Valence electron separation energies and momentum distributions for N2O

Journal of Electron Spectroscopy and Related Phenomena, 27 (1982) l-14 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

VALENCE ELECTRON SEPARATION ENERGIES AND MOMENTUM DISTRIBUTIONS FOR Nz 0

A. MINCHINTON, I. FUSS* and E. WEIGOLD Institute of Atomic Studies, The Flinders University of South Australia, Bedford Park, S.A..5042 (Australia) (Fist received 28 December 1981; in final form 5 March 1982)

ABSTRACT The nitrous oxide (Nz 0) molecule has been studied by binary (e,2e) coincidence spectroscopy at 1200 eV using noncoplanar symmetric kinematics. Separation energy spectra have been determined in the energy range up to 55 eV at azimuthal angles of O’, 7’ and loo. The separation energies of the main transitions belonging to the two inner valence orbitals have been determined as 35 eV (50) and 38.7 eV (40). Momentum distributions measured for all the valence orbit& are compared with LCAO MO calculations. The spectra show considerable satellite structure due to electron correlation effects, and the spectroscopic splitting is compared with pole strengths derived from a many-body two-particle-hole Tamm-Dancoff calculation.

INTRODUCTION

Detailed investigations of the valence structure of atoms and molecules [l-4] have been carried out in recent years in this laboratory and elsewhere [5,6] using binary (e,2e) coincidence spectroscopy. The experiment comprises basically electron-impact ionization with simultaneous determination of the_ energies and momenta of the incident and outgoing electrons [4] . The binding or separation energies of the target electrons are determined by energy conservation. Further, since the incident and outgoing energies are large compared with the separation energy and there is large momentum transfer to the ejected electron, the reaction can be described by the plane wave impulse approximation (PWIA) [4]. Under these conditions the momentum of an electron prior to knockout can be determined simply by momentum conservation principles [4]. The differential cross-section for * Permanent address: Defence Research Centre, Salisbury, South Australia.

0368-2048/82/0000-0000/$02.75

o 1982

Elsevier Scientific Publishing Company

the (e,2e) reaction is related to the momentum distribution of the ejected electrons defined by the square of the Fourier transform of the overlap integral between the wavefunction of the target atom or molecule in its ground state I g> and the residual ion in an eigenstate 1f ). In the independent-particle model (for closed shells) this is simply the momentum distribution of the orbital occupied by the ejected electron in the Hartree-Fock ground state of the target. The (e,2e) technique is thus a sensitive probe of the momentum space wavefunction and provides detailed information on orbital symmetry [4], especially since the momentum space wavefunction is directly related to the configuration space wavefunction by a Fourier transformation. The (e,2e) momentum distributions can thus be used to resolve orbital assignments both for main transitions [7,8] and for correlation satellites [ 1,2] as well as providing a comparison for momentum distributions derived from molecular orbital (MO) wavefunctions. The momentum distribution near the origin in momentum space is determined largely by the value of the configuration space wavefunction in the chemically interesting region far from the nuclei. The (e,2e) method is particularly sensitive to these low-momentum components and has repeatedly shown that energy-optimized MO wavefunctions are in serious error in this region [ 7,9] . Tests of the accuracy of different many-body calculations have also been achieved using (e,2e) spectroscopy [2,4,8,10,11] through the determination of spectroscopic strengths or pole strengths for ion eigenstates of a particular orbital [4]. Such electron correlation effects can be readily observed using the (e,2e) technique, since the relative intensities of satellite structures are independent of energy at high incident energy. Noncoplanar symmetric binary (e,2e) results for nitrous oxide have recently been reported by the Frascati group [12]. Measurements were performed at a total energy of 2600 eV with an instrumental energy resolution of -3.1 eV FWHM and a momentum resolution of > 0.1 ~0’. This broad energy resolution combined with a deconvolution of the separation energy spectra that was based partly on predicted CI states has apparently produced some.‘ erroneous corrections to some of the momentum distributions obtained by these workers. In this report we present binary (e,2e) separation energy spectra and electron momentum distributions for the valence region of nitrous oxide. The results are presented and compared directly with (e,2e) cross-sections calculated using two different MO wavefunctions as well as pole strengths derived from a many-body Green’s function calculation. Where applicable, direct comparison is also made with the work of the Frascati group.

