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Rotational Spectroscopy of HB33S: The Quadrupole Coupling Constant of 33S in Thioborine
Journal of Molecular Spectroscopy 215, 228–233 (2002) doi:10.1006/jmsp.2002.8649
Rotational Spectroscopy of HB33 S: The Quadrupole Coupling Constant of 33 S in Thioborine L. Bizzocchi, C. Degli Esposti, and L. Dore Dipartimento di Chimica “G. Ciamician,” Universit`a di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Received February 28, 2002; in revised form June 27, 2002
The unstable HBS molecule has been produced in the gas phase by a high-temperature reaction between crystalline boron and hydrogen sulfide. Ground state rotational spectra have been observed in the millimeter-wave region, from 75 to 460 GHz, for the previously unobserved H11 B33 S and H10 B33 S isotopic species. The analysis of the hyperfine structure produced by the 10/11 B and 33 S nuclear spins in the low-J rotational transitions has yielded the first evaluation of the quadrupole coupling constant of 33 S in the thioborine molecule, which was 6.361(15) MHz in H11 B33 S and 6.329(17) MHz in H10 B33 S. In addition, further measurements have been performed for the most abundant isotopomers H10/11 B32/34 S, for which improved values of rotational, C 2002 Elsevier Science (USA) centrifugal, and hyperfine structure constants have been determined. Key Words: rotational spectroscopy; thioborine; HBS; pyrolysis; quadrupole coupling constants; sulfur-33. I. INTRODUCTION
II. EXPERIMENTAL DETAILS
The sulfidoboron compounds (X–B==S) constitute a small class of moderately unstable molecules, which are typically produced in the gas phase by high-temperature reactions between crystalline boron and a suitable Sn Xm sulfur-containing compound. Thioborine (HBS) was first detected by Kirk and Timms who observed its mass spectrum in the products of the action of hydrogen sulfide on boron at high temperature (1), and its rotational spectrum was subsequently studied by Pearson and McCormick using a millimeter-wave (mm-wave) spectrometer (2). Ground-state spectra of eight isotopic species 1/2 10/11 32/34 H B S were analyzed and the complete rs structure (3) was calculated. A following work, focused on the study of the J = 1 ← 0 rotational transition for the H11 B32 S, D11 B32 S, and D10 B32 S isotopomers, yielded a determination of the 10 B and 11 B nuclear hyperfine coupling constants in thioborine (4). The present work extends the study of the rotational spectra of HBS to the scarcely abundant and so far unobserved 33 Scontaining species, having as main objective the determination of the quadrupole coupling constant of the 33 S nucleus in the thioborine molecule, from which information on the nature of the rather unusual B==S bond can be derived. The rotational spectra of H10 B33 S and H11 B33 S have been recorded in the frequency range 75–460 GHz, which includes rotational transitions from J = 2 ← 1 to J = 12 ← 11. The hyperfine structures given by both 10/11 B and 33 S nuclei have been detected and analyzed for lines up to J = 3, thus obtaining a sufficiently precise evaluation of the quadrupole coupling constant of 33 S in thioborine. The value determined has been compared with those previously obtained for related molecules containing a multiple-bonded terminal sulfur atom.
HBS has been produced in the gas phase by a pyrolysis reaction between hydrogen sulfide and crystalline boron (2). The same pyrolysis system already used to produce FBS (5) was also employed to generate HBS. Gaseous H2 S (Matheson) was flowed through a quartz tube, whose central part, 30 cm long and 1 cm in diameter, was filled with pieces of crystalline boron (Aldrich) and held in a tubular oven at a temperature of 1100◦ C. The quartz reactor was directly connected to the glass-made absorption cell of the mm-wave spectrometer (3 m long, 10 cm in diameter), through which the reaction products were continuously pumped using a diffusion pump connected to the cell with a flexible pipe 2.5 cm in diameter. The H2 S flow rate was adjusted by means of a stainless steel needle valve and the weakest HBS lines were recorded using an inlet pressure of 1 Torr (measured before the boron-filled part of the tube), corresponding to 5 mTorr of gaseous products flowing through the absorption cell. Large amounts of sulfur and a white solid were deposited just out of the heated part of the quartz tube. The rotational spectra of HBS were observed in selected frequency regions between 75 and 460 GHz using a source modulation mm-wave spectrometer which employed Gunn oscillators (Farran and Carlstrom) and klystrons (Varian) as main radiation sources to cover the fundamental frequency range 52–116 GHz. Higher frequencies were generated using two different frequency multipliers, one for the band 50–75 GHz, and a quadrupler optimized for the band 75–110 GHz (Radiometer Physics). The oscillators were phase-locked to the suitable harmonic of the fundamental frequency emitted by a cm-wave signal generator (Wavetek) which was driven by a personal computer. A Schottky barrier diode (Millitech) and a liquid-helium-cooled InSb detector (QMC) were respectively used to record the spectra below
0022-2852/02 $35.00 C 2002 Elsevier Science (USA) All rights reserved.
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ROTATIONAL SPECTROSCOPY OF HB33 S
229
and above 200 GHz. The oscillators were frequency modulated at 16.7 kHz, and the detected signals were demodulated by a lock-in amplifier tuned at 33.3 kHz, so that the second derivative of the actual spectrum profile was displayed by the computercontrolled acquisition system. The accuracy of the frequency measurements was about 20 kHz. A 10 times smaller modulation frequency was employed to perform a few measurements with sub-Doppler resolution (see below). III. OBSERVED SPECTRA AND ANALYSIS
Ground-state rotational spectra have been recorded and analyzed for six isotopomers, H11 B32 S, H10 B32 S, H11 B34 S, H10 B34 S, H11 B33 S, and H10 B33 S, covering the J range from 1 to 11. Several transition frequencies were already known for the 32 S- and 34 S-containing species (2), while no information was available for the two 33 S isotopomers, which are respectively 125 and 500 times less abundant than the main H11 B32 S species. The lines of the 33 S isotopomers were, however, easily identified by means of accurate predictions obtained from an r0 structure (3), which was calculated by fitting the two bond lengths to the ground-state rotational constants of the four most abundant species, H10/11 B32/34 S (2). The calculation gives r0 ˚ and r0 (B–S) = 1.59984(15) A, ˚ from (H–B) = 1.17805(92) A which the very reliable values B000 0 (H11 B33 S) = 18 932.75 MHz and B000 0 (H10 B33 S) = 19 932.17 MHz were obtained. The low-J transitions (up to J = 3) of all the isotopic species investigated exhibit a hyperfine structure due to the 11 B (I = 3/2) or 10 B (I = 3) nuclei, which becomes considerably more complicated when the 33 S (I = 3/2) isotope is also present. An example is given in Fig. 1, where the recordings of the J = 2 ← 1 transitions of H11 B34 S and H11 B33 S are compared. The measured transition frequencies have been analyzed using Pickett’s SPFIT program (6) adopting the Hamiltonian H = H R + HQ (B) + HQ (S) + HSR (B) + HSR (S),
[1]
where H R is the rotational Hamiltonian for a linear molecule in a state, HQ (B) and HQ (S) describe the interaction of the 10/11 B and 33 S nuclear electric quadrupole moments with the respective electric field gradients, and HSR (B) and HSR (S) describe the weak interaction of the boron and sulfur nuclear spins with the magnetic field produced by the rotational motion. Since in HBS the quadrupole coupling constants of 10/11 B and 33 S are of comparable magnitude, the analysis of the hyperfine structure of the HB33 S species was based on the coupling scheme I = IB + IS , and F = I + J, so that each energy level was designated using the three quantum numbers J, I , and F. For two intense lines belonging to the H10 B32 S isotopomer the Lamb-dip technique (7, 8) was used to improve the resolution, making possible the measurement of hyperfine components whose separation was less than the Doppler half-width of the lines. An example is given in Fig. 2, which shows the recording of the J = 4 ← 3 transition of H10 B32 S, performed at very low
1
FIG. 1. Comparison between the J = 2 ← 1 transitions of H11 B34 S and H11 B33 S. The increased complexity of the hyperfine structure produced by the 33 S nucleus is clearly apparent. The absorption features marked by asterisk are unidentified and do not belong to the indicated transitions.
