Quantitative studies of the photoabsorption of carbonyl sulphide in the valence-shell, S 2p, 2s and C 1s inner-shell regions (4–360 eV) by dipole electron impact spectroscopies

Chemical Physics 252 Ž2000. 359–378 www.elsevier.nlrlocaterchemphys

Quantitative studies of the photoabsorption of carbonyl sulphide in the valence-shell, S 2p, 2s and C 1s inner-shell regions ž4–360 eV / by dipole electron impact spectroscopies Renfei Feng, Glyn Cooper, C.E. Brion

)

Department of Chemistry, UniÕersity of British Columbia, VancouÕer, BC, Canada V6T 1Z1 Received 2 September 1999

Abstract Electronic excitation spectra and absolute photoabsorption oscillator strengths Žcross-sections. have been measured in the UV, VUV and soft X-ray energy regions for the valence- and inner- ŽS 2p, 2s, C 1s. shell photoabsorption of carbonyl sulphide ŽOCS. from 5 to 360 eV using low-resolution Ž; 1 eV fwhm. dipole Že, e. spectroscopy. The absolute oscillator strength scale has been determined using valence-shell TRK Ži.e., SŽ0.. sum-rule normalization. The discrete structures, as well as the continuum structures, in the valence region also have been studied at high resolution Ž; 0.05 eV fwhm. from 4 to 32 eV. The presently reported high- and low-resolution absolute photoabsorption oscillator strengths are compared with previously published data Žfrom the direct photoabsorption measurements. in those limited energy regions where such data exist. Evaluation of the SŽy2. sum using the presently reported absolute differential photoabsorption oscillator strength data gives a static dipole polarizability for carbonyl sulphide in excellent agreement Žwithin 2%. with previously reported polarizability values. Other dipole sums SŽ u. Ž u s y1, y3 to y6, y8, y10. and logarithmic dipole sums LŽ u. Ž u s y1 to y6. are also determined from the presently reported absolute differential photoabsorption oscillator strength data. q 2000 Elsevier Science B.V. All rights reserved.

1. Introduction Carbonyl sulphide plays an important role in the global cycling of sulphur w1–5x and is released into the Earth’s atmosphere by both natural w6–8x and anthropogenic w9–11x emissions. To model equilibrium conditions in the stratosphere and troposphere, the electronic transition probability and cross-section Žabsolute photoabsorption oscillator strength. data )

Corresponding author. E-mail: [email protected]

for carbonyl sulphide are required w1–5x. Also, carbonyl sulphide has been observed in the deep atmosphere of Venus w12x, in Jupiter’s atmosphere following the impact of comets w13x and in dense molecular clouds w14,15x. The electronic structure and excited states of carbonyl sulphide, as well as its electronic transition probabilities and cross-sections Žabsolute photoabsorption oscillator strengths. are therefore useful to analyze observed data from planetary atmospheres and interstellar space. Thus, quantitative studies of the electronic structure of carbonyl sul-

0301-0104r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 9 . 0 0 3 6 3 - 8

360

R. Feng et al.r Chemical Physics 252 (2000) 359–378

phide and its interaction with visible, UV, VUV and soft X-ray radiation are of great interest in areas such as environmental, astronomical and fundamental science w16x. In the valence-shell region of carbonyl sulphide, the photoabsorption spectrum was first reported by Lochte-Holtgreven and Bawn w17x. It has been studied photographically by Price and Simpson w18x in ˚ Ž7.3–12.4 eV., by Tanaka the region 1000–1700 A ˚ Ž7.3–20.7 eV., et al. w19x in the region 600–1700 A ˚ Ž8.73–9.18 by Kopp w20x in the region 1350–1420 A eV. and by Rocin et al. w21x in the region 1600–1800 ˚ Ž6.89–7.75 eV. at high resolution. However, none A of these measurements w17–20x reported absolute intensities. Absolute photoabsorption oscillator strengths Žphotoabsorption coefficients or cross-sections. have been measured by Matsunaga and Watanabe w22x in ˚ Ž7.3–11.6 eV., by Cook the region 1070–1700 A ˚ Ž12.9–20.7 and Ogawa w23x in the region 600–960 A eV. and by Rabalais et al. w24x in the region 1240– ˚ Ž5.0–10.0 eV.. A higher-energy region 2500 A ˚ i.e., 16.3–70.5 eV. absolute photoabŽ175–760 A, sorption measurement has been reported by Wu and Judge w25x using synchrotron radiation. In the region ˚ Ž4.77–6.20 eV., a number of absolute 2000–2600 A photoabsorption studies w26–30x have also been reported. In addition, the temperature-dependent photoabsorption cross-sections of OCS have been measured in this region by Molina et al. w29x, Ferro and Reuben w31x, Locker et al. w32x and very recently by Wu et al. w33x. A valence-shell low-resolution Ž; 0.9 eV fwhm. absolute photoabsorption oscillator strength measurement Ž5–100 eV. has been reported earlier from our laboratory by White et al. w34x using a magic-angle dipole Že, 2e. spectrometer in the non-coincident, forward energy loss mode with an electron impact energy of 3.5 keV. However, this spectrum w34x, obtained using instrumentation and techniques predating the presently available and much more accurate high-resolution ŽHR. and low-resolution ŽLR. dipole Že, e. spectrometers and operating procedures w35–38x, is only expected to be semiquantitative. It was for these reasons that this earlier data set w34x for OCS was not included in our recent compilation w38x. Several other electron energy loss studies of OCS have been performed by Foo et al. w39x, Flicker et al. w40x and Leclerc et al. w41x. In

these experiments, in which low impact energies were used to measure electron energy loss spectra at 08 scattering angle w39x or at varying scattering angles w40,41x, absolute intensities were not obtained. In the inner-shell regions of carbonyl sulphide, some photon and electron impact studies w42–50x have been reported both in the sulphur 2p, 2s ŽL-shell. w42,43,45,46,49,50x and carbon 1s ŽK-shell. w42,44– 49x regions. The electron energy loss studies for both C K-shell and S L-shell excitations of OCS have been reported by Wight and Brion w42x. The C K-shell excitations have also been studied by Tronc et al. w44x using electron energy loss spectroscopy at high resolution and also by Harrison and King w46x with low electron impact energy. The cross-sections and angular-distribution asymmetry parameters of OCS have been measured by Truesdale et al. w45x for CŽKVV. and SŽLVV. Auger electrons, as well as C 1s and S 2p photoelectrons using synchrotron radiation. A relative near-edge ŽL 2, 3 . photoabsorption spectrum of OCS has been recorded by Krasnoperova et al. w43x using synchrotron radiation. A review of the spectral studies of core Žas well as valence. excited states has been published by Nenner et al. w47x. More recently, the carbon K near-edge X-ray absorption fine structures ŽNEXAFS. of OCS have been investigated by Sham et al. w48x. However, no absolute photoabsorption oscillator strengths of carbonyl sulphide in the inner-shell ŽS 2p, 2s and C 1s. regions have been reported, to the best of our knowledge. It is well known that the photoabsorption oscillator strength Žcross-section. distribution can be used to determine various atomic and molecular properties using dipole sum-rules w38,51–53x. Kumar and Meath w54x have constructed a dipole Žphotoabsorption. oscillator strength distribution ŽDOSD. of OCS from a consideration of published experimental data ŽRabalais et al. w24x, 4.96–9.91 eV; White et al. w34x, 6.6–100 eV; Matsunaga and Watanabe w22x, 7.71– 11.59 eV; Foo et al. w39x, 6.66–17.98 eV; Cook and Ogawa w23x, 12.91–18.96 eV; Wu and Judge w25x, 16.24–69.18 eV. and the summation of experimental andror theoretical atomic photoabsorption oscillator strengths or group oscillator strengths derived from mixture rules for photon energies above 100 eV. It should be noted that very low electron impact energy Ž60 eV. was used in the electron energy loss mea-