3 EXPERIMENTAL

The experiments were carried out using a noncoplanar symmetric coincidence spectrometer at a total energy of 1200 eV [ll]. The relative azimuthal angles were varied from 0’ to 25” at fixed polar angles of 45’. Variations of incident energy (for separation energy spectra), of angle (for momentum distributions), and acquisition of data were achieved under computer control. The gas sample was obtained commercially and used as supplied. No spurious peaks were observed in the separation energy spectra. The instrumental energy resolution was 1.8 eV FWHM and the momentum resolution < 0.1 ai’ .

RESULTS

AND DISCUSSION

The nitrous oxide molecule, which belongs to the C,, point group, has 22 electrons and is characterized by its two nonequivalent nitrogen atoms. The calculated valence-shell configuration can be written as (40)~ (50)’ (60)~ (1~)~ (70)~ (27r)4 in order of decreasing separation energy. This ordering has been determined by photoelectron spectroscopy [13] and confirmed by both binary [12] and dipole [14] (e,2e) coincidence spectroscopy . The binary (e,2e) separation energy spectra over the energy range 5-55 eV at azimuthal angles 4 of O”, 7’ and 10’ are shown in Fig. 1. At 1200 eV these angles correspond to average electron momenta q of -0.07 ai’ , -0.6 ai’ and -0.8 a;’ respectively. Using the peak positions and widths for the four outer valence orbitals derived from photoelectron spectra [ 13,15 3 we have performed a deconvolution of the spectra using a Gaussian fitting programme which includes the instrumental energy bandwidth of 1.8 eV FWHM. The spectral deconvolutions are shown in Fig. 1 together with the sum of the peaks for the energy range lo-43 eV. The photoelectron spectra indicate that considerable vibrational structure is associated with the four outer valence states, especially the 1~ transition. This splitting is, however, well below the resolution of the present apparatus. The positions and widths of the two inner valence orbitals were determined from the best relative fits of broadened Gaussians to the three sets of data. The separation energy for the main 4u-’ transition is 38.7 +0.5 eV with[a natural width of 3.0 eV, while the separation energy for the main 50-l transition is -35.0 eV with an estimated natural width of 3.0 eV also. These separation energies can be compared with values determined previously from He(I1) photoelectron spectra [16] (37.3 and 33.7 eV), X-ray photoelectron spectra [17] (-39 and -36 eV), and dipole (e,2e) spectroscopy [14 ] (-38.0 and -35.5 eV). Two SCF MO calculations for the nitrous oxide molecule were employed.

Separatron enerw

(eV)

Fii. 1,.1200eV Noncoplanar symmetric separation energy spectra of nitrous oxide at e= O0 (Q N 0.07 ai’ ), Pp= 7O (q 2 0.6 a;’ ) and 4 = 10’ (q N 0.8 co1 ). The dominant single-hole valence orbital transitions are as indicated. The Gaussian deconvolution curves were determined ss discussed in the text. The vertical bars give the standard-deviation statIstical errors.

The first, SB, was the double-zeta basis set calculation of Snyder and Basch [i8f ; the second, G76, used the GAUSS-76 ST04 basis set [ 19 1. A comparison between the resulting one-electron orbital energies and total energies {in au.) is given in Table 1 together with the expe~en~ separation energies. Table 1 also lists the separation energies for the main transitions (and their spectroscopic strengths) obtained by a many-body Green’s

5 TABLE 1 SEPARATION ENERGIES (eV) FOR THE MAIN TRANSITIONS SHELL OF NITROUS OXIDEa

Orbital ($0 )-’

Expt.

SB

G76

GFb

2n 70 17r 60 50

12.9 16.5 18.3 20.1 35.0 (3.0)

13.25 18.94 21.36 22.37 39.93

10.2 16.3 19.4 20.0 37.1

40

38.7 (3.0)

44.85

42.2

12.15 15.23 17.69 18.92 34.75 34.83 36.29 38.46 38.63

E::F(a.u.)