pressure and frequency modulation amplitude values. Ten dips are observable on the Doppler-broadened profile of the line. Owing to the large number of hyperfine-structure components produced by the 10/11 B and 33 S nuclei, many of the recorded lines actually envelop several unresolved transitions, and the corresponding peak frequencies were therefore assigned to the set of components blended in the observed absorption profile. In these cases, an intensity-averaged calculated frequency was compared with the experimental value in the fitting procedure. Typically, all hyperfine structure transitions whose frequencies were predicted to lie within ±100 kHz from the peak of a measured line were used to calculate the corresponding average frequency, but excluding those components whose intensity was less than 10% of that of the strongest one. No evidence of any hyperfine structure was apparent in the lines recorded above 300 GHz, and in these cases the measured peak frequencies were simply assigned to the most intense hyperfine component.
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BIZZOCCHI, DEGLI ESPOSTI, AND DORE
TABLE 2 Measured Transition Frequencies and Least-Squares Deviations (MHz) for the H10 B32 S and H10 B34 S Isotopomers H10 B32 S J F ← J F
FIG. 2. Recording of the J = 4 ← 3 transition of H10 B32 S obtained using the Lamb-dip technique. Ten dips (indicated by arrows) are visible on the Doppler-broadened profile of the line. The stick spectrum was drawn using frequencies and intensities calculated by Pickett’s SPCAT program (Ref. (6)).
The transition frequencies measured and analyzed for the six thioborine isotopomers are listed in Tables 1–4, where for simplicity the lines corresponding to blended transitions are labeled using the set of quantum numbers relative to the most intense TABLE 1 Measured Transition Frequencies and Least-Squares Deviations (MHz) for the H11 B32 S and H11 B34 S Isotopomers H11 B32 S J F ← J 1 1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 5 5 5 9 10 11 12
1.5 2.5 0.5 2.5 3.5 1.5 0.5 3.5 2.5 4.5 2.5 1.5 1.5 4.5 5.5 2.5 5.5 6.5 3.5 10.5 11.5 12.5 13.5
0 0 0 1 1 1 1 2 2 2 2 2 2 3 3 3 4 4 4 8 9 10 11
H11 B34 S
obs.−calc. Na
F
observed
1.5 1.5 1.5 2.5 2.5 1.5 1.5 3.5 1.5 3.5 2.5 1.5 2.5 4.5 4.5 2.5 5.5 5.5 3.5 9.5 10.5 11.5 12.5
38165.176b 38166.127b 38166.837b 76330.453 76331.432 76332.076 76332.992 114494.788
−0.008 0.000 −0.017 0.006c 0.003c −0.003 −0.011 −0.014
114495.748 114496.157 114496.447
0.004c −0.011 0.013
190818.237 190819.184 190820.057 343430.421 381572.727 419709.800 457841.100
0.000 0.016c 0.021 −0.008 −0.013 −0.002 0.010
observed
1 1 1 2 75164.904 2 75165.880 1 75166.523 1 75167.440 1 112746.505 112747.208 2 112747.462 1 112747.888 1 112748.144 112748.778 150326.595 150327.510 150328.337 1 4 1 1 338187.232 1 375747.460 1 413302.602 1 450852.144
obs.−calc. Na
0.005c 0.005c 0.001 −0.001 −0.011 −0.014c 0.001c 0.014 0.005 −0.011 0.006 −0.014c 0.003
2 2 1 1 1 2 2 1 1 1 1 4 1
−0.008 −0.008 −0.001 0.008
1 1 1 1
a Number of hyperfine structure components used to calculate the intensityaveraged frequency (see text). b From Ref. (4). c Observed minus average calculated frequency.
2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 8 9 10 11
3 4 3 2 5 4 3 2 5 2 3 4 4 6 2 5 3 1 2 6 3 4 5 5 7 6 1 4 2 3 11 12 13 14
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 7 8 9 10
2 4 4 2 4 3 3 3 5 1 2 3 4 5 2 4 3 2 3 6 2 3 5 4 6 5 1 4 2 3 10 11 12 13
observed 80318.670 80318.984 80319.217 80319.603 80320.385 80320.548 80320.752 80321.682 120477.666 120478.020 120478.290 120478.679 120478.926c 120478.976c 120479.031c 120479.066c 120479.218c 120479.695 120479.980 160634.650 160635.467c 160635.589c 160635.644c 160635.783c 160635.870c 160635.931c 160636.010c 160636.091c 160636.124c 160636.209c 321234.719 361374.332 401508.770 441637.448
H10 B34 S
obs.−calc. Na −0.005 −0.007 0.011 −0.007 0.006 0.004 −0.007 −0.012 −0.005 −0.015 0.007 −0.027b 0.003 0.008 0.005 0.007 0.001 0.002 0.019 0.023 0.001b −0.001 0.003b 0.003 0.003 0.007 −0.009 −0.009 −0.013 0.002 0.004 −0.008 −0.005 0.006
1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1
observed
obs.−calc. Na
79170.427 79170.746 79170.985 79171.366 79172.141 79172.314 79172.527 79173.441 118755.361 118755.707 118755.987 118756.379
−0.010 −0.008 0.016 −0.007 −0.002 0.006 0.004 −0.018 0.006 −0.012 0.020 −0.012b
1 1 1 1 1 1 1 1 1 1 1 2
118756.703
0.020b
4
118757.379 −0.001 118757.674 0.027 158338.296 0.016
1 1 1
158339.159 −0.021b
3
0.004b
2
158339.550
316643.025 −0.014 356209.098 −0.011 395770.124 −0.007 435325.561 0.016
1 1 1 1
a Number of hyperfine structure components used to calculate the intensityaveraged frequency (see text). b Observed minus average calculated frequency. c Lamb-dip measurements.
hyperfine component. The measurements previously reported by Pearson et al. in (4) for the J = 1 ← 0 transition of H11 B32 S have been also included in the data set analyzed for this isotopomer. Equal weights were given to the various measurements employed in the least-squares analyses, whose complete details are available from the authors. Table 5 contains the results obtained from the least-squares analyses of the line frequencies measured for all the six isotopomers investigated. The fitted parameters are the rotational constant B, the quartic centrifugal distortion constant D, and the quadrupole and spin–rotation coupling constants for the 10 B, 11 B, and 33 S nuclei. The reliability of the results obtained is well illustrated in Fig. 3, which shows the comparison between experimental and
C 2002 Elsevier Science (USA)
ROTATIONAL SPECTROSCOPY OF HB33 S
TABLE 4 Measured Transition Frequencies and Least-Squares Deviations (MHz) for H10 B33 S
TABLE 3 Measured Transition Frequencies and Least-Squares Deviations (MHz) for H11 B33 S J I F ← J I F 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 5 9 10 11 12
3 1 1 3 1 2 3 3 2 3 1 1 2 3 3 2 3 2 3 3 1 3 3 3 3 3 3 3
2 1 2 3 3 3 5 3 3 4 2 3 2 2 3 1 6 1 4 5 4 5 7 8 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 4 8 9 10 11
3 2 2 3 2 1 3 2 3 3 1 2 2 3 3 2 3 2 2 3 2 3 3 3 3 3 3 3
3 2 1 3 2 2 4 3 2 4 1 3 3 3 3 1 5 0 4 5 4 5 6 7 11 12 13 14
231
observed
obs.−calc.
