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ESCA studies of CO2, CS2 and COS
Journal of Electron
Spectroscopy
and ReIated Phenomena
Elsevier Publishing Company, Amsterdam - Printed in The Netherlands
ESCA
STUDIES
C. J. ALLAN*, K. SIEGBAHN
OF C02,
U. GELIUS,
Institute of Physics,
University
CS2 AND
COS
D. A. ALLISON**, of Uppsala, P.0.
Box
G. JOHANSSON,
H. SIEGBAHN
and
530, S-751 21 Uppsala I (Sweden)
(Received 19 June 1972)
ABSTRACT
The core level electron spectra of COz, CS2 and COS excited by Mg Ka radiation have been studied to identify shake-up satellite lines associated with ionization from these levels. A number of such lines have been seen and possible assignments have been suggested using the excited states of the molecule as a guide. The valence spectra have also been recorded and they too were found to be rich in shake-up structure. The observed variation of the valence line intensities is discussed and compared with predictions made from an intensity model. The validity of distinguishing between 5~ and 0 symmetries in linear molecules in applying the intensity model is confirmed_
INTRODUCTION
During the past few years the use of soft X-rays to excite electron spectra from the valence region of molecules has proven to be very useful’ -‘. Not only is it possible to excite electrons from all orbitals, including those which cannot be reached with ultraviolet sources, but it was found that the intensities of the observed lines were dependent on the atomic character of the orbital. Thus, for example, for second row elements “2s” character is seen roughly ten times as strongly as “2~” character4. Although this property was used qualitatively, little quantitative work was done. Recently, however, Gelius et ale5 -’ have attempted to make quantitative predictions of line intensities based on the atomic parentage of the molecular orbitals obtained from ab i~itio LCAO-SCF calculations, with encouraging results. In a continuation of this study we have recorded the valence orbital spectra of CO,, CS2 and COS to * National Research Council of Canada Postdoctoral Fellow. ** Gillette International Research Postdoctoral Fellow. J. Electron
Spectrosc.,
1 (1972j73)
131
compare with line intensities predicted from the atomic populations from a recent set of ab initio calculations on these molecules*. In addition to studying the spectra from the valence orbitals of these molecules, we have investigated the shake-up spectra associated with ionization from the various atomic core levels for this series. This phenomenon occurs when a valence electron is promoted from a filled orbital to an unfilled orbital as a result of the perturbation caused by the removal of another electron, in this case, a core electron. Experimentally, one observes a sharp line to the lower kinetic energy side of the normal photo-peak, at an energy
E =
hv
- E, - E’
where EB is the ionization energy for the given orbital and E’ is the additional energy needed to excite the valence electron. EXPERIMENTAL
Electron spectra were acquired using a double-focussing magnetic analyzer’ and were excited with Mg Ka X-radiation, 1253.6 eV. All samples were run in the gaseous phase. CO2 (99.99 % pure) was introduced into the sample chamber, directly from the supply cylinder, using appropriate reduction valves for pressure control prior to the spectrometer needle valve. CS2 (> 99.5 % pure) normally a liquid at room temperature, was introduced into the sample chamber via the needle valve. COS (> 97.5 % pure) normally a gas at room temperature, was liquefied, using a trichloroethylene bath, and the vapour fed into the sample chamber through the needle valve. In studying shake-up one must be careful to eliminate or minimize contributions from discrete energy loss peaks caused by electrons being inelastically scattered from neutral molecules. One can correct for such contributions by obtaining, independently, the inelastic scattering spectrum1 O:,or as we have done in the present work, by acquiring core spectra over a range of sample pressures to identify pressure dependent peaks. The shake-up data was then collected at a sample pressure well below that at which the pressure dependence was eliminated. Typically this meant a gas pressure of 1.0-1.5 x lo-’ torr. The counting rates were very low in the region of interest and successive scans were added together to obtain adequate spectra. The vaIence region spectra were acquired in a similar manner, again to minimize inelastic scattering background. THE SHAKE-UP
SPECTRA
ASSOCIATED
WITH
IONIZATION
FROM
THE CORE
LEVELS
As we shall see, the valence spectra of the present series exhibit extra structure which is due to shake-up associated with ionization from the valence orbitals. Therefore it is reasonable to begin with a discussion of shake-up. When a core electron is suddenly removed from a molecule, by photoionization or some other process, the 132
J. Electron
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valence electrons experience a sudden change in their potential as a result of which an electron may be promoted from a filled level to an unoccupied orbital or to the continuum. In the former case one observes a line spectrum to the lower kinetic energy side of the normal ESCA peak, the normal peak corresponding to no excitation of a valence electron, and in the latter case one observes a continuum. The first process is called shake-up and the second process is termed shake-off and is analogous to shake-off associated with nuclear p-decay. Manne and Abergil and later Meldner and Perezi have shown that the Hartree-Fock orbital energies are more directly comparable to the experimental mean ionization energy, including shake-up and shake-off contributions, than to the normal ionization energy. The difference between the two experimental energies is then a measure of the reorganization energy. Consequently, it is of interest to determine the shake-up and shake-off spectra associated with a given core level. In the
10 0 t
IO 0
100
k
co2
I
I
I
I
0 Is
I,,
CIS
1
”
1 1 cos
I
I
S2P
10 0 10
0 IO 0
I
L
I
II
L
Ok
Cls
I I
I
20 SHAKE-UP
I
I
10 ENERGY
-. 1
0 I.?‘.‘1
Figure 1. Summw of the shake-up lines observed in the present study. The vertical lines indicate the position of the lines and their heights their intensity relative to the main core line. J. Electron
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1 (1972/73)
I33
TABLE
1
SUMMARY
OF THE CORE
LEVEL SHAKE-UP
DATA
FOR COz, CSz AND
COS
Relative energies are estimated to be accurate to +-0.2 eV and relative intensities to *20°A otherwise stated.
c
0 Is Relative intensity
Shake-up energy (eV)
(%I
unless
Is
Shake-up energy CeV)
Relative intensity (%)
co2 0.0 11.5 12.7 13.8 16.1 17.9 19.9 22.3 f
c
100 0.9 1.4 3.6 5.8 3.1 2.x 0.2 * 0.1
0.4
0.0 10.8 12.4 15.0 18.0 20.2 f
0.4&
s 2s
Is
S/aake-ug energy (e V)
Shake-up energy (e V)
Relative intensity (%)
-
100 2.6 3.0 7.6 3.9 0.4
s & Shake-up energy (e V)
Relative intensity ( %)
Relative intensity (%I
cs2 0.0 6.5 9.1 12.2 15.8 17.7 19.7
0
* * k &
0.5 0.4 0.3 0.3
100 7.0 16.4 N 2 5.5 f 1.5 4.0 & 1.5 3.7 & 1.0
c
is
Shake-up energy (eV)
cos 0.0 8.8 13.8 i 0.3 15.5 & 0.3
Rel. int.
0.0 7.3 13.1 + 0.3 15.0 f 0.3
0.0 7.3 13.6 + 0.3 16.4 & 0.3
s 2s
IS Rel. int.
(%I
Shake-up energy CeV)
100 16 4.3 * 9.5
0.0 8.3 12.2 17.8
100 9.2 9.7 3.8 & 1.0
1.0
100 12 ZL 2 ,-u 2 N 2.5
(%I
Shake-up energy feV)
Rd. int.
0.0 9.4 14.8 rtr:0.5
100 -5 -1
(%)
S 2P Shake-up energy (eV)
0.0 9.6 15.3
100 19 7.0 f 2.0 f
1.0 0.5
Rel. int. f%)
100 6.4 f 4.8 f
2.4 1.5
8 Taken from the C 1s spectrum reported by Carlson et al.16.
present experiment we have measured the shake-up spectra associated with each of the core levels in the series. We have not attempted to determine the corresponding shakeoff continua since, with our present intensity, the time required, to accumulate the requisite data would be prohibitive. Furthermore, in determining the shape of the 134
J. Electron Spectrosc., 1 (1972173)
O-
I/\
. -10
-M
0
ci8oos 3oct-
1
cos-
s2p
zmloa,-
O-20 I__L__+._AL RELATIVE
KINETIC
0 ENERGY
Wfl
I
Figure 2. Sample shake-up spectra observed for the core levels of COz, CSZ and COS.
continua, continuum contributions from inelastically scattered electrons and from core electrons excited by the bremsstrahiung continuum present in the X-ray source can be more important than for the corresponding shake-up peaks. The shake-up process can be described in terms of the sudden approximation, where we treat the transition as occurring between two states of the ion13- 15. The transition is then of the monopole type and the probability depends on a matrix element of the form < Y&V- 1)1Yi(N1)) w here Y(N1) is the wave function describing the N- 1 electron system formed by removing an electron from the appropriate core level. Since we are considering a transition between two valence .7. Electron Spectrosc., 1 (1972/73)
135
orbitals
we can assume
that
the other
orbitals
are relatively
unaffected
so that
= where pf and cpl are the two orbitals involved in the transition. For a non-zero overlap the two wave functions must have the same symmetry. Thus, for example, a nngelectron can only be excited to another nngorbital. With this introduction let us now consider the results of the present experiment, which are summarized in Figure 1 and Table 1. Figure 2 shows a sampIe spectrum for one of the core levels of each molecule in the series. Let us begin with a discussion of the CO2 data. Carlson et al. l6 have previously obtained the shake-up spectra of COZ. They have not presented a detailed analysis of their data but the appearance of the spectra obtained in the present work agrees well with their data including the existence of the weak peak at -22.3 eV in the 0 1s spectrum. They have swept over a wider energy region and their spectra show evidence of an additional peak in the C 1s run and this has been included in Figure 1. The broad structure observed in the 0 1s shake-up spectrum, see Figure 2, has been deconvoluted into six peaks of approximately equal widths. The C 1s spectrum also showed a broad shakeup structure which was resolved into four lines. However the line at - 15 eV was considerably broader than the other three lines and so may contain contributions from more than one shake-up transition. It should be pointed out, though, that we could not resolve this peak into two lines with the same separation as that of the third and fourth oxygen lines. From Figure 1 one can see a considerable similarity between the oxygen and carbon data. A point of interest is that the additional line observed by Carlson et al-l6 in the carbon spectrum corresponds very well with the sixth 0 1s line observed in the present work. It is, of course, interesting to try to identify the levels involved in the shake-up transitions. Lacking anything better we have used optical data on the neutral molecules as a guide. It is not clear that such data will correlate very well with the shake-up transitions since the removal of a core electron represents a strong perturbation on the system. However if all orbitals relax by approximately the same amount the errors introduced in estimating transition energies should not be too large. Lindholm has surveyed the literature on Rydberg series for small molecules, and has analyzed the data in terms of the quantum defects to identify the levels involved ’’. Using Lindholm’s results plus the results of Meyer and Lassettrel’ we have constructed an energy level diagram for CO2 shown in Figure 3 which we have used in an attempt to assign the shake-up transitions. The first two shake-up peaks in the C 1s spectrum occur at - 10.8 eV and - 12.4 eV and in the 0 1s spectrum at - 11.5 and - 12.7 eV. These energies are close to that for a nng+ng transition, 12.2 eV, so one or both of the first two shake-up peaks in the C Is and 0 Is spectra may involve this type of a transition. Here it is worth noting that the two 7t, electrons can couple with their spins parallel or anti-parallel which will result in two peaks. In the Ne Is shake-up spectrum the splitting is observed to be a few electron volts” so the first two shake-up peaks may in fact correspond to these two spin configurations. The 136
J.