-183.5761

-182.9466

IN THE VALENCE

GF=

[0.90] [0.83] [0.69] [0.84] [0.19] [0.34] [O.lO] to.131 IO.171

12.72 16.38 18.93 20.53

-183.6466

a Natural widths are shown in parentheses. The calculated spectroscopic strengths are given in square brackets, only transitions having spectroscopic strengths of 0.1 or greater being included. b 2ph-TDA ionixation potentials and spectroscopic strengths [ 201. c Green’s function method especially adapted to the outer valence region [ 201.

function calculation by Domcke et al. [20] employing the nondiagonal twoparticle-hole Tamm-Dancoff approximation (Bph-TDA). Also included are these authors’ results obtained using an outer-valence-type (OVT) Green’s function calculation. The separation energies and pole strengths for the satellite peaks obtained from the 2ph-TDA calculation can be found in Table 3 of ref. 20. As shown in Table 1 the MO calculations are not in good overall agreement with the experimental separation energies, especially for those orbitals (lx, 50, 40) predicted by the Green’s function calculation to exhibit strong splitting of their spectroscopic strengths (see ref. 20). In the target HartreeFock approximation the energy of an orbital is given by the weighted centroid of the separation energies for all transitions belonging to the orbital [4] . Significant differences between the calculated and measured separation energies can be indicative of significant splitting of the spectroscopic strengths of the orbital concerned by electron correlation effects (such differences may also be due to an inadequate calculation). That such correlation effects are important in nitrous oxide has been noted previously [12] and is readily apparent in Fig. 1 in the excess structure between 21 and 33 eV and above 40 eV. The separation energies for the main transitions of each of the four outer valence orbitals predicted by the OVT Green’s function calculation show excellent agreement with the experimental values. Agreement with the

corresponding Zph-TDA separation energies (for the transitions having the greatest spectroscopic strengths) is, as expected, not as good, although it is considerably better than obtained with either of the MO calculations. The separation energies predicted by the Bph-TDA calculation for the main 50-l and 40-r transitions (inner valence orbit&) are, however, in excellent agreement with the experimental values of 35.0 and 38.7 eV. Relative (e,2e) cross-sections determined from the peak areas of the energy spectra at each angle are given in Table 2 and are compared with the cross-sections predicted by the PWIA using the SB and G76 MO wavefunctions. The calculated spectroscopic strengths for the main In-‘, 50-r and 40-l transitions [20] are all well below unity. Since the cross-section for a given transition is directly proportional to the spectroscopic factor [4], the intensities of these transitions should be lower than those given by the simple MO calculations which assume spectroscopic factors of unity. The spectroscopic factors for a particular orbital must sum to unity, the partial intensities being assigned to satellite lines due to final-state correlations. Momentum distributions for nitrous oxide have been determined from measurements of the angular correlations at separation energies of 12.8, 15.8, 18.8, 20.3, 34.3 and 40.3eV. These values are all very close to the separation energies for the main transitions. Corrections have been made to account for background contributions from neighboring transitions. Although absolute cross-sections were not determined, relative normalizations have been maintained. The results are shown in Figs. 2 and 3 and are compared there with the (e,2e) cross-sections generated by the SB (full curves) and G76 (dashed curves) MO wavefunctions. The calculated crosssections are normalized to the integral over momentum space of the measured 27r momentum distribution, i.e., to the ground-state transition. The overall shapes and widths of the calculated momentum profiles show significant differences when compared with the measurements, although they are in accordance with the symmetry designations given. The Snyder and Basch wavefunctions [18] give a slightly better fit to the experimental data. Apart from the two inner valence states, the G70 wavefunctions give generally lower cross-sections at low momentum than the SB wavefunctions, and cross-sections that are peaked at higher momenta. The present momentum distributions can be compared with the results of the’ Frascati group, who compared their measurements with cross-sections calculated using the Snyder and Basch wavefunctions but who used different normalizations for each transition to obtain the best fit to each experimental momentum distribution. However, as mentioned earlier, major corrections to their angular correlations based on deconvolutions may have produced inaccurate momentum profiles. This is particularly evident for the 7u, la and 60 momentum profiles, for which there is a large degree of overlap of the three states in the energy spectra given the 3.1 eV energy resolution. The

12.9 16.5 18.3 20.1 35.0 38.7

2a 70 lff 6a 50 4a

0 35 4 23 12 30

(4) (1) (3) (1) (4)

0 9 1 19 8;:

1 26 6:

1: 0 13 1 22 2 33

GFb 12(2) 26 (4) 17 (2) 12(2) 16 (2) 20 (3)

Expt.