Na
J I
75727.372 75728.453 75728.782 75729.070 75729.524 75729.738 75730.298 75731.089 75731.430 75731.702 75731.913 75732.164 75732.502 113592.376 113592.926 113593.326 113594.113 113594.961 113595.382 113595.655 113596.079 151455.477 151456.459 189316.690 340726.599 378568.750 416405.725 454237.025
0.001 −0.012 −0.011b 0.010 −0.018 0.011b 0.011b −0.024 0.009b −0.011b −0.014b 0.001b 0.001 0.003b 0.007b 0.009b −0.009b 0.000b 0.000b 0.020 0.006 0.011 0.007b 0.006b −0.017 −0.008 −0.003 0.013
1 1 5 1 1 2 9 1 2 2 6 5 1 3 11 4 14 4 3 1 1 1 17 16 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 8 9 10 11
4.5 3.5 2.5 2.5 3.5 2.5 4.5 4.5 3.5 2.5 1.5 4.5 3.5 4.5 3.5 2.5 4.5 2.5 4.5 3.5 4.5 4.5 1.5 4.5 4.5 4.5 4.5
F ← J 2.5 3.5 3.5 3.5 4.5 2.5 4.5 5.5 4.5 4.5 1.5 6.5 5.5 4.5 4.5 4.5 3.5 4.5 5.5 4.5 7.5 1.5 4.5 12.5 13.5 14.5 15.5
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 7 8 9 10
I
F
observed
obs.−calc.
Na
3.5 3.5 4.5 3.5 3.5 4.5 3.5 4.5 2.5 4.5 1.5 4.5 3.5 4.5 3.5 2.5 4.5 4.5 3.5 4.5 4.5 4.5 3.5 4.5 4.5 4.5 4.5
2.5 4.5 3.5 2.5 4.5 3.5 4.5 5.5 3.5 3.5 0.5 5.5 4.5 4.5 3.5 3.5 4.5 4.5 5.5 4.5 6.5 2.5 4.5 11.5 12.5 13.5 14.5
79724.418 79724.984 79725.224 79725.407 79725.642 79726.051 79726.512 79726.899 79727.140 79727.370 79727.601 79728.077 79728.303 79728.850 79729.088 79729.464 79730.165 79730.336 119589.287 119589.708 119590.696 119591.843 119592.459 318866.836 358710.695 398549.435 438382.496
0.000 −0.005b −0.010 0.005 −0.008 −0.016b −0.015b −0.014 0.018b 0.000b 0.001 −0.010b 0.014b −0.020 −0.010b −0.022b −0.004b −0.007 −0.003b 0.020b 0.007b 0.015b 0.003 0.025 0.017 0.001 −0.020
1 3 1 1 1 2 6 1 3 6 1 9 6 1 3 2 5 1 8 10 19 12 1 1 1 1 1
a
a
Number of hyperfine structure components used to calculate the intensityaveraged frequency (see text). b Observed minus average calculated frequency.
simulated spectrum profiles for the J = 2 ← 1 transition of H10 B33 S. The simulated spectrum was calculated assuming a frequency modulated Voigt profile (9) for each of the 113 hyperfine structure components included in the frequency interval recorded. A Doppler half-width of 74 kHz and a collisional half-width of 70 kHz have been assumed for all the components, whose peak frequencies and relative intensities were predicted using Pickett’s SPCAT program (6) and the spectroscopic parameters listed in Table 5. The second Fourier component of the simulated Voigt spectrum profile (lower trace) has been computed assuming a modulation depth of 100 kHz, i.e., the value used for the second harmonic detection of the experimental absorption profile (upper trace). The new measurements described in this work yielded an improved set of spectroscopic parameters for the thioborine molecule. In comparison with the previous experimental results (2, 4) the precision of the rotational and quartic centrifugal distortion constants B and D for the H10/11 B32/34 S isotopomers, even in the less favorable case, has been improved by a factor of 5 and 10, respectively. We have also determined for the first time precise values of the quadrupole coupling constants
Number of hyperfine structure components used to calculate the intensityaveraged frequency (see text). b Observed minus average calculated frequency.
TABLE 5 Rotational, Centrifugal Distortion, and Hyperfine-Structure Constants Determined for the Six Isotopic Species H10/11 B32/33/34 S: Standard Errors in Units of the Last Quoted Digit Are Given in Parentheses for the Fitted Parameters H11 B32 S
H11 B33 S
H11 B34 S
B D eQq (B) eQq (S) C (B) C (S) σ
(MHz) (kHz) (MHz) (MHz) (kHz) (kHz) (kHz)
19083.01082(75) 21.8722(36) −3.725(15) — −4.6(15) — 12.2
18932.74583(51) 21.5418(26) −3.715a 6.361(15) −4.6a −3.7(12) 11.8
18791.61730(59) 21.2226(28) −3.704(13) — −4.6(12) — 9.5
B D eQq (B) eQq (S) C(B) C(S) σ
(MHz) (kHz) (MHz) (MHz) (kHz) (kHz) (kHz)
H10 B32 S 20080.24457(37) 24.0333(25) −7.733(21) — −1.43(65) — 10.2
H10 B33 S 19932.20388(66) 23.6639(39) −7.738a 6.329(17) −1.43a −3.4(12) 14.1
H10 B34 S 19793.18021(65) 23.3724(38) −7.742(31) — −1.43a — 14.5
a
Fixed in the analysis.
