
0
18008.065(-20) IW.m1(-7) 18009.%0(17) 18010.748(6) IR011.472(17)
18006.877(-23) 18006.647(.1) 18006.293(22) ls(wH.790(22)
I 2
3 4
K;= 1 c K ; ’ = O
A
J
J 0 1
18004.628(*20) 1%003.320(.9) 18001.920(-4)
2 3 4 5
6 K;=OcK;’=
I 2
3 4
17990.483(1I ) 17991.263(0) 17991.913(-17) 17992.W.13)
5
1812bW9(-3) 18129.167(-5) 18127.447(-8) 18127.W(- IO) 18125.W2(0) 18126354(-3) 18124.095(1) I8124.815(-16)
RfJI 18117.175(-3) 18118.105(4) 18118.908(-4) 18119.612(0) 18120.1%(-4) 18120.686(8) 18121.038(-7)
I
17988.441(13) 17988.265(15) 17987.997(14) 17987.621(-6) 17987.167(-14)
PfJI
O(J)
18116.060(-1) 18115.895(1) I81 15.654(IO) 181 15.294(-18) 18114.897(0)
18113.73y-6) 181123790) 181 10.88fX-7)
K;=OtK;‘=l
17987.370(16) 17986.072(5) 17984.652(-4) 17983.117(-4) 17981.447(-15)
J
R(JI
I
*18100.436(31) *18101.314(21) *18102.127(26) 1810.2.841(13) 1810).478(4)
2 3 4 5
PfJ)
O(J)
...
18098.275(1) 18098.033(-11) 18097.701(2) 18097.245(6) 18096.663(0)
18096045(-7) 18094.762(-2) I8093.393(-2) 18091.942(-5) 18090.413(.5)
6 $J(’, Band
K;=2eK;’=l J 2 3 4
5
R(J)
O(J)
18416.775(-1)
18413.692(10) 18413.793(6) 18413.284(-3) 18413.502(6) 18412.759(0) 18413.1 1q2) 1 84 12.09I(-9) 18412.615(-8) I 8 4 1 1.322(11)
18416.876(-5) 18417.413(2) 184 17.626(5) 18417.917(2) 184 I8.286(21) 184 I8.286(0) 1 R418.809(-3)
h
P(J) 1
2 18410.185(-8) 184 10.397(-5)
18408.634(0) 1 R408.98q-3) I 8406.934(-9) 18407.449(-18) I &405.126(5) 18405.857(2)
3
18572.207(-3) 18572.996(-4) 18573.086(-19) 18573.683(*6) 18573.886(-13)
4
K;= I e K ; ’ = O
K;=IcK;’=O
J 0
I 2 1 4
5
18398.693(-9) 1R399.603(5) 1 R400.369(0) 1R401.CW-9) IR401.542(5) 1 R401.933(-2)
18397.582(6) 18397.370(2) 18397.O48(-7) 183%.656(17) I8396.103(-17) K;=O+K;’=
18395.258(-6) 1 R393.887(18) 1 R392.340(-9)
K(J)
O(J)
Unarsignshlc
R(J)
0
18557.117(19)
1
18557.985(-26) 18558.774(-34) 18559.483(-6)
2 3
1
O(J)
I’(J)
J 1
2 3 4 5
R1J) iR541.017(-135) 18541.814(-214) I R542.58W.24 I ) *lR543.216(-314)
P(JI
18556.010(28) 18555.806(-4) I 8555.555(2)
K;=OcK;’=
. ..
L-
18569.885(19) 18569.987(16) 18569.512(1) 18569.727(7) 18569.038(I ) 18569.388(3)
18553.677(16) 18552.2651-17)
1
OIJ) *18538.949(-78) * 18538.650(-140) I R538.221(-213) *18537.695(-264)
PIJI
___
.-
18436.731(-75) 18435.383(-127) *18433.907(-223) 18432.414(-253)
Dunlop et al.