Eiecdron
Spectrosc.,
1 (1972/73)
co: 9.3 6.5
509
8g:E- 3ng CEi 7.3 6.7_
0
1n9
-3.8 -4.3-
1TtU 3ou
-5.6
cos
-2
4w
0
9.2
- a.3
4Tt 106
709
0
2n9
-2.8
2Tiu
-L.fa
5ol.l
-6.1
6W
-4.3
3ii
-4.8
z
-6.8
8~
Figure 3. Energy level diagram of the COZ, CSZ and COS molecules deduced from observed Rydberg series. For details refer to the text.
C 1s peak at - 15.0 eV may contain contributions
from several shake-up transitions, k9+5as = 14.5 eV, 17r,+2~, = 15.2 eV and 3a,+4a, = 15.5 eV and the two 0 1s shake-up lines at - 13.8 and - 16.0 eV may arise from similar transitions. Finally the line at - 18.0 eV, seen in both the 0 1s and C Is spectra may be a transition between the 4a, and 6a, orbitals, excitation energy, 17.5 eV. Turning to the CS2 data, one can see a close correlation between the S 2p and S 2s data, as would be expected, but not such a close correlation between the carbon and sulphur data. There are several points of interest which should be noted. Firstly, the innermost shake-up line observed in the S 2s and S 2p spectra do not occur at the same relative position but are separated by about 1.4 eV. Secondly, a deconvolution of the first and second S 2p shake-up structure into two components does not result in the same separation as for the normal line. This is to be expected since in addition to the spin-orbit splitting, the states will be split by the different spin configurations of the three unpaired electrons, thus resulting in four lines. Since the relative intensities of these components are not known we have not attempted a deconvolution but in Figure 1 and Table 1 have reported the structures as single lines. Thirdly, the C 1s spectrum shows evidence of considerable structure to the lower kinetic energy side of the first two shake-up lines. See Figure 2. We have assigned this structure to four different contributions but in view of the statistics these assignments can only be considered tentative. This is especially true of the line at - 12.2 eV. In an attempt to assign the shake-up peaks we have used the optical data of Tanaka et al. lg. We have assig ned the orbitals involved in the Rydberg series from the quantum defects, using Lindholm’s work on COZ as a guide. The results of this analysis together with data on the vertical ionization potentials taken from the present work and that of Turner et al.“, summarized in Table 2, have been used to construct J. Electron
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1 (1972/73)
137
TABLE
2
RYDBERG
SERIES
OF CSz
The quantum defects, 6, for CSz used to identify the Rydberg orbitals, were obtained from the work Also shown, in parentheses, are of Tanaka et al.lB according to the formula, En = A -R/(n-Q2. the quantum defects for the corresponding Rydberg series of COZ. taken from the work of Lindhohnl’. Transition energies enclosed in parentheses have been determined from the Rydberg formula since the corresponding transitions were not directly observed. Initial orbital
Orbital binding energy (e V)
Rydberg orbital
6
2-j% 5CU
10.1 14.5
6%
16.2
npnc, ?rsue ndog npcu n&E
0.45 0.94 0.58 0.31 0.10
np%l
0.48 (0.56)
Transition energy
Intensity
(0.56) (0.93) (0.31) (0.71) (0.05)
strong strong strong strong apparent emission apparent emission
n=3
4
5
(8.01) 11.10 11.97 (13.35) 14.60
9.03 12.92 13.30 14.94 15.30
9.43 13.63 13.78 15.42 15.62
14.06
15.09
15.52
an energy level diagram of CS2, shown in Figure 3. Using this level diagram we can estimate the following shake-up energies: 2~,+37c, = 10.8 eV, 50,+6m, = 11.7 eV and 6g*+ 70, = 12.8 eV. The second shake-up lines in the S 2s, and S 2p spectra lie 13.1 eV and 13.7 eV below the main lines so we have tentatively assigned these lines to the 6a,+7a, excitation. None of the other shake-up peaks observed in CS2 correlate with the above transition energies. The identification of the levels involved in the second Rydberg series converging to the ionization potential of the 6a, orbital is not straight forward. However, the quantum defect indicates that it is the forbidden TABLE
3
RYDBERG
SERIES
OF COS
The quantum defects, 6, for COS, used to identify the Rydberg orbitals, were obtained from the work of Tanaka et al.19 according to the formula, E,, = A - R/(n - c?)~.Also shown, in parentheses, are the quantum defects for the corresponding Rydberg series of CO, taken from the work of Lindholmrr. Transition energies enclosed in brackets have been determined from the Rydberg formula and the corresponding transitions were not observed directly by Tanaka et al. Initial orbital
Orbital binding energy (e VJ
Rydberg orbita!
6
3n 9a
11.2 16.0
8u
18.0
nPn nsb nP0 nPn ndx nsa
0.48 (0.65) 0.96 (0.90) 0.68 (0.66) 0.49 (0.63) 0.12 (0.1 I) 0.90 (0.90)
138
Transition energy (e V) n-3
4
5
( 9.25) (12.76) 13.29 13.89 14.39 (14.85)
(10.20) (14.50) 14.79 14.94 15.15 16.52
10.60 (15.18) 15.31 15.37 15.47 17.10
J. Electron Spectrosc., 1 (1972/73)
-3~~ excitation energy is 8.5 eV. The most intense series 6a,+n&,. Then the 27rn, shake-up lines observed in the S 2s and S 2p spectra lie 7.4 eV below the main peaks, so it is possible that these lines are associated with this type of transition. Finally, let us consider COS. One can, again, see similarities among the data, particularly between oxygen and sulphur. We have identified the orbitals involved in the Rydberg series observed by Tanaka et al. I9 ‘by comparing the quantum defects of a given series with those for CO I’. See Table 3. Again we have used the vertical ionization potentials taken from the present work and that of Turner et aL2’. The result is the partial energy level diagram of COS shown in Figure 3. From this diagram we have estimated the following shake-up energies: 3x+4~ = 9.2 eV, 2n+4n = 13.5 eV, 9a-+lOa w 13 eV and 8a-tlOa E 15 eV. From Figure 1 we can see that the first of the shake-up lines observed in the 0 Is, C Is, S 2s and S 2p spectra lies about 9 eV below the main line so it is probably associated with a 37c+4rc transition. The peaks observed in the 0 Is, S 2s and S 2p spectra at x - 15 eV are then assigned to an 8a+lOa excitation. The shake-up lines observed in the C 1s and 0 1s spectra at - 12.2 eV and - 13.8 eV, respectively, may then be associated with the 2~+4~, and/or the 90 -+ 100 excitations. To summarize, we have used optical data as a guide in interpreting the shakeup spectra associated with ionization from core levels of CO,, CS2 and COS. Although it is not at all certain that such optical data for the neutral species should correlate with transitions in the highly perturbed system, formed by removing a core electron, we have been able to suggest assignments for a number of the observed shake-up lines. In fact, the correlation between the optical and shake-up data seems to be rather too good to be purely coincidental. Since the core level binding energies of COS have not been previously measured, we did so in the present set of experiments for completeness. We used a mixed CO, plus COS sample and calibrated the C 1s and S 2p levels of COS against the C 1s level of CO 2 (297.5 ev) and the 0 Is level against the 0 1s level of COZ (540.8 eV), as described previously 5. The C Is and S 2p binding energies of CS, are known2’ but in the present work we have determined the S 2s binding energies of this molecule and of COS using the S 2p lines of the respective molecules as calbration standards. These binding energies are tabulated in Table 6. VALENCE
ORBITAL
SPECTRA
Figure 4 shows the valence orbitat spectra obtained from the isoelectronic series CO,, CS, and COS. As is to be expected, the spectra are noticeably similar, particularly in the region associated with the outer orbitals. It is interesting to compare the spectra of CO2 and CS, in this region. In particular, the intensity of the outer lcg line relative to that of the outer cg peak is remarkably different in the two spectra. This difference is a striking demonstration of the different dependence of the photoionization cross-section on the atomic s and p character of the molecular orbitals for J. Electrun Spectrosc., 1 (1972f73)
139
I
LO
I
I
30 BINDING
I
I
20 ENERGY (&‘I
I
I 10
Figure 4. Valence orbital spectra of COz, CSa and COS. The insert shows the higher binding energy region of the COS spectrum, following a straight line background subtraction, as an aid in the discussion.
second and third row elements. Qualitatively, “2s” character is seen roughly ten times as strongly as “2~” character for second row elements whereas for third row elements “3s” and “3~” character have approximately the same cross-section. The electron spectra of COZ, CS2 and COS excited by ultraviolet radiation, have been studied previouslyzls “, and there is a large body of information on the ionization potentials of these molecules based on optical spectroscopylgs 23, 24 and inelastic electron scattering experiments’ 8* 25P26. Th us, the binding energies of the four outer orbitals are well known, but the binding energies of the lower lying orbitals which cannot be reached by ultraviolet radiation have not been previously determined. In the region in which one expects contributions from the two innermost CJorbitals the spectra show considerable structure the interpretation of which is discussed below. We begin with CO,. In the binding energy region of the spectrum between x 30 eV and x40 eV one can observe a broad, complex structure. In this energy region 140
J. EZectrun
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one expects to find contributions from only two orbitals, the 3a, and 217, levels, which are essentially the gerade and ungerade combinations of the 0 2s orbitals. The ub initio calculation predicts the 30~ and 20, orbitals to be separated by 1.4 eV. Since the spacing of the ab irzitio orbital energies and the observed ionization potentials agree very well for the outer orbitals (see Table 6) the predicted separation of the 3~, and 217, peaks is probably quite good. The innermost valence peaks observed in ESCA are normally quite wide as a result of life-time broadening. Thus, for example, the widths of the innermost (0 2s) lines of C,H,O and C,O, are 2 4 eV full width at halfmaximum intensity 59 6 . One would therefore expect the contributions from the 3a, and 20, orbitals to give rise to a single unresolved peak and hence the existence of several lines in the high binding energy portion of the CO, spectrum is an anomaly. To assign the peak from the 3a, and 2a, levels we have used the ab initio calculation as a guide. It has been observed in several cases that, in the valence region, the calculated orbital energies are approximately linearly related to the ionization energies, which relation can be used to obtain more accurate estimates of ionization energies from calculation. Such a straight line is shown in Figure 5 for CO, where the ionization energies have been taken from the work of Siegbahn et a1.27 and the orbital energies from a calculation by one of us’8. Since the calculation for CO2 employed the same basis set, one would expect the orbital energies to approximately follow the same straight line and indeed when one plots the points for the outer four orbitals, (whose binding energies are well known), they do follow the curve. See Figure 5.