R. Feng et al.r Chemical Physics 252 (2000) 359–378

surements reported by Foo et al. w39x for OCS, and therefore it is not possible to convert the data to a photoabsorption oscillator strength scale. This is because the momentum transfers w39x for the energy loss region 5–18 eV were in the range 0.09–0.34 a.u. which cannot be considered to be negligible. In a recent major article w38x reviewing and assessing our absolute photoabsorption oscillator strength measurements by dipole Že, e. methods for 5 noble gas atoms and 52 small molecules, molecular and intermolecular properties were also calculated from the oscillator strength distributions using dipole sum rules. Similar results have also been very recently reported for SO 2 w55x and H 2 S w37x. These w38x and the subsequent w37,55x studies used the much improved LR dipole Že, e. w38,56x and the new HR dipole Že, e. w35,36x spectroscopies and operating procedures developed w35,36,56x for obtaining very accurate w38x absolute photoabsorption oscillator strengths. In the present work, absolute photoabsorption oscillator strengths for the valence-shell discrete and continuum excitations of carbonyl sulphide have been determined using the high-resolution Ž; 0.05 eV fwhm. dipole Že, e. method w35,36x in the energy range 4–32 eV. This method is capable of producing very accurate absolute photoabsorption oscillator strengths for discrete and continuum processes, as shown, for example, by the studies of He w35x and molecular hydrogen w57x. Also, the HR dipole Že, e. technique is not subject to ‘line-saturation’ Žbandwidthrlinewidth interaction. effects which can cause serious errors in direct Beer–Lambert law photoabsorption determinations of cross-sections for discrete excitation processes w58,59x. A discussion of the different dependencies of experimental resolution with energy in photon and electron impact experiments has been given by Brion et al. w60x. A comparison of the synchrotron radiation and dipole Že, e. photoabsorption methods has been given by Gallagher et al. w16x and by Olney et al. w38,61x. In addition to the HR dipole Že, e. spectra, new wide-range Ž5–360 eV. measurements of both the valence- and inner- ŽS 2p, 2s and C 1s. shell absolute photoabsorption oscillator strengths for carbonyl sulphide at lower resolution Ž; 1 eV fwhm. are also reported in the present work using the modified LR dipole Že, e. instrumentation with improved differen-

361

tial pumping w56x. The present results are compared with previously published data where such data are available.

2. Experimental The experimental procedures employed in the present work are similar to those used in previously reported oscillator strength measurements for the noble gases w35,36,62x and several diatomic w57, 58,63–65x and polyatomic molecules w37,38,55,56, 66–68x, therefore only a brief description will be given here. A low-resolution dipole Že, e. spectrometer w69,70x, using 8 keV electron impact energy, zerodegree mean scattering angle and a two-stage differentially pumped electron gun vacuum chamber w56x, was employed to obtain electron energy loss spectra of carbonyl sulphide in the energy ranges 5–40, 30–90, 80–170, 156–190, 180–260, 255–310, 283– 308 and 305–360 eV at intervals of 0.5, 1.0, 2.0, 0.5, 1.0, 1.0, 0.5 and 1.0 eV, respectively. These spectra were then normalized to each other in the overlapping energy regions. The resultant electron energy loss spectrum was converted to a relative photoabsorption spectrum by multiplying by the known Bethe–Born conversion factor for the spectrometer w70x. Valence-shell TRK sum rule normalization w38,71x was used to obtain absolute values of the photoabsorption oscillator strength. In order to estimate the contribution to the valence-shell oscillator strength above 160 eV, a curve of the form AEy2 q BEy3 q CEy4 Žwhere E is the photon energy, and A, B and C are best-fit parameters. was fitted to the experimental data from 70–160 eV and integrated from 160 eV to infinite energy. On this basis, the fraction of the valence-shell oscillator strength above 160 eV was found to be 8.9%. The total area under the valence-shell spectrum from 5 eV to infinity was then normalized to a value of 16.52, which includes the total number of valence electrons Ž16. plus a small estimated contribution for the Pauli-excluded transitions Žto the already occupied valence orbitals. w72–74x. A high-resolution dipole Že, e. spectrometer, using 3 keV impact energy and zero-degree mean scattering angle, was employed to obtain electron energy

R. Feng et al.r Chemical Physics 252 (2000) 359–378

362

loss spectra of carbonyl sulphide in the equivalent photon energy range 4–32 eV Žat ; 0.05 eV fwhm resolution.. Details of the construction and operation of this spectrometer can be found in Refs. w35,75x. All regions of the spectrometer, i.e. electron gun, monochromator, collision chamber and analyzer, are in separate differentially pumped vacuum chambers. The energy loss spectrum was converted to a relative photoabsorption spectrum by multiplying by the energy-dependent kinematic Bethe–Born conversion factor for the spectrometer, which was obtained as described in Refs. w35,36,56x. This relative photoabsorption spectrum was then normalized in the smooth continuum region to the presently reported low-resolution absolute oscillator strength data. Any contributions from background gases remaining at the base pressures of the spectrometers Ž; 2 = 10y7 Torr. and from non-spectral electrons were removed by subtracting the signal when the sample pressure was quartered. The energy scale of the high-resolution spectrum was calibrated in a separate experiment by admitting helium simultaneously with carbonyl sulphide and referencing to the 11 S 21 P transition of helium at 21.218 eV w76x. Using this procedure the energy scale is estimated to be accurate to better than "0.02 eV. The low-resolution spectrum was compared with the high-resolution data Žconvoluted with 1 eV fwhm Gaussian. in order to calibrate the LR energy scale. The sample of carbonyl sulphide was obtained commercially from the Matheson Gas Products and was used without further purification. The uncertainty of the absolute oscillator strength scale is estimated to be "5%.

™

3. Results and discussion 3.1. Electronic structure of carbonyl sulphide Carbonyl sulphide is a linear triatomic molecule with C`v symmetry. Its ground-state independent particle electron configuration may be written as: core: Ž 1s . 2 S 1s

Ž2 s . 2 O 1s

Ž 3s . 2 C 1s

Ž 4s . 2 S 2s

Ž 5s . 2 Ž 1p . 4 S 2p

valence shell: Ž 6s . 2

Ž 7s . 2

Ž 8s . 2

Ž 9s . 2

Ž 2 p . 4 Ž 3p . 4 :

X 1 Sq

virtual molecular orbitals ŽMOs.:

Ž4p .

0

Ž 10s .

0

Ž 11s .

0...

™™

The terms of the electronic transitions excited for the valence shell are: 3, 1 Sq, 3, 1 Sy and 3 ,1D for np 4 p; 3, 1 P for np 10s and 11s; 3, 1 Sq for 8s 10s. Only the transitions to 1 Sq and 1 P states are optically allowed for OCS w41x. The oscillator strength spectrum of OCS is conveniently discussed with reference to these ground state electron configurations. The ionization energies for the outer four orbitals of OCS are: Ž3p .y1 X 2 P 3r2, 1r2 – 11.183, 11.229 eV, Ž2 p .y1 A 2 P – 15.078 eV, Ž9s .y1 B 2 Sq – 16.042 eV, and Ž8s .y1 C 2 Sq–17.957 eV, respectively, as given by high-resolution PES measurements w77,78x. The ionization spectrum of the Ž7s .y1 and Ž6s .y1 inner-valence orbitals is split into several peaks by extensive many-body Želectron correlation. effects over the energy range 19–40 eV w79–81x. In the S 2p and 2s regions of carbonyl sulphide, the S 2p ionization energies have been reported to be 170.72 eV Ž2p 3r2 . and 171.93 eV Ž2p1r2 . w82x, respectively, by X-ray photoelectron studies, and the S 2s ionization energy to be ; 235.0 eV w83,84x. The C 1s ionization energy has been reported as ; 295.2 eV w83,84x.

™

3.2. Low-resolution absolute photoabsorption oscillator strengths in the Õalence-shell and inner-shell (S 2p, 2s and C 1s) regions (5–360 eV) Fig. 1 shows the presently determined absolute photoabsorption oscillator strengths Žcross-sections. for carbonyl sulphide in the energy range 5–360 eV obtained using the low-resolution Ž; 1 eV fwhm. dipole Že, e. spectrometer. The inset in Fig. 1 is an expanded view of the present results in the energy range 140–360 eV with the fitted curves to the valence-shell Žlong-dashed line. and S 2p, 2s innershell Žshort-dashed line. region data. Numerical values of the presently determined absolute photoabsorption oscillator strengths are given in Table 1. These data encompass both the valence shell and the inner shells ŽS 2p, 2s and C 1s..

R. Feng et al.r Chemical Physics 252 (2000) 359–378

363

Fig. 1. Absolute total photoabsorption oscillator strengths for the valence and inner ŽS 2p, 2s and C 1s. shells of carbonyl sulphide in the energy range 5–360 eV obtained at ; 1 eV fwhm resolution. The inset shows an expanded view of the inner-shell ŽS 2p, 2s and C 1s. regions in the energy range 140–360 eV. The long- and short-dashed lines represent the extrapolations of the fits to the valence-shell and S L-shell ŽS 2p, 2s q valence. oscillator strengths, respectively Žsee text for details..

