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Quantitative photoabsorption of diethyl ether in the valence and carbon 1s inner shell regions (5–360 eV)
Chemical Physics 284 (2002) 615–623 www.elsevier.com/locate/chemphys
Quantitative photoabsorption of diethyl ether in the valence and carbon 1s inner shell regions (5–360 eV) Renfei Feng, C.E. Brion * Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1 Received 4 June 2002
Abstract Absolute photoabsorption oscillator strengths (cross-sections) in the valence-shell discrete and continuum regions of diethyl ether C2 H5 OC2 H5 have been measured from 5 to 32 eV using high-resolution (HR) (0.05 eV fwhm) dipole ðe; eÞ spectroscopy. Wide-range spectra, spanning the UV, VUV and soft X-ray regions, have also been obtained at lowresolution (LR) (1 eV fwhm) from 5 to 360 eV which covers the valence-shell and C 1s inner-shell regions. The LR spectrum has been used to determine the absolute oscillator strength scale by employing valence-shell TRK (i.e., Sð0Þ) sum-rule normalization. Evaluation of the Sð2Þ sum using the presently reported absolute differential photoabsorption oscillator strength data gives a static dipole polarizability for diethyl ether in good agreement with previously reported polarizability values obtained by other methods. Other dipole sums SðuÞ, ðu ¼ 1; 3; 4; 5; 6; 8; 10Þ, and logarithmic dipole sums LðuÞ, (u ¼ 1 to 6), are also determined from the presently reported absolute differential photoabsorption oscillator strength data using dipole sum-rules. The presently reported absolute photoabsorption oscillator strength data are web-accessible at ftp.chem.ubc.ca/pub/cooper. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Quantitative studies of photoabsorption processes are of fundamental importance in understanding the interaction between photons and molecules and the action of ionizing radiation on matter [1]. They also provide useful information in a large number of scientific contexts, including studies in aeronomy, astrophysics, planetary science, fusion, and radiation chemistry, physics and biology [1]. Accurate photoabsorption absolute *
Corresponding author. Tel.: +1-604-822-3266; fax: +1-604822-2847. E-mail address: [email protected] (C.E. Brion).
oscillator strengths (cross-sections) are also required over wide spectral regions for use in modeling studies, while the experimental oscillator strength data can be used to evaluate theoretical concepts and computational approximations used in modeling molecular photoabsorption processes [1]. In a previous publication [2], we have reported absolute photoabsorption oscillator strengths (cross-sections) for one of the ethers, dimethyl ether CH3 OCH3 [2], using both high- and lowresolution (HR and LR) dipole ðe; eÞ spectroscopies from 5 to 32 eV and 5 to 200 eV, respectively. In the present work, we report absolute photoabsorption oscillator strengths for diethyl ether
0301-0104/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 2 ) 0 0 7 8 8 - 7
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C2 H5 OC2 H5 , in the valence-shell and inner-shell regions, determined using the same methods [3–5]. HR (0.05 eV fwhm) dipole ðe; eÞ [3,4] measurements were carried out in the energy range 5–32 eV. Much wider range (up to 360 eV) measurements, which cover both the valence-shell and C 1s innershell regions, were carried out at LR (1 eV fwhm) using the modified LR dipole ðe; eÞ instrumentation with improved differential pumping [5,6]. To the best of our knowledge, no photoabsorption oscillator strength data have previously been published for diethyl ether. It is well known now that dipole ðe; eÞ spectroscopy has been demonstrated [3–5] to provide a very accurate method of determining absolute optical oscillator strengths (cross-sections) for photoabsorption. The dipole ðe; eÞ method provides an entirely independent method to the use of direct photoabsorption [1,3,5], and furthermore it avoids the major sources of error (line saturation and the presence of higher order radiation) which can occur when photon techniques are employed. In addition, the wide-range photoabsorption oscillator strength (cross-section) distribution can be used to determine a range of atomic and molecular properties using dipole sum-rules [5,7–9]. Such procedures also provide an independent evaluation of the accuracy of the experimentally determined photoabsorption oscillator strength (cross-section) scale by comparing the dipole polarizability derived from the Sð2Þ sum-rule to directly determined experimental values obtained by other techniques. In a recent paper [5] reviewing and assessing our absolute photoabsorption oscillator strength measurements by dipole ðe; eÞ methods for five noble gas atoms and 52 small molecules, molecular and inter-molecular properties were calculated from the wide-range oscillator strength distributions using dipole sum-rules. Similar results have also very recently been reported for SO2 [10], H2 S [11], OCS [12], CH3 OCH3 [2], C6 H6 [13] and C2 H5 OH [14].
2. Experimental The instrumentation and experimental procedures employed in the present work are similar to
those used in our earlier reported photoabsorption oscillator strength measurements for a wide selection of atoms and molecules [2–6,10–14], and therefore only a brief description will be given below. A LR dipole ðe; eÞ spectrometer [15,16], using 8 keV electron impact energy, zero degree mean scattering angle and a two stage differentially pumped electron gun vacuum chamber [6], was employed to obtain electron energy loss spectra of diethyl ether in the energy ranges 5–40, 35–90, 80– 200, 190–290, 280–310 and 300–360 eV at intervals of 0.5, 1.0, 2.0, 2.0, 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. Valence shell TRK sum-rule normalization [5,17] was used to obtain absolute values of the photoabsorption oscillator strength. In order to estimate the contribution to the valence shell oscillator strength above 200 eV, a curve of the form AE2 þ BE3 þ CE4 (where E is the photon energy, and A, B and C are best fit parameters) was fitted to the experimental data from 120 to 280 eV and integrated from 280 eV to infinite energy. On this basis, the fraction of the valence shell oscillator strength above the limit of measurements at 280 eV was found to be 5.4%. The total area under the valence shell spectrum from 5 eV to infinity was then normalized to a value of 32.57, which includes the total number of valence electrons (32) of diethyl ether plus a small estimated contribution for the Pauli-excluded transitions (to the already occupied valence orbitals) [18–20]. A HR dipole ðe; eÞ spectrometer, using 3 keV impact energy and zero degree mean scattering angle, was employed to obtain electron energy loss spectra of diethyl ether in the equivalent photon energy range 5–32 eV at 0.05 eV fwhm resolution. Details of the construction and operation of this spectrometer can be found in [3,21]. 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
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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 [3–6]. This relative HR photoabsorption spectrum was then normalized in the smooth continuum region (at 18.0 eV) to the presently reported LR absolute oscillator strength data obtained as described above. Any contributions from background gases remaining at the base pressures of the spectrometers (2 107 Torr) and from non-spectral electrons were removed by subtracting the signal when the sample pressure was quartered [3,4]. The energy scale of the HR energy loss spectrum was calibrated in a separate experiment by admitting helium simultaneously with diethyl ether and referencing to the 11 S ! 21 P transition of helium at 21.218 eV [22]. Using this procedure the energy scale is estimated to be accurate to better than 0.02 eV. The LR spectrum was compared with the HR data (convoluted with 1 eV fwhm G) in order to calibrate the LR energy scale. The sample of diethyl ether was obtained commercially and degassed thoroughly by freeze– pump–thaw cycles. No impurity peaks were observed in the electron energy loss spectra after this purification. The uncertainty of the absolute oscillator strength scale is estimated to be at most 5%.