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Intensity (arbitrary units)
BIZZOCCHI, DEGLI ESPOSTI, AND DORE
for eQq(33 S) in these two isotopomers differ by 0.032 MHz, an amount equal to the sum of the respective standard uncertainties. In order to reduce the correlation effects between the fitted parameters, the boron quadrupole constants of the H11 B33 S and H10 B33 S isotopomers have been constrained to the values calculated by linear interpolation of the results obtained for 32 S and 34 S containing species. However, only small changes in the value of the 33 S quadrupole constants (≈30 kHz) are produced if both eQq (B) and eQq (33 S) are simultaneously adjusted in the least-squares analyses.
experimental
79724
79726
79728
79730
79732
IV. CONCLUSION
Intensity (arbitrary units)
Frequency (MHz)
calculated
79724
79726
79728
79730
79732
Frequency (MHz) FIG. 3. Comparison between experimental and simulated spectrum profile for the J = 2 ← 1 transition of the H10 B33 S isotopomer. The stick spectrum was drawn using frequencies and intensities calculated by Pickett’s SPCAT program (Ref. (6)).
of the 10/11 B nuclei for the isotopomers H10 B32 S, H11 B34 S, and H10 B34 S. As expected, the quadrupole coupling constants determined for 10 B and 11 B in the 32/34 S isotopic species are coincident within the experimental uncertainties; the average value of their ratios turns out to be
eQq(10 B) eQq(11 B)
This paper presents the first identification of the rotational spectra of the 33 S-containing species of thioborine. Very accurate rotational and centrifugal distortion constants have been determined and, more importantly, a sufficiently precise estimate of the 33 S quadrupole coupling constant has been obtained. The average value determined for the two HB33 S isotopomers is compared in Table 6 with those of the related molecules OC33 S (10), H2 C33 S (11), and C33 S (12), in which a terminal sulfur atom forms an unsaturated bond, as in HBS. It is reasonable to expect that the sulfur atom has sp2 hybridization in HBS, OCS, and H2 CS (with two pairs of nonbonding electrons), while it should be better described as sp hybridized in the CS molecule. Inspection of Table 6 shows clearly that eQqzz (33 S) can assume very different values in different molecules, and this indicates a strong dependence on the polarity of the unsaturated bond and on the type of hybridization of the sulfur atom. This behaviour can be discussed qualitatively using the Townes–Dailey theory (13). If one relates the quadrupole constant of 33 S to the unbalanced p-electron density in the valence shell, then nx + n y eQqzz = −(U p )z eQq310 = − − n z eQq310 . [3] 2
By assuming a sp2 hybridization in the xz plane, the valence shell orbitals of the sulfur atom can be described by the linear
= 2.083 ± 0.015,
[2]
avg
which is well comparable with the value of 2.084(2) obtained from the ratio of the nuclear quadrupole moments of 10 B and 11 B (3). Although affected by a large uncertainty, the ratio of the boron spin–rotation constants C(10 B)/C(11 B) is consistent with the ratio of the boron nuclear g values, g I (10 B)/g I (11 B) = 0.335, as predicted by theory (4). Finally, the analysis of the so-far-unobserved rotational spectra of the 33 S-containing species allowed us to obtain the first experimental evaluation of the quadrupole coupling constants of the 33 S nucleus in H11 B33 S and H10 B33 S. The values determined
TABLE 6 Comparison between the eQqzz Values of the 33 S Nucleus Determined for HBS and the Related Molecules OCS, H2 CS, and CS
a
Ref. (10). Ref. (11). c Ref. (12). b
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Molecule
eQqzz (MHz)
O==C==Sa H2 C==Sb H–B==S C≡Sc
−29.12 −11.90 6.35 12.83
ROTATIONAL SPECTROSCOPY OF HB33 S
combinations of atomic orbitals (3s, 3 px , 3 p y , 3 pz ) 1/2 1/2 ψ1 = 1 − 2as2 ψs + 2as2 ψ pz 1/2 1 − 2as2 1/2 1 ψ2 = as ψs − ψ pz + ψ px 2 2 1/2 1 − 2as2 1/2 1 ψ3 = as ψs − ψ pz − ψ px 2 2 ψ4 = ψ p y ,
[4a] [4b] [4c] [4d]
where as2 represents the “weight” of the s-type basis function in the hybridized orbitals. The equivalent orbitals ψ2 and ψ3 contain the two unshared pairs of electrons, ψ1 forms the σ bond along the z axis, and ψ4 , perpendicular to the x z plane, engages in the π bond. Neglecting any ionic effect in the X==S bond, the electronic populations of the p orbitals are n x = 2, n y = 1, n z = 2 1 − as2 .
[5]
If one assumes perfect sp 2 hybridization in the x z plane (as2 = 0.33), then n z = 1.33, from which a value of (U p )z = 0.167 can be calculated. Taking eQq310 = 52 MHz for 33 S (3), the value eQqzz = −8.7 MHz can be obtained, which is not far from that experimentally found for H2 C33 S. The trend exhibited by eQqzz (33 S) in OCS, H2 CS, and HBS can be tentatively rationalized by considering the different polarity of the X==S bonds (X = C, B) in these molecules. The value of eQqzz becomes more negative if n z decreases in comparison with n x + n y , while it can change sign if n z increases with respect to n x + n y . This simplified picture could account for the large negative eQqzz value of 33 S in OCS, because of the noticeable electronegativity of the OC group. In contrast, sulfur is much more electronegative than boron, and in the thioborine molecule it can withdraw electron density along the σ bond, thus producing a positive value of the quantity −(U p )z in Eq. [3]. On the other hand, Eq. [5] shows that the value of n z is very sensitive to the weight of the s-type function in the hybridized atomic orbital. An increase in the value of as2 gives to the ψ 1 orbital a more pronounced p character: the value as2 = 0.5 corresponds to consider the ψ 1 orbital as a pure pz and the value of eQqzz , calculated using Eq. [3] turns out to be −26 MHz. In contrast, a decrease in the absolute value of the quadrupole coupling constant can be obtained if one assumes the orbital which engages in the σ bond to have more s character (eQqzz vanishes if as2 = 0.25, corresponding to consider the ψ 1 orbital as a perfect sp hybrid).
233
As already pointed out before, the electronic structure of the diatomic molecule CS is more properly described by considering the sp hybridization of the valence atomic orbitals. This leads us to calculate, neglecting any ionic effect, a zero value for eQqzz (33 S), but the experimentally found value of 12.83 MHz can be exactly matched by admitting a certain degree of back-donation from the p-type electron pairs of the sulfur atom. It is very likely that the effects of both bond ionicity and orbital hybridization can contribute to some extent to the observed values of the 33 S quadrupole coupling constant in HBS. A qualitative description of the bond properties of thioborine based on the boron quadrupole coupling constant was given by Gordy and Cook (3). They considered the electronegativity difference between boron and sulfur atoms to derive reasonable assumptions regarding the bond ionicity but, in order to reproduce satisfactorily the experimental value of the 11 B quadrupole constant, a small difference in the ionic character of the σ and π B==S bonds had to be admitted. By assuming the values reported in (3) for i σ and i π ionic characters of the boron–sulfur bond, i.e., i σ = 0.2 and i π = 0.3, the 33 S quadrupole coupling constant can be exactly reproduced if as2 = 0.135, which means that the sulfur hybridized orbital involved in the σ bond should have a noticeable weight of the s-type atomic orbital. ACKNOWLEDGMENTS Thanks are due to G. Cazzoli for valuable suggestions in the course of the measurements. Financial support from MURST and from the University of Bologna (Funds for Selected Research Topics) is gratefully acknowledged.