G76

Expt. SB

$J= 7O

G=O”

12 24 29 8 14 35

SB 5 16 20 6 16 41

G76 11 20 20 7 9 18

GFb 15(2) 13 (2) 19(3) 9 (1) 7 (1) 11(2)

Expt.

f$ = loo

20 13 28 9 14 19

SB

10 10 23 8 16 21

G76

18 11 19 8 9 10

GFb

a Experimental errors are given in parentheses. The MO (SB and G76) calculated cross-sectionsare normalized to the measured 2z momentum distributionintegratedover momentum space. b SB cross-sectioncorrected by the Green’s function spectroscopic strength [ 201.

e(eV)

Orbital (tie)-’

CALCULATED RELATIVE DIFFERENTIAL CROSS-SECTIONS FOR THE REMOVAL OF A VALENCE ORBITAL ELECTRON AT 1200 eV AND d = O”, 7’ AND 10’ COMPARED WITH OBSERVED RELATIVE INTENSITIES FOR THE TRANsITIoNsAT THE GIVEN SEPARATION ENERGIES ~a

TABLE 2

-a

8

0

0.4

0.6

1.2

Momentum

1.6

(0 u

20

2.4

;2.t

1

Fig. 2. Measured and calculated momentum distributions for the main 2x-‘, 70-r and la-’ transitions in nitrous oxide. The full circles represent results obtained from the angular correlation measurements and open triangles those from the separation energy spectra. The full curve is the calculated cross-section obtained using the MO wavefunctions of Snyder and Basch [ 18 1, and the dashed curve that obtained using the G76 MO wavefunctions [19]. The dashed-dotted curve for the In orbital is the SB curve multiplied by 0.7. Relative normalizations are preserved and the calculated cross-sections have been normalized to the integrated 27~cross-section.

contribution of the l?r orbital, which peaks at q * 0.7 a;‘, has apparently been overestimated in the 70 momentum profile, with a resultant loss of intensity between 0.2 and 0.9 a; 1 . Similarly the contributions of the lowmomentum components from the 70 -r transition to the In momentum profile appear to be underestimated, resulting in excess intensity below -0.8 ai’. The 60 intensity below - 0.6 a;’ is thus probably too low because of corrections for the low-momentum components from the 1~ momentum profile. The present measurements do not agree well with the Frascati data, there being good agreement only for the 2a-’ and 40-l transitions. As stated

9

6cr

Momentum

(au

)

Fig. 3. Experimental and calculated momentum distributions for the main 60-l, 50-l and 40-l transitions in nitrous oxide. The calculated cross-sections for the 40 orbital have been multiplied by 0.5. Details as in Fig. 2.

above, between 0.2 and 0.9 ai’ the Frascati 70 cross-section lies below the present results by an average of 30%, agreement outside this range being quite good. Similarly the Frascati lx cross-section peaks at lower momentum and lies considerably above the present measurements below 0.9 a;’ . The Frascati 60 momentum profile shows similar trends to the 70 profile, in that it lies below the present results below -0.6 ai1 but is similar in shape and magnitude above this value. On a scale relative to the present measurements the 5a momentum profile reported by the Frascati group is in serious disagreement with the present results in the region of the maximum between 0.4 and 1.0 aol . Instead of exhibiting a well-defined peak at q N 0.8 ai’ , the F’rascati data are essentially flat below 1 a,’ , with a relative magnitude of only one-half that of the present results. This may be due either to an overcorrection for the overlap of the 40-l transition in their data, or to poor counting statistics. The present results contain twice as many experimental