3. Results and discussion 3.1. Low-resolution absolute photoabsorption oscillator strengths in the valence-shell and C 1s innershell regions (5–360 eV) Fig. 1 shows the presently determined absolute photoabsorption oscillator strengths (cross-sections) for diethyl ether in the energy range 5–360 eV obtained using the LR (1 eV fwhm) dipole ðe; eÞ spectrometer. The inset on Fig. 1 is an expanded view of the present results in the energy range above 240 eV (valence continuum and C 1s inner-shell regions). The dashed line in the figure represents the fitted polynomial curve to the valence shell continuum region. Numerical values of
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Fig. 1. Absolute photoabsorption oscillator strengths (crosssections) for diethyl ether in the energy range 5–360 eV obtained at 1 eV fwhm resolution. The inset shows an expanded view in the energy range above 240 eV. The dashed line represents the extrapolation of the fit to the valence shell continuum oscillator strengths (see text for details).
the presently determined absolute photoabsorption oscillator strengths are given in Table 1. These data encompass both the valence shell and C 1s inner shells. Fig. 2 shows the presently determined LR (1 eV fwhm) photoabsorption differential oscillator strength spectrum for diethyl ether in three energy regions of (a) 5–32, (b) 32–270 and (c) 270–360 eV. In Fig. 2(a), the presently determined HR photoabsorption oscillator strength spectrum has also been shown for comparison. It is clear that the presently determined HR and LR data sets are in excellent agreement. Figs. 2(b) and (c) show the presently determined LR absolute photoabsorption oscillator strengths in valence continuum region and the C 1s inner-shell region, respectively. Since no previously published absolute photoabsorption oscillator strengths for diethyl ether have been reported in this energy region only estimated oscillator strengths, obtained from atomic data (4C+ 10H+O) [23–25], can be shown for comparison. Absolute oscillator strength values for the hydrogen atom, derived from the exact formula for the oscillator strength distribution for transitions from the ground electronic state to the continuum as given by Inokuti [8], were used to supplement the calculated data for the carbon and oxygen atoms
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Table 1 Absolute differential total photoabsorption oscillator strengthsa for diethyl ether at low resolution (1 eV fwhm) Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
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 30.5
0.86 0.35 0.06 1.14 3.93 5.69 7.32 16.37 28.96 35.93 42.96 49.42 56.20 68.23 83.91 98.2413 107.8 114.6 121.9 126.2 128.4 129.9 131.1 130.6 128.7 127.7 125.6 122.9 119.4 116.4 112.6 107.3 103.7 99.85 96.03 91.86 89.07 85.26 82.38 79.43 76.25 72.81 69.70 67.10 64.62 62.39 60.12 58.34 55.50 54.37 51.85 49.49
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 72.0 73.0
48.48 46.69 45.08 43.35 42.00 40.13 39.45 37.80 37.46 35.73 34.43 33.64 32.26 31.28 30.28 29.66 28.64 27.45 26.68 25.47 24.12 22.77 21.58 20.37 19.28 18.50 17.57 16.80 15.94 15.36 14.72 14.05 13.51 12.89 12.33 11.82 11.44 11.03 10.56 10.21 9.87 9.51 9.19 8.98 8.48 8.28 7.93 7.62 7.38 7.26 7.04 6.69
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 98.0 100.0 102.0 104.0 106.0 108.0 110.0 112.0 114.0 116.0 118.0 120.0 122.0 124.0 126.0 128.0 130.0 132.0 134.0 136.0 138.0 140.0 142.0 144.0 146.0 148.0 150.0 152.0 154.0 156.0 158.0 160.0
6.37 6.35 6.11 5.94 5.90 5.59 5.44 5.27 5.12 5.03 4.79 4.77 4.48 4.47 4.26 4.28 4.11 3.89 3.72 3.54 3.38 3.22 3.10 2.99 2.87 2.74 2.63 2.53 2.45 2.34 2.29 2.19 2.15 2.07 1.97 1.93 1.86 1.81 1.73 1.69 1.63 1.61 1.54 1.51 1.47 1.41 1.36 1.33 1.31 1.28 1.25 1.20
162.0 164.0 166.0 168.0 170.0 172.0 174.0 176.0 178.0 180.0 182.0 184.0 186.0 188.0 190.0 192.0 194.0 196.0 198.0 200.0 202.0 204.0 206.0 208.0 210.0 212.0 214.0 216.0 218.0 220.0 222.0 224.0 226.0 228.0 230.0 232.0 234.0 236.0 238.0 240.0 242.0 244.0 246.0 248.0 250.0 252.0 254.0 256.0 258.0 260.0 262.0 264.0
1.19 1.19 1.13 1.10 1.10 1.06 1.05 1.02 1.02 0.98 0.96 0.96 0.94 0.93 0.89 0.88 0.87 0.85 0.84 0.82 0.81 0.79 0.78 0.76 0.74 0.75 0.72 0.70 0.71 0.71 0.70 0.67 0.66 0.66 0.65 0.65 0.65 0.63 0.64 0.62 0.62 0.59 0.60 0.57 0.61 0.59 0.57 0.60 0.56 0.57 0.57 0.55
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Table 1 (continued) Photon energy (eV) 266.0 268.0 270.0 272.0 274.0 276.0 278.0 280.0 280.5 281.0 281.5 282.0 282.5 283.0 283.5 284.0 284.5 285.0 285.5 286.0 286.5 287.0 287.5 288.0 288.5 289.0 289.5 290.0 290.5 291.0 a
Oscillator strength ð102 eV1 Þ 0.54 0.54 0.55 0.50 0.52 0.52 0.52 0.52 0.52 0.53 0.51 0.52 0.52 0.50 0.52 0.51 0.51 0.50 0.50 0.54 0.55 0.58 0.70 1.24 2.01 3.32 4.55 5.48 6.06 6.09
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
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
6.26 6.42 6.44 6.59 6.81 6.86 6.80 6.72 6.55 6.44 6.21 6.00 5.79 5.63 5.49 5.27 5.11 4.99 4.93 4.75 4.63 4.64 4.55 4.46 4.36 4.32 4.26 4.21 4.12 4.14
306.5 307.0 307.5 308.0 308.5 309.0 309.5 310.0 311.0 312.0 313.0 314.0 315.0 316.0 317.0 318.0 319.0 320.0 321.0 322.0 323.0 324.0 325.0 326.0 327.0 328.0 329.0 330.0 331.0 332.0
4.06 3.99 3.94 3.91 3.88 3.83 3.78 3.74 3.68 3.61 3.52 3.47 3.45 3.36 3.33 3.35 3.28 3.22 3.22 3.10 3.11 3.10 3.04 2.99 3.04 2.92 2.89 2.89 2.82 2.82
333.0 334.0 335.0 336.0 337.0 338.0 339.0 340.0 341.0 342.0 343.0 344.0 345.0 346.0 347.0 348.0 349.0 350.0 351.0 352.0 353.0 354.0 355.0 356.0 357.0 358.0 359.0 360.0
2.77 2.79 2.79 2.79 2.78 2.71 2.70 2.70 2.66 2.64 2.60 2.60 2.60 2.64 2.56 2.63 2.56 2.60 2.57 2.57 2.46 2.55 2.51 2.41 2.60 2.51 2.52 2.47
rðMbÞ ¼ 1:0975 102 ðdf =dEÞ ðeV1 Þ.