3058 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 TABLE XI (continued) Bmd
96'0
K;=2cK;'=l J 1 2
3
R(n *18839.114(2.621) *18MO.054(2.789) *l8839.987(2.622) *18MO.955(3.023) I8esO.W.715)
an *18836.901(2.752) 18836.78q2.532) 18113&717(2.732) l8836.4aq2.4l5)
p(n
___
.--
K;=ItK;'=O J 1 2
3
an
R(n *18817.133(45) *18818.W(-ll4) *18818.745(-345)
4 5
18815.824(-17) *18815.59w6) 18815.067(22) l8814.414(6) 18813.598(-12)
wn *1u)13.700(M) *1881227q*I19) *I 8810.699(-371)
K;=OtK;'= I J
om
RIn
1 2 3
18799.564(-3) I8soO.3so(0)
4
I880l.5zo(z)
18797.527(-1) 1mn347(1) 18797.M5(-4) l87%.@3(-4) 187%.231(5)
18801.002(1)
5
334'0
PO l87%.468(12) 18795.l72(5) 18793.74q-1I)
1 2 3 4 5 6
189913.62!T(IO) I89I4JlqIf) lWI5.264(6) l8915.993(27) *18916.6l1(47) *189917.148(78)
Bwd
$#e
K;=2tK;'= I
J 1
2
3 4
an
Rfn 19215.04 I( IO) 19215.781(4) 19215.887(5) I9216.404(-3) 19216.591(-26) 19216.908(3) *19217.202(-52)
I9212.W) 19212.800(8) 19212.284(-3) 19212.507(10) 19211.732(-23) 19212096(-8) K;.:
J 0 I 2
3 4 5
6
R(n 19197.51M-18) 19198.436(-16) 19199.244(4) 19199.932(-5) 19200.521(14) 19200.968(4) 19201.321(15)
1c
Pfn
J
RUl
2
19374.887(-5) 19374.m-9) 193755$0(15) 1937S.750(3)
3 19209.Zar(lO) 19209.417(10) 19207.652(17) 192U7.979(-5)
4
..-
19376.402(-1)
1 2
3 4
R(n '19180512(-224) 19181.I 3 l (-438) *l9181.591(-713)
I
an 19371.800(-1) 193713 S y - I 2) 19371.415(8) 19371.625(13) 19370.8991(6) 19371.m)
Pm 19368.292(-19) 19361524(3) 19366.744(-6) 19367.102(.1)
K ; ' = O
an
p(n
191%.389(0) 191%.167(30) I9 1%.827( 19) 19195.344(0) *191W.808(44)
191W.OSy-5) 19192.727(4)
K;=OtK;'=l J
Bad
Kir2-K;'~
an *19178.5M(-91) 19178.136(-238) *19177.534(-441) *19176.721(-721)
K;=OtK;'= I
p(n
J
--_
1 2 3 4 5
*19176.326(-93) *19174.863(-231) *19173.238(.433)
6
R(n 19342.847(10) 19343.686(17) 19344.384(-15) 19345.013(-9) 19345.538(2) 19345.945(9)
an 19340.73%-2) 19340.483(7) l9340.064(-11) 19339.521(-16) l9338.846(-12)
P(J)
19339.749(3) 19338.52qO) 19337.212(17) 19335.771(0)
Pyrolysis Jet Spectroscopy of Thioformaldehyde
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3059
TABLE XI (continued) 2'84'.
