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198 No Sauerwald et alo/Journal of Electron Spectroscopy and Related Phenomena 70 (1995) 197-206

[16-18]. We used both ab initio and semiempiricalwave functions of the model system Ni-N-N. Thesemiempirical method employed was the completeneglect of differential overlap (CNDO) method.For the ab initio calculations the program CADPAC4.2 was used which was installed on the Cray Y -MPof the Forschungszentrum lillich. It is well knownthat CNDO eigenvalues are shifted to higher bind-ing energies by 3 to 5 eV [19]. These values enterdirectly into the Dyson equation resulting in rela-tively high binding energies for the satellite states (2hole 1 particle (2hlp». The satellite states cannotbe shifted to lower binding energies because of asingularity in the real part of the self energy. There-fore, in this work we have used the eigenvaluesobtained by the ab initio calculations. For thesecalculations a basis set published by Ohno andvon Niessen [20] was used which is an extendedWachters set [21] for the nickel atom and a basisset of Salez and VeilIard [22] for the nitrogen. Thiscluster has a linear geometry because each nitrogenmolecule sits perpendicularly to the surface on topof a nickel atom in the case of Ni(llO) [10,23] aswell as Ni(IOO) [24]. Two different sets of param-eters were used for our calculations. The internaldistancesdNi-N = I.82A and dN-N = I.I3Awhichare equivalent to those in the Ni(CO)4-complexand well known from the literature [17] and acluster with dNi-N = I.64A and dN-N = I.IOAwhich are the parameters used by Ohno and vonNiessen [20] were used for comparison. The resultspresented are calculated using the first clusterbecause there was only a small difference in theoverall dependence of the calculated values byvarying the bond length.

The description of the autoionization spectra isas follows. The probability of a population of aspecial state is described as

lab OC L l(wfonel,mlit'lw~eutraUfl,m

(1)

\I!~eutral represents the initial state which is thehighly excited neutral state after the core tobound excitation; \I!fon is the final state after theradiationless decay of the initial state, and el,mrepresents the leaving electron. it is the Hamilto-nian for the described process. The initial state

wave function is approximated as

IW:eutral) ~ 1ct>ls--+1r.) (2)

i.e. a single determinant representation was chosenfor the core to bound excited neutral state. Tech-nically this was done in the equivalent coreapproximation [25]. For this system configurationinteraction effects were omitted because they are ofnegligible importance. This conclusion was drawnfrom the narrow 7r resonance in the near-edge X-ray adsorption fine structure (NEXAFS) spectrum.This simplification is not possible in the descriptionof the final state wave function. In terms of config-uration interaction it has to be described as

Iwfonel,m) ~ IA L L cfJblct>fJ)1/JI,m (3)I,m fJ

where A represents the antisymmetrizer, 1/JI,m arespherical waves centered at the core hole sitecharacterized by a set of angular momentumquantum numbers (I, m), describing the emittedelectron. The index J1, in Eq. (3) enumerates thepossible final state configurations of the ion stateCI eigenvectors obtained by the Green's functioncalculation. Within this approximation the inten-sity is given as

lab = L L C~,bCv,b(Act>fJ1/JI,ml.ifIct>;)I,m fJ,V

X (ct>il.ifIAct>v1/JI,m) (4)

Introducing the abbreviation1m ..

M ~ = (ct>ilJft'IAct>fJ1/JI,m) (5)

it is possible to write

I = ~~c* C MI,m* MI,m ( 6 )ab L.., L.., fJb vb fJ v

I,m fJ,V

The doublet states originating from the autoioni-zation process may be classified according to fourdifferent types under the assumption that theground state of the molecule is I>:::. The firstpossibility is a relaxation where the spectator elec-tron is taking part. The corresponding state is asingle hole state. The matrix elements are a combi-nation of integrals of the type

V1s1/l1r.i = (ct>IS(I)1/JI,m(2) 1~1ct>1r.(I)ct>i(2)) (7)

'12

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200 N. Sauerwald et al./Journal of Electron Spectroscopy and Related Phenomena 70 (1995) 197-206

have been fitted. These curves were fitted to each ofthe spectra at identical positions with the same fullwidth at half maximum and using the samefunctional form. To solve the fitting problem anew routine was programmed to obtain optimalresults for every angle. We developed a two-dimensional simplex algorithm fitting all of thespectra at the same time, obeying the boundaryconditions described before [23]. In this way itwas possible to optimize the localization andshape of the distributions.

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4. Results and discussion

The autoionization spectrum of N2(2 x 1)/Ni(110) and the photoelectron spectrum of cleannickel are shown in Fig. 1. The autoionizationspectrum is dominated by four intense features inaddition to emission from the d band. The firstfeature is located at about 13eV. The second isthe most intense and is located at 21 eV bindingenergy. The third maximum at about 27eV, inenergy directly above the major peak, is followedby the fourth structure which is a broad peakat about 42eV. It is obvious that not each ofthese spectral features represents single states.