from [25]. From Fig. 2(b), it is found that the photoabsorption oscillator strengths for diethyl ether estimated from the atomic sums are generally lower than the presently determined photoabsorption oscillator strengths below 50 eV, then a little higher below 180 eV and lower again above 180 eV, respectively. Comparing with the results estimated from the two theoretical data sets [24,25], the atomic estimates resulting from the experimental data of Henke et al. [23] show closer agreement with the present data. Fig. 2(c) gives an expanded view in the C 1s inner-shell region (270– 360 eV). The oscillator strengths from the atomic data give reasonable estimates only at the region far above the C 1s edge (J310 eV). At the near-
edge region, where significant near-edge molecular effects are expected to occur, the atomic estimates are significantly lower than the presently determined experimental data. In addition, the atomic estimates also underestimate the valence contributions for diethyl ether in the C 1s inner-shell region (see up-triangles and dashed line in Fig. 2(c)). By subtracting the underlying valence distributions (estimated from the polynomial curve fit and shown as the dashed line in Fig. 2(c)) from the total absolute photoabsorption oscillator strengths, the absolute partial photoabsorption oscillator strengths for the C 1s inner shell have been deduced, and these values are given numerically in Table 2.
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oscillator strength spectrum shows four main discrete band features at 6.57, 7.23, 8.13 and 9.02 eV, respectively. Above the first ionization threshold, a very broad continuum distribution occurs with a maximum at 16.5 eV and two superimposed structures at 10.2 and 13 eV, respectively. In order to carefully 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 fwhm (to mathematically degrade its resolution to that of the LR data) and compared with the LR spectrum. Extremely good quantitative agreement is found between these two data sets over the entire energy range of the HR spectrum (5–32 eV). This very good quantitative agreement gives confidence in the overall accuracy of the absolute oscillator strengths determined in the present work, and therefore of the Bethe–Born factors previously determined [3,16] for our HR and LR dipole ðe; eÞ spectrometers. A further and more stringent test of the accuracy of the absolute oscillator strength scale is to apply the Sð2Þ sum rule [5] and to compare the results with published experimental values of the static dipole polarizability as described in the following section. Fig. 2. Low-resolution (1 eV fwhm) absolute photoabsorption oscillator strengths for diethyl ether in the energy regions: (a) 5–32, (b) 32–270 and (c) 270–360 eV. The presently determined high-resolution absolute photoabsorption oscillator strengths for diethyl ether are shown as a solid line in panel (a). For the higher energy regions (b) and (c), the sum of atomic data 4C+10H+O [23–25] are shown for comparison. See text for details.
3.2. High-resolution absolute photoabsorption oscillator strengths (5–32 eV) Fig. 3 shows the presently determined absolute photoabsorption oscillator strength spectrum for diethyl ether in the energy range 5–32 eV, obtained using HR (0.05 eV fwhm) dipole ðe; eÞ spectroscopy. The positions of the valence shell (vertical) ionization potentials [26] are indicated as vertical lines in Fig. 3. Below the first ionization threshold, the presently determined HR photoabsorption
3.3. 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 [5,7–9] resulting from the integration of excitation energy weighted dipole differential oscillator strength spectra over all discrete and continuum electronic states. Table 3 lists the dipole sums S(u) and logarithmic dipole sums L(u) for u 6 1, obtained from the presently determined differential photoabsorption oscillator strength spectra of diethyl ether (the HR spectrum was used from 5–32 eV and the LR spectrum from 32–360 eV). The static dipole polarizabilities, i.e., Sð2Þ, previously determined from refractive index measurements [27] and by the empirical additivity methods of ahc (atomic hybrid component) and ahp (atomic hybrid polarizability), which are reported in recently published studies [28], are also
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Table 2 Absolute differential photoabsorption oscillator strengthsa for C 1s inner-shell regionb of diethyl ether at low resolution (1 eV fwhm) Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
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
0.03 0.03 0.07 0.08 0.11 0.23 0.78 1.55 2.85 4.09 5.02 5.60 5.63 5.80 5.96 5.98 6.13 6.35 6.41 6.35 6.27 6.10 6.00 5.77 5.56 5.35
298.0 298.5 299.0 299.5 300.0 300.5 301.0 301.5 302.0 302.5 303.0 303.5 304.0 304.5 305.0 305.5 306.0 306.5 307.0 307.5 308.0 308.5 309.0 309.5 310.0 311.0
5.19 5.05 4.84 4.67 4.56 4.50 4.32 4.20 4.21 4.12 4.03 3.94 3.90 3.83 3.79 3.70 3.72 3.64 3.57 3.52 3.49 3.47 3.41 3.37 3.32 3.27
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
3.20 3.11 3.06 3.05 2.96 2.93 2.95 2.89 2.83 2.83 2.71 2.72 2.72 2.65 2.61 2.66 2.54 2.51 2.51 2.45 2.45 2.40 2.42 2.43 2.43 2.42
338.0 339.0 340.0 341.0 342.0 343.0 344.0 345.0 346.0 347.0 348.0 349.0 350.0 351.0 352.0 353.0 354.0 355.0 356.0 357.0 358.0 359.0 360.0
2.35 2.34 2.34 2.31 2.29 2.24 2.25 2.25 2.29 2.22 2.29 2.22 2.26 2.23 2.23 2.12 2.22 2.18 2.08 2.27 2.18 2.19 2.14
a b
rðMbÞ ¼ 1:0975 102 ðdf =dEÞ ðeV1 Þ. Note that the estimated underlying valence shell contribution has been subtracted.