9. B d
B d
K;=2tK;'= I
J
RIn
am
1
2
19757.53I(2) 19758.331(15) 1971.415(-6)
I9755.192(7)
3
19759.012(11)
4
19759.227(15) 19759.549(-18) 19759.943(23)
5
6
_._
19760.540(-5) 39760.355(14) l9761.089(1)
7
19755.31I@) 19754.6335) 19755.048(12) 19754.364(14) 19754.712(14) 19753.753-4)
___
K;32+K;'=1
m
I
m
1
19SU3.616 19504.594 19504.666
2
19751.66w-6) l9751.693(-11) l97SO.l54(-a)
3
19750.501(-22) l9748.498(-35) 19749.01q-44)
19753.033(-10)
.__
19752.193(-22) 19753.155(-22)
J
RUl
0
19740.347(0) 19741.2.56(4) 19742.03q-4) 19742.703(-1) 19743.23q-21) *19743.649(-29) 19743.996(9)
2 3 4 5
6
Rn
19497.762 19497.973 19496433 19496797
19w.491
K;=l c K ; ' = O
K;= I t K ; ' = O
1
om
an 19739.21q-26) O19739.03 1(-37) *19738.744(-72) *l9738.389(-91) *19737.915(-146)
pm
19736.m-9) 19735.5270) 19734.01l ( 4 ) 19732.401(6)
I 1 2 3 4
RUl
___
om
PU)
1 9 4 6 s . m lW.856
19463.266
IW2W 19462440
19481.030 19479.972
K;=OtK;'= I
J
Rln
an
1
19723.7Iq5) 19724.587(1) 19725.398(23) *19726.114(36) *19726.758(63)
I97215 l9(-70) 19721.343-8) 19720.999(8) I9720.S44@2) *19719.9M(56)
2 3 4 5
2 3
4 5
___
.._ 16398.028(0) 16397.940(-4) 16398.683(1) 16398.595(2) 16399.240(2)
16399.142(-4)
Pm 19720.549(-21) 19719.365(-2) I97 l8.063(-7) 19716.667(0) 19715.235(15)
16391.%1(-1) 16392029(-8) 16390.592(-4) 16390.719(2) 16389.I%@) 16389.310(8) 16387.553(-7) I6387.796(6)
I72 15.986(-5) I72 15.938(-4) 17216.63%-3) l7216373(- I) 17217.574(-2) 17217.505(-I) 17216.21~1) 17218.142(1) I7218.710(3) 17218.678(2) 37219.173(14) 17219.119(6) 17219.4739)
17213.84y4) 17213.906(-3) 17213.577y-3) 17213 . 7 ~ - 3 ) l7213.180(0) 17213 . m 4 ) 17212642(-2) 17213.273( I )
__.
17211.545(.4) I7211.622(-4) 17210.17 l ( 4 ) 17210.298(-2) 17208.689(-5) 17208.874(-2) 172O7.107(0) 172O7.355(3) 17205.4I4(-2) 17205.73q-I) 17203.619(0) 17204.009(-?)
17219.690(1) K; = 0 c K ; ' = 0 J
n 1
2 3 4
5
16395.679(-1) 163%.627(-1) 16397.486(8) 16398.244(16) 16398.818(-2) 16399.427(-6)
___ I6392.233(-10) 16390.898(-2) 16389.446(7) 16307.912(-7)
R(J) 17215.318(14) 17216.255(10) 17217.088(4) 17217.818(- I ) 17218.441(-12) *17218.%3(-21) * 17219.378(-35) *17219.690(-51) * 17219.945(-21)
an
PfJ) 17213.132(17) 1721I.SSO(l3) 172l0.527( 10) I7209.069(5) 17207.51O(0) 17205.84I (. 1.i) 17204.07~(.2.1)
3060 The Journal of Physical Chemistry, Vol. 95, No. 8,1991
Dunlop et al.
TABLE X I (continued) B8d
J
Rm
1
*17230.362(-27) 1723O.341(-9) 17231.242(-3) 17231.201(-1) 17232.q4) 17231.958(-4) *17232.653(12)
2 3 4
4'4'0 B u d
(High R d u t l o n )
(HI@ RaduUon)
K;= I cK;'= 1
K;= 1 t K ; ' =1
an
pm
an
1
17565.18q-6) 17565.113(-3) 17%.oM(2) 17545.948(5) 17S66.8lq5) 17566.67q- I) 17567.475(2) 17567.298@) 17566.036@ 17567.826(1) 17W.495(-3) I7568.24q-5)
17563.0280) 17563.098(4) 17562.710(36) 17562.958(-6) 1756235WI) 17562752(-16) 17561.808(-1)
mn
an
2
*I7224.548(.25)
3
___ *l7U0.231(1 I )
6
BUL
17225.996(56) 172%.092(72) *17224.lw7(-11) 17223.101(-2) 17223.3W(O) 17221.534(3) 17221.804(-4)
5
J
4
5 6
PfJ)
17560.736(3) 17560.806(3) 17559.364(-5) 17559.472(-2) 17557.WO) 17558.049(4) 17556.345(2) 17556.519(2) 17554.678(-1) 17554.887(-I ) 17552917(0)
7
J 0 1
2 3 4 5 6
an
Rm
PiJl
17230.3w) 17231.3M(O) 17232.189(-1) 17232.w-1) 17233.602(-4)
I 0
17228.191(1) 17226.947(0) 17225.61q3) 17224.17qo) 17222.639(2) 17221.006(*2)
1
2 3 4
5 6
1756).413(-5) 17S65.360(-4) 175&.199(-9) 17%.959(6) 17567.614(17) *17566.161(21) 17568.572(-10)
17562-223(-4) 17560.976(-5) 17559.634(-I ) 17558.181(-8) 17556.651(7) 17555.015( 16) 3'&
K;r 1 c K ; ' = I J
an
Bmd
K;= 1 t K ; ' =1
pIn
J
Rm
ocn
sOZa76l(l5)