Fig. 2 shows the presently determined photoabsorption differential oscillator strength spectrum for carbonyl sulphide in the energy range 5–120 eV Žvalence shell. in comparison with the previously published data reported by Wu and Judge Ž16.3–70.5 eV. w25x. Two peaks below and above the first ionization threshold ŽX 2 P ., respectively, on Fig. 2 are comprised of overlapping discrete transitions and autoionizing Rydberg series Žsee HR spectra in Figs. 4–6 below.. Above the C 2 Sq ionization threshold, the absolute photoabsorption oscillator strengths decrease monotonically with increasing photon energy. The absolute photoabsorption oscillator strengths reported by Wu and Judge w25x are in agreement Ž; 5% lower. with the presently reported data within their quoted experimental error Ž"10%. in the region ; 16–24 eV, but are lower than the present data in the ; 24–36 eV region and higher in the ; 36–70 eV region. The reason that the data of Wu and Judge w25x are lower in the ; 24–36 eV region may be due to an overestimated contribution from second-order light, since such a correction was re-

˚ . when an Al film quired in this region Ž345–520 A was used w25x. Fig. 3 shows the features observed in the presently determined oscillator strength spectrum for carbonyl sulphide in the energy region 140–360 eV, which corresponds to valence-shell, S 2p, 2s and C 1s inner-shell photoabsorption. The contribution of the valence-shell photoabsorption to the total above 150 eV, estimated from the polynomial fit, is shown in Fig. 3 as the long-dashed line. This was obtained by extrapolating the polynomial fit to the valence-shell continuum data above 160 eV Žsee Section 2 for details of the fit.. A similar extrapolation process has also been used to estimate the underlying contribution of the S 2p, 2s plus valence-shell photoabsorption to the total above 287 eV, and this is shown in Fig. 3 as the short-dashed line. In addition, considering this extrapolation, the total summed oscillator strength ŽTRK sum-rule. for the valence shell plus S 2p, 2s inner shell up to infinite energy is found to be 25.45, which is in good agreement Žwithin ; 2.5%. with the expected value of 24.84 Žestimated from the

R. Feng et al.r Chemical Physics 252 (2000) 359–378

364

Table 1 Absolute differential oscillator strengthsa for the total photoabsorption of carbonyl sulphide at low resolution Ž; 1 eV fwhm. Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0

0.00 0.00 0.72 2.16 10.24 30.83 55.41 38.26 26.09 24.66 20.21 23.04 27.20 35.99 57.88 63.14 70.97 75.43 74.47 62.55 58.77 55.18 51.50 49.10 47.56 47.15 46.99 46.79 46.08 44.10 41.84 39.73 38.52 37.11 35.50 34.03 32.61 31.09 29.34 28.97 27.95 27.17 26.37 25.43 24.49 23.55 22.86 21.83 20.91 20.40 19.46

30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 48.0 49.0 50.0 51.0 52.0 53.0 54.0 55.0 56.0 57.0 58.0 59.0 60.0 61.0 62.0 63.0 64.0 65.0 66.0 67.0 68.0 69.0 70.0 71.0

19.01 18.37 17.64 16.90 16.30 16.12 15.66 15.43 15.13 14.60 14.41 14.17 13.64 13.30 13.30 12.89 12.65 12.33 12.23 12.17 11.82 11.62 11.33 11.12 10.71 10.48 10.26 9.99 9.69 9.45 9.15 8.85 8.61 8.44 8.24 7.94 7.72 7.53 7.29 7.06 6.93 6.55 6.51 6.20 6.13 5.80 5.71 5.53 5.48 5.25 5.07

72.0 73.0 74.0 75.0 76.0 77.0 78.0 79.0 80.0 81.0 82.0 83.0 84.0 85.0 86.0 87.0 88.0 89.0 90.0 92.0 94.0 96.0 98.0 100.0 102.0 104.0 106.0 108.0 110.0 112.0 114.0 116.0 118.0 120.0 122.0 124.0 126.0 128.0 130.0 132.0 134.0 136.0 138.0 140.0 142.0 144.0 146.0 148.0 150.0 152.0 154.0

4.98 4.90 4.74 4.47 4.39 4.31 4.27 4.14 4.06 3.87 3.84 3.83 3.65 3.60 3.51 3.44 3.43 3.33 3.22 3.10 2.97 2.86 2.75 2.64 2.53 2.44 2.34 2.25 2.16 2.08 2.00 1.92 1.87 1.81 1.74 1.68 1.62 1.56 1.51 1.46 1.42 1.37 1.32 1.29 1.25 1.22 1.18 1.15 1.13 1.08 1.07

156.0 156.5 157.0 157.5 158.0 158.5 159.0 159.5 160.0 160.5 161.0 161.5 162.0 162.5 163.0 163.5 164.0 164.5 165.0 165.5 166.0 166.5 167.0 167.5 168.0 168.5 169.0 169.5 170.0 170.5 171.0 171.5 172.0 172.5 173.0 173.5 174.0 174.5 175.0 175.5 176.0 176.5 177.0 177.5 178.0 178.5 179.0 179.5 180.0 180.5 181.0

1.05 1.05 1.04 1.04 1.03 1.01 1.00 1.00 0.99 0.98 1.00 0.98 0.97 0.96 0.95 0.95 0.99 1.14 1.44 1.45 1.68 2.00 1.98 2.09 2.10 1.79 1.79 1.74 1.70 1.76 1.85 1.92 2.01 2.12 2.32 2.57 2.82 3.02 3.24 3.46 3.52 3.61 3.69 3.74 3.75 3.72 3.70 3.68 3.58 3.57 3.53

R. Feng et al.r Chemical Physics 252 (2000) 359–378

365

Table 1 Žcontinued. Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

181.5 182.0 182.5 183.0 183.5 184.0 184.5 185.0 185.5 186.0 186.5 187.0 187.5 188.0 188.5 189.0 189.5 190.0 191.0 192.0 193.0 194.0 195.0 196.0 197.0 198.0 199.0 200.0 201.0 202.0 203.0 204.0 205.0 206.0 207.0 208.0 209.0 210.0 211.0 212.0 213.0 214.0 215.0 216.0 217.0 218.0 219.0 220.0 221.0 222.0 223.0

3.54 3.51 3.45 3.44 3.41 3.43 3.36 3.31 3.35 3.27 3.27 3.26 3.20 3.22 3.23 3.23 3.19 3.24 3.24 3.24 3.29 3.36 3.46 3.49 3.50 3.53 3.54 3.55 3.55 3.48 3.51 3.46 3.42 3.40 3.40 3.36 3.27 3.28 3.25 3.21 3.18 3.14 3.12 3.17 3.13 3.12 3.05 3.10 3.07 3.04 3.02

224.0 225.0 226.0 227.0 228.0 229.0 230.0 231.0 232.0 233.0 234.0 235.0 236.0 237.0 238.0 239.0 240.0 241.0 242.0 243.0 244.0 245.0 246.0 247.0 248.0 249.0 250.0 251.0 252.0 253.0 254.0 255.0 256.0 257.0 258.0 259.0 260.0 261.0 262.0 263.0 264.0 265.0 266.0 267.0 268.0 269.0 270.0 271.0 272.0 273.0 274.0

3.01 2.97 2.97 3.02 3.13 3.25 3.29 3.16 3.01 3.01 3.00 2.96 2.96 2.94 2.97 2.86 2.93 2.92 2.86 2.86 2.88 2.87 2.85 2.85 2.76 2.80 2.77 2.77 2.73 2.79 2.74 2.68 2.70 2.63 2.65 2.64 2.61 2.63 2.60 2.56 2.53 2.55 2.50 2.53 2.50 2.47 2.42 2.41 2.40 2.40 2.39

275.0 276.0 277.0 278.0 279.0 280.0 281.0 282.0 283.0 283.5 284.0 284.5 285.0 285.5 286.0 286.5 287.0 287.5 288.0 288.5 289.0 289.5 290.0 290.5 291.0 291.5 292.0 292.5 293.0 293.5 294.0 294.5 295.0 295.5 296.0 296.5 297.0 297.5 298.0 298.5 299.0 299.5 300.0 300.5 301.0 301.5 302.0 302.5 303.0 303.5 304.0

2.40 2.37 2.31 2.34 2.33 2.26 2.34 2.33 2.30 2.28 2.23 2.26 2.23 2.27 2.30 2.23 2.20 2.33 2.51 4.82 8.71 7.62 4.94 3.57 3.02 2.98 2.88 2.83 2.51 2.45 2.44 2.63 2.94 3.06 2.89 2.71 2.80 2.80 2.80 2.92 3.11 2.93 2.99 2.80 2.83 2.85 2.90 2.91 2.90 2.90 2.88