REFERENCES 1. R. W. Kirk and P. L. Timms, J. Chem. Soc. Chem. Commun. 18–19 (1967). 2. E. F. Pearson and R. V. McCormick, J. Chem. Phys. 58, 1619–1621 (1973). 3. W. Gordy and R. L. Cook, “Microwave Molecular Spectra.” Wiley, New York, 1984. 4. E. F. Pearson, C. L. Norris, and W. H. Flygare, J. Chem. Phys. 60, 1761– 1764 (1974). 5. L. Bizzocchi and C. Degli Esposti, J. Chem. Phys. 115, 7041–7050 (2001). 6. H. M. Pickett, J. Mol. Spectrosc. 148, 371–377 (1991). 7. W. E. Lamb, Jr., Phys. Rev. A 134, 1429–1450 (1964). 8. C. C. Costain, Can. J. Phys. 47, 2431–2433 (1969). 9. G. Cazzoli and L. Dore, J. Mol. Spectrosc. 141, 49–58 (1990). 10. I. Merke and H. Dreizler, Z. Naturforsch. A 42, 1043–1044 (1987). 11. A. P. Cox, S. D. Hubbard, and H. Kato, J. Mol. Spectrosc. 93, 196–208 (1982). 12. M. Bogey, C. Demuynck, and J. L. Destombes, Chem. Phys. Lett. 81, 256– 260 (1981). 13. C. H. Townes and B. P. Dailey, J. Chem. Phys. 17, 782–796 (1949).
C 2002 Elsevier Science (USA)
Rotational Spectroscopy of HB33 S: The Quadrupole Coupling Constant of 33 S in Thioborine L. Bizzocchi, C. Degli Esposti, and L. Dore Dipartimento di Chimica “G. Ciamician,” Universit`a di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Received February 28, 2002; in revised form June 27, 2002
The unstable HBS molecule has been produced in the gas phase by a high-temperature reaction between crystalline boron and hydrogen sulfide. Ground state rotational spectra have been observed in the millimeter-wave region, from 75 to 460 GHz, for the previously unobserved H11 B33 S and H10 B33 S isotopic species. The analysis of the hyperfine structure produced by the 10/11 B and 33 S nuclear spins in the low-J rotational transitions has yielded the first evaluation of the quadrupole coupling constant of 33 S in the thioborine molecule, which was 6.361(15) MHz in H11 B33 S and 6.329(17) MHz in H10 B33 S. In addition, further measurements have been performed for the most abundant isotopomers H10/11 B32/34 S, for which improved values of rotational, C 2002 Elsevier Science (USA) centrifugal, and hyperfine structure constants have been determined. Key Words: rotational spectroscopy; thioborine; HBS; pyrolysis; quadrupole coupling constants; sulfur-33. I. INTRODUCTION
II. EXPERIMENTAL DETAILS
The sulfidoboron compounds (X–B==S) constitute a small class of moderately unstable molecules, which are typically produced in the gas phase by high-temperature reactions between crystalline boron and a suitable Sn Xm sulfur-containing compound. Thioborine (HBS) was first detected by Kirk and Timms who observed its mass spectrum in the products of the action of hydrogen sulfide on boron at high temperature (1), and its rotational spectrum was subsequently studied by Pearson and McCormick using a millimeter-wave (mm-wave) spectrometer (2). Ground-state spectra of eight isotopic species 1/2 10/11 32/34 H B S were analyzed and the complete rs structure (3) was calculated. A following work, focused on the study of the J = 1 ← 0 rotational transition for the H11 B32 S, D11 B32 S, and D10 B32 S isotopomers, yielded a determination of the 10 B and 11 B nuclear hyperfine coupling constants in thioborine (4). The present work extends the study of the rotational spectra of HBS to the scarcely abundant and so far unobserved 33 Scontaining species, having as main objective the determination of the quadrupole coupling constant of the 33 S nucleus in the thioborine molecule, from which information on the nature of the rather unusual B==S bond can be derived. The rotational spectra of H10 B33 S and H11 B33 S have been recorded in the frequency range 75–460 GHz, which includes rotational transitions from J = 2 ← 1 to J = 12 ← 11. The hyperfine structures given by both 10/11 B and 33 S nuclei have been detected and analyzed for lines up to J = 3, thus obtaining a sufficiently precise evaluation of the quadrupole coupling constant of 33 S in thioborine. The value determined has been compared with those previously obtained for related molecules containing a multiple-bonded terminal sulfur atom.
HBS has been produced in the gas phase by a pyrolysis reaction between hydrogen sulfide and crystalline boron (2). The same pyrolysis system already used to produce FBS (5) was also employed to generate HBS. Gaseous H2 S (Matheson) was flowed through a quartz tube, whose central part, 30 cm long and 1 cm in diameter, was filled with pieces of crystalline boron (Aldrich) and held in a tubular oven at a temperature of 1100◦ C. The quartz reactor was directly connected to the glass-made absorption cell of the mm-wave spectrometer (3 m long, 10 cm in diameter), through which the reaction products were continuously pumped using a diffusion pump connected to the cell with a flexible pipe 2.5 cm in diameter. The H2 S flow rate was adjusted by means of a stainless steel needle valve and the weakest HBS lines were recorded using an inlet pressure of 1 Torr (measured before the boron-filled part of the tube), corresponding to 5 mTorr of gaseous products flowing through the absorption cell. Large amounts of sulfur and a white solid were deposited just out of the heated part of the quartz tube. The rotational spectra of HBS were observed in selected frequency regions between 75 and 460 GHz using a source modulation mm-wave spectrometer which employed Gunn oscillators (Farran and Carlstrom) and klystrons (Varian) as main radiation sources to cover the fundamental frequency range 52–116 GHz. Higher frequencies were generated using two different frequency multipliers, one for the band 50–75 GHz, and a quadrupler optimized for the band 75–110 GHz (Radiometer Physics). The oscillators were phase-locked to the suitable harmonic of the fundamental frequency emitted by a cm-wave signal generator (Wavetek) which was driven by a personal computer. A Schottky barrier diode (Millitech) and a liquid-helium-cooled InSb detector (QMC) were respectively used to record the spectra below
0022-2852/02 $35.00 C 2002 Elsevier Science (USA) All rights reserved.
228
ROTATIONAL SPECTROSCOPY OF HB33 S
229
and above 200 GHz. The oscillators were frequency modulated at 16.7 kHz, and the detected signals were demodulated by a lock-in amplifier tuned at 33.3 kHz, so that the second derivative of the actual spectrum profile was displayed by the computercontrolled acquisition system. The accuracy of the frequency measurements was about 20 kHz. A 10 times smaller modulation frequency was employed to perform a few measurements with sub-Doppler resolution (see below). III. OBSERVED SPECTRA AND ANALYSIS
Ground-state rotational spectra have been recorded and analyzed for six isotopomers, H11 B32 S, H10 B32 S, H11 B34 S, H10 B34 S, H11 B33 S, and H10 B33 S, covering the J range from 1 to 11. Several transition frequencies were already known for the 32 S- and 34 S-containing species (2), while no information was available for the two 33 S isotopomers, which are respectively 125 and 500 times less abundant than the main H11 B32 S species. The lines of the 33 S isotopomers were, however, easily identified by means of accurate predictions obtained from an r0 structure (3), which was calculated by fitting the two bond lengths to the ground-state rotational constants of the four most abundant species, H10/11 B32/34 S (2). The calculation gives r0 ˚ and r0 (B–S) = 1.59984(15) A, ˚ from (H–B) = 1.17805(92) A which the very reliable values B000 0 (H11 B33 S) = 18 932.75 MHz and B000 0 (H10 B33 S) = 19 932.17 MHz were obtained. The low-J transitions (up to J = 3) of all the isotopic species investigated exhibit a hyperfine structure due to the 11 B (I = 3/2) or 10 B (I = 3) nuclei, which becomes considerably more complicated when the 33 S (I = 3/2) isotope is also present. An example is given in Fig. 1, where the recordings of the J = 2 ← 1 transitions of H11 B34 S and H11 B33 S are compared. The measured transition frequencies have been analyzed using Pickett’s SPFIT program (6) adopting the Hamiltonian H = H R + HQ (B) + HQ (S) + HSR (B) + HSR (S),
[1]
where H R is the rotational Hamiltonian for a linear molecule in a state, HQ (B) and HQ (S) describe the interaction of the 10/11 B and 33 S nuclear electric quadrupole moments with the respective electric field gradients, and HSR (B) and HSR (S) describe the weak interaction of the boron and sulfur nuclear spins with the magnetic field produced by the rotational motion. Since in HBS the quadrupole coupling constants of 10/11 B and 33 S are of comparable magnitude, the analysis of the hyperfine structure of the HB33 S species was based on the coupling scheme I = IB + IS , and F = I + J, so that each energy level was designated using the three quantum numbers J, I , and F. For two intense lines belonging to the H10 B32 S isotopomer the Lamb-dip technique (7, 8) was used to improve the resolution, making possible the measurement of hyperfine components whose separation was less than the Doppler half-width of the lines. An example is given in Fig. 2, which shows the recording of the J = 4 ← 3 transition of H10 B32 S, performed at very low
1
FIG. 1. Comparison between the J = 2 ← 1 transitions of H11 B34 S and H11 B33 S. The increased complexity of the hyperfine structure produced by the 33 S nucleus is clearly apparent. The absorption features marked by asterisk are unidentified and do not belong to the indicated transitions.