10

points over the region of the maximum in the momentum profile. It is interesting to note that there are also some differences between the present cross-sections calculated using the Snyder and Basch wavefunctions [ 181 and those obtained by Fantoni et al. (121. This is particularly so in the case of the 50~‘ , 6a-1 and ‘7~~1 transitions. Table 2 summarizes the relative differential cross-sections of the different transitions in the three energy spectra in some detail. The main inner valence 40-i transition clearly shows the ~po~ce of correlation effects, since at each angle the measured cross-section is approx~a~ly one-half the calculated MO value. The 50 experimental intensity is considerably higher than the calculated value at @ = 0’. The low experimental value at Cp= loo is in disagreement with the measured momentum profile, which suggests a value of N 15 (Fig. 3, to be discussed later), The In -i transition also exhibits lower measured intensities at Cp= 7’ and 10’ when compared with the calculated MO intensities. The higher measured intensity at @ = 0’ may be due in part to the finite momentum resolution of the apparatus, as the In momentum distribution has a sharp minimum at Cp= 0’. Table 2 also gives the cross-sections determined using the Green’s function (GF) spectroscopic factors as corrections to the MO values. The SB inanities at each angle have been m~tip~ed by the summ~ spectroscopic strengths of the satellites within the range of the experimental energy resolution. The summed spectroscopic strength is limited by the values given by Domcke et al. 1201, which include only spectroscopic factors > 0.01. The GF-corrected cross-sections for the 40 orbital are in good agreement with experiment at all angles, However, the GF-corrected values for the 50 orbital are seriously in error at all @. Significant contributions from other transitions are not predicted around the “main” 4u-’ transition at 38.63 eV. In Fig. 1, if the intensity at Q,= 0’ over the entire energy range from -5 to 48 eV is summed to unity, then the relative strength of the summed intensity between 40 and 48 eV is 0.16. Relative to the total intensity at Q = 0’ the respective values at 4 = 7O and r#= 10’ between 40 and 48 eV are 0.13 and 0.06. This means that the density above 40 eV belongs to either the 40 orbital or the 70 orbital, since these are the only transitions which have a maximum in their cross-section at Q,= 0’ and similar ratios between the cross-sections at the three angles. The GF calculation predicts that the broad inner valence band at -31 eV is dominated by 40 components at the higher energies and 50 components at the lower energies. If it is assumed that all the intensity between 40 and 48 eV (the data for Cp= 0’ extend only to 48 eV) is associated purely with the 4u-’ transition, then relative to the total 40 strength of unity the 38.7 eV peak has a strength of 0.52 kO.05 at Cp= O”, 0.48 kO.07 at 9 = 7’, and 0.51+0.07 at $J= 10’. Given the distinct 4u momentum profile or angular correlation (Fig. 3), the results indicate that the 40 state is severely split, with -50% of the spectroscopic strength contained in the main peak at

11

38.7 eV and -50% in the structure above - 40 eV. The spectroscopic factors calculated using the 2ph-TDA [20] for the 4a satellites which contribute to the intensity centered around the “main” 40 peak sum to -0.5. This “GFcorrection” factor which is used in Table 2 also implies that the main 4a-i transition comprises -50% of the total 40 strength, in excellent agreement with the above arguments. According to the GF calculations of Domcke et al. [20], the structure above 40 eV is predominantly 40 in character, with only small contributions (l-4%) from 50, 60 and 70 satellites. The weighted mean separation energy of the data between 36 and 48 eV is 40.6 &l.OeV at @ = O”, 40.7 ?l.OeV at $J = 7’, and 41.0 ?l.OeV at $ = 10’. If all the structure above 40 eV is attributed to the 40 orbital then the orbital separation energy is -41 eV, rather than 38.7 eV as observed for the main transition. This is in better agreement with the orbital energy values of 44.85 and 42.2 eV predicted by the MO calculations. The 50 experimental cross-section determined from the peak area at $I = loo (q = 0.8 ai’ ) is anomalous when compared with the cross-section given by the measured 5u momentum distribution at the same angle (Fig. 3). The momentum profile cross-section compares favorably with the MO calculations whereas the peak area cross-section compares better with the GFcorrected value (Table 2). However, the GF values are seriously in error at both r#~= 7’ and $I = 0’. The measured momentum profile (Fig. 3) indicates that the 50 transition either does not have its spectroscopic strength as severely split as predicted by the 2ph-TDA calculation, or that the split states lie predominantly within the range of the present experimental resolution. Both the SB and G76 calculations predict the correct maximum in the momentum distribution for the 50 transition (Fig. 3), but both underestimate the probability of low-momentum components. Even though the overall agreement with experiment is not good the results indicate that most of the spectroscopic strength is contained in the “main” transition with a width of -3eV, compared with the 63% predicted by the GF calculation. The 2ph-TDA calculation of Domcke et al. [20] predicts some 4u-1 satellite intensity around the main 50-l transition at 34.8 eV. This may explain the excess of low-momentum components in the measured 5u-’ momentum profile. The GF calculation predicts two 50 satellites, at 29.4 and 30.7 eV, -4 eV below the main peak. Evidence for this is seen in the excess intensity centered around 31 eV. This structure is similar to the peak labeled MET II observed by Brion et al. [14] and some structure observed by the Frascati group

WI -

Owing to the finite ing statistics we have action (CI) states to correlation with the

energy resolution of the apparatus and the low countnot attempted to assign definite configurationinterthe structure between 22 and 32 eV. There is good peaks observed in the dipole (e,2e) spectra of Brion