Fig. 3. Absolute oscillator strengths (present work) for the valence shell photoabsorption of diethyl ether in the energy range 5–32 eV at 0.05 eV fwhm resolution. The vertical lines indicate the positions of the valence shell ionization potentials [26].
listed for comparison. Since the presently reported dipole ðe; eÞ measurements were obtained only up to 360 eV, accurate calculation of the u P 0 sums is not possible because of the heavy weighting of the high-energy regions of the oscillator strength distribution in them. To our knowledge, no such dipole sum data set for diethyl ether has been published previously. It should be noted that because of the weighting terms Eu and Eu lnðE=EH Þ in the SðuÞ and LðuÞ sums [5], the contributions to the sums from lower energy region data become more important as u decreases (e.g., u 6 3). Fig. 4 shows the ðdf = dEÞ/E2 spectrum (i.e., the Sð2Þ spectrum) obtained from the presently determined HR (5–32 eV) and LR (5–360 eV) photoabsorption oscillator strength data for diethyl ether. It can be seen that this spectrum decreases very rapidly with increasing
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Table 3 Dipole sums SðuÞ and LðuÞ of diethyl ether, obtained from the presently reported absolute differential oscillator strengths, compared with dipole sums from other sources. (All valuesa are given in a.u.) Dipole sums
From present dipole ðe; eÞ work
Sð1Þ Sð2Þc
3.646(1) 5.577(1)
Sð3Þ Sð4Þ Sð5Þ Sð6Þ Sð8Þ Sð10Þ Lð1Þ Lð2Þ Lð3Þ Lð4Þ Lð5Þ Lð6Þ
1.016(2) 2.103(2) 4.845(2) 1.224(3) 9.828(3) 9.975(4) )1.110(1) )2.922(1) )6.788(1) )1.649(2) )4.277(2) )1.186(3)
From refraction [27]
Additivity [28]b
5.891(1)
5.870(1) 5.904(1)
a
MðnÞ represents M 10n . The first entry is obtained using the ahc (atomic hybrid component) method and the second entry is from the ahp (atomic hybrid polarizability) method [28]. c Sð2Þ gives aN , the static dipole polarizability. b
perimental photoabsorption oscillator strength data above 360 eV will have negligible effect on the Sð2Þ dipole sum, or on the other sums with u 6 2. In fact, the static dipole polarizability ðSð2ÞÞ of diethyl ether, 55.77 a.u., derived from the presently determined differential photoabsorption oscillator strength spectra, is in good agreement (within <6%) with the previously reported experimental static dipole polarizability (58.91 a.u.) [27], and also with the empirical ahc and ahp values [28]. These Sð2Þ comparisons also strongly support the quoted 5% accuracy of the presently reported HR and LR absolute oscillator strength data and lend confidence to the accuracy of the other SðuÞ and LðuÞ sums given in Table 3. In addition to the dipole polarizability, the normal Verdet constant, which is involved in the Faraday effect [29,30], could also be calculated from the presently determined differential oscillator strengths or dipole sums [5]. Finally, the rotationally averaged van der Waals C6 coefficients (dipole–dipole dispersion energy coefficients) [5,31] for the long-range interaction of diethyl ether with a wide range of other atoms and molecules can be obtained from the absolute dipole (photoabsorption) oscillator strength distribution or various combinations of SðuÞ and LðuÞ values for each of the species involved, using the dipole sums given in the previous publications for five noble atoms and 57 molecules, and the appropriate equations [2,5,10–14].
Acknowledgements This work was financially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. Fig. 4. The ðdf =dEÞ/E2 spectrum (i.e., Sð2Þ) obtained from the presently determined high-resolution (0.05 eV fwhm) (5– 32 eV) and low-resolution (1 eV fwhm) (32–360 eV) absolute photoabsorption oscillator strengths for diethyl ether. The published value ðaPub Þ of the static dipole polarizability is taken from [27].
energy, and in fact the values above 32 eV (32– 360 eV) contribute only 5.7 of the total Sð2Þ sum from 5 to 360 eV. Therefore, the lack of ex-
References [1] J.W. Gallagher, C.E. Brion, J.A.R. Samson, P.W. Langhoff, J. Phys. Chem. Ref. Data 17 (1988) 9, and references therein. [2] R. Feng, G. Cooper, C.E. Brion, Chem. Phys. 260 (2000) 391. [3] W.F. Chan, G. Cooper, C.E. Brion, Phys. Rev. A 44 (1991) 186.
R. Feng, C.E. Brion / Chemical Physics 284 (2002) 615–623 [4] W.F. Chan, G. Cooper, X. Guo, C.E. Brion, Phys. Rev. A 45 (1992) 1420. [5] T.N. Olney, N.M. Cann, G. Cooper, C.E. Brion, Chem. Phys. 223 (1997) 59. [6] X. Guo, G. Cooper, W.F. Chan, G.R. Burton, C.E. Brion, Chem. Phys. 161 (1992) 453. [7] U. Fano, J.W. Cooper, Rev. Mod. Phys. 40 (1968) 441. [8] M. Inokuti, Rev. Mod. Phys. 43 (1971) 297. [9] J. Berkowitz, Photoabsorption, Photoionization and Photoelectron Spectroscopy, Academic Press, New York, 1979. [10] R. Feng, G. Cooper, G.R. Burton, C.E. Brion, L. Avaldi, Chem. Phys. 240 (1999) 371. [11] R. Feng, G. Cooper, C.E. Brion, Chem. Phys. 244 (1999) 127. [12] R. Feng, G. Cooper, C.E. Brion, Chem. Phys. 252 (2000) 359. [13] R. Feng, G. Cooper, C.E. Brion, J. Electron Spectrosc. Relat. Phenom. 123 (2002) 199. [14] R. Feng, C.E. Brion, Chem. Phys. 282 (2002) 419. [15] C. Backx, P.R. Tol, G.R. Wight, M.J. van der Wiel, J. Phys. B 8 (1975) 2050. [16] F. Carnovale, C.E. Brion, Chem. Phys. 74 (1983) 253. [17] G.R. Burton, W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 177 (1993) 217. [18] J.A. Wheeler, J. Bearden, Phys. Rev. 46 (1934) 755. [19] J.L. Dehmer, M. Inokuti, R.P. Saxon, Phys. Rev. A 12 (1975) 102.