.--
I
__.
18042513(23)
8027.455(-16)
2
I8045.4l4(l)
3
18046.124(-1)
Rfn
PU)
..-
___
pm
18042534(-11)
... ... _--
I(uwo.171(-13) IsoSo.Ua(-IO)
...
18042155(13)
*18(n8.902(-36)
18037.282(2)
4
18037.5 l q 4 )
18035.651(-3)
5
K; = 0-
J
Rtn
0
I 2 3
K;'
K; = 0 cK;'= 0
0
an
pIn
J
Rln
an
1802&270(-26) 18027.188(27)
18042.513(1 I ) 10041.244(-4)
2'$'0
Band
K;= 1 c K ; ' =
I
2
18379.284(22) 18379.106(-11) 18380.106(6)
___ 18374.872(10) 18373.465(4) I8373.465(4) I8371.94q-20) 18371.946(-20)
3 4
J
Rm
an
1
18546.475(-11) 18546.419(-4) 18547.331(-6) 18547.241(-4) *18548.131(48) 18547.%2(-4) 18548.728(2) 18548.593(9)
... __.
2
3 4
J
2
3 4
18378.617(-3) I8379.495(-38) 18380.340(12)
1
18544.(nZ(IO) 18544.263(-1) _._
18544.072(15)
_..
18543.779(-1)
P(J1
I8542.03W-6) 18542114(0) 18540.67I ( 1 ) 18540.782(1) 18539.197(?) I8539.343(-4)
K; = 0 c K ; ' = 0
K; = 0 cK;'= 0
0 I
p(n
0 1
18375.206(23) I 8373.77I (-33) I8372.347(38)
2 3 4
Rm 18545.641(8) 18546.576(3) lU47.410(1) 18548.131(-11)
OfJ)
PfJ)
...
Pyrolysis Jet Spectroscopy of Thioformaldehyde
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3061
TABLE XI (coatinwd) #('e
Bmd
4l&
K;= 1 -IC;'=
K;= I c&'= I J 1
RlJl
an
18550.383 18550.248
2
___
3
I8S51.095 18552.265 18552.130
___ ___
1
J
19820.085
2
19820.935
18543.216 18541.814 18541.978
19812.881 1981 1.363 19809.950 19809.580
___
0
18552.130
18544.522
2
1
5 6
3 4
18828.858 18828.8% 18829.607 18829.607 18830.220 18830.220 111830.720
K(JI
_..
19819.833
___
..19822.398
_.. 19816.389 19815.045 19813.602 19812.077 19810.439
18824.466 18824.547 18823.052 18823.189 I 8821.480 18819.763 1 RR 19.R79
I 8830.W
-J
.._ __.
4 5 6
...
18550.248
PlJ)
19814.258
3
2
--.
O(Jl
I
3
4
1
R(Jl
1
18544.601
5
2 3
P(JI
.__ ._.
4
Band
O(J)
P(J)
I
18829.233
2 7
...
...
...
4
...