304.5 305.0 305.5 306.0 306.5 307.0 307.5 308.0 309.0 310.0 311.0 312.0 313.0 314.0 315.0 316.0 317.0 318.0 319.0 320.0 321.0 322.0 323.0 324.0 325.0 326.0 327.0 328.0 329.0 330.0 331.0 332.0 333.0 334.0 335.0 336.0 337.0 338.0 339.0 340.0 341.0 342.0 343.0 344.0 345.0 346.0 347.0 348.0 349.0 350.0 351.0

3.01 2.93 2.91 2.98 2.89 2.96 2.93 2.89 2.92 2.93 2.81 2.86 2.74 2.73 2.77 2.80 2.75 2.68 2.71 2.65 2.59 2.58 2.53 2.60 2.42 2.42 2.52 2.36 2.34 2.36 2.33 2.24 2.36 2.24 2.28 2.30 2.21 2.30 2.16 2.09 2.15 2.17 2.11 2.14 2.19 2.14 2.01 2.02 2.06 2.24 1.99

R. Feng et al.r Chemical Physics 252 (2000) 359–378

366 Table 1 Žcontinued. Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

352.0 353.0 354.0

2.11 2.10 2.08

355.0 356.0

2.05 1.96

357.0 358.0

2.05 1.94

359.0 360.0

1.88 2.05

a

s ŽMbarn. s 1.0975 = 10 2 Žd frd E . ŽeVy1 ..

total number of electrons Ž24. in the valence shell and S 2p, 2s inner shell, plus a small estimated contribution Ž0.84. for the Pauli-excluded transitions to the already occupied valence orbitals. w72–74x. This good agreement provides strong support for the accuracy Ž"5%. of the presently determined absolute photoabsorption oscillator strength scale. A consideration of the total absolute photoabsorption oscillator strength spectrum together with these extrapolations permits the absolute partial photoabsorption oscillator strengths for the S 2p q 2s and C 1s subshells to be deduced individually, and these values are given numerically in Tables 2 and 3, respectively. One pre-edge feature is observed at ; 168 eV just below the S 2p 3r2, 1r2 ionization thresholds in

™

the low-resolution spectrum shown in Fig. 3. This can be assigned to the unresolved 2p 3r2, 1r2 4 p Ž p ) . and 10s Ž s ) . transitions to antibonding valence orbitals and to Rydberg transitions w42,43,47x. Three broad features are also observed between the S 2p 3r2, 1r2 ionization thresholds and the S 2s ionization threshold. The first two, around ; 178 and ; 200 eV, probably correspond to the 11s Ž s ) . shape resonances and shake-up processes w42,47x, respectively, and the third one just below the 2s ionization threshold Žat ; 230 eV. corresponds to the overlapping 2s 4 p Ž p ) ., 10s Ž s ) . and Rydberg transitions. Three peaks are also found around the C 1s ionization threshold. The very intense peak at ; 288 eV is from the C 1s 4 p Ž p ) . transition, which shows significant enhancement effect due to

™

™

Fig. 2. Comparison of the present low-resolution Ž; 1 eV fwhm. absolute photoabsorption oscillator strengths of carbonyl sulphide with previously published data w25x in the valence-shell region Ž5–80 eV.. The valence ionization potentials w77,78x are indicated by the vertical lines.

R. Feng et al.r Chemical Physics 252 (2000) 359–378

367

Fig. 3. Comparison of the present low-resolution Ž; 1 eV fwhm. absolute photoabsorption oscillator strengths of carbonyl sulphide with the sum of atomic data O q C q S w85–87x in the inner-shell ŽS 2p, 2s and C 1s. regions Ž150–360 eV.. The S 2p, 2s and C 1s ionization potentials w82–84x are indicated by the vertical lines. The long- and short-dashed lines represent the extrapolations of the fits to the valence-shell and S L-shell ŽS 2p, 2s q valence. oscillator strengths, respectively Žsee text for details..

the existence of an effective potential barrier in OCS w42,46x. The small shoulder on the right-hand side of this peak corresponds to the unresolved transitions of C 1s 10s Ž s ) . and Rydberg series w46,47x. Another peak below the C 1s ionization threshold Žat ; 295 eV. is formed by other overlapping Rydberg transitions. A peak above the C 1s ionization threshold Žat ; 298 eV. may correspond to the C 1s 11s Ž s ) . shape resonance. Since no previously published absolute photoabsorption oscillator strengths for carbonyl sulphide have been reported in this energy region, only estimated atomic oscillator strength data ŽO q C q S. w85–87x can be shown for comparison in Fig. 3. It is found that the estimated photoabsorption and photoionization oscillator strengths Žcross-sections. for OCS, based on the atomic data reported by Yeh and Lindau w86x using the Hartree–Fock–Slater one-electron central potential model, are significantly higher than the presently determined oscillator strengths for the S 2p and 2s subshell below the C 1s threshold. However, the presently determined photoionization oscillator strengths in the valence-shell and C 1s

™

™

subshell regions are in good agreement with the respective estimates from the atomic data. Similar results are given from another theoretical data set reported by Reilman and Manson w87x. In contrast, good agreement is found between the estimates from the experimental and theoretical atomic data reported by Henke et al. w85x and the presently determined absolute oscillator strength data, except for the S 2p near-edge region where significant near-edge molecular effects are expected to occur. Similar behaviour has also been found in our recently reported sulphur L-shell studies of SO 2 w55x and H 2 S w37x. 3.3. High-resolution absolute photoabsorption oscillator strengths in the Õalence-shell regions (4–32 eV) Fig. 4 shows the presently determined absolute photoabsorption oscillator strength spectrum for the valence shell of carbonyl sulphide in the energy range 4–32 eV obtained using high-resolution Ž; 0.05 eV fwhm. dipole Že, e. spectroscopy. The positions of the valence-shell ionization potentials w78,79x

R. Feng et al.r Chemical Physics 252 (2000) 359–378

368

Table 2 Absolute differential oscillator strengthsa for the S 2p and 2s inner-shell photoabsorptionb of carbonyl sulphide at low resolution Ž; 1 eV fwhm. Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

160.0 160.5 161.0 161.5 162.0 162.5 163.0 163.5 164.0 164.5 165.0 165.5 166.0 166.5 167.0 167.5 168.0 168.5 169.0 169.5 170.0 170.5 171.0 171.5 172.0 172.5 173.0 173.5 174.0 174.5 175.0 175.5 176.0 176.5 177.0 177.5 178.0 178.5 179.0 179.5 180.0 180.5 181.0 181.5 182.0 182.5 183.0 183.5 184.0 184.5 185.0

0.00 0.00 0.02 0.01 0.00 0.01 0.00 0.01 0.05 0.21 0.51 0.53 0.77 1.09 1.07 1.19 1.21 0.90 0.91 0.87 0.82 0.89 0.99 1.06 1.16 1.27 1.48 1.74 1.99 2.19 2.42 2.64 2.71 2.81 2.89 2.94 2.96 2.94 2.92 2.90 2.81 2.80 2.77 2.78 2.75 2.70 2.70 2.67 2.69 2.62 2.58

185.5 186.0 186.5 187.0 187.5 188.0 188.5 189.0 189.5 190.0 191.0 192.0 193.0 194.0 195.0 196.0 197.0 198.0 199.0 200.0 201.0 202.0 203.0 204.0 205.0 206.0 207.0 208.0 209.0 210.0 211.0 212.0 213.0 214.0 215.0 216.0 217.0 218.0 219.0 220.0 221.0 222.0 223.0 224.0 225.0 226.0 227.0 228.0 229.0 230.0 231.0

2.62 2.55 2.56 2.55 2.49 2.51 2.53 2.53 2.50 2.55 2.56 2.56 2.62 2.70 2.80 2.84 2.86 2.90 2.92 2.93 2.93 2.87 2.91 2.86 2.83 2.81 2.82 2.79 2.70 2.72 2.70 2.66 2.64 2.60 2.59 2.64 2.61 2.60 2.53 2.59 2.56 2.54 2.52 2.52 2.48 2.49 2.55 2.66 2.78 2.83 2.70

232.0 233.0 234.0 235.0 236.0 237.0 238.0 239.0 240.0 241.0 242.0 243.0 244.0 245.0 246.0 247.0 248.0 249.0 250.0 251.0 252.0 253.0 254.0 255.0 256.0 257.0 258.0 259.0 260.0 261.0 262.0 263.0 264.0 265.0 266.0 267.0 268.0 269.0 270.0 271.0 272.0 273.0 274.0 275.0 276.0 277.0 278.0 279.0 280.0 281.0 282.0