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[20] M. Inokuti, private communication. [21] S. Daviel, C.E. Brion, A.P. Hitchcock, Rev. Sci. Instrum. 55 (1984) 182. [22] W.L. Wiese, M.W. Smith, B.M. Glenon, Atomic Transition Probabilities, Vol. 1, Hydrogen Through Neon, NSRDS-NBS circular no. 4, US GPO, Washington, DC, 1966. [23] B.L. Henke, P. Lee, T.J. Tanaka, R.L. Shimabukuro, B.K. Fujikawa, At. Data Nucl. Data Tables 27 (1982) 1. [24] J.J. Yeh, I. Lindau, At. Data Nucl. Data Tables 32 (1985) 1. [25] R.F. Reilman, S.T. Manson, Astrophys. J. Suppl. Ser. 40 (1979) 815. [26] K. Kimura, S. Katsumata, Y. Achiba, T. Yamazaki, S. Iwata, Handbook of HeI Photoelectron Spectra of Fundamental Organic Molecules, Halsted Press, New York, 1981. [27] Landolt-Bornstein, in: Atom und Molekularphysik, Vol. 1, Part 3, Springer-Verlag, West Berlin, 1951, pp. 511–513. [28] K.J. Miller, J. Am. Chem. Soc. 112 (1990) 8533. [29] R. Serber, Phys. Rev. A 41 (1932) 489. [30] H. Becquerel, C.R. Acad. Sci. 125 (1897) 679. [31] G.C. Maitland, M. Rigby, E.B. Smith, W.A. Wakeman, Intermolecular Forces, Oxford Science Publications, Oxford, 1987.
Quantitative photoabsorption of diethyl ether in the valence and carbon 1s inner shell regions (5–360 eV) Renfei Feng, C.E. Brion * Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1 Received 4 June 2002
Abstract Absolute photoabsorption oscillator strengths (cross-sections) in the valence-shell discrete and continuum regions of diethyl ether C2 H5 OC2 H5 have been measured from 5 to 32 eV using high-resolution (HR) (0.05 eV fwhm) dipole ðe; eÞ spectroscopy. Wide-range spectra, spanning the UV, VUV and soft X-ray regions, have also been obtained at lowresolution (LR) (1 eV fwhm) from 5 to 360 eV which covers the valence-shell and C 1s inner-shell regions. The LR spectrum has been used to determine the absolute oscillator strength scale by employing valence-shell TRK (i.e., Sð0Þ) sum-rule normalization. Evaluation of the Sð2Þ sum using the presently reported absolute differential photoabsorption oscillator strength data gives a static dipole polarizability for diethyl ether in good agreement with previously reported polarizability values obtained by other methods. Other dipole sums SðuÞ, ðu ¼ 1; 3; 4; 5; 6; 8; 10Þ, and logarithmic dipole sums LðuÞ, (u ¼ 1 to 6), are also determined from the presently reported absolute differential photoabsorption oscillator strength data using dipole sum-rules. The presently reported absolute photoabsorption oscillator strength data are web-accessible at ftp.chem.ubc.ca/pub/cooper. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Quantitative studies of photoabsorption processes are of fundamental importance in understanding the interaction between photons and molecules and the action of ionizing radiation on matter [1]. They also provide useful information in a large number of scientific contexts, including studies in aeronomy, astrophysics, planetary science, fusion, and radiation chemistry, physics and biology [1]. Accurate photoabsorption absolute *
Corresponding author. Tel.: +1-604-822-3266; fax: +1-604822-2847. E-mail address: [email protected] (C.E. Brion).
oscillator strengths (cross-sections) are also required over wide spectral regions for use in modeling studies, while the experimental oscillator strength data can be used to evaluate theoretical concepts and computational approximations used in modeling molecular photoabsorption processes [1]. In a previous publication [2], we have reported absolute photoabsorption oscillator strengths (cross-sections) for one of the ethers, dimethyl ether CH3 OCH3 [2], using both high- and lowresolution (HR and LR) dipole ðe; eÞ spectroscopies from 5 to 32 eV and 5 to 200 eV, respectively. In the present work, we report absolute photoabsorption oscillator strengths for diethyl ether
0301-0104/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 2 ) 0 0 7 8 8 - 7
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C2 H5 OC2 H5 , in the valence-shell and inner-shell regions, determined using the same methods [3–5]. HR (0.05 eV fwhm) dipole ðe; eÞ [3,4] measurements were carried out in the energy range 5–32 eV. Much wider range (up to 360 eV) measurements, which cover both the valence-shell and C 1s innershell regions, were carried out at LR (1 eV fwhm) using the modified LR dipole ðe; eÞ instrumentation with improved differential pumping [5,6]. To the best of our knowledge, no photoabsorption oscillator strength data have previously been published for diethyl ether. It is well known now that dipole ðe; eÞ spectroscopy has been demonstrated [3–5] to provide a very accurate method of determining absolute optical oscillator strengths (cross-sections) for photoabsorption. The dipole ðe; eÞ method provides an entirely independent method to the use of direct photoabsorption [1,3,5], and furthermore it avoids the major sources of error (line saturation and the presence of higher order radiation) which can occur when photon techniques are employed. In addition, the wide-range photoabsorption oscillator strength (cross-section) distribution can be used to determine a range of atomic and molecular properties using dipole sum-rules [5,7–9]. Such procedures also provide an independent evaluation of the accuracy of the experimentally determined photoabsorption oscillator strength (cross-section) scale by comparing the dipole polarizability derived from the Sð2Þ sum-rule to directly determined experimental values obtained by other techniques. In a recent paper [5] reviewing and assessing our absolute photoabsorption oscillator strength measurements by dipole ðe; eÞ methods for five noble gas atoms and 52 small molecules, molecular and inter-molecular properties were calculated from the wide-range oscillator strength distributions using dipole sum-rules. Similar results have also very recently been reported for SO2 [10], H2 S [11], OCS [12], CH3 OCH3 [2], C6 H6 [13] and C2 H5 OH [14].