1 RR23.497 I R822.057
all of the 39 model parameters were varied and the quadratic term of the potential was also allowed to vary. The resulting fitting produced results almost indistinguishable from the fitting presented in this paper, in which the quadratic term f12) was fixed to zero. In particular, f12)was found to have the small value of 28 cm-'/rad2 (Le., only contributing a maximum of 28 cm-' to the potential over the classically allowed region of about 1 rad for the inversional states studied here). More importantly, the standard error on f12)was found to be 29 cm-I rad2. That is, the experimental results are consistent with fl2{ equal to zero. Therefore, for all practical purposes, the first contributing term to the pure inversional potential in H2CS is the term quartic in the inversional coordinate p. This, together with the quartic dependence of the bond lengths on p , goes a long way in explaining the difficulties that Jensen and Bunker42experienced in trying, unsuccessfully, to fit H2CS and D2CS as semirigid invertors using quadratic semirigidity and fitting the quadratic term of the inversional potential function. It is interesting to note that, if the ab initio potential function obtained by Goddard and Clouthier4* for the @A2triplet state of H2CS (as reported in Table I of Jensen and Bunker42) is fitted to a constant plus quadratic plus quartic power series, then the quartic coefficient obtained, 2126 f 5 1 cm-'/rad4, agrees to within about twice the stangard error of the difference with the quartic term obtained for the A'A2 singlet state in this work, viz. 2288 f 60 cm-'/rad4. Indeed, Jensen and Bunker use a quartic coefficient of 2292.8 cm-'/rad4 for the Z3A2state potential function.
An additional complete semirigid invertor fitting was done using a quartic plus sextic form for the pure inversional potential. Although this led to the pure inversional levels being somewhat better accounted for (rms errors of 1.8 and 3.1 cm-I for H2CS and D2CS, respectively, as compared to 2.3 and 3.8 cm-l in the fitting with the purely quartic potential), the quality of the fitting to the other types of levels was unaffected and the overall standard deviation decreased insignificantly from 3.35 to 3.34 cm-I. More importantly, the coefficient of the sextic term of the potential energy function was barely determined, with f16)= 177 f 121 cm-'/rad6. (The quartic coefficient was found to be 2188 f 92 cm-'/rad4.) For these reasons, this fitting was discarded. It was also possible to fit a quartic plus sextic plus octic potential. The resulting constants, however, are rather poorly determined and the improvement in overall fit is small. It does not seem that anything additional is obtained in such a fitting, and it too was discarded. Finally, a fitting was done to the vibrational levels using the standard anharmonicity expansion, modified 5s done by Frisoli et aL51 for the case of the inversional motion in A'A2 D2C0. This provides an easy-to-use formula to calculate levels not included in Table VIII. The formula is the same as the ordinary anharmonicity expansion, except that the energies of the pure largeamplitude inversional motion are not expressed in terms of har(51) Frisoli, J. K.;Polik, W.F.; Moore, C. B. J . Phys. Chem. 1988, 92, 5417.
3062 The Journal of Physical Chemistry, Vol. 95, No. 8,1991
I
L
1
Figure 8. Geometric changes on S,-So excitation in formaldehyde and thioformaldehyde.
monic and diagonal anharmonic constants but are instead considered as molecular constants, E(u4). Thus, in this empirical expression, the term value of a state is written as E(ul~2,~~,u~,u= 5 , uE(u4) , ) + C (ui)ui i#4
+ C
(uj)(u,)xj,
(8)
iSj (xu4
This simple idea is quite successful, and the resulting constants are given in Table X. All determinable constants were included in the fitting. Those constants that were undetermined were successively eliminated until only determined constants were left in the model, all others being fixed to zero.