1 t ‘&
&Gu
c 1
L L
i OBSERVED
IONIZATtON
to
30
ENERGY
(eV1
Figure 5. Comparison of the ab initio orbital energies and measured ionization energies for CO, CO%, CS2 and COS. The straight line was drawn using only the CO data and was used as an aid in identifying the electron lines from the lower lying valence orbitals of COz, CSZ and COS. For CO2 and COS the points corresponding to these orbitals have also been placed on the figure. J. Electron Specfrosc., 1 (1972/73)
141
One can therefore use this straight line to obtain a quite accurate estimate of the 3a, and 20, binding energies and in this way we predict the peaks from these orbitals to lie at 39.7 and 37.5 eV. We have therefore concluded that the peak observed at 37.6 eV binding energy corresponds to these orbitals as indicated in Figure 4. This line appears to contain two components, the intense peak from the 31s~ and 20, orbitals plus a considerably weaker and more narrow peak which is centred at z 38 eV thus resulting in its asymmetric appearance. We have studied the COZ spectrum in considerable detail to try to establish the origin of the additional structure. As a result of these investigations we have been able to establish that the structure is associated with the Mg Ka radiation and not some other X-ray and we have eliminated the possibilities that it results from a sample impurity, from inelastically scattered electrons, or from electrons excited from the walls of the source compartment. Thus it seems conclusive that the anomalous structure is associated with COZ itself. One explanation for these lines is to assign them to shake-up transitions associated with ionization from the valence orbitals. Aberg has shown that the sudden approximation is also valid for systems for which electron correlation is important, such as the valence electrons of a molecule, provided the excitation energy is sufficiently highi3. Since we excite with Mg Kct this condition is fulfilled and we need only consider monopole transitions. As a guide we may use the energy level diagram of Figure 3. Here it seems more probable that shake-up transitions associated with valence ionization will correlate with data for the neutral molecule except for those cases for which we have both excitation and ionization from the same orbital, although this is by no means certain. Disregarding this difficulty one can then assign the structure centred at x 32.5 eV binding energy to a shake-up transition from the 17t, to the 27~”orbital associated with ionization from the 3~” orbital, which gives a peak at 33.3 eV binding energy, a transition from 40, to 5~, also associated with ionization from the 3a, level, which gives a peak at x 32.5 eV binding energy and/or a transition from the 17~~to the 2n, levels associated with ionization from the 4a, orbital, which gives a peak at 31.6 eV. An additional contribution may arise from a transition between the 4a, and 50, levels associated with ionization from the 4a, orbital which would give rise to a peak at w 34 eV. The positions of these peaks have been indicated in Figure 4 by vertical bars. Here, it can be seen that they cover the anomalous structure and may explain its broad appearance. The additional structure at 38 eV binding energy may possibly correspond to a shake-up transition between the 40, and 6a, levels and ionization from the 4~, which would give a peak at 36.9 eV. Although this explanation of the additional structure seems to fit reasonably well, energetically, the relative intensities of the peaks are unusually high for shake-up. Considering next the CS, spectrum, we expect to find two peaks in the higher binding energy portion of the spectrum originating from the 50, and 4a, orbitaIs’. Again the spectrum appears anomalous. We see two rather narrow peaks, S, and S,, lying on what appears to be an extremely broad structure (Fig. 4). We have concluded 142
J. Electron S’ectrosc., 1 (1972173)
that S 1and SZ are not from the 50, and 40, orbitals but are in fact shake-up peaks. Based on previous experience these lines are too narrow to originate from the 50, and 4~, levels. For example, the innermost valence orbital of C4H4S is x 5 eV wide5. To predict the binding energies of the 50, and 4a, orbitals from the calculation we have used the linear relation between the ab initio orbital energies and experimental ionization energies of Figure 5. It is not obvious that the same linear relation should hold for CS2 but when one plots the data for the four outer orbitals of CS2 it follows the CO-CO2 data reasonably well. See Figure 5. Further, the COS data also follows this straight line, as will be discussed later, so the CO-CO2 line would appear to be generally valid for this isoelectronic series. On this basis we predict the ionization energies of the 5a, and 40, orbitals to be 25.4 and 28.4 eV. From Figure 4 one can see a broad peak at 26.5 eV which we then attribute to these two orbitals. Above this peak one can observe an extremely broad structure which may consist of a series of shake-up lines and/or which may be part of a shake-off continuum. As for C02, we have attempted to assign the shake-up peaks, S 1 and S2, using the energy level diagram for the neutral molecule, see Figure 3. As with shake-up from the core levels a given transition will give rise to a spin doublet depending on whether the electron in the excited orbital has its spin parallel or anti-parallel to that of the original unpaired electron. Of course, if the photo-electron and the shake-up electron originate from the same 0 level only a single line will be observed. For ionization from orbital a and excitation from b to c the two-spin combinations may be written schematically. 1. a b c or 2. a b c ttS_
-ITT
If a is a core orbital the exchange energy for 1 will be considerably smaller than for 2 resulting in a relatively widely spaced doublet. On the other hand if a is a valence orbital the exchange energies for 1 and 2 may be comparable resulting in a closely spaced doublet. At the present time we have no estimate of the splitting one might expect which makes the assignment of S, and S2 rather tentative. However if we assume the doublet splitting is small so that S 1 and SZ are associated with different transitions we may reason as follows: S2 lies 10.8 eV below the line from the 27c,orbital which suggests it may originate from a 27~” + 37~”shake-up transition, AE = 10.8 eV (Figure 3), associated with ionization from the 27c, orbital. S, lies 8.5 eV below the 2~” peak. If we assume the 3n, level lies 8.5 eV above the 2n, level, as indicated in Figure 3, then S, would be assigned to a 2np+3xs transition associated with ionization from the 27~~level. The predicted energy for a 5~,+6a, transition is 11.7 eV. Since S, also lies 11.3 eV below the 2ng peak it may also contain a contribution from such a transition associated with ionization from the 2ng orbital. If, on the other hand, we assume that the doublet splitting is of the order of a few electron volts then S 1 and S 2 would be assigned to such a doublet arising from some given shake-up transition. Energetically a 2n,+3~, or 2np+3xB transition J. Electron
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1 (1972/73)
143
associated with ionization from the 27rUorbital or a 5a,+6aU transition associated with ionization from the 2n, orbital are most likely. Finally let us consider the COS data. In the higher binding energy portion of the spectrum we expect to see two peaks from the 70 and 8a orbitals but as with CO2 and CS2 we observe a considerable amount of structure. In Figure 4 we have subtracted a straight line background from the data to facilitate the discussion. From the ab initio calculation, using the linear relation between orbital energies and ionization energies (Figure 5) the predicted ionization energies for the 70 and 6a orbitals are 26.7 and 36.4 eV respectively. Consequently we have assigned the peaks at 27.4 and 35.7 eV binding energies to these orbitals as indicated in Figure 4. We have fitted these peaks to gaussians, as indicated by the solid lines and have subtracted these contributions to obtain the remaining spectrum indicated by the dotted lines. We are left with two peaks S 1 and SZ centred at 25.0 and 26.6 eV binding energies and a broad structure centred at x 33 eV binding energy which would appear to consist of two or more Iines. We have used the energy level diagram for the neutral molecule (Figure 3) as a guide in assigning the peaks. If we assume S I and SZ are associated with different shake-up transitions then since SZ lies 9.3 eV below the 27~line it is assigned to a 3n+4n transition, (AE = 9.2 eV), associated with ionization from the 27~ orbital. Although SZ can be assigned S1 does not fit very well with any proposed placement. It lies 12.2 eV below the 37~peak and may correspond to a 27c+4rc transition, (AE = 13.5 eV) and/or a 9o+lOa transition (AE x 13 ev) associated with ionization from the 37~level. Energetically, however, these suggestions are not very satisfactory. It should be noted that we have a rather limited knowledge of excited states in COS with which to assign shake-up peaks so it may well be that S1 corresponds to a transition involving some state which has not been located on the level diagram of Figure 3. If we assume S 1 and S2 are an exchange doublet then they may arise from a 37r+4n transition associated with ionization from the 2~ orbital, or a 2x+4x and/or 90+10a transition associated with ionization from the 3n level. The broad structure at ~33 eV binding energy corresponds very well with a 8a-+ lOa shake-up transition, AE x 15 eV, associated with ionization from both the 8a and the 9o orbitals. THE
INTENSITY
MODEL
In previous papers we have assumed that the observed intensity of the line from the ith molecular orbital was related to the gross atomic populations of that orbital via an expression of the form 1; = 2 cAI P’(AA) Al
where cAL is the photoionization cross-section for a ;1 type atomic orbital on atom A and P’(Ai) is the gross atomic population of symmetry il on atom A for the ith I44
J. Electron
Spectrosc.,
1 (1972/73)
molecular orbital. If we use photoionization cross-sections relative to that of a particular atomic symmetry, in the present case C 2s, the intensity of a given line is then given by
(1) This expression then allows us to predict the relative intensities of the lines in the X-ray induced electron spectrum. In a previous application of this model to C,O, it was found necessary to reduce the predicted intensities of the x orbitals by a factor of two in order to obtain good agreement with experiment 6 - Lohrz9 has recently outlined a method of calculating photoionization cross-sections using orthogonalized plane-waves to describe the free electron. For unpolarized radiation, the cross-section, at an angle perpendicular to the inc:dent radiation, is given by fl=;
[
29
B
1
where
-11/312.