pressure and frequency modulation amplitude values. Ten dips are observable on the Doppler-broadened profile of the line. Owing to the large number of hyperfine-structure components produced by the 10/11 B and 33 S nuclei, many of the recorded lines actually envelop several unresolved transitions, and the corresponding peak frequencies were therefore assigned to the set of components blended in the observed absorption profile. In these cases, an intensity-averaged calculated frequency was compared with the experimental value in the fitting procedure. Typically, all hyperfine structure transitions whose frequencies were predicted to lie within ±100 kHz from the peak of a measured line were used to calculate the corresponding average frequency, but excluding those components whose intensity was less than 10% of that of the strongest one. No evidence of any hyperfine structure was apparent in the lines recorded above 300 GHz, and in these cases the measured peak frequencies were simply assigned to the most intense hyperfine component.
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BIZZOCCHI, DEGLI ESPOSTI, AND DORE
TABLE 2 Measured Transition Frequencies and Least-Squares Deviations (MHz) for the H10 B32 S and H10 B34 S Isotopomers H10 B32 S J F ← J F
FIG. 2. Recording of the J = 4 ← 3 transition of H10 B32 S obtained using the Lamb-dip technique. Ten dips (indicated by arrows) are visible on the Doppler-broadened profile of the line. The stick spectrum was drawn using frequencies and intensities calculated by Pickett’s SPCAT program (Ref. (6)).
The transition frequencies measured and analyzed for the six thioborine isotopomers are listed in Tables 1–4, where for simplicity the lines corresponding to blended transitions are labeled using the set of quantum numbers relative to the most intense TABLE 1 Measured Transition Frequencies and Least-Squares Deviations (MHz) for the H11 B32 S and H11 B34 S Isotopomers H11 B32 S J F ← J 1 1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 5 5 5 9 10 11 12
1.5 2.5 0.5 2.5 3.5 1.5 0.5 3.5 2.5 4.5 2.5 1.5 1.5 4.5 5.5 2.5 5.5 6.5 3.5 10.5 11.5 12.5 13.5
0 0 0 1 1 1 1 2 2 2 2 2 2 3 3 3 4 4 4 8 9 10 11
H11 B34 S
obs.−calc. Na
F
observed
1.5 1.5 1.5 2.5 2.5 1.5 1.5 3.5 1.5 3.5 2.5 1.5 2.5 4.5 4.5 2.5 5.5 5.5 3.5 9.5 10.5 11.5 12.5
38165.176b 38166.127b 38166.837b 76330.453 76331.432 76332.076 76332.992 114494.788
−0.008 0.000 −0.017 0.006c 0.003c −0.003 −0.011 −0.014
114495.748 114496.157 114496.447
0.004c −0.011 0.013
190818.237 190819.184 190820.057 343430.421 381572.727 419709.800 457841.100
0.000 0.016c 0.021 −0.008 −0.013 −0.002 0.010
observed
1 1 1 2 75164.904 2 75165.880 1 75166.523 1 75167.440 1 112746.505 112747.208 2 112747.462 1 112747.888 1 112748.144 112748.778 150326.595 150327.510 150328.337 1 4 1 1 338187.232 1 375747.460 1 413302.602 1 450852.144
obs.−calc. Na
0.005c 0.005c 0.001 −0.001 −0.011 −0.014c 0.001c 0.014 0.005 −0.011 0.006 −0.014c 0.003
2 2 1 1 1 2 2 1 1 1 1 4 1
−0.008 −0.008 −0.001 0.008
1 1 1 1
a Number of hyperfine structure components used to calculate the intensityaveraged frequency (see text). b From Ref. (4). c Observed minus average calculated frequency.
2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 8 9 10 11
3 4 3 2 5 4 3 2 5 2 3 4 4 6 2 5 3 1 2 6 3 4 5 5 7 6 1 4 2 3 11 12 13 14
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 7 8 9 10
2 4 4 2 4 3 3 3 5 1 2 3 4 5 2 4 3 2 3 6 2 3 5 4 6 5 1 4 2 3 10 11 12 13
observed 80318.670 80318.984 80319.217 80319.603 80320.385 80320.548 80320.752 80321.682 120477.666 120478.020 120478.290 120478.679 120478.926c 120478.976c 120479.031c 120479.066c 120479.218c 120479.695 120479.980 160634.650 160635.467c 160635.589c 160635.644c 160635.783c 160635.870c 160635.931c 160636.010c 160636.091c 160636.124c 160636.209c 321234.719 361374.332 401508.770 441637.448
H10 B34 S
obs.−calc. Na −0.005 −0.007 0.011 −0.007 0.006 0.004 −0.007 −0.012 −0.005 −0.015 0.007 −0.027b 0.003 0.008 0.005 0.007 0.001 0.002 0.019 0.023 0.001b −0.001 0.003b 0.003 0.003 0.007 −0.009 −0.009 −0.013 0.002 0.004 −0.008 −0.005 0.006
1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1
observed
obs.−calc. Na
79170.427 79170.746 79170.985 79171.366 79172.141 79172.314 79172.527 79173.441 118755.361 118755.707 118755.987 118756.379
−0.010 −0.008 0.016 −0.007 −0.002 0.006 0.004 −0.018 0.006 −0.012 0.020 −0.012b
1 1 1 1 1 1 1 1 1 1 1 2
118756.703
0.020b
4
118757.379 −0.001 118757.674 0.027 158338.296 0.016
1 1 1
158339.159 −0.021b
3
0.004b
2
158339.550
316643.025 −0.014 356209.098 −0.011 395770.124 −0.007 435325.561 0.016
1 1 1 1
a Number of hyperfine structure components used to calculate the intensityaveraged frequency (see text). b Observed minus average calculated frequency. c Lamb-dip measurements.