2.56 2.56 2.56 2.52 2.52 2.50 2.54 2.43 2.51 2.50 2.45 2.45 2.47 2.46 2.45 2.45 2.36 2.40 2.38 2.39 2.35 2.41 2.37 2.31 2.33 2.27 2.29 2.28 2.25 2.28 2.25 2.21 2.18 2.21 2.15 2.19 2.17 2.14 2.09 2.08 2.08 2.07 2.07 2.08 2.06 2.00 2.03 2.02 1.96 2.03 2.02

283.0 283.5 284.0 284.5 285.0 285.5 286.0 286.5 287.0 287.5 288.0 288.5 289.0 289.5 290.0 290.5 291.0 291.5 292.0 292.5 293.0 293.5 294.0 294.5 295.0 295.5 296.0 296.5 297.0 297.5 298.0 298.5 299.0 299.5 300.0 300.5 301.0 301.5 302.0 302.5 303.0 303.5 304.0 304.5 305.0 305.5 306.0 306.5 307.0 307.5 308.0

2.00 1.98 1.93 1.97 1.93 1.97 2.01 1.93 1.91 1.92 1.92 1.91 1.90 1.90 1.89 1.89 1.88 1.88 1.87 1.87 1.86 1.86 1.85 1.85 1.84 1.83 1.83 1.82 1.82 1.81 1.81 1.80 1.80 1.79 1.79 1.78 1.78 1.77 1.77 1.76 1.76 1.75 1.75 1.74 1.74 1.73 1.73 1.72 1.72 1.72 1.71

R. Feng et al.r Chemical Physics 252 (2000) 359–378

369

Table 2 Žcontinued. Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

309.0 310.0 311.0 312.0 313.0 314.0 315.0 316.0 317.0 318.0 319.0 320.0 321.0

1.70 1.69 1.68 1.67 1.66 1.65 1.65 1.64 1.63 1.62 1.61 1.60 1.59

322.0 323.0 324.0 325.0 326.0 327.0 328.0 329.0 330.0 331.0 332.0 333.0 334.0

1.58 1.58 1.57 1.56 1.55 1.54 1.53 1.53 1.52 1.51 1.50 1.49 1.49

335.0 336.0 337.0 338.0 339.0 340.0 341.0 342.0 343.0 344.0 345.0 346.0 347.0

1.48 1.47 1.46 1.45 1.45 1.44 1.43 1.42 1.42 1.41 1.40 1.39 1.39

348.0 349.0 350.0 351.0 352.0 353.0 354.0 355.0 356.0 357.0 358.0 359.0 360.0

1.38 1.37 1.37 1.36 1.35 1.35 1.34 1.33 1.32 1.32 1.31 1.30 1.30

a

s ŽMbarn. s 1.0975 = 10 2 ŽdfrdE. ŽeVy1 .. Note that the estimated underlying valence-shell contribution has been subtracted and the data above 287 eV have been estimated by a polynomial fitting Žsee text for details..

b

are indicated as vertical lines in the figure. In order to check the consistency of the HR and LR absolute

photoabsorption oscillator strength data sets, this HR spectrum was convoluted with a Gaussian of 1 eV

Table 3 Absolute differential oscillator strengthsa for the C 1s inner-shell photoabsorptionb of carbonyl sulphide at low resolution Ž; 1 eV fwhm. Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

Energy ŽeV.

Oscillator strength Ž10y2 eVy1 .

287.0 287.5 288.0 288.5 289.0 289.5 290.0 290.5 291.0 291.5 292.0 292.5 293.0 293.5 294.0 294.5 295.0 295.5 296.0 296.5 297.0 297.5 298.0 298.5 299.0

0.000 0.115 0.305 2.618 6.519 5.437 2.760 1.396 0.859 0.821 0.729 0.687 0.373 0.318 0.310 0.512 0.826 0.952 0.785 0.609 0.709 0.718 0.718 0.849 1.046

299.5 300.0 300.5 301.0 301.5 302.0 302.5 303.0 303.5 304.0 304.5 305.0 305.5 306.0 306.5 307.0 307.5 308.0 309.0 310.0 311.0 312.0 313.0 314.0 315.0

0.874 0.934 0.755 0.787 0.814 0.865 0.883 0.884 0.886 0.868 1.004 0.937 0.923 0.999 0.910 0.988 0.963 0.927 0.970 0.992 0.884 0.947 0.835 0.840 0.889

316.0 317.0 318.0 319.0 320.0 321.0 322.0 323.0 324.0 325.0 326.0 327.0 328.0 329.0 330.0 331.0 332.0 333.0 334.0 335.0 336.0 337.0 338.0 339.0 340.0

0.928 0.886 0.826 0.867 0.813 0.767 0.767 0.732 0.812 0.634 0.646 0.753 0.604 0.595 0.628 0.605 0.529 0.649 0.542 0.591 0.617 0.539 0.637 0.511 0.447

341.0 342.0 343.0 344.0 345.0 346.0 347.0 348.0 349.0 350.0 351.0 352.0 353.0 354.0 355.0 356.0 357.0 358.0 359.0 360.0

0.514 0.546 0.489 0.530 0.594 0.552 0.423 0.444 0.493 0.684 0.439 0.569 0.563 0.551 0.532 0.449 0.551 0.442 0.398 0.571

a

s ŽMbarn. s 1.0975 = 10 2 Žd frd E . ŽeVy1 .. Note that the estimated underlying valence-shell and S 2p, 2s inner-shell contributions have been subtracted Žsee text for details..

b

R. Feng et al.r Chemical Physics 252 (2000) 359–378

370

Fig. 4. Absolute oscillator strengths for the valence-shell photoabsorption of carbonyl sulphide in the energy range 4–32 eV at ; 0.05 eV fwhm resolution. The vertical lines indicate the positions of the valence-shell ionization potentials w77,78x.

fwhm Žto mathematically degrade its resolution to that of the LR data. and compared with the LR spectrum. The extremely good quantitative agreement found between these two data sets over the whole energy range of the high-resolution spectrum Ž4–32 eV. lends confidence to the overall accuracy of the absolute photoabsorption oscillator strengths and the energy scale determined in the present work. The presently determined HR photoabsorption oscillator strength spectrum in the region below the first ionization threshold is shown in Fig. 5, together with assignments taken from Refs. w41x and w47x. The main features of this spectrum correspond to the three excitation bands Ž3p 4 p .1D, Ž3p 1 1 q 10s . P and Ž3p 4 p . S located around the maxima at 5.54, 7.38 and 8.12 eV, respectively, as well as to a number of Rydberg series converging to X 2 P limits. The very weak photoabsorption oscillator strength spectrum for the formally dipole forbid1 q den 1D S band is also compared with the most recently reported data by Wu et al. w33x in Fig. 5. Because of the nearly structureless, Gaussian-shaped, broad continuum spectral feature of this band, the differences in experimental energy resolution of the

™

§

™

™

two measurements do not result in much difference in spectral shape or magnitude. Therefore, the presently reported data can be compared directly with the previously published experimental data in this region. Excellent agreement in both the magnitude and the spectral shape is found between the presently determined HR absolute photoabsorption oscillator strengths with the data reported by Wu et al. w33x, as well as these reported by Rabalais et al. w24x, by Breckenridge and Taube w28x, and by others w27,29,30x. In order to preserve the clarity of Fig. 5, only the most recently reported data by Wu et al. w33x are shown Žbold solid line. for comparison. The available integrated photoabsorption oscillator strengths for this band are listed in Table 4. The presently determined oscillator strength for the 1D 1 q S band is 0.00175, which is consistent with the experimental values of 0.0018 and 0.002 reported by Rabalais et al. w24x and by Breckenridge and Taube w28x, respectively. A very small peak at ; 6.25 eV observed in this spectral region is due to the 1 Sq u excitation band from a very small CS 2 impurity, and corresponds to the most intense band in the CS 2 spectrum. Using the photoabsorption spectra reported

§

R. Feng et al.r Chemical Physics 252 (2000) 359–378

371

§

Fig. 5. The presently determined HR photoabsorption oscillator strength spectrum below the first ionization threshold, together with 1 q assignments taken from Refs. w41x and w47x. The data reported by Wu et al. w33x for 1D S are shown as the bold solid line for comparison. The ionization potentials w77,78x are indicated by the vertical lines.

by Rabalais et al. w24x, the amount of impurity CS 2 in the presently used sample is estimated to be ; 0.1%. Such a low impurity level will not make any effective differences in the spectrum other than in the ; 6.0–6.5 eV region. Fig. 6 shows a comparison of the presently determined HR photoabsorption oscillator strength spectrum of OCS with two previously reported higherresolution direct photoabsorption measurement data sets w22,24x below the first ionization threshold. These two experimental photoabsorption data sets w22,24x

have each been convoluted with a Gaussian function of 0.05 eV fwhm to degrade their resolution so that they can be compared to the presently reported data in a meaningful fashion. For the 1 P transitions, all three data sets are in good agreement with each other. The integrated oscillator strength for the 1 P band determined in the present work is 0.130, which is exactly the same value as that reported by Rabalais et al. w24x Žsee Table 4.. Notwithstanding this good agreement, the spectrum reported by Rabalais et al. w24x Ždotted-line. shows ; 40% lower intensi-

Table 4 Absolute photoabsorption oscillator strengthsa for the 1D, 1 P and 1 Sq excitation bands of carbonyl sulphide State Ženergy at peak maximum.