Lohr investigated the energy dependence of j? for ionization from the bg and 7~” orbitals of the linear CZ system over the free electron energy range O-200 eV. The j? value for the bg electron reached an asymptotic value of 2 at about 100 eV while for the 7rUorbital j? was found to decrease monotonically for energies above 50 eV and may be close to - 1 at 1200 eV. If this asymptotic behaviour of /3 is general for all linear molecules then the cross-section for Q orbitals, predicted from eqn. (I), relative to that of z orbitals, is underestimated by a factor of two. This has lead GeIius’ to express the intensity model in the form P’(AA)
(2)
It is in this form which we have used the intensity model taking b = 2 for Q orbitals and/3 = -. 1 for n orbitals. From eqn. (2) we have calculated the relative line intensities for ionization from the various orbitals of COZ, CS2 and COS using the gross atomic populations from the ab initio calculations on these molecules* and using atomic photoionization TABLE
4
SUMMARY CARBON,
OF THE RELATIVE ATOMIC PHOTOIONIZATION OXYGEN AND SULPHUR USED IN THE PRESENT
CROSS-SECTIONS PAPER
FOR
dC2S
GO%
csas
fJc2s
CGZZS
m2p
002P
m3p
cJO28
cm.38
13.3/l
8.8/l
1.1/l
0.77/l
2.1/l
J. Electron
Spectrosc.,
1 (1972/73)
145
TABLE
5
SUMMARY OF THE GROSS ATOMIC RELATIVE AND THE CALCULATED Molecule
Orbital
POPULATIONS OF THE MOLECULAR LINE INTENSITIES OF CO2, CS2 AND
Gross atomic populafion
ORBITALS COS Relative
in fen&y
co2
cs2
3% 2% 4% 3% In, 1%
C2.S 0.279 0.0 0.190 0.0 0.0 9.0
c2p 0.0 0.282 0.0 0.168 0.754 0.0
02s 0.639 0.653 0.297 0.272 0.0 0.0
5% 4% 6% 5Bu 2% 2%
c 2s 0.369 0.0 0.166 0.0 0.0 0.0
C 2P 0.0 0.293 0.0 0.226 0.832 0.0
s 3s 0.498 0.663 0.461 0.273 0.0 0.0
0.034 0.360 0.484 1.128 1.996
0.019 0.009 0.013 0.017 0.040 0.004
6a 70 80 9u 276 376
c 2s 0.125 0.199 0.101 0.079 0.0 0.0
C 2P 0.046 0.173 0.052 0.122 0.689 0.083
0 2s 0.743 0.020 0.207 0.012 0.0 0.0
0 2P 0.089 0.003 0.542 0.074 1.196 0.366
s 3s 0.0 0.524 0.090 0.332 0.0 0.0
I/-
cos
0 2P 0.082 0.065 0.513 0.560 1.246 2.000 S 3P 0.115
1.00 0.78 0.58 0.40 0.11 0.13 S3d
1.00 0.54 0.83 0.54 0.42 0.66
0.0
S 3d 0.0
0.066 0.009 0.366 0.107 1.539
0.015 0.0 0.016 0.008 0.012
S 3P
1.00 0.47 0.45 0.39
0.12 0.33
cross-sections previously determined5’ 6. These cross-sections are summarized in Table 4 while in TabIe 5 the ab initio populations and the calculated relative line intensities are given. For CS2 and COS sulphur 3d polarization functions were used in the basis set and we have included the populations of these orbitals in Table 5. Since, however, the S 3d functions are more diffuse than the s and p functions and their populations are small their contributions have been neglected in calculating the intensities. To make a more direct comparison with experiment we have used the relative intensities to calculate theoretical spectra assuming a gaussian shape for each line. The widths and positions of the gaussians were adjusted to agree with experiment but the areas of the gaussians were fixed to the calculated relative intensities. For the outer orbitals we have used the vertical ionization potentials determined from the electron spectrum due to Turner et al.‘l using ultraviolet excitation and for the inner orbitals we have used the present results. These energies are listed in Table 6 compared to the a& inifio orbital energies, where for completeness we have also included the core levels. Figure 6 shows a comparison of the calculated specfra with experiment. Here, we have subtracted a straight line background and correct&d for Ka, , 4 satellites 146
J.
Electron
Specfrosc.,
1 (1972173)
4 I??
2ff” 4% 3au In, 1%
3%
19.4 18.1 17.6 13.8
37.6 & 0.2 41.3 21.6 20.2 20.1 14.7
42.7
562.5 313.0
541.1 & 0.1 297.5 f 0.1
0 IS c 1s s 2PJ11 s 2P’,* 50,
s 2s
c 1s
Ab initio orb. Orbital energy (e V)
Ionization energy (e V)
CSZ
Orbital
CQZ
16.2 14.5 12.9 10.1
26.5 k 0.8
293.1 * 0.1 234.2 + 0.2 169.8 & 0.1 171.0 k 0.1
Ionization energy (e V)
27.8 18.4 15.7 14.3 9.9
31.2
310.3 244.5 181.6
70 8a 9a 2n 371
S 2P’I, S 2Plll 60
0 1s c IS S2s
Ab initioorb. Orbital energy (eV)
CQS
0.1 0.1 0.2 0.1 0.1 0.4 27.4 f 0.4 18.0 16.0 15.5 11.2
540.3 f 295.2 + 235.0 & 170.6 & 171.8 f 35.8 f
Ionization energy (e V)
29.1 21.0 17.0 17.7 11.2
40.8
562.5 311.1 244.3 181.5
Ab initioorb. energy (e V)
SUMMARY OF THE OBSERVED IONIZATION ENERGIES AND THE ab initio ORBITAL ENERGIES OF COz, CSz AND COS
TABLE 6
-___
Figure 6. Comparison of the experimental valence orbital spectra of COz, CSx and COS and the spectra predicted from the intensity model (solid lines). The experimental data have been corrected for Mg KUS, 4 satellites where necessary, and a straight line background has been subtracted. The dotted lines shown in the higher binding energy region of the spectra have been obtained from the predicted spectraby appropiate normalization.
where necessary. Since we have not been able to determine the separation of the innermost c8 and flu orbitals of CO, and CS1 experimentally we have used the predicted separation of these orbitals 1.2 eV and 3.0 eV (see previous discussion) respectively in the calculated spectrum. For COS we have used the ordering given by Turner et a1.21 for the outer three levels, 37c,27cand 90. The ab initio ordering reverses the position of the 9m and 2~ orbitals, which ordering was also found by McLean and Yoshimine3’ in their ab initio calculation very close to the HartreeFock limit. 14s
J. Electron Sgectrosc.,1 (1972/73)
However, the unresolved peak from the 9a and 23~orbitals, which is dominated by the 9a level (see Table 5) is centred 4.9 eV below the 37~peak in agreement with the assignment of Turner et al. 21 . For CS2 we have chosen the widths of the 5a, and 4a, lines to be the same as that of the 70 line of COS, 3.2 eV, which occurs at about the same energy. A point of interest with respect to CS2 is that Tanaka et al.’ ’ have observed a Rydberg series converging to an ionization potential of 19.5 eV and suggested this was the “Zz state. We have found no evidence for an orbital with this binding energy and therefore suggest that this assignment is incorrect. The agreement between the calculated spectra and experiment is generally good for the outer four orbitals. However, the intensities of the innermost orbitals are overpredicted by 3O-4Oo/O.The agreement is not too significant in view of the large amount of shake-up observed in the valence spectra. The intensity of the shake-up lines observed is not negligible. One expects the intensity of the normal line from a given orbital to be correspondingly reduced if ionization from this level gives rise to appreciable shake-up. Thus for example the over-prediction of the intensity of the 27~”line of CS2 may result from a decrease in the intensity of the normal line because of a large amount of shake-up associated with ionization from this orbital. (See the previous discussion.) No corrections have been applied for this effect in applying the intensity model in view of the uncertainty of precisely what levels are involved in the shake-up lines and what their relative contributions are. It may be noted that ionization from the innermost d orbitals may also give rise to appreciable shake-up. However, because of the broad nature of these lines, the time required to acquire adequate statistics would be prohibitive with our present intensity. A large amount of shake-up associated with these levels might explain the disagreement between the calculated and observed intensities. Considering only the outer four orbitals, the results do indicate that one must distinguish between the n: and cr symmetries in calculating the relative intensities. It appears that using the asymptotic values of the /?parameter, +2 for o orbitals and - 1 for x orbitals is generally valid for linear molecules, in this kinetic energy range. Without applying the j? parameter the intensity of the rc orbitals would be overpredieted by a factor of two which is considerably greater than any errors introduced by neglecting shake-up effects. The rest&s obtained here and in previous applications of the intensity model indicate that it is a field of research which should be more fully investigated. The relative photoionization cross-sections used here cannot be considered definitive since they were based, in large part, on experimental valence spectra which were not intended to be used for intensity measurements. Two additional points should also be examined. Firstly, is the use of different /3parameters for different orbital symmetries important only for linear systems or should it be applied to other geometries? Secondly, would it be better to use net atomic populations in calculating intensities instead of gross atomic populations? A recent paper by one of us7 indicates that this might be the case. In the near future improveJ. Electron Spectrosc., 1 (1972/73)
149
ments at this laboratory in both resolution investigations of these phenomena.
and effective intensity
will greatly facilitate
CONCLUSION
The shake-up associated with ionization from the core levels of CO,, CS, and COS is fairly complex but for a given molecule a considerable similarity can be seen between the shake-up spectra of two different core levels. Using the energy levels of the neutral molecuIe, deduced from observed Rydberg series, we have been able to make tentative assignments of a number of the shake-up peaks. The present results show that shake-up processes may also be an important effect in the valence regior when exciting with soft X-rays. The intensity model predicts the observed valence orbital intensities surprisingly well in view of the large amount of shake-up observed in the valence spectra, but for the inner Q orbitals the agreement is not very good. Nonetheless the validity of using different #I parameters for different symmetries has been established for linear molecules.