hyperfine component. The measurements previously reported by Pearson et al. in (4) for the J = 1 ← 0 transition of H11 B32 S have been also included in the data set analyzed for this isotopomer. Equal weights were given to the various measurements employed in the least-squares analyses, whose complete details are available from the authors. Table 5 contains the results obtained from the least-squares analyses of the line frequencies measured for all the six isotopomers investigated. The fitted parameters are the rotational constant B, the quartic centrifugal distortion constant D, and the quadrupole and spin–rotation coupling constants for the 10 B, 11 B, and 33 S nuclei. The reliability of the results obtained is well illustrated in Fig. 3, which shows the comparison between experimental and
C 2002 Elsevier Science (USA)
ROTATIONAL SPECTROSCOPY OF HB33 S
TABLE 4 Measured Transition Frequencies and Least-Squares Deviations (MHz) for H10 B33 S
TABLE 3 Measured Transition Frequencies and Least-Squares Deviations (MHz) for H11 B33 S J I F ← J I F 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 5 9 10 11 12
3 1 1 3 1 2 3 3 2 3 1 1 2 3 3 2 3 2 3 3 1 3 3 3 3 3 3 3
2 1 2 3 3 3 5 3 3 4 2 3 2 2 3 1 6 1 4 5 4 5 7 8 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 4 8 9 10 11
3 2 2 3 2 1 3 2 3 3 1 2 2 3 3 2 3 2 2 3 2 3 3 3 3 3 3 3
3 2 1 3 2 2 4 3 2 4 1 3 3 3 3 1 5 0 4 5 4 5 6 7 11 12 13 14
231
observed
obs.−calc.
Na
J I
75727.372 75728.453 75728.782 75729.070 75729.524 75729.738 75730.298 75731.089 75731.430 75731.702 75731.913 75732.164 75732.502 113592.376 113592.926 113593.326 113594.113 113594.961 113595.382 113595.655 113596.079 151455.477 151456.459 189316.690 340726.599 378568.750 416405.725 454237.025
0.001 −0.012 −0.011b 0.010 −0.018 0.011b 0.011b −0.024 0.009b −0.011b −0.014b 0.001b 0.001 0.003b 0.007b 0.009b −0.009b 0.000b 0.000b 0.020 0.006 0.011 0.007b 0.006b −0.017 −0.008 −0.003 0.013
1 1 5 1 1 2 9 1 2 2 6 5 1 3 11 4 14 4 3 1 1 1 17 16 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 8 9 10 11
4.5 3.5 2.5 2.5 3.5 2.5 4.5 4.5 3.5 2.5 1.5 4.5 3.5 4.5 3.5 2.5 4.5 2.5 4.5 3.5 4.5 4.5 1.5 4.5 4.5 4.5 4.5
F ← J 2.5 3.5 3.5 3.5 4.5 2.5 4.5 5.5 4.5 4.5 1.5 6.5 5.5 4.5 4.5 4.5 3.5 4.5 5.5 4.5 7.5 1.5 4.5 12.5 13.5 14.5 15.5
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 7 8 9 10
I
F
observed
obs.−calc.
Na
3.5 3.5 4.5 3.5 3.5 4.5 3.5 4.5 2.5 4.5 1.5 4.5 3.5 4.5 3.5 2.5 4.5 4.5 3.5 4.5 4.5 4.5 3.5 4.5 4.5 4.5 4.5
2.5 4.5 3.5 2.5 4.5 3.5 4.5 5.5 3.5 3.5 0.5 5.5 4.5 4.5 3.5 3.5 4.5 4.5 5.5 4.5 6.5 2.5 4.5 11.5 12.5 13.5 14.5
79724.418 79724.984 79725.224 79725.407 79725.642 79726.051 79726.512 79726.899 79727.140 79727.370 79727.601 79728.077 79728.303 79728.850 79729.088 79729.464 79730.165 79730.336 119589.287 119589.708 119590.696 119591.843 119592.459 318866.836 358710.695 398549.435 438382.496
0.000 −0.005b −0.010 0.005 −0.008 −0.016b −0.015b −0.014 0.018b 0.000b 0.001 −0.010b 0.014b −0.020 −0.010b −0.022b −0.004b −0.007 −0.003b 0.020b 0.007b 0.015b 0.003 0.025 0.017 0.001 −0.020
1 3 1 1 1 2 6 1 3 6 1 9 6 1 3 2 5 1 8 10 19 12 1 1 1 1 1
a
a
Number of hyperfine structure components used to calculate the intensityaveraged frequency (see text). b Observed minus average calculated frequency.
simulated spectrum profiles for the J = 2 ← 1 transition of H10 B33 S. The simulated spectrum was calculated assuming a frequency modulated Voigt profile (9) for each of the 113 hyperfine structure components included in the frequency interval recorded. A Doppler half-width of 74 kHz and a collisional half-width of 70 kHz have been assumed for all the components, whose peak frequencies and relative intensities were predicted using Pickett’s SPCAT program (6) and the spectroscopic parameters listed in Table 5. The second Fourier component of the simulated Voigt spectrum profile (lower trace) has been computed assuming a modulation depth of 100 kHz, i.e., the value used for the second harmonic detection of the experimental absorption profile (upper trace). The new measurements described in this work yielded an improved set of spectroscopic parameters for the thioborine molecule. In comparison with the previous experimental results (2, 4) the precision of the rotational and quartic centrifugal distortion constants B and D for the H10/11 B32/34 S isotopomers, even in the less favorable case, has been improved by a factor of 5 and 10, respectively. We have also determined for the first time precise values of the quadrupole coupling constants
Number of hyperfine structure components used to calculate the intensityaveraged frequency (see text). b Observed minus average calculated frequency.
TABLE 5 Rotational, Centrifugal Distortion, and Hyperfine-Structure Constants Determined for the Six Isotopic Species H10/11 B32/33/34 S: Standard Errors in Units of the Last Quoted Digit Are Given in Parentheses for the Fitted Parameters H11 B32 S
H11 B33 S
H11 B34 S
B D eQq (B) eQq (S) C (B) C (S) σ
(MHz) (kHz) (MHz) (MHz) (kHz) (kHz) (kHz)
19083.01082(75) 21.8722(36) −3.725(15) — −4.6(15) — 12.2
18932.74583(51) 21.5418(26) −3.715a 6.361(15) −4.6a −3.7(12) 11.8
18791.61730(59) 21.2226(28) −3.704(13) — −4.6(12) — 9.5
B D eQq (B) eQq (S) C(B) C(S) σ
(MHz) (kHz) (MHz) (MHz) (kHz) (kHz) (kHz)
H10 B32 S 20080.24457(37) 24.0333(25) −7.733(21) — −1.43(65) — 10.2
H10 B33 S 19932.20388(66) 23.6639(39) −7.738a 6.329(17) −1.43a −3.4(12) 14.1
H10 B34 S 19793.18021(65) 23.3724(38) −7.742(31) — −1.43a — 14.5
a
Fixed in the analysis.