V. Discussion This study provides a detailed picture of the rovibrational energy level structure of SI H2CS up to about 3000 cm-’ above the vibrationless level. The semirigid invertor model was used to perform a single simultaneous fitting of all of the vibrational and inversional levels, and of all those rotational levels built on the pure inversional structure, of both isotopic species H2CS and D2CS. The results clearly show that thioformaldehyde has a planar equilibrium structure in the SI state, in agreement with the previous conclusions of Jensen and Bunker.42 Comparing the results of this work with semirigid invertor parameters of S I H2C041is instructive. Formaldehyde adopts a nonplanar equilibrium geometry with an out-of-plane angle of 34O. The H C H angle is 1 18.l0, almost identical with the thioformaldehyde value of l I8.28O. The thioformaldehyde C-H bond is about 0.02 A shorter than that of formaldehyde. The geometric changes on SI-Soexcitation in the two molecules are shown in Figure 8. In formaldehyde the C=X bond elongates more on excitation and there is a large change in the out-of-plane angle. There is a large difference in the semirigidity parameters in HzCO and H2CS. These parameters model the dependence of the bond lengths and the HCH angle on the out-of-plane inversion angle p . In H2C0, the Xco parameter was constrained to a value of zero and the fitted parameters were XCH= -0.0141 (35) A rad-2 and X , = 0.8 1 (1 7) deg rad-2. The trend is exactly opposite to our findings of H2CS/D2CS (see Table V), in which the C-H and C-S bond lengths increase and the HCH angle decreases with p . Although the reasons for the differences between the thioformaldehyde and formaldehyde results are not thoroughly understood, we can speculate on some possibilities. In the H 2 C 0 work, the isotopes were fitted independently and three of the four potential constants used were held fixed. Similarly, one of the three semirigidity parameters was fixed in the least-squares fitting. These restrictions may make comparisons between the semirigidity constants of the two molecules unwarranted. It is also possible that the semirigidity effects in H 2 C 0 might parallel the form of the potential function. The geometry may only start changing
Dunlop et al. dramatically at larger values of p than in H2CS, and at small values of p it could actually change in the opposite direction. The resulting semirigidity parameters would then be much smaller than for H2CS (as is found in the calculations) and could reflect finer details of the semirigidity around the planar configuration. It is gratifying that our results for the SIstate of H2CS parallel the previous ab initio predictions of Goddard and Clouthie#* for the TI state. In the a b initio work, the molecular geometry was optimized a t the DZ** S C F level for various values of the outof-plane angle. The results indicate a slight elongation of the C-S and C-H bonds, with a concomitant decrease in the HCH angle as the out-of-plane angle is increased from the equilibrium value. Few substantial perturbations are observed in the jet spectra. A notable exception is the 5’,level which is shifted up 25.4 cm-I from its calculated position. Small deviations in the rotational struture of the bands become increasingly evident with vibrational energy. These can often be rationalized in terms of the near degeneracy of u3’, 2u4, and ug/. There is no evidence signaling the onset of massive interstate perturbations involving So or TI. These observations have important implications for dynamics studies. Using pyrolysisjet techniques and an extended observation zone to accommodate the expected long fluorescence lifetimes,52 it should be possible to study the rovibrational level dependence of the excited-state decay, now that the spectrum has been characterized. Magnetic field effects could be used to probe the extent of mixing with TI levels, as observed in the Ooo band.27 Further MODR studiesI3 may also be possible. Several of the bands examined in this work occur in the high-frequency end of the tuning range of rhodamine 6G ring dye lasers, making them especially attractive for more detailed study. Acknowledgment. We thank Prof. A. K. Ray for generously giving us access to his ring dye laser and Prof. R. H. Judge for the laser data acquisition programs. Stimulating discussions with R. H. Judge and D. C. Moule are also acknowledged. The authors are grateful to Debra Clouthier for proofreading the entire manuscript. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U S . Department of Energy, under Contract DE-FG05-86ER13544. S.C.R. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada. Appendix Subband tables for the rotationally analyzed bands in the pyrolysis jet spectrum of H2CS are collected in Table XI. The subband tables are organized according to J”values. In cases where transitions can be observed from both even and odd parity asymmetry components the transition from the even component is listed first. All numerical values are in cm-I. Numbers in parentheses are observed minus calculated values right justified to the last figure quoted for the measured transition frequency. An asterisk denotes a line not used in the least-squares fit. Bands without observed minus calculated values could not be satisfactorily fitted. A dashed line indicates a line in a progression which was expected but not assignable due to perturbations, overlapping lines, or abnormally low intensity. Registry No. H,CS, 865-36-1, (52) Dunlop, J. R.; Clouthier, D. J . J . Chem. fhys. 1990, 93, 6371.