REFERENCES
2 3 4 5
6 7
8 9
10 11 12 13 14 15 16 17 1X 19 20 150
K. Siegbahn, C!. Nordling, G. Johansson, J. Hedman, P. F. Hed&n, K. Hamrin, U. Gelius, T. Bergmark, L. 0. Werme, R. Manne and Y. Baer, ESCA Appiied to Free Molecules, NorthHolland Publ. Co., Amsterdam, 1969. T. D. Thomas, J. Cfiem. Ph_w., 52 (1970) 1373. R. Prins and T. Novakov, Chem. Phys. Lett., 9 (1971) 593. Ref. 1, pp. 31 and 63. U. Gelius, C. J. Allan, G. Johansson, H. Siegbahn, D. A. Allison and K. Siegbahn, Physica Scripta, 3 (1971) 237. U. Gelius, C. J. Allan, D. A. Allison, H. Siegbahn and K. Siegbahn, Chem. Phys. L&t., 11 (1971) 224. U. Gelius, in D. A. Shirley (editor), Electron Spectroscopy (Proc. Int. Conf. at Asilomar, Cu1iJ, 2971) North-Holland Publ. Co., Amsterdam, 1972, p. 311. U. Gelius, B. Roos and P. Siegbahn, unpublished results. K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hatnrin, J. Hedman, G. Johansson, T. Bergmark, S.-E. Karlsson, I. Lindgren and B. Lindberg, ESCA, Atomic, Mo!eculur, and Solid State Structure Studied by Means of EIectron Spectroscopy, Nova Acta Regiae Sot. Sci. Upsaliensis, Ser. IV, Vol 20, 1967. M. 0. Krause, T. A. Carlson and R. D. Dismukes, Phys. Rev., 170 (196X) 37. 8. Manne and T. Aberg, Chem. Phys. Lett. 7 (1970) 282. SC. Meldner and J. D. Perez, Phys. Rev. A, 4 (1971) 1388. T. &erg, Ann. Acad. Sci. Fem., A6, 308 (1967). T. A. Carlson, C. W. Nestor Jr., T. C. Tucker and F. S. Malik, Phys. Rev., 169 (1968) 27. Ref. 1, p. 32. T. A. Carlson, M. 0. Krause and W. E. Moddeman, J. Phys. (Paris), 32 (1971) C4-76. E. Lindholm, Ark. Fys., 40 (1969) 97, 103, 125. V. D. Meyer and E. N. Lassettre, J. Chem. Phys., 42 (1965) 3436. Y. Tanaka, A. S. Jursa and F. J. LeBlanc, f. Chem. Phys., 32 (1960) 1205. Ref. 1, pp. 119 and 132. J. Electron Spectrosc., 1 (1972173)
21 22 23 24 25 26 27 28 29 30
D. W. Turner, C. Baker, A. D. Baker and C. R. Brundle, Mokculur Photoefectron Spectroscopy, Wiley-Interscience, London, 1970, p. 6 1. J. E. Collin and P. Natalis, Znt. J. Mczss Spectrom. Zon Phys., 1 (1968) 121. Y. Tanaka, A. S. Jursa and F. J. LeBlanc, J. Chem. Phys., 32 (1960) 1199. Y. Tanaka and M. Ogawa, Can. J. Phys., 40 (1962) 879. E. N. Lassettre and J. C. Shiloff, J. Chem. Phys., 43 (1965) 560. J. D. Carette, Can. J. Ph_vs., 45 (1967) 2931. Ref. 1, p. 75. U. Gelius, unpublished results. L. L. Lohr Jr., in D. A. Shirley (editor), Electron Spectroscopy (Proc. Znt. Co& at Asilomar, Cal%), North-Holland Publ. Co., Amsterdam, 1972, p. 245. A. D. McLean and M. Yoshimine, Tables of Linear Molecule Wave Functions, I.B.M. Research Laboratory, San Jo&, Calif., 1967.
f. Electron Spectrosc.,
1 (1972/73)
151
Spectroscopy
and ReIated Phenomena
Elsevier Publishing Company, Amsterdam - Printed in The Netherlands
ESCA
STUDIES
C. J. ALLAN*, K. SIEGBAHN
OF C02,
U. GELIUS,
Institute of Physics,
University
CS2 AND
COS
D. A. ALLISON**, of Uppsala, P.0.
Box
G. JOHANSSON,
H. SIEGBAHN
and
530, S-751 21 Uppsala I (Sweden)
(Received 19 June 1972)
ABSTRACT
The core level electron spectra of COz, CS2 and COS excited by Mg Ka radiation have been studied to identify shake-up satellite lines associated with ionization from these levels. A number of such lines have been seen and possible assignments have been suggested using the excited states of the molecule as a guide. The valence spectra have also been recorded and they too were found to be rich in shake-up structure. The observed variation of the valence line intensities is discussed and compared with predictions made from an intensity model. The validity of distinguishing between 5~ and 0 symmetries in linear molecules in applying the intensity model is confirmed_
INTRODUCTION
During the past few years the use of soft X-rays to excite electron spectra from the valence region of molecules has proven to be very useful’ -‘. Not only is it possible to excite electrons from all orbitals, including those which cannot be reached with ultraviolet sources, but it was found that the intensities of the observed lines were dependent on the atomic character of the orbital. Thus, for example, for second row elements “2s” character is seen roughly ten times as strongly as “2~” character4. Although this property was used qualitatively, little quantitative work was done. Recently, however, Gelius et ale5 -’ have attempted to make quantitative predictions of line intensities based on the atomic parentage of the molecular orbitals obtained from ab i~itio LCAO-SCF calculations, with encouraging results. In a continuation of this study we have recorded the valence orbital spectra of CO,, CS2 and COS to * National Research Council of Canada Postdoctoral Fellow. ** Gillette International Research Postdoctoral Fellow. J. Electron
Spectrosc.,
1 (1972j73)
131
compare with line intensities predicted from the atomic populations from a recent set of ab initio calculations on these molecules*. In addition to studying the spectra from the valence orbitals of these molecules, we have investigated the shake-up spectra associated with ionization from the various atomic core levels for this series. This phenomenon occurs when a valence electron is promoted from a filled orbital to an unfilled orbital as a result of the perturbation caused by the removal of another electron, in this case, a core electron. Experimentally, one observes a sharp line to the lower kinetic energy side of the normal photo-peak, at an energy
E =
hv
- E, - E’
where EB is the ionization energy for the given orbital and E’ is the additional energy needed to excite the valence electron. EXPERIMENTAL
Electron spectra were acquired using a double-focussing magnetic analyzer’ and were excited with Mg Ka X-radiation, 1253.6 eV. All samples were run in the gaseous phase. CO2 (99.99 % pure) was introduced into the sample chamber, directly from the supply cylinder, using appropriate reduction valves for pressure control prior to the spectrometer needle valve. CS2 (> 99.5 % pure) normally a liquid at room temperature, was introduced into the sample chamber via the needle valve. COS (> 97.5 % pure) normally a gas at room temperature, was liquefied, using a trichloroethylene bath, and the vapour fed into the sample chamber through the needle valve. In studying shake-up one must be careful to eliminate or minimize contributions from discrete energy loss peaks caused by electrons being inelastically scattered from neutral molecules. One can correct for such contributions by obtaining, independently, the inelastic scattering spectrum1 O:,or as we have done in the present work, by acquiring core spectra over a range of sample pressures to identify pressure dependent peaks. The shake-up data was then collected at a sample pressure well below that at which the pressure dependence was eliminated. Typically this meant a gas pressure of 1.0-1.5 x lo-’ torr. The counting rates were very low in the region of interest and successive scans were added together to obtain adequate spectra. The vaIence region spectra were acquired in a similar manner, again to minimize inelastic scattering background. THE SHAKE-UP
SPECTRA
ASSOCIATED
WITH
IONIZATION
FROM
THE CORE
LEVELS
As we shall see, the valence spectra of the present series exhibit extra structure which is due to shake-up associated with ionization from the valence orbitals. Therefore it is reasonable to begin with a discussion of shake-up. When a core electron is suddenly removed from a molecule, by photoionization or some other process, the 132
J. Electron
Spectrosc.,
1 (1972/73)
valence electrons experience a sudden change in their potential as a result of which an electron may be promoted from a filled level to an unoccupied orbital or to the continuum. In the former case one observes a line spectrum to the lower kinetic energy side of the normal ESCA peak, the normal peak corresponding to no excitation of a valence electron, and in the latter case one observes a continuum. The first process is called shake-up and the second process is termed shake-off and is analogous to shake-off associated with nuclear p-decay. Manne and Abergil and later Meldner and Perezi have shown that the Hartree-Fock orbital energies are more directly comparable to the experimental mean ionization energy, including shake-up and shake-off contributions, than to the normal ionization energy. The difference between the two experimental energies is then a measure of the reorganization energy. Consequently, it is of interest to determine the shake-up and shake-off spectra associated with a given core level. In the
10 0 t
IO 0
100
k
co2
I
I
I
I
0 Is
I,,
CIS
1
”
1 1 cos
I
I
S2P
10 0 10
0 IO 0
I
L
I
II
L
Ok
Cls
I I
I
20 SHAKE-UP
I
I
10 ENERGY
-. 1
0 I.?‘.‘1
Figure 1. Summw of the shake-up lines observed in the present study. The vertical lines indicate the position of the lines and their heights their intensity relative to the main core line. J. Electron
Spectrosc.,
1 (1972/73)
I33
TABLE
1
SUMMARY
OF THE CORE
LEVEL SHAKE-UP
DATA
FOR COz, CSz AND
COS
Relative energies are estimated to be accurate to +-0.2 eV and relative intensities to *20°A otherwise stated.
c
0 Is Relative intensity
Shake-up energy (eV)
(%I
unless
Is
Shake-up energy CeV)
Relative intensity (%)
co2 0.0 11.5 12.7 13.8 16.1 17.9 19.9 22.3 f
c
100 0.9 1.4 3.6 5.8 3.1 2.x 0.2 * 0.1
0.4
0.0 10.8 12.4 15.0 18.0 20.2 f
0.4&
s 2s
Is
S/aake-ug energy (e V)
Shake-up energy (e V)
Relative intensity (%)
-
100 2.6 3.0 7.6 3.9 0.4
s & Shake-up energy (e V)
Relative intensity ( %)
Relative intensity (%I
cs2 0.0 6.5 9.1 12.2 15.8 17.7 19.7
0
* * k &
0.5 0.4 0.3 0.3
100 7.0 16.4 N 2 5.5 f 1.5 4.0 & 1.5 3.7 & 1.0
c
is
Shake-up energy (eV)
cos 0.0 8.8 13.8 i 0.3 15.5 & 0.3
Rel. int.
0.0 7.3 13.1 + 0.3 15.0 f 0.3
0.0 7.3 13.6 + 0.3 16.4 & 0.3
s 2s
IS Rel. int.
(%I
Shake-up energy CeV)
100 16 4.3 * 9.5
0.0 8.3 12.2 17.8
100 9.2 9.7 3.8 & 1.0
1.0
100 12 ZL 2 ,-u 2 N 2.5
(%I
Shake-up energy feV)
Rd. int.