12

et al., but detailed comparison with the binary (e,2e) Frascati data is not possible owing to the very broad energy resolution of the latter measurements. In Fig. 3 the calculated and measured momentum profiles for the 6a-’ transition are compared. The SB calculation is in reasonable agreement with the data whereas the G76 calculation underestimates the intensity up to the second maximum at g N 1 .O ai1 . The additional intensity observed at -0.6 ai’ could be due in part to contributions from the In orbital, the GF calculation predicting at In satellite at 19.2 eV having approximately the extra intensity required. Thus in Table 2 the GF-corrected cross-section shows excellent agreement with experiment at each angle. The GF-corrected cross-section for the 1~ orbital is in excellent agreement with experiment at all angles, the excess experimental intensity at Q N 0 being due to the finite instrumental resolution. The G76 momentum profile (Fig. 2) agrees well with experiment below 0.6 ai’, although both MO calculations overestimate the higher-momentum components and overestimate the position of the maximum by nearly 0.2 a<‘. In Fig. 2 the dashed--dotted curve is the calculated lx SB cross-section multiplied by 0.7, which is the pole strength for the main In transition obtained using the 2ph-TDA [20]. This curve is in excellent agreement with experiment over the complete momentum range, indicating that the In state has its spectroscopic strength split as predicted by the 2ph-T.DA calculation, with -70% of the strength found in the main transition at 18.3 eV. The missing spectroscopic strength of Il symmetry is evident in the structure at -23 eV corresponding to the peak MET I in ref. 14. The 2ph-TDA predicts a In-’ peak at -26 eV. Table 2 and Fig. 2 show that the calculations seriously underestimate the low-momentum cross-section (@ % 0’) for the 7a-’ transition, and slightly underestimate the cross-sections at larger momenta. This suggests that this orbital is more extended in configuration space than indicated by the calculations. Since 1I+!J (q) I2 1s * weighted by the momentum space volume element 4rq2dq in the normalization of the cross-section, a small excess of largemomentum components leads to a correspondingly large reduction in the cross-section in the low-momentum region and vice versa. For the 277 ground-state transition (Fig. 2) both calculations give the position of the maximum in the momentum profile at too high a momentum and underestimate the probability of momentum components below 0.4 ai’ . This means that the probability of electrons being far from the nucleus is underestimated by the MO wavefunctions. The SB calculation overestimates the cross-section around the region of the maximum whereas the G76 calculation significantly underestimates the cross-section up to 1 .O a;’ . Figure 3 also compares the calculated and measured momentum profiles for the 40 transition. There is good agreement in shape at all momenta, although both MO calculations predict somewhat sharper peaking at low

13

momentum than is observed. The calculated momentum distributions have been multiplied by 0.5 to produce reasonable agreement between theory and experiment. This implies that the spectroscopic strength for the 40 orbital is severely split, with the main peak at 38.7 eV having -50% of the total spectroscopic strength. This value is in good agreement with the value of -50% obtained earlier from a consideration of the separation energy spectra and the 40-r pole strength obtained in the 2ph-TDA calculations. Absorption effects in the inner valence region can account for at most a small reduction in the 4a cross-section [4].

CONCLUSIONS

The ionization of the valence electrons of nitrous oxide has been studied using binary (e,2e) spectroscopy and the results compared with SCF MO and 2ph-TDA many-body GF calculations. The results clearly show the breakdown of the MO picture of ionization, especially for the inner valence orbit&, and confirm the assignment of valence band structure predicted by the GF calculation. In particular the results have confirmed the nature of the inner valence band structure. The peak at 35 eV is assigned to the 50-i transition and the peak at 38.7 eV to the 40 ml transition. Higher-energy spectral intensity (above 40 eV) can be assigned largely to the 40 orbital, which shows considerable splitting of its spectroscopic strength, the spectroscopic strength of the main transition at 38.7 eV being -0.5, in good agreement with the calculated 2ph-TDA pole strength. It is difficult to assign the correlation structure between 22 and 32 eV to definite transitions. However, the results indicate that the structure at -23 eV is due to the In transition and the structure at -31 eV to the 50-l transition. The calculated MO momentum profiles are generally not in good agreement with experiment, although better agreement is obtained when the spectroscopic strengths calculated using the GF technique are taken into account. The data indicate that the 2r and 70 orbitals are rather more extended in configuration space than predicted by the rather simple MO calculations.

ACKNOWLEDGEMENTS

Acknowledgement is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, as well as to the Australian Research Grants Committee, for financial support of this work.

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