2. Experimental The instrumentation and experimental procedures employed in the present work are similar to
those used in our earlier reported photoabsorption oscillator strength measurements for a wide selection of atoms and molecules [2–6,10–14], and therefore only a brief description will be given below. A LR dipole ðe; eÞ spectrometer [15,16], using 8 keV electron impact energy, zero degree mean scattering angle and a two stage differentially pumped electron gun vacuum chamber [6], was employed to obtain electron energy loss spectra of diethyl ether in the energy ranges 5–40, 35–90, 80– 200, 190–290, 280–310 and 300–360 eV at intervals of 0.5, 1.0, 2.0, 2.0, 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. Valence shell TRK sum-rule normalization [5,17] was used to obtain absolute values of the photoabsorption oscillator strength. In order to estimate the contribution to the valence shell oscillator strength above 200 eV, a curve of the form AE2 þ BE3 þ CE4 (where E is the photon energy, and A, B and C are best fit parameters) was fitted to the experimental data from 120 to 280 eV and integrated from 280 eV to infinite energy. On this basis, the fraction of the valence shell oscillator strength above the limit of measurements at 280 eV was found to be 5.4%. The total area under the valence shell spectrum from 5 eV to infinity was then normalized to a value of 32.57, which includes the total number of valence electrons (32) of diethyl ether plus a small estimated contribution for the Pauli-excluded transitions (to the already occupied valence orbitals) [18–20]. A HR dipole ðe; eÞ spectrometer, using 3 keV impact energy and zero degree mean scattering angle, was employed to obtain electron energy loss spectra of diethyl ether in the equivalent photon energy range 5–32 eV at 0.05 eV fwhm resolution. Details of the construction and operation of this spectrometer can be found in [3,21]. 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
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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 [3–6]. This relative HR photoabsorption spectrum was then normalized in the smooth continuum region (at 18.0 eV) to the presently reported LR absolute oscillator strength data obtained as described above. Any contributions from background gases remaining at the base pressures of the spectrometers (2 107 Torr) and from non-spectral electrons were removed by subtracting the signal when the sample pressure was quartered [3,4]. The energy scale of the HR energy loss spectrum was calibrated in a separate experiment by admitting helium simultaneously with diethyl ether and referencing to the 11 S ! 21 P transition of helium at 21.218 eV [22]. Using this procedure the energy scale is estimated to be accurate to better than 0.02 eV. The LR spectrum was compared with the HR data (convoluted with 1 eV fwhm G) in order to calibrate the LR energy scale. The sample of diethyl ether was obtained commercially and degassed thoroughly by freeze– pump–thaw cycles. No impurity peaks were observed in the electron energy loss spectra after this purification. The uncertainty of the absolute oscillator strength scale is estimated to be at most 5%.
3. Results and discussion 3.1. Low-resolution absolute photoabsorption oscillator strengths in the valence-shell and C 1s innershell regions (5–360 eV) Fig. 1 shows the presently determined absolute photoabsorption oscillator strengths (cross-sections) for diethyl ether in the energy range 5–360 eV obtained using the LR (1 eV fwhm) dipole ðe; eÞ spectrometer. The inset on Fig. 1 is an expanded view of the present results in the energy range above 240 eV (valence continuum and C 1s inner-shell regions). The dashed line in the figure represents the fitted polynomial curve to the valence shell continuum region. Numerical values of
617
Fig. 1. Absolute photoabsorption oscillator strengths (crosssections) for diethyl ether in the energy range 5–360 eV obtained at 1 eV fwhm resolution. The inset shows an expanded view in the energy range above 240 eV. The dashed line represents the extrapolation of the fit to the valence shell continuum oscillator strengths (see text for details).
the presently determined absolute photoabsorption oscillator strengths are given in Table 1. These data encompass both the valence shell and C 1s inner shells. Fig. 2 shows the presently determined LR (1 eV fwhm) photoabsorption differential oscillator strength spectrum for diethyl ether in three energy regions of (a) 5–32, (b) 32–270 and (c) 270–360 eV. In Fig. 2(a), the presently determined HR photoabsorption oscillator strength spectrum has also been shown for comparison. It is clear that the presently determined HR and LR data sets are in excellent agreement. Figs. 2(b) and (c) show the presently determined LR absolute photoabsorption oscillator strengths in valence continuum region and the C 1s inner-shell region, respectively. Since no previously published absolute photoabsorption oscillator strengths for diethyl ether have been reported in this energy region only estimated oscillator strengths, obtained from atomic data (4C+ 10H+O) [23–25], can be shown for comparison. Absolute oscillator strength values for the hydrogen atom, derived from the exact formula for the oscillator strength distribution for transitions from the ground electronic state to the continuum as given by Inokuti [8], were used to supplement the calculated data for the carbon and oxygen atoms
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Table 1 Absolute differential total photoabsorption oscillator strengthsa for diethyl ether at low resolution (1 eV fwhm) Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
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 30.5
0.86 0.35 0.06 1.14 3.93 5.69 7.32 16.37 28.96 35.93 42.96 49.42 56.20 68.23 83.91 98.2413 107.8 114.6 121.9 126.2 128.4 129.9 131.1 130.6 128.7 127.7 125.6 122.9 119.4 116.4 112.6 107.3 103.7 99.85 96.03 91.86 89.07 85.26 82.38 79.43 76.25 72.81 69.70 67.10 64.62 62.39 60.12 58.34 55.50 54.37 51.85 49.49