0.0 9.4 14.8 rtr:0.5
100 -5 -1
(%)
S 2P Shake-up energy (eV)
0.0 9.6 15.3
100 19 7.0 f 2.0 f
1.0 0.5
Rel. int. f%)
100 6.4 f 4.8 f
2.4 1.5
8 Taken from the C 1s spectrum reported by Carlson et al.16.
present experiment we have measured the shake-up spectra associated with each of the core levels in the series. We have not attempted to determine the corresponding shakeoff continua since, with our present intensity, the time required, to accumulate the requisite data would be prohibitive. Furthermore, in determining the shape of the 134
J. Electron Spectrosc., 1 (1972173)
O-
I/\
. -10
-M
0
ci8oos 3oct-
1
cos-
s2p
zmloa,-
O-20 I__L__+._AL RELATIVE
KINETIC
0 ENERGY
Wfl
I
Figure 2. Sample shake-up spectra observed for the core levels of COz, CSZ and COS.
continua, continuum contributions from inelastically scattered electrons and from core electrons excited by the bremsstrahiung continuum present in the X-ray source can be more important than for the corresponding shake-up peaks. The shake-up process can be described in terms of the sudden approximation, where we treat the transition as occurring between two states of the ion13- 15. The transition is then of the monopole type and the probability depends on a matrix element of the form < Y&V- 1)1Yi(N1)) w here Y(N1) is the wave function describing the N- 1 electron system formed by removing an electron from the appropriate core level. Since we are considering a transition between two valence .7. Electron Spectrosc., 1 (1972/73)
135
orbitals
we can assume
that
the other
orbitals
are relatively
unaffected
so that
J.
Eiecdron
Spectrosc.,
1 (1972/73)
co: 9.3 6.5
509
8g:E- 3ng CEi 7.3 6.7_
0
1n9
-3.8 -4.3-
1TtU 3ou
-5.6
cos
-2
4w
0
9.2
- a.3
4Tt 106
709
0
2n9
-2.8
2Tiu
-L.fa
5ol.l
-6.1
6W
-4.3
3ii
-4.8
z
-6.8
8~
Figure 3. Energy level diagram of the COZ, CSZ and COS molecules deduced from observed Rydberg series. For details refer to the text.
C 1s peak at - 15.0 eV may contain contributions
from several shake-up transitions, k9+5as = 14.5 eV, 17r,+2~, = 15.2 eV and 3a,+4a, = 15.5 eV and the two 0 1s shake-up lines at - 13.8 and - 16.0 eV may arise from similar transitions. Finally the line at - 18.0 eV, seen in both the 0 1s and C Is spectra may be a transition between the 4a, and 6a, orbitals, excitation energy, 17.5 eV. Turning to the CS2 data, one can see a close correlation between the S 2p and S 2s data, as would be expected, but not such a close correlation between the carbon and sulphur data. There are several points of interest which should be noted. Firstly, the innermost shake-up line observed in the S 2s and S 2p spectra do not occur at the same relative position but are separated by about 1.4 eV. Secondly, a deconvolution of the first and second S 2p shake-up structure into two components does not result in the same separation as for the normal line. This is to be expected since in addition to the spin-orbit splitting, the states will be split by the different spin configurations of the three unpaired electrons, thus resulting in four lines. Since the relative intensities of these components are not known we have not attempted a deconvolution but in Figure 1 and Table 1 have reported the structures as single lines. Thirdly, the C 1s spectrum shows evidence of considerable structure to the lower kinetic energy side of the first two shake-up lines. See Figure 2. We have assigned this structure to four different contributions but in view of the statistics these assignments can only be considered tentative. This is especially true of the line at - 12.2 eV. In an attempt to assign the shake-up peaks we have used the optical data of Tanaka et al. lg. We have assig ned the orbitals involved in the Rydberg series from the quantum defects, using Lindholm’s work on COZ as a guide. The results of this analysis together with data on the vertical ionization potentials taken from the present work and that of Turner et al.“, summarized in Table 2, have been used to construct J. Electron
Spectrosc.,
1 (1972/73)
137
TABLE
2
RYDBERG
SERIES
OF CSz
The quantum defects, 6, for CSz used to identify the Rydberg orbitals, were obtained from the work Also shown, in parentheses, are of Tanaka et al.lB according to the formula, En = A -R/(n-Q2. the quantum defects for the corresponding Rydberg series of COZ. taken from the work of Lindhohnl’. Transition energies enclosed in parentheses have been determined from the Rydberg formula since the corresponding transitions were not directly observed. Initial orbital
Orbital binding energy (e V)
Rydberg orbital
6
2-j% 5CU
10.1 14.5
6%
16.2
npnc, ?rsue ndog npcu n&E
0.45 0.94 0.58 0.31 0.10
np%l
0.48 (0.56)
Transition energy
Intensity
(0.56) (0.93) (0.31) (0.71) (0.05)
strong strong strong strong apparent emission apparent emission
n=3
4
5
(8.01) 11.10 11.97 (13.35) 14.60
9.03 12.92 13.30 14.94 15.30
9.43 13.63 13.78 15.42 15.62
14.06
15.09
15.52
an energy level diagram of CS2, shown in Figure 3. Using this level diagram we can estimate the following shake-up energies: 2~,+37c, = 10.8 eV, 50,+6m, = 11.7 eV and 6g*+ 70, = 12.8 eV. The second shake-up lines in the S 2s, and S 2p spectra lie 13.1 eV and 13.7 eV below the main lines so we have tentatively assigned these lines to the 6a,+7a, excitation. None of the other shake-up peaks observed in CS2 correlate with the above transition energies. The identification of the levels involved in the second Rydberg series converging to the ionization potential of the 6a, orbital is not straight forward. However, the quantum defect indicates that it is the forbidden TABLE
3
RYDBERG
SERIES
OF COS
The quantum defects, 6, for COS, used to identify the Rydberg orbitals, were obtained from the work of Tanaka et al.19 according to the formula, E,, = A - R/(n - c?)~.Also shown, in parentheses, are the quantum defects for the corresponding Rydberg series of CO, taken from the work of Lindholmrr. Transition energies enclosed in brackets have been determined from the Rydberg formula and the corresponding transitions were not observed directly by Tanaka et al. Initial orbital
Orbital binding energy (e VJ
Rydberg orbita!
6
3n 9a
11.2 16.0
8u
18.0
nPn nsb nP0 nPn ndx nsa
0.48 (0.65) 0.96 (0.90) 0.68 (0.66) 0.49 (0.63) 0.12 (0.1 I) 0.90 (0.90)
138
Transition energy (e V) n-3
4
5
( 9.25) (12.76) 13.29 13.89 14.39 (14.85)
(10.20) (14.50) 14.79 14.94 15.15 16.52
10.60 (15.18) 15.31 15.37 15.47 17.10
J. Electron Spectrosc., 1 (1972/73)
-3~~ excitation energy is 8.5 eV. The most intense series 6a,+n&,. Then the 27rn, shake-up lines observed in the S 2s and S 2p spectra lie 7.4 eV below the main peaks, so it is possible that these lines are associated with this type of transition. Finally, let us consider COS. One can, again, see similarities among the data, particularly between oxygen and sulphur. We have identified the orbitals involved in the Rydberg series observed by Tanaka et al. I9 ‘by comparing the quantum defects of a given series with those for CO I’. See Table 3. Again we have used the vertical ionization potentials taken from the present work and that of Turner et aL2’. The result is the partial energy level diagram of COS shown in Figure 3. From this diagram we have estimated the following shake-up energies: 3x+4~ = 9.2 eV, 2n+4n = 13.5 eV, 9a-+lOa w 13 eV and 8a-tlOa E 15 eV. From Figure 1 we can see that the first of the shake-up lines observed in the 0 Is, C Is, S 2s and S 2p spectra lies about 9 eV below the main line so it is probably associated with a 37c+4rc transition. The peaks observed in the 0 Is, S 2s and S 2p spectra at x - 15 eV are then assigned to an 8a+lOa excitation. The shake-up lines observed in the C 1s and 0 1s spectra at - 12.2 eV and - 13.8 eV, respectively, may then be associated with the 2~+4~, and/or the 90 -+ 100 excitations. To summarize, we have used optical data as a guide in interpreting the shakeup spectra associated with ionization from core levels of CO,, CS2 and COS. Although it is not at all certain that such optical data for the neutral species should correlate with transitions in the highly perturbed system, formed by removing a core electron, we have been able to suggest assignments for a number of the observed shake-up lines. In fact, the correlation between the optical and shake-up data seems to be rather too good to be purely coincidental. Since the core level binding energies of COS have not been previously measured, we did so in the present set of experiments for completeness. We used a mixed CO, plus COS sample and calibrated the C 1s and S 2p levels of COS against the C 1s level of CO 2 (297.5 ev) and the 0 Is level against the 0 1s level of COZ (540.8 eV), as described previously 5. The C Is and S 2p binding energies of CS, are known2’ but in the present work we have determined the S 2s binding energies of this molecule and of COS using the S 2p lines of the respective molecules as calbration standards. These binding energies are tabulated in Table 6. VALENCE
ORBITAL
SPECTRA
Figure 4 shows the valence orbitat spectra obtained from the isoelectronic series CO,, CS, and COS. As is to be expected, the spectra are noticeably similar, particularly in the region associated with the outer orbitals. It is interesting to compare the spectra of CO2 and CS, in this region. In particular, the intensity of the outer lcg line relative to that of the outer cg peak is remarkably different in the two spectra. This difference is a striking demonstration of the different dependence of the photoionization cross-section on the atomic s and p character of the molecular orbitals for J. Electrun Spectrosc., 1 (1972f73)
139
I
LO
I
I
30 BINDING
I
I
20 ENERGY (&‘I
I
I 10
Figure 4. Valence orbital spectra of COz, CSa and COS. The insert shows the higher binding energy region of the COS spectrum, following a straight line background subtraction, as an aid in the discussion.