Present work ŽHR dipole Že, e.. Rabalais et al. w24x Žphotoabsorption. Breckenridge and Taube w28x Žphotoabsorption. a

s ŽMbarn. s 1.0975 = 10 2 Žd frd E . ŽeVy1 ..

1 D Ž; 5.54 eV.

1 P Ž; 7.38 eV.

1 q S Ž; 8.12 eV.

0.00175 0.0018 0.002

0.130 0.13

0.601 0.38

372

R. Feng et al.r Chemical Physics 252 (2000) 359–378

Fig. 6. Comparison of the present high-resolution Ž; 0.05 eV fwhm. absolute photoabsorption oscillator strengths of carbonyl sulphide with previously published data w22,24x below the first ionization threshold X 2 P. These data w22,24x have each been convoluted with a Gaussian function of 0.05 eV fwhm and are shown as the dashed-line and the dotted-line, respectively. The ionization potentials w77,78x are indicated by the vertical lines.

ties than the present work for the 1 Sq band Žtheir integrated oscillator strength value for the 1 Sq band is 0.38, compared with the presently determined value of 0.601.. This difference is most probably attributable to Beer–Lambert law ‘line-saturation’ Žbandwidthrlinewidth interaction. errors w35,58x in the optical work w24x which lead to a lowering of the measured cross-section. It also seems that some background contribution exists in the higher-energy region of their spectrum w24x above ; 9 eV. As mentioned before, the HR dipole Že, e. technique is not subject to these ‘line-saturation’ Žbandwidthr linewidth interaction. effects which are well known to cause serious errors in direct Beer–Lambert law photoabsorption determinations, particularly for narrow and intense discrete absorption peaks w58–60x. Another data set reported by Matsunaga and Watanabe w22x shows oscillator strengths ; 10% higher than those in the present work for most of the discrete transitions, but in quite good agreement with the present work in the higher-energy ‘quasi-continuum’ region above ; 10 eV. It should be noted

these data were digitized from modest quality figure Žon a logarithmic scale. in the originally published spectrum w22x. Therefore, errors in the digitizing process may lead to the higher values shown in Fig. 6. The most intense photoabsorption band below the first ionization threshold is due to the 3p 4p excitations to the individual vibronic states of the 1 q S manifold Žsee Figs. 5 and 7.. In order to obtain absolute photoabsorption oscillator strengths for the individual vibronic states of 1 Sq, a single Gaussian profile for the whole broad 1 P photoabsorption band and a Lorentzian profile for each of the vibronic states of 1 Sq have been used to curve fit the present experimental data. The small shoulder around 7.84 eV is considered to be a photoabsorption peak from one of the 3p nss series Ž3p 11s . w41x. Fig. 7 shows the presently deconvoluted results Žas dashed-lines.. The detailed information from this deconvolution, i.e., the energies Žpositions. and oscillator strengths Žintensities., are listed in Table 5. The previously published energies and relative intensities

™

™

™

R. Feng et al.r Chemical Physics 252 (2000) 359–378

373

Fig. 7. The absolute photoabsorption oscillator strength spectra for production of the 1 P electronic state and the individual vibronic states of the 1 Sq state of carbonyl sulphide deconvoluted from the present high-resolution Ž; 0.05 eV fwhm. spectrum.

for the 1 Sq band from the electron impact studies by Leclerc et al. w41x and photoabsorption studies by Rabalais et al. w24x are also listed in Table 5 for comparison. Excellent agreement between these three data sets is found for the excitation energies, but not for the relative intensities.

The presently determined absolute HR photoabsorption oscillator strength spectrum of OCS between the X 2 P and C 2 Sq ionization thresholds is shown in Fig. 8, together with assignments taken from Ref. w41x. The main features of the spectrum in this region consist of the autoionizing Rydberg series

Table 5 Comparison of the excitation energies, relative intensities and absolute oscillator strengthsa for the vibronic states of the 1 Sq of carbonyl sulphide Present HR dipole Že, e.

Electron impact w41x

Photoabsorption w24x

§S

energy ŽeV.

relative intensity

oscillator strengthb

energy ŽeV.

relative intensity

energy ŽeV.

relative intensity

Ž7.842. c 7.916 8.017 8.119 8.220 8.319 8.413 8.504 8.588 8.674

Ž0.275. c 0.783 0.927 1.00 0.863 0.565 0.357 0.159 0.0586 0.0115

Ž3.305. c 9.414 11.141 12.017 10.373 6.788 4.269 1.910 0.704 0.138

7.916 8.016 8.120 8.221 8.317 8.414 8.502 8.584 8.668

0.49 0.80 1.00 0.89 0.64 0.37 0.19 0.10 0.06

7.907 8.014 8.118 8.215 8.311 8.407 8.498 8.587 8.675

0.34 0.93 1.00 0.76 0.72 0.38 0.21 0.10 0.07

a

s ŽMbarn. s 1.0975 = 10 2 Žd frd E . ŽeVy1 .. = 10y2 eVy1 . c Corresponds to one band of the 3p nss series Ž3p b

™

™ 11s . w41x.

1

q

band

374

R. Feng et al.r Chemical Physics 252 (2000) 359–378

Fig. 8. Comparison of the present high-resolution Ž; 0.05 eV fwhm. absolute photoabsorption oscillator strengths of carbonyl sulphide with previously published data w23x between the ionization thresholds X 2 P and C 2 Sq. The data from Ref. w23x have been convoluted with a Gaussian function of 0.05 eV fwhm and are shown as the dashed line. The ionization potentials w77,78x are indicated by the vertical lines.

converging towards the B 2 Sq state of OCSq. Some very small peaks superimposed on the continuum spectrum at ; 12.9 eV are due to the very strong transitions to the b 1 P u state of N2 from a very small nitrogen impurity w58x Žand possibly also some impurity CO 2 , which has strong transitions in this energy region w67x.. The amount of impurity N2 is estimated to be ; 1%, according to the absolute HR photoabsorption oscillator strength spectrum reported by Chan et al. w58x, therefore no significant N2 contributions are expected other than in the ; 12.6–13.2 eV region. The previously published absolute photoabsorption spectrum reported by Cook and Ogawa w23x, convoluted with a Gaussian function of 0.05 eV fwhm, is also shown in Fig. 8 for comparison with the present work. Generally, the results reported by Cook and Ogawa w23x are ; 10% lower than the presently determined data, except for the first peak of the RIII series at ; 13.29 eV. No previously published absolute photoabsorption data are available to compare with the present work for the first peak of the RV series at ; 12.21 eV, to the best of our knowledge.

Above the C 2 Sq ionization threshold at 17.957 eV, the presently determined absolute photoabsorption oscillator strength spectrum consists mainly of broad continuum structure which decreases monotonically with increasing photon energy. Fig. 9 shows the present HR photoabsorption oscillator strength spectrum in this region and the previously published results that are available. Since differences in experimental energy resolution do not result in appreciable differences in spectral shape or magnitude in the continuum region, the present and previously published experimental results can be compared directly with each other in this energy region. The data reported by Cook and Ogawa w23x are generally ; 10% lower than the presently reported measurements. The absolute photoabsorption oscillator strengths reported by Wu and Judge w25x are in agreement with the presently reported data within their quoted experimental error Ž"10%. in the region ; 16–23 eV Ž; 3–10% lower., but are significantly lower in the region above ; 24 eV. As mentioned above, the reason for these data w25x being lower than the presently reported values above ; 24

R. Feng et al.r Chemical Physics 252 (2000) 359–378

375

Fig. 9. Comparison of the present high-resolution Ž; 0.05 eV fwhm. absolute photoabsorption oscillator strengths of carbonyl sulphide with the previously published data w23,25x in the valence-shell continuum region.

eV may be due to an overestimation of the contribution from second-order light. A correction for second-order light was required in this region Ž345–520 ˚ . when an Al film was used w25x. A Very good quantitative agreement is found between the presently reported HR and LR absolute photoabsorption differential oscillator strength spectra up to 32 eV. This, together with the excellent agreement with other previously published experi1 q mental results down to 5 eV Ž1D S ., gives confidence in the overall accuracy of the absolute oscillator strengths determined in the present work, and therefore of the Bethe–Born factors w35,36x determined for our HR and LR spectrometers. A further stringent test of the accuracy of the absolute oscillator strength scale is to apply the SŽy2. sum rule w38x and compare the results with experimental values of the static dipole polarizability as described in the following section.