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 72.0 73.0
48.48 46.69 45.08 43.35 42.00 40.13 39.45 37.80 37.46 35.73 34.43 33.64 32.26 31.28 30.28 29.66 28.64 27.45 26.68 25.47 24.12 22.77 21.58 20.37 19.28 18.50 17.57 16.80 15.94 15.36 14.72 14.05 13.51 12.89 12.33 11.82 11.44 11.03 10.56 10.21 9.87 9.51 9.19 8.98 8.48 8.28 7.93 7.62 7.38 7.26 7.04 6.69
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 98.0 100.0 102.0 104.0 106.0 108.0 110.0 112.0 114.0 116.0 118.0 120.0 122.0 124.0 126.0 128.0 130.0 132.0 134.0 136.0 138.0 140.0 142.0 144.0 146.0 148.0 150.0 152.0 154.0 156.0 158.0 160.0
6.37 6.35 6.11 5.94 5.90 5.59 5.44 5.27 5.12 5.03 4.79 4.77 4.48 4.47 4.26 4.28 4.11 3.89 3.72 3.54 3.38 3.22 3.10 2.99 2.87 2.74 2.63 2.53 2.45 2.34 2.29 2.19 2.15 2.07 1.97 1.93 1.86 1.81 1.73 1.69 1.63 1.61 1.54 1.51 1.47 1.41 1.36 1.33 1.31 1.28 1.25 1.20
162.0 164.0 166.0 168.0 170.0 172.0 174.0 176.0 178.0 180.0 182.0 184.0 186.0 188.0 190.0 192.0 194.0 196.0 198.0 200.0 202.0 204.0 206.0 208.0 210.0 212.0 214.0 216.0 218.0 220.0 222.0 224.0 226.0 228.0 230.0 232.0 234.0 236.0 238.0 240.0 242.0 244.0 246.0 248.0 250.0 252.0 254.0 256.0 258.0 260.0 262.0 264.0
1.19 1.19 1.13 1.10 1.10 1.06 1.05 1.02 1.02 0.98 0.96 0.96 0.94 0.93 0.89 0.88 0.87 0.85 0.84 0.82 0.81 0.79 0.78 0.76 0.74 0.75 0.72 0.70 0.71 0.71 0.70 0.67 0.66 0.66 0.65 0.65 0.65 0.63 0.64 0.62 0.62 0.59 0.60 0.57 0.61 0.59 0.57 0.60 0.56 0.57 0.57 0.55
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Table 1 (continued) Photon energy (eV) 266.0 268.0 270.0 272.0 274.0 276.0 278.0 280.0 280.5 281.0 281.5 282.0 282.5 283.0 283.5 284.0 284.5 285.0 285.5 286.0 286.5 287.0 287.5 288.0 288.5 289.0 289.5 290.0 290.5 291.0 a
Oscillator strength ð102 eV1 Þ 0.54 0.54 0.55 0.50 0.52 0.52 0.52 0.52 0.52 0.53 0.51 0.52 0.52 0.50 0.52 0.51 0.51 0.50 0.50 0.54 0.55 0.58 0.70 1.24 2.01 3.32 4.55 5.48 6.06 6.09
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
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
6.26 6.42 6.44 6.59 6.81 6.86 6.80 6.72 6.55 6.44 6.21 6.00 5.79 5.63 5.49 5.27 5.11 4.99 4.93 4.75 4.63 4.64 4.55 4.46 4.36 4.32 4.26 4.21 4.12 4.14
306.5 307.0 307.5 308.0 308.5 309.0 309.5 310.0 311.0 312.0 313.0 314.0 315.0 316.0 317.0 318.0 319.0 320.0 321.0 322.0 323.0 324.0 325.0 326.0 327.0 328.0 329.0 330.0 331.0 332.0
4.06 3.99 3.94 3.91 3.88 3.83 3.78 3.74 3.68 3.61 3.52 3.47 3.45 3.36 3.33 3.35 3.28 3.22 3.22 3.10 3.11 3.10 3.04 2.99 3.04 2.92 2.89 2.89 2.82 2.82
333.0 334.0 335.0 336.0 337.0 338.0 339.0 340.0 341.0 342.0 343.0 344.0 345.0 346.0 347.0 348.0 349.0 350.0 351.0 352.0 353.0 354.0 355.0 356.0 357.0 358.0 359.0 360.0
2.77 2.79 2.79 2.79 2.78 2.71 2.70 2.70 2.66 2.64 2.60 2.60 2.60 2.64 2.56 2.63 2.56 2.60 2.57 2.57 2.46 2.55 2.51 2.41 2.60 2.51 2.52 2.47
rðMbÞ ¼ 1:0975 102 ðdf =dEÞ ðeV1 Þ.
from [25]. From Fig. 2(b), it is found that the photoabsorption oscillator strengths for diethyl ether estimated from the atomic sums are generally lower than the presently determined photoabsorption oscillator strengths below 50 eV, then a little higher below 180 eV and lower again above 180 eV, respectively. Comparing with the results estimated from the two theoretical data sets [24,25], the atomic estimates resulting from the experimental data of Henke et al. [23] show closer agreement with the present data. Fig. 2(c) gives an expanded view in the C 1s inner-shell region (270– 360 eV). The oscillator strengths from the atomic data give reasonable estimates only at the region far above the C 1s edge (J310 eV). At the near-
edge region, where significant near-edge molecular effects are expected to occur, the atomic estimates are significantly lower than the presently determined experimental data. In addition, the atomic estimates also underestimate the valence contributions for diethyl ether in the C 1s inner-shell region (see up-triangles and dashed line in Fig. 2(c)). By subtracting the underlying valence distributions (estimated from the polynomial curve fit and shown as the dashed line in Fig. 2(c)) from the total absolute photoabsorption oscillator strengths, the absolute partial photoabsorption oscillator strengths for the C 1s inner shell have been deduced, and these values are given numerically in Table 2.
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oscillator strength spectrum shows four main discrete band features at 6.57, 7.23, 8.13 and 9.02 eV, respectively. Above the first ionization threshold, a very broad continuum distribution occurs with a maximum at 16.5 eV and two superimposed structures at 10.2 and 13 eV, respectively. In order to carefully 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 fwhm (to mathematically degrade its resolution to that of the LR data) and compared with the LR spectrum. Extremely good quantitative agreement is found between these two data sets over the entire energy range of the HR spectrum (5–32 eV). This very good quantitative agreement gives confidence in the overall accuracy of the absolute oscillator strengths determined in the present work, and therefore of the Bethe–Born factors previously determined [3,16] for our HR and LR dipole ðe; eÞ spectrometers. A further and more stringent test of the accuracy of the absolute oscillator strength scale is to apply the Sð2Þ sum rule [5] and to compare the results with published experimental values of the static dipole polarizability as described in the following section. Fig. 2. Low-resolution (1 eV fwhm) absolute photoabsorption oscillator strengths for diethyl ether in the energy regions: (a) 5–32, (b) 32–270 and (c) 270–360 eV. The presently determined high-resolution absolute photoabsorption oscillator strengths for diethyl ether are shown as a solid line in panel (a). For the higher energy regions (b) and (c), the sum of atomic data 4C+10H+O [23–25] are shown for comparison. See text for details.