second and third row elements. Qualitatively, “2s” character is seen roughly ten times as strongly as “2~” character for second row elements whereas for third row elements “3s” and “3~” character have approximately the same cross-section. The electron spectra of COZ, CS2 and COS excited by ultraviolet radiation, have been studied previouslyzls “, and there is a large body of information on the ionization potentials of these molecules based on optical spectroscopylgs 23, 24 and inelastic electron scattering experiments’ 8* 25P26. Th us, the binding energies of the four outer orbitals are well known, but the binding energies of the lower lying orbitals which cannot be reached by ultraviolet radiation have not been previously determined. In the region in which one expects contributions from the two innermost CJorbitals the spectra show considerable structure the interpretation of which is discussed below. We begin with CO,. In the binding energy region of the spectrum between x 30 eV and x40 eV one can observe a broad, complex structure. In this energy region 140
J. EZectrun
Spectrosc.,
1 (1972/73)
one expects to find contributions from only two orbitals, the 3a, and 217, levels, which are essentially the gerade and ungerade combinations of the 0 2s orbitals. The ub initio calculation predicts the 30~ and 20, orbitals to be separated by 1.4 eV. Since the spacing of the ab irzitio orbital energies and the observed ionization potentials agree very well for the outer orbitals (see Table 6) the predicted separation of the 3~, and 217, peaks is probably quite good. The innermost valence peaks observed in ESCA are normally quite wide as a result of life-time broadening. Thus, for example, the widths of the innermost (0 2s) lines of C,H,O and C,O, are 2 4 eV full width at halfmaximum intensity 59 6 . One would therefore expect the contributions from the 3a, and 20, orbitals to give rise to a single unresolved peak and hence the existence of several lines in the high binding energy portion of the CO, spectrum is an anomaly. To assign the peak from the 3a, and 2a, levels we have used the ab initio calculation as a guide. It has been observed in several cases that, in the valence region, the calculated orbital energies are approximately linearly related to the ionization energies, which relation can be used to obtain more accurate estimates of ionization energies from calculation. Such a straight line is shown in Figure 5 for CO, where the ionization energies have been taken from the work of Siegbahn et a1.27 and the orbital energies from a calculation by one of us’8. Since the calculation for CO2 employed the same basis set, one would expect the orbital energies to approximately follow the same straight line and indeed when one plots the points for the outer four orbitals, (whose binding energies are well known), they do follow the curve. See Figure 5.
1 t ‘&
&Gu
c 1
L L
i OBSERVED
IONIZATtON
to
30
ENERGY
(eV1
Figure 5. Comparison of the ab initio orbital energies and measured ionization energies for CO, CO%, CS2 and COS. The straight line was drawn using only the CO data and was used as an aid in identifying the electron lines from the lower lying valence orbitals of COz, CSZ and COS. For CO2 and COS the points corresponding to these orbitals have also been placed on the figure. J. Electron Specfrosc., 1 (1972/73)
141
One can therefore use this straight line to obtain a quite accurate estimate of the 3a, and 20, binding energies and in this way we predict the peaks from these orbitals to lie at 39.7 and 37.5 eV. We have therefore concluded that the peak observed at 37.6 eV binding energy corresponds to these orbitals as indicated in Figure 4. This line appears to contain two components, the intense peak from the 31s~ and 20, orbitals plus a considerably weaker and more narrow peak which is centred at z 38 eV thus resulting in its asymmetric appearance. We have studied the COZ spectrum in considerable detail to try to establish the origin of the additional structure. As a result of these investigations we have been able to establish that the structure is associated with the Mg Ka radiation and not some other X-ray and we have eliminated the possibilities that it results from a sample impurity, from inelastically scattered electrons, or from electrons excited from the walls of the source compartment. Thus it seems conclusive that the anomalous structure is associated with COZ itself. One explanation for these lines is to assign them to shake-up transitions associated with ionization from the valence orbitals. Aberg has shown that the sudden approximation is also valid for systems for which electron correlation is important, such as the valence electrons of a molecule, provided the excitation energy is sufficiently highi3. Since we excite with Mg Kct this condition is fulfilled and we need only consider monopole transitions. As a guide we may use the energy level diagram of Figure 3. Here it seems more probable that shake-up transitions associated with valence ionization will correlate with data for the neutral molecule except for those cases for which we have both excitation and ionization from the same orbital, although this is by no means certain. Disregarding this difficulty one can then assign the structure centred at x 32.5 eV binding energy to a shake-up transition from the 17t, to the 27~”orbital associated with ionization from the 3~” orbital, which gives a peak at 33.3 eV binding energy, a transition from 40, to 5~, also associated with ionization from the 3a, level, which gives a peak at x 32.5 eV binding energy and/or a transition from the 17~~to the 2n, levels associated with ionization from the 4a, orbital, which gives a peak at 31.6 eV. An additional contribution may arise from a transition between the 4a, and 50, levels associated with ionization from the 4a, orbital which would give rise to a peak at w 34 eV. The positions of these peaks have been indicated in Figure 4 by vertical bars. Here, it can be seen that they cover the anomalous structure and may explain its broad appearance. The additional structure at 38 eV binding energy may possibly correspond to a shake-up transition between the 40, and 6a, levels and ionization from the 4~, which would give a peak at 36.9 eV. Although this explanation of the additional structure seems to fit reasonably well, energetically, the relative intensities of the peaks are unusually high for shake-up. Considering next the CS, spectrum, we expect to find two peaks in the higher binding energy portion of the spectrum originating from the 50, and 4a, orbitaIs’. Again the spectrum appears anomalous. We see two rather narrow peaks, S, and S,, lying on what appears to be an extremely broad structure (Fig. 4). We have concluded 142
J. Electron S’ectrosc., 1 (1972173)
that S 1and SZ are not from the 50, and 40, orbitals but are in fact shake-up peaks. Based on previous experience these lines are too narrow to originate from the 50, and 4~, levels. For example, the innermost valence orbital of C4H4S is x 5 eV wide5. To predict the binding energies of the 50, and 4a, orbitals from the calculation we have used the linear relation between the ab initio orbital energies and experimental ionization energies of Figure 5. It is not obvious that the same linear relation should hold for CS2 but when one plots the data for the four outer orbitals of CS2 it follows the CO-CO2 data reasonably well. See Figure 5. Further, the COS data also follows this straight line, as will be discussed later, so the CO-CO2 line would appear to be generally valid for this isoelectronic series. On this basis we predict the ionization energies of the 5a, and 40, orbitals to be 25.4 and 28.4 eV. From Figure 4 one can see a broad peak at 26.5 eV which we then attribute to these two orbitals. Above this peak one can observe an extremely broad structure which may consist of a series of shake-up lines and/or which may be part of a shake-off continuum. As for C02, we have attempted to assign the shake-up peaks, S 1 and S2, using the energy level diagram for the neutral molecule, see Figure 3. As with shake-up from the core levels a given transition will give rise to a spin doublet depending on whether the electron in the excited orbital has its spin parallel or anti-parallel to that of the original unpaired electron. Of course, if the photo-electron and the shake-up electron originate from the same 0 level only a single line will be observed. For ionization from orbital a and excitation from b to c the two-spin combinations may be written schematically. 1. a b c or 2. a b c ttS_
-ITT
If a is a core orbital the exchange energy for 1 will be considerably smaller than for 2 resulting in a relatively widely spaced doublet. On the other hand if a is a valence orbital the exchange energies for 1 and 2 may be comparable resulting in a closely spaced doublet. At the present time we have no estimate of the splitting one might expect which makes the assignment of S, and S2 rather tentative. However if we assume the doublet splitting is small so that S 1 and SZ are associated with different transitions we may reason as follows: S2 lies 10.8 eV below the line from the 27c,orbital which suggests it may originate from a 27~” + 37~”shake-up transition, AE = 10.8 eV (Figure 3), associated with ionization from the 27c, orbital. S, lies 8.5 eV below the 2~” peak. If we assume the 3n, level lies 8.5 eV above the 2n, level, as indicated in Figure 3, then S, would be assigned to a 2np+3xs transition associated with ionization from the 27~~level. The predicted energy for a 5~,+6a, transition is 11.7 eV. Since S, also lies 11.3 eV below the 2ng peak it may also contain a contribution from such a transition associated with ionization from the 2ng orbital. If, on the other hand, we assume that the doublet splitting is of the order of a few electron volts then S 1 and S 2 would be assigned to such a doublet arising from some given shake-up transition. Energetically a 2n,+3~, or 2np+3xB transition J. Electron
Sped-ox.,
1 (1972/73)
143
associated with ionization from the 27rUorbital or a 5a,+6aU transition associated with ionization from the 2n, orbital are most likely. Finally let us consider the COS data. In the higher binding energy portion of the spectrum we expect to see two peaks from the 70 and 8a orbitals but as with CO2 and CS2 we observe a considerable amount of structure. In Figure 4 we have subtracted a straight line background from the data to facilitate the discussion. From the ab initio calculation, using the linear relation between orbital energies and ionization energies (Figure 5) the predicted ionization energies for the 70 and 6a orbitals are 26.7 and 36.4 eV respectively. Consequently we have assigned the peaks at 27.4 and 35.7 eV binding energies to these orbitals as indicated in Figure 4. We have fitted these peaks to gaussians, as indicated by the solid lines and have subtracted these contributions to obtain the remaining spectrum indicated by the dotted lines. We are left with two peaks S 1 and SZ centred at 25.0 and 26.6 eV binding energies and a broad structure centred at x 33 eV binding energy which would appear to consist of two or more Iines. We have used the energy level diagram for the neutral molecule (Figure 3) as a guide in assigning the peaks. If we assume S I and SZ are associated with different shake-up transitions then since SZ lies 9.3 eV below the 27~line it is assigned to a 3n+4n transition, (AE = 9.2 eV), associated with ionization from the 27~ orbital. Although SZ can be assigned S1 does not fit very well with any proposed placement. It lies 12.2 eV below the 37~peak and may correspond to a 27c+4rc transition, (AE = 13.5 eV) and/or a 9o+lOa transition (AE x 13 ev) associated with ionization from the 37~level. Energetically, however, these suggestions are not very satisfactory. It should be noted that we have a rather limited knowledge of excited states in COS with which to assign shake-up peaks so it may well be that S1 corresponds to a transition involving some state which has not been located on the level diagram of Figure 3. If we assume S 1 and S2 are an exchange doublet then they may arise from a 37r+4n transition associated with ionization from the 2~ orbital, or a 2x+4x and/or 90+10a transition associated with ionization from the 3n level. The broad structure at ~33 eV binding energy corresponds very well with a 8a-+ lOa shake-up transition, AE x 15 eV, associated with ionization from both the 8a and the 9o orbitals. THE
INTENSITY
MODEL
In previous papers we have assumed that the observed intensity of the line from the ith molecular orbital was related to the gross atomic populations of that orbital via an expression of the form 1; = 2 cAI P’(AA) Al
where cAL is the photoionization cross-section for a ;1 type atomic orbital on atom A and P’(Ai) is the gross atomic population of symmetry il on atom A for the ith I44
J. Electron
Spectrosc.,
1 (1972/73)
molecular orbital. If we use photoionization cross-sections relative to that of a particular atomic symmetry, in the present case C 2s, the intensity of a given line is then given by
(1) This expression then allows us to predict the relative intensities of the lines in the X-ray induced electron spectrum. In a previous application of this model to C,O, it was found necessary to reduce the predicted intensities of the x orbitals by a factor of two in order to obtain good agreement with experiment 6 - Lohrz9 has recently outlined a method of calculating photoionization cross-sections using orthogonalized plane-waves to describe the free electron. For unpolarized radiation, the cross-section, at an angle perpendicular to the inc:dent radiation, is given by fl=;
[
29
B
1
where
-11/312.