§

3.4. Sum-rule analysis and static dipole polarizability It is well known that many important properties of atoms and molecules can be obtained from dipole

sum-rules w47–52x resulting from the integration of excitation energy weighted dipole differential oscillator strength spectra over all discrete and continuum electronic states. Table 6 lists the dipole sums SŽ u. and logarithmic dipole sums LŽ u. for u F y1, obtained from the presently determined differential photoabsorption oscillator strength spectra of carbonyl sulphide Žthe HR spectrum was used from 4 to 32 eV and the LR spectrum from 32 to 360 eV.. The dipole sums, derived from semi-empirical DOSD procedures w54x and the experimental static dipole polarizability extrapolated by Alms et al. w88x from the experimental refractive index data of Huxley and Lowery w89x listed in the Landolt–Bornstein tables ¨ w90x, are also shown for comparison. Since the presently reported dipole Že, e. measurements were obtained only up to 360 eV, accurate prediction of the u G 0 sums is not possible because of the heavy weighting of the high-energy regions of the oscillator strength distribution. From Table 6, it can be seen that the dipole sums SŽ u. determined from the present dipole Že, e. work are generally smaller than those from DOSD semiempirical procedures w54x, except for the good agree-

R. Feng et al.r Chemical Physics 252 (2000) 359–378

376

Table 6 Dipole sums SŽ u. and LŽ u. obtained from the presently reported absolute differential oscillator strengths compared with dipole sums from other sources. All values a are given in atomic units Dipole sums SŽy1. SŽy2. c SŽy3. SŽy4. SŽy5. SŽy6. SŽy8. SŽy10. LŽy1. LŽy2. LŽy3. LŽy4. LŽy5. LŽy6.

From present dipole Že, e. work

From DOSD b

1.953Ž1. 3.396Ž1. 7.542Ž1. 1.937Ž2. 5.492Ž2. 1.669Ž3. 1.762Ž4. 2.087Ž5.

1.927Ž1. 3.372Ž1. 7.928Ž1. 2.169Ž2. 6.543Ž2. 2.106Ž3. 2.461Ž4. 3.166Ž5.

y6.906Ž0. y2.382Ž1. y6.639Ž1. y1.934Ž2. y5.936Ž2. y1.900Ž3.

y5.426Ž0. y2.522Ž1.

Literature value 3.435Ž1. d

a

M Ž n. represents M =10 n. From Ref. w54x. c SŽy2. gives a N , the static dipole polarizability. d Extrapolated by Alms et al. w88x from the experimental refractive index data of Huxley and Lowery w89x listed in the Landolt–Born¨ stein tables w90x. b

ment for u s y1, y2. It should be noted that because of the weighting terms E u and E u lnŽ ErEH .

in the SŽ u. and LŽ u. sums w38x, the contributions to the sums from lower-energy region data become more important as u decreases Ž u F y3.. Fig. 10 shows the Žd frd E .rE 2 spectrum obtained from the present HR Ž4–32 eV. and LR Ž16–360 eV. photoabsorption oscillator strength data. It can be clearly seen that this spectrum decreases very quickly with increasing energy and, in fact, the values above ; 32 eV contribute only ; 4.8% of the total SŽy2. sum from 4–360 eV. Therefore, the lack of experimental photoabsorption oscillator strength data above 360 eV makes no effective difference to the SŽy2. dipole sum, or to the other sums with u F y2. In fact, the static dipole polarizability Ž SŽy2.. of OCS, derived from the presently determined differential photoabsorption oscillator strength spectra, is in extremely good agreement Žwithin ; 2%. with both the experimental static dipole polarizability extrapolated by Alms et al. w88x from the experimental data of Huxley and Lowery w89x listed in the Landolt– Bornstein tables w90x, and the semi-empirical value ¨ derived from DOSD procedures w54x. These SŽy2. comparisons also support the quoted "5% accuracy of the presently reported high- and low-resolution absolute oscillator strength data and lend confidence to the accuracy of the other SŽ u. and LŽ u. sums given in Table 6.

Fig. 10. The Žd frd E .rE 2 spectrum obtained from the high-resolution Ž; 0.05 eV fwhm. Ž4–32 eV. and low-resolution Ž; 1 eV fwhm. Ž16–360 eV. photoabsorption oscillator strengths for the valence shell and inner shells ŽS 2p, 2s and C 1s. of carbonyl sulphide.

R. Feng et al.r Chemical Physics 252 (2000) 359–378

Finally, van der Waals C6 coefficients for the interaction of OCS with a wide range of other atoms and molecules can also be obtained from the absolute dipole Žphotoabsorption. oscillator strength distributions or various combinations of SŽ u. and LŽ u. values for each of the species, using the dipole sums given in a previous publication for 5 noble atoms and 52 molecules, and the appropriate equations w37,38,55x. Acknowledgements This work was supported by the Natural Sciences and Engineering Research Council ŽNSERC. of Canada. One of us ŽR.F.. gratefully acknowledges financial support from the Chinese Academy of Sciences for part of his stay at UBC. References w1x M. Pham, J.-F. Mueller, G.P. Brasseur, C. Granier, G. Megie, J. Geophys. Res., wAtmos.x 100 Ž1995. 26061. w2x E. Kjellstrom, J. Atmos. Chem. 29 Ž1998. 151. w3x M. Chin, D.D. Davis, J. Geophys. Res., wAtmos.x 100 Ž1995. 8993. w4x J.E. Johnson, T.S. Bates, J. Geophys. Res., wAtmos.x 98 Ž1993. 23443. w5x D.C. Thornton, A.R. Bandy, B.W. Blomquist, B.E. Anderson, J. Geophys. Res., wAtmos.x 101 Ž1996. 1873. w6x T.S. Bates, B.K. Lamb, A. Guenther, J. Dignon, R.E. Stoiber, J. Atmos. Chem. 14 Ž1992. 315. w7x B. Lamb, H. Westberg, G. Allwine, L. Bamesberger, A. Guenther, J. Atmos. Chem. 5 Ž1987. 469. w8x P.D. Golden, W.C. Kuster, D.L. Albritton, F.C. Fehsenfeld, J. Atmos. Chem. 5 Ž1987. 439. w9x H.G. Bingemer, S. Buergermeister, R.L. Zimmermann, H.W. Georgii, J. Geophys. Res., wAtmos.x 95 Ž1990. 20617. w10x B.C. Nguyen, N. Mihalopoulos, J.P. Putaud, B. Bonsang, J. Atmos. Chem. 22 Ž1995. 55. w11x B.C. Nguyen, N. Mihalopoulos, J.P. Putaud, J. Geophys. Res., wAtmos.x 99 Ž1994. 16435. w12x B. Bezard, C. De Bergh, D. Crisp, J.P. Maillard, Nature ŽLondon. 345 Ž1990. 508. w13x E. Lellouch, G. Paubert, R. Moreno, M. Festou, B. Bezard, D. Bockelee-Morven, P. Colom, J. Crovisier, T. Encrenac et al., Nature ŽLondon. 373 Ž1995. 592. w14x M.E. Palumbo, A.G.G.M. Tielens, A.T. Tokunaga, Astrophys. J. 449 Ž1995. 674. w15x M.E. Palumbo, T.R. Geballe, A.G.G.M. Tielens, Astrophys. J. 479 Ž1997. 839. w16x J.W. Gallagher, C.E. Brion, J.A.R. Samson, P.W. Langhoff, J. Phys. Chem. Ref. Data 17 Ž1988. 9, and references therein.