3.2. High-resolution absolute photoabsorption oscillator strengths (5–32 eV) Fig. 3 shows the presently determined absolute photoabsorption oscillator strength spectrum for diethyl ether in the energy range 5–32 eV, obtained using HR (0.05 eV fwhm) dipole ðe; eÞ spectroscopy. The positions of the valence shell (vertical) ionization potentials [26] are indicated as vertical lines in Fig. 3. Below the first ionization threshold, the presently determined HR photoabsorption
3.3. 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 [5,7–9] resulting from the integration of excitation energy weighted dipole differential oscillator strength spectra over all discrete and continuum electronic states. Table 3 lists the dipole sums S(u) and logarithmic dipole sums L(u) for u 6 1, obtained from the presently determined differential photoabsorption oscillator strength spectra of diethyl ether (the HR spectrum was used from 5–32 eV and the LR spectrum from 32–360 eV). The static dipole polarizabilities, i.e., Sð2Þ, previously determined from refractive index measurements [27] and by the empirical additivity methods of ahc (atomic hybrid component) and ahp (atomic hybrid polarizability), which are reported in recently published studies [28], are also
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Table 2 Absolute differential photoabsorption oscillator strengthsa for C 1s inner-shell regionb of diethyl ether at low resolution (1 eV fwhm) Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
Photon energy (eV)
Oscillator strength ð102 eV1 Þ
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
0.03 0.03 0.07 0.08 0.11 0.23 0.78 1.55 2.85 4.09 5.02 5.60 5.63 5.80 5.96 5.98 6.13 6.35 6.41 6.35 6.27 6.10 6.00 5.77 5.56 5.35
298.0 298.5 299.0 299.5 300.0 300.5 301.0 301.5 302.0 302.5 303.0 303.5 304.0 304.5 305.0 305.5 306.0 306.5 307.0 307.5 308.0 308.5 309.0 309.5 310.0 311.0
5.19 5.05 4.84 4.67 4.56 4.50 4.32 4.20 4.21 4.12 4.03 3.94 3.90 3.83 3.79 3.70 3.72 3.64 3.57 3.52 3.49 3.47 3.41 3.37 3.32 3.27
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
3.20 3.11 3.06 3.05 2.96 2.93 2.95 2.89 2.83 2.83 2.71 2.72 2.72 2.65 2.61 2.66 2.54 2.51 2.51 2.45 2.45 2.40 2.42 2.43 2.43 2.42
338.0 339.0 340.0 341.0 342.0 343.0 344.0 345.0 346.0 347.0 348.0 349.0 350.0 351.0 352.0 353.0 354.0 355.0 356.0 357.0 358.0 359.0 360.0
2.35 2.34 2.34 2.31 2.29 2.24 2.25 2.25 2.29 2.22 2.29 2.22 2.26 2.23 2.23 2.12 2.22 2.18 2.08 2.27 2.18 2.19 2.14
a b
rðMbÞ ¼ 1:0975 102 ðdf =dEÞ ðeV1 Þ. Note that the estimated underlying valence shell contribution has been subtracted.
Fig. 3. Absolute oscillator strengths (present work) for the valence shell photoabsorption of diethyl ether in the energy range 5–32 eV at 0.05 eV fwhm resolution. The vertical lines indicate the positions of the valence shell ionization potentials [26].
listed for comparison. Since the presently reported dipole ðe; eÞ measurements were obtained only up to 360 eV, accurate calculation of the u P 0 sums is not possible because of the heavy weighting of the high-energy regions of the oscillator strength distribution in them. To our knowledge, no such dipole sum data set for diethyl ether has been published previously. It should be noted that because of the weighting terms Eu and Eu lnðE=EH Þ in the SðuÞ and LðuÞ sums [5], the contributions to the sums from lower energy region data become more important as u decreases (e.g., u 6 3). Fig. 4 shows the ðdf = dEÞ/E2 spectrum (i.e., the Sð2Þ spectrum) obtained from the presently determined HR (5–32 eV) and LR (5–360 eV) photoabsorption oscillator strength data for diethyl ether. It can be seen that this spectrum decreases very rapidly with increasing
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Table 3 Dipole sums SðuÞ and LðuÞ of diethyl ether, obtained from the presently reported absolute differential oscillator strengths, compared with dipole sums from other sources. (All valuesa are given in a.u.) Dipole sums
From present dipole ðe; eÞ work
Sð1Þ Sð2Þc
3.646(1) 5.577(1)
Sð3Þ Sð4Þ Sð5Þ Sð6Þ Sð8Þ Sð10Þ Lð1Þ Lð2Þ Lð3Þ Lð4Þ Lð5Þ Lð6Þ
1.016(2) 2.103(2) 4.845(2) 1.224(3) 9.828(3) 9.975(4) )1.110(1) )2.922(1) )6.788(1) )1.649(2) )4.277(2) )1.186(3)
From refraction [27]
Additivity [28]b
5.891(1)
5.870(1) 5.904(1)
a
MðnÞ represents M 10n . The first entry is obtained using the ahc (atomic hybrid component) method and the second entry is from the ahp (atomic hybrid polarizability) method [28]. c Sð2Þ gives aN , the static dipole polarizability. b
perimental photoabsorption oscillator strength data above 360 eV will have negligible effect on the Sð2Þ dipole sum, or on the other sums with u 6 2. In fact, the static dipole polarizability ðSð2ÞÞ of diethyl ether, 55.77 a.u., derived from the presently determined differential photoabsorption oscillator strength spectra, is in good agreement (within <6%) with the previously reported experimental static dipole polarizability (58.91 a.u.) [27], and also with the empirical ahc and ahp values [28]. These Sð2Þ comparisons also strongly support the quoted 5% accuracy of the presently reported HR and LR absolute oscillator strength data and lend confidence to the accuracy of the other SðuÞ and LðuÞ sums given in Table 3. In addition to the dipole polarizability, the normal Verdet constant, which is involved in the Faraday effect [29,30], could also be calculated from the presently determined differential oscillator strengths or dipole sums [5]. Finally, the rotationally averaged van der Waals C6 coefficients (dipole–dipole dispersion energy coefficients) [5,31] for the long-range interaction of diethyl ether with a wide range of other atoms and molecules can be obtained from the absolute dipole (photoabsorption) oscillator strength distribution or various combinations of SðuÞ and LðuÞ values for each of the species involved, using the dipole sums given in the previous publications for five noble atoms and 57 molecules, and the appropriate equations [2,5,10–14].
Acknowledgements This work was financially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. Fig. 4. The ðdf =dEÞ/E2 spectrum (i.e., Sð2Þ) obtained from the presently determined high-resolution (0.05 eV fwhm) (5– 32 eV) and low-resolution (1 eV fwhm) (32–360 eV) absolute photoabsorption oscillator strengths for diethyl ether. The published value ðaPub Þ of the static dipole polarizability is taken from [27].
energy, and in fact the values above 32 eV (32– 360 eV) contribute only 5.7 of the total Sð2Þ sum from 5 to 360 eV. Therefore, the lack of ex-
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