Lohr investigated the energy dependence of j? for ionization from the bg and 7~” orbitals of the linear CZ system over the free electron energy range O-200 eV. The j? value for the bg electron reached an asymptotic value of 2 at about 100 eV while for the 7rUorbital j? was found to decrease monotonically for energies above 50 eV and may be close to - 1 at 1200 eV. If this asymptotic behaviour of /3 is general for all linear molecules then the cross-section for Q orbitals, predicted from eqn. (I), relative to that of z orbitals, is underestimated by a factor of two. This has lead GeIius’ to express the intensity model in the form P’(AA)
(2)
It is in this form which we have used the intensity model taking b = 2 for Q orbitals and/3 = -. 1 for n orbitals. From eqn. (2) we have calculated the relative line intensities for ionization from the various orbitals of COZ, CS2 and COS using the gross atomic populations from the ab initio calculations on these molecules* and using atomic photoionization TABLE
4
SUMMARY CARBON,
OF THE RELATIVE ATOMIC PHOTOIONIZATION OXYGEN AND SULPHUR USED IN THE PRESENT
CROSS-SECTIONS PAPER
FOR
dC2S
GO%
csas
fJc2s
CGZZS
m2p
002P
m3p
cJO28
cm.38
13.3/l
8.8/l
1.1/l
0.77/l
2.1/l
J. Electron
Spectrosc.,
1 (1972/73)
145
TABLE
5
SUMMARY OF THE GROSS ATOMIC RELATIVE AND THE CALCULATED Molecule
Orbital
POPULATIONS OF THE MOLECULAR LINE INTENSITIES OF CO2, CS2 AND
Gross atomic populafion
ORBITALS COS Relative
in fen&y
co2
cs2
3% 2% 4% 3% In, 1%
C2.S 0.279 0.0 0.190 0.0 0.0 9.0
c2p 0.0 0.282 0.0 0.168 0.754 0.0
02s 0.639 0.653 0.297 0.272 0.0 0.0
5% 4% 6% 5Bu 2% 2%
c 2s 0.369 0.0 0.166 0.0 0.0 0.0
C 2P 0.0 0.293 0.0 0.226 0.832 0.0
s 3s 0.498 0.663 0.461 0.273 0.0 0.0
0.034 0.360 0.484 1.128 1.996
0.019 0.009 0.013 0.017 0.040 0.004
6a 70 80 9u 276 376
c 2s 0.125 0.199 0.101 0.079 0.0 0.0
C 2P 0.046 0.173 0.052 0.122 0.689 0.083
0 2s 0.743 0.020 0.207 0.012 0.0 0.0
0 2P 0.089 0.003 0.542 0.074 1.196 0.366
s 3s 0.0 0.524 0.090 0.332 0.0 0.0
I/-
cos
0 2P 0.082 0.065 0.513 0.560 1.246 2.000 S 3P 0.115
1.00 0.78 0.58 0.40 0.11 0.13 S3d
1.00 0.54 0.83 0.54 0.42 0.66
0.0
S 3d 0.0
0.066 0.009 0.366 0.107 1.539
0.015 0.0 0.016 0.008 0.012
S 3P
1.00 0.47 0.45 0.39
0.12 0.33
cross-sections previously determined5’ 6. These cross-sections are summarized in Table 4 while in TabIe 5 the ab initio populations and the calculated relative line intensities are given. For CS2 and COS sulphur 3d polarization functions were used in the basis set and we have included the populations of these orbitals in Table 5. Since, however, the S 3d functions are more diffuse than the s and p functions and their populations are small their contributions have been neglected in calculating the intensities. To make a more direct comparison with experiment we have used the relative intensities to calculate theoretical spectra assuming a gaussian shape for each line. The widths and positions of the gaussians were adjusted to agree with experiment but the areas of the gaussians were fixed to the calculated relative intensities. For the outer orbitals we have used the vertical ionization potentials determined from the electron spectrum due to Turner et al.‘l using ultraviolet excitation and for the inner orbitals we have used the present results. These energies are listed in Table 6 compared to the a& inifio orbital energies, where for completeness we have also included the core levels. Figure 6 shows a comparison of the calculated specfra with experiment. Here, we have subtracted a straight line background and correct&d for Ka, , 4 satellites 146
J.
Electron
Specfrosc.,
1 (1972173)
4 I??
2ff” 4% 3au In, 1%
3%
19.4 18.1 17.6 13.8
37.6 & 0.2 41.3 21.6 20.2 20.1 14.7
42.7
562.5 313.0
541.1 & 0.1 297.5 f 0.1
0 IS c 1s s 2PJ11 s 2P’,* 50,
s 2s
c 1s
Ab initio orb. Orbital energy (e V)
Ionization energy (e V)
CSZ
Orbital
CQZ
16.2 14.5 12.9 10.1
26.5 k 0.8
293.1 * 0.1 234.2 + 0.2 169.8 & 0.1 171.0 k 0.1
Ionization energy (e V)
27.8 18.4 15.7 14.3 9.9
31.2
310.3 244.5 181.6
70 8a 9a 2n 371
S 2P’I, S 2Plll 60
0 1s c IS S2s
Ab initioorb. Orbital energy (eV)
CQS
0.1 0.1 0.2 0.1 0.1 0.4 27.4 f 0.4 18.0 16.0 15.5 11.2
540.3 f 295.2 + 235.0 & 170.6 & 171.8 f 35.8 f
Ionization energy (e V)
29.1 21.0 17.0 17.7 11.2
40.8
562.5 311.1 244.3 181.5
Ab initioorb. energy (e V)
SUMMARY OF THE OBSERVED IONIZATION ENERGIES AND THE ab initio ORBITAL ENERGIES OF COz, CSz AND COS
TABLE 6
-___
Figure 6. Comparison of the experimental valence orbital spectra of COz, CSx and COS and the spectra predicted from the intensity model (solid lines). The experimental data have been corrected for Mg KUS, 4 satellites where necessary, and a straight line background has been subtracted. The dotted lines shown in the higher binding energy region of the spectra have been obtained from the predicted spectraby appropiate normalization.
where necessary. Since we have not been able to determine the separation of the innermost c8 and flu orbitals of CO, and CS1 experimentally we have used the predicted separation of these orbitals 1.2 eV and 3.0 eV (see previous discussion) respectively in the calculated spectrum. For COS we have used the ordering given by Turner et a1.21 for the outer three levels, 37c,27cand 90. The ab initio ordering reverses the position of the 9m and 2~ orbitals, which ordering was also found by McLean and Yoshimine3’ in their ab initio calculation very close to the HartreeFock limit. 14s
J. Electron Sgectrosc.,1 (1972/73)
However, the unresolved peak from the 9a and 23~orbitals, which is dominated by the 9a level (see Table 5) is centred 4.9 eV below the 37~peak in agreement with the assignment of Turner et al. 21 . For CS2 we have chosen the widths of the 5a, and 4a, lines to be the same as that of the 70 line of COS, 3.2 eV, which occurs at about the same energy. A point of interest with respect to CS2 is that Tanaka et al.’ ’ have observed a Rydberg series converging to an ionization potential of 19.5 eV and suggested this was the “Zz state. We have found no evidence for an orbital with this binding energy and therefore suggest that this assignment is incorrect. The agreement between the calculated spectra and experiment is generally good for the outer four orbitals. However, the intensities of the innermost orbitals are overpredicted by 3O-4Oo/O.The agreement is not too significant in view of the large amount of shake-up observed in the valence spectra. The intensity of the shake-up lines observed is not negligible. One expects the intensity of the normal line from a given orbital to be correspondingly reduced if ionization from this level gives rise to appreciable shake-up. Thus for example the over-prediction of the intensity of the 27~”line of CS2 may result from a decrease in the intensity of the normal line because of a large amount of shake-up associated with ionization from this orbital. (See the previous discussion.) No corrections have been applied for this effect in applying the intensity model in view of the uncertainty of precisely what levels are involved in the shake-up lines and what their relative contributions are. It may be noted that ionization from the innermost d orbitals may also give rise to appreciable shake-up. However, because of the broad nature of these lines, the time required to acquire adequate statistics would be prohibitive with our present intensity. A large amount of shake-up associated with these levels might explain the disagreement between the calculated and observed intensities. Considering only the outer four orbitals, the results do indicate that one must distinguish between the n: and cr symmetries in calculating the relative intensities. It appears that using the asymptotic values of the /?parameter, +2 for o orbitals and - 1 for x orbitals is generally valid for linear molecules, in this kinetic energy range. Without applying the j? parameter the intensity of the rc orbitals would be overpredieted by a factor of two which is considerably greater than any errors introduced by neglecting shake-up effects. The rest&s obtained here and in previous applications of the intensity model indicate that it is a field of research which should be more fully investigated. The relative photoionization cross-sections used here cannot be considered definitive since they were based, in large part, on experimental valence spectra which were not intended to be used for intensity measurements. Two additional points should also be examined. Firstly, is the use of different /3parameters for different orbital symmetries important only for linear systems or should it be applied to other geometries? Secondly, would it be better to use net atomic populations in calculating intensities instead of gross atomic populations? A recent paper by one of us7 indicates that this might be the case. In the near future improveJ. Electron Spectrosc., 1 (1972/73)
149
ments at this laboratory in both resolution investigations of these phenomena.
and effective intensity
will greatly facilitate
CONCLUSION
The shake-up associated with ionization from the core levels of CO,, CS, and COS is fairly complex but for a given molecule a considerable similarity can be seen between the shake-up spectra of two different core levels. Using the energy levels of the neutral molecuIe, deduced from observed Rydberg series, we have been able to make tentative assignments of a number of the shake-up peaks. The present results show that shake-up processes may also be an important effect in the valence regior when exciting with soft X-rays. The intensity model predicts the observed valence orbital intensities surprisingly well in view of the large amount of shake-up observed in the valence spectra, but for the inner Q orbitals the agreement is not very good. Nonetheless the validity of using different #I parameters for different symmetries has been established for linear molecules.
REFERENCES
2 3 4 5
6 7
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10 11 12 13 14 15 16 17 1X 19 20 150
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