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Intensity (arbitrary units)
BIZZOCCHI, DEGLI ESPOSTI, AND DORE
for eQq(33 S) in these two isotopomers differ by 0.032 MHz, an amount equal to the sum of the respective standard uncertainties. In order to reduce the correlation effects between the fitted parameters, the boron quadrupole constants of the H11 B33 S and H10 B33 S isotopomers have been constrained to the values calculated by linear interpolation of the results obtained for 32 S and 34 S containing species. However, only small changes in the value of the 33 S quadrupole constants (≈30 kHz) are produced if both eQq (B) and eQq (33 S) are simultaneously adjusted in the least-squares analyses.
experimental
79724
79726
79728
79730
79732
IV. CONCLUSION
Intensity (arbitrary units)
Frequency (MHz)
calculated
79724
79726
79728
79730
79732
Frequency (MHz) FIG. 3. Comparison between experimental and simulated spectrum profile for the J = 2 ← 1 transition of the H10 B33 S isotopomer. The stick spectrum was drawn using frequencies and intensities calculated by Pickett’s SPCAT program (Ref. (6)).
of the 10/11 B nuclei for the isotopomers H10 B32 S, H11 B34 S, and H10 B34 S. As expected, the quadrupole coupling constants determined for 10 B and 11 B in the 32/34 S isotopic species are coincident within the experimental uncertainties; the average value of their ratios turns out to be
eQq(10 B) eQq(11 B)
This paper presents the first identification of the rotational spectra of the 33 S-containing species of thioborine. Very accurate rotational and centrifugal distortion constants have been determined and, more importantly, a sufficiently precise estimate of the 33 S quadrupole coupling constant has been obtained. The average value determined for the two HB33 S isotopomers is compared in Table 6 with those of the related molecules OC33 S (10), H2 C33 S (11), and C33 S (12), in which a terminal sulfur atom forms an unsaturated bond, as in HBS. It is reasonable to expect that the sulfur atom has sp2 hybridization in HBS, OCS, and H2 CS (with two pairs of nonbonding electrons), while it should be better described as sp hybridized in the CS molecule. Inspection of Table 6 shows clearly that eQqzz (33 S) can assume very different values in different molecules, and this indicates a strong dependence on the polarity of the unsaturated bond and on the type of hybridization of the sulfur atom. This behaviour can be discussed qualitatively using the Townes–Dailey theory (13). If one relates the quadrupole constant of 33 S to the unbalanced p-electron density in the valence shell, then nx + n y eQqzz = −(U p )z eQq310 = − − n z eQq310 . [3] 2
By assuming a sp2 hybridization in the xz plane, the valence shell orbitals of the sulfur atom can be described by the linear
= 2.083 ± 0.015,
[2]
avg
which is well comparable with the value of 2.084(2) obtained from the ratio of the nuclear quadrupole moments of 10 B and 11 B (3). Although affected by a large uncertainty, the ratio of the boron spin–rotation constants C(10 B)/C(11 B) is consistent with the ratio of the boron nuclear g values, g I (10 B)/g I (11 B) = 0.335, as predicted by theory (4). Finally, the analysis of the so-far-unobserved rotational spectra of the 33 S-containing species allowed us to obtain the first experimental evaluation of the quadrupole coupling constants of the 33 S nucleus in H11 B33 S and H10 B33 S. The values determined
TABLE 6 Comparison between the eQqzz Values of the 33 S Nucleus Determined for HBS and the Related Molecules OCS, H2 CS, and CS
a
Ref. (10). Ref. (11). c Ref. (12). b
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Molecule
eQqzz (MHz)
O==C==Sa H2 C==Sb H–B==S C≡Sc
−29.12 −11.90 6.35 12.83
ROTATIONAL SPECTROSCOPY OF HB33 S
combinations of atomic orbitals (3s, 3 px , 3 p y , 3 pz ) 1/2 1/2 ψ1 = 1 − 2as2 ψs + 2as2 ψ pz 1/2 1 − 2as2 1/2 1 ψ2 = as ψs − ψ pz + ψ px 2 2 1/2 1 − 2as2 1/2 1 ψ3 = as ψs − ψ pz − ψ px 2 2 ψ4 = ψ p y ,
[4a] [4b] [4c] [4d]
where as2 represents the “weight” of the s-type basis function in the hybridized orbitals. The equivalent orbitals ψ2 and ψ3 contain the two unshared pairs of electrons, ψ1 forms the σ bond along the z axis, and ψ4 , perpendicular to the x z plane, engages in the π bond. Neglecting any ionic effect in the X==S bond, the electronic populations of the p orbitals are n x = 2, n y = 1, n z = 2 1 − as2 .
[5]
If one assumes perfect sp 2 hybridization in the x z plane (as2 = 0.33), then n z = 1.33, from which a value of (U p )z = 0.167 can be calculated. Taking eQq310 = 52 MHz for 33 S (3), the value eQqzz = −8.7 MHz can be obtained, which is not far from that experimentally found for H2 C33 S. The trend exhibited by eQqzz (33 S) in OCS, H2 CS, and HBS can be tentatively rationalized by considering the different polarity of the X==S bonds (X = C, B) in these molecules. The value of eQqzz becomes more negative if n z decreases in comparison with n x + n y , while it can change sign if n z increases with respect to n x + n y . This simplified picture could account for the large negative eQqzz value of 33 S in OCS, because of the noticeable electronegativity of the OC group. In contrast, sulfur is much more electronegative than boron, and in the thioborine molecule it can withdraw electron density along the σ bond, thus producing a positive value of the quantity −(U p )z in Eq. [3]. On the other hand, Eq. [5] shows that the value of n z is very sensitive to the weight of the s-type function in the hybridized atomic orbital. An increase in the value of as2 gives to the ψ 1 orbital a more pronounced p character: the value as2 = 0.5 corresponds to consider the ψ 1 orbital as a pure pz and the value of eQqzz , calculated using Eq. [3] turns out to be −26 MHz. In contrast, a decrease in the absolute value of the quadrupole coupling constant can be obtained if one assumes the orbital which engages in the σ bond to have more s character (eQqzz vanishes if as2 = 0.25, corresponding to consider the ψ 1 orbital as a perfect sp hybrid).
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As already pointed out before, the electronic structure of the diatomic molecule CS is more properly described by considering the sp hybridization of the valence atomic orbitals. This leads us to calculate, neglecting any ionic effect, a zero value for eQqzz (33 S), but the experimentally found value of 12.83 MHz can be exactly matched by admitting a certain degree of back-donation from the p-type electron pairs of the sulfur atom. It is very likely that the effects of both bond ionicity and orbital hybridization can contribute to some extent to the observed values of the 33 S quadrupole coupling constant in HBS. A qualitative description of the bond properties of thioborine based on the boron quadrupole coupling constant was given by Gordy and Cook (3). They considered the electronegativity difference between boron and sulfur atoms to derive reasonable assumptions regarding the bond ionicity but, in order to reproduce satisfactorily the experimental value of the 11 B quadrupole constant, a small difference in the ionic character of the σ and π B==S bonds had to be admitted. By assuming the values reported in (3) for i σ and i π ionic characters of the boron–sulfur bond, i.e., i σ = 0.2 and i π = 0.3, the 33 S quadrupole coupling constant can be exactly reproduced if as2 = 0.135, which means that the sulfur hybridized orbital involved in the σ bond should have a noticeable weight of the s-type atomic orbital. ACKNOWLEDGMENTS Thanks are due to G. Cazzoli for valuable suggestions in the course of the measurements. Financial support from MURST and from the University of Bologna (Funds for Selected Research Topics) is gratefully acknowledged.
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