377

w17x W. Lochte-Holtgreven, C.E.H. Bawn, Trans. Faraday Soc. 28 Ž1932. 698. w18x W.C. Price, D.M. Simpson, Proc. R. Soc. London, Ser. A 169 Ž1939. 50. w19x Y. Tanaka, A.S. Jursa, F.J. LeBlanc, J. Chem. Phys. 32 Ž1960. 1205. w20x I. Kopp, Can. J. Phys. 45 Ž1967. 4011. w21x J.-Y. Rocin, N. Damany, B. Vodar, Chem. Phys. Lett. 3 Ž1969. 197. w22x F.M. Matsunaga, K. Watanabe, J. Chem. Phys. 46 Ž1967. 4457. w23x G.R. Cook, M. Ogawa, J. Chem. Phys. 51 Ž1969. 647. w24x J.W. Rabalais, J.M. McDonald, V. Scherr, S.P. McGlynn, Chem. Rev. 71 Ž1971. 73. w25x C.Y.R. Wu, D.L. Judge, J. Chem. Phys. 76 Ž1982. 2871. w26x G.S. Forbes, J.E. Cline, J. Am. Chem. Soc. 61 Ž1939. 151. w27x K.S. Sidhu, I.G. Csizmadia, O.P. Strausz, H.E. Gunning, J. Am. Chem. Soc. 88 Ž1966. 2412. w28x W.H. Breckenridge, H. Taube, J. Chem. Phys. 52 Ž1970. 1713. w29x L.T. Molina, J.J. Lamb, M.J. Molina, Geophys. Res. Lett. 8 Ž1981. 1008. w30x R.N. Rudolph, E.C.Y. Inn, J. Geophys. Res. 86 Ž1981. 9891. w31x B.M. Ferro, B.G. Reuben, Trans. Faraday Soc. 67 Ž1971. 2847. w32x J.R. Locker, J.B. Burkholder, E.J. Bair, H.A. Webster III, J. Chem. Phys. 87 Ž1983. 1864. w33x C.Y.R. Wu, F.Z. Chen, D.L. Judge, J. Quant. Spectrosc. Radiat. Transfer 61 Ž1999. 265. w34x M.G. White, K.T. Leung, C.E. Brion, J. Electron Spectrosc. Relat. Phenom. 23 Ž1981. 127. w35x W.F. Chan, G. Cooper, C.E. Brion, Phys. Rev. A 44 Ž1991. 186. w36x W.F. Chan, G. Cooper, X. Guo, C.E. Brion, Phys. Rev. A 45 Ž1992. 1420. w37x R. Feng, G. Cooper, C.E. Brion, Chem. Phys. 244 Ž1999. 127. w38x T.N. Olney, N.M. Cann, G. Cooper, C.E. Brion, Chem. Phys. 223 Ž1997. 59. w39x V.Y. Foo, C.E. Brion, J.B. Hasted, Proc. R. Soc. London, Ser. A 322 Ž1971. 535. w40x W.M. Flicker, O.A. Mosher, A. Kuppermann, J. Chem. Phys. 69 Ž1978. 3910. w41x B. Leclerc, A. Poulin, D. Roy, M.-J. Hubin-Franskin, J. Delwiche, J. Chem. Phys. 75 Ž1981. 5329. w42x G.R. Wight, C.E. Brion, J. Electron Spectrosc. Relat. Phenom. 4 Ž1974. 335. w43x A.A. Krasnoperova, E.S. Gluskin, L.N. Mazalov, J. Struct. Chem. 18 Ž1977. 206. w44x M. Tronc, G.C. King, F.H. Read, J. Phys. B 12 Ž1979. 137. w45x C.M. Truesdale, D.W. Lindle, P.H. Kobrin, U.E. Becker, H.G. Kerkhoff, P.A. Heimann, T.A. Ferrett, D.A. Shirley, J. Chem. Phys. 80 Ž1984. 2319. w46x I. Harrison, G.C. King, J. Electron. Spectrosc. Relat. Phenom. 43 Ž1987. 155. w47x I. Nenner, M.J. Hubin-Franskin, J. Delwiche, P. Morin, S. Bodeur, J. Mol. Struct. 173 Ž1988. 269.

378

R. Feng et al.r Chemical Physics 252 (2000) 359–378

w48x T.K. Sham, B.X. Yang, J. Kirz, J.S. Tse, Phys. Rev. A 40 Ž1989. 652. w49x P. Millie, A.P. Hitchcock, S. Bodeur, I. Nenner, unpublished. w50x U. Ankerhold, B. Esser, F. von Busch, Chem. Phys. 220 Ž1997. 393. w51x U. Fano, J.W. Cooper, Rev. Mod. Phys. 40 Ž1968. 441. w52x M. Inokuti, Rev. Mod. Phys. 43 Ž1971. 297. w53x J. Berkowitz, Photoabsorption, Photoionization and Photoelectron Spectroscopy, Academic Press, New York, 1979. w54x A. Kumar, W.J. Meath, Can. J. Phys. 63 Ž1985. 417. w55x R. Feng, G. Cooper, G.R. Burton, C.E. Brion, L. Avaldi, Chem. Phys. 240 Ž1999. 371. w56x X. Guo, G. Cooper, W.F. Chan, G.R. Burton, C.E. Brion, Chem. Phys. 161 Ž1992. 453. w57x W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 168 Ž1992. 375. w58x W.F. Chan, G. Cooper, R.N.S. Sodhi, C.E. Brion, Chem. Phys. 170 Ž1993. 81. w59x R.D. Hudson, Rev. Geophys. Space Phys. 6 Ž1971. 305. w60x C.E. Brion, S. Daviel, R.N.S. Sodhi, A.P. Hitchcock, in: B. Crasemann ŽEd.., AIP Conference Proceedings No. 94: X-ray and Inner Shell Physics, Am. Inst. Phys., New York, 1982, p. 429. w61x T.N. Olney, G. Cooper, W.F. Chan, G.R. Burton, C.E. Brion, Chem. Phys. 189 Ž1994. 733. w62x W.F. Chan, G. Cooper, X. Guo, G.R. Burton, C.E. Brion, Phys. Rev. A 46 Ž1992. 149. w63x W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 170 Ž1993. 99. w64x W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 170 Ž1993. 111. w65x W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 170 Ž1993. 123. w66x W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 178 Ž1993. 387. w67x W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 178 Ž1993. 401. w68x W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 180 Ž1994. 77. w69x C. Backx, P.R. Tol, G.R. Wight, M.J. van der Wiel, J. Phys. B 8 Ž1975. 2050.

w70x F. Carnovale, C.E. Brion, Chem. Phys. 74 Ž1983. 253. w71x G.R. Burton, W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 177 Ž1993. 217. w72x J.A. Wheeler, J. Bearden, Phys. Rev. 46 Ž1934. 755. w73x J.L. Dehmer, M. Inokuti, R.P. Saxon, Phys. Rev. A. 12 Ž1975. 102. w74x M. Inokuti, private communication. w75x S. Daviel, C.E. Brion, A.P. Hitchcock, Rev. Sci. Instrum. 55 Ž1984. 182. w76x W.L. Wiese, M.W. Smith, B.M. Glenon, Atomic Transition Probabilities, Vol. 1, Hydrogen through Neon, NSRDS-NBS Circ. No. 4, US Gov. Print. Off., Washington, DC, 1966. w77x L.S. Wang, J.E. Reutt, Y.T. Lee, D.A. Shirley, J. Electron Spectrosc. Relat. Phenom. 47 Ž1988. 167. w78x S. Stimson, M. Evans, C.Y. Ng, C.-W. Hsu, P. Heimann, C. Destandau, G. Chambaud, P. Rosmus, J. Chem. Phys. 108 Ž1998. 6205. w79x M.G. White, K.T. Leung, C.E. Brion, J. Electron Spectrosc. Relat. Phenom. 23 Ž1981. 127. w80x K.T. Leung, C.E. Brion, Chem. Phys. 1996 Ž1985. 241. w81x D.M.P. Holland, M.A. MacDonald, Chem. Phys. 144 Ž1990. 279. w82x M. Coville, T.D. Thomas, J. Electron Spectrosc. Relat. Phenom. 71 Ž1995. 21. w83x C.J. Allan, U. Gelius, D.A. Allison, G. Johansson, H. Siegbahn, K. Siegbahn, J. Electron Spectrosc. Relat. Phenom. 1 Ž1972. 131. w84x W.L. Jolly, K.D. Bomben, C.J. Eyermann, At. Data Nucl. Data Tables 31 Ž1984. 433. w85x B.L. Henke, P. Lee, T.J. Tanaka, R.L. Shimabukuro, B.K. Fujikawa, At. Data Nucl. Data Tables 27 Ž1982. 1. w86x J.J. Yeh, I. Lindau, At. Data Nucl. Data Tables 32 Ž1985. 1. w87x R.F. Reilman, S.T. Manson, Astrophys. J. Suppl. Ser. 40 Ž1979. 815. w88x G.R. Alms, A.K. Burnham, W.H. Flygare, J. Chem. Phys. 63 Ž1975. 3321. w89x H. Huxley, H. Lowery, Proc. R. Soc. London, Ser. A 182 Ž1944. 207. w90x Landolt–Bornstein, Zahlenwerte und Funktionen, vol. 2, part ¨ 6, Springer, Berlin, 1962, p. 871.