"to'

-ap

~~~.E

hv=400.1eV

Fig. 2. Comparison between the calculated and measured auto-ionization spectra. The calculated line spectrum has beenconvoluted with a Lorentzian line of 2 e V FWHM.

Therefore, a more detailed and theoretical modelof the process and the system is needed. Itstheoretical background has been summarized inSection 2 and is discussed elsewhere [32].

The measured autoionization spectrum afterbackground subtraction and the calculated spec-trum are shown in Fig. 2. The latter was obtainedby convoluting the calculated states with Lorentzianfunctions of 2 e V full width at half maximum. Thecalculated spectrum has been shifted by about 7 eV(about 5eV workfunction of the surface [10]) tolower binding energies. The general features of theautoionization spectrum are very well reproduced byour simplified model.

For a first overview it is not necessary to considerthe exact assignments of the individual lines.Rather we consider distinct transition regimes.The first one is situated at energies lower than10eV. It contains the single hole states of the 50--and 17r-orbital. The second regime, at around13 eV, contains states which are formed when ametal orbital (M7r) takes part in the relaxationprocess. Those screened states of the type(. ..M7r-I7r*) are referred to as charge transfer(CT) states below. The most intense feature in the

Substrate','i';\.,'.,.,)",;",

!;;:v, 40: -B1nding Energy[eV]

Fig. I. Series 6r photoelectron spectra and autoionizationspectra:

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202 N. Sauerwa/d et al./Journal of Electron Spectroscopy and Related Phenomena 70 (1995) 197-206

CNDO-GF

-=;::::;1,.1,) 111".,10 20 40

Binding Energy reV]

00

'Sp-2~E00

~:E

Fig. 4. Calculated autoionization spectrum after Nls -+ !T*excitation of the inner nitrogen atom. The line spectrum hasbeen convoluted with a Lorentzian line of 2eV FWHM.

the autoionization spectra of the two chemicallydifferent nitrogen atoms of N2 on Ni(lOO). Theyfitted the NEXAFS resonance with two peaks forthe two chemically different nitrogen atoms andtook autoionization spectra of the outer nitrogenat 399.4eV and one with an increased contributionof the inner nitrogen at 40l.0eV. Their autoioni-zation spectra agree well with ours for theN2/Ni(IIO) system. In addition, it is possibleto model the spectra with our calculations. Aninteresting fact is that the CT states at about13 e V appear in the spectrum of the outer and dis-appear in the spectrum of the inner nitrogen. Bjor-neholm et al. [33] point out that one reason for this

rise to the largest intensities. Since Ni-N-N hastwo chemically inequivalent nitrogen atoms, wehave performed two separate calculations. Thetheoretical results shown in Fig. 2 are a super-position of both spectra. In our experimentalwork, it has not been possible to resolve the twodifferent contributions (see, however, the work bythe Uppsala group [33,34]).

In order to qualitatively interpret the results weremember that an important factor for determiningthe size ot the matrix elements, i.e. the intensity,is the degree of overlap between the 7r* orbital, thevalence, and the Is orbitals. We have plottedthe orbitals of the different nitrogen atoms in theequivalent core approximation in Fig. 3. It is clearfrom the diagram that the electron density at thesite of the excited nitrogen atom depends onthe final orbital. For example it is larger for theinner nitrogen atom in the case of the 17r decayand for the outer atom in the case of thedecay into the Sa and the M7r orbitals. The directconclusion from this finding is that ion states witha high degree of participation of the 17r orbitalhave a higher intensity for excitation of the inneratom, and states with a high degree of participationof the Sa or M7r orbital have a higher intensityfor excitation of the outer nitrogen atom. Further-more, the overall intensity should be slightlyhigher after excitation of the inner than of theouter nitrogen atom. Table 2, which showsthe assignment of the most intense states in thespectra, verifies this conclusion.

Bjorneholm et a1. [33,34] succeeded in resolving

Table 2Assignment of the autoionization spectra

9.312.716.819.9

(+)(+)+

+

00+"oSP

~~~o§Q)

~H

24.226.5

0 20 40Binding Energy [eV]

Fig. 5. Calculated autoionization spectrum after Nls -+ 7r*excitation of the outer nitrogen atom. The line spectrum hasbeen convoluted with a Lorentzian line of 2 eV FWHM.

(+)

a With reference to Ef. b CT, decay with metal orbital takingpart. C +, Angular dependence fits very well; (+), angulardepen-

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204 N. Sauerwald et al.jJournal of Electron Spectroscopy and Related Phenomena 70 (1995) 197-206

The results of the fitting procedure describedin Section 2 are shown for the angle integratedspectrum in Fig. 6. Figure 7 shows the results ofthe angular dependence in the experiment and thecalculations for eight peaks. Peaks 9-12 are onlynecessary to model the high energy range of thespectra and will not be addressed further.

The first experimental peak is located at 9.3 e V.The states in the calculations between 7 and 11 eVare considered. In this region the intensity is domi-nated by the three single hole states 50--1, 171"-1 and40--1. The experimental dependence of angle is notvery significant and is very similar for the pureconfigurations 50--1 and 40--1 while the calculationis dominated by the 171"-1 angular dependence. Wemay say that the intensity of the 171"-1 state is esti-mated to be too high in the calculations. With alower contribution for that state we can obtainthe experimental curve almost exactly because forlow angles the 171"-1 state creates some intensity butthe maximum is deterntined from the 50--1 and40--1 states at about 40 to 50° (Fig. 7(a».

The second distribution is situated at 12.7 e V.Therefore the states from 11 to 15 eV aresummed. This region is governed by the chargetransfer satellites of the 171" and 50- orbitals. Thecharge transfer satellites of the 40- orbital domi-nate the next peak. The angular dependence doesnot fit very well with the experimental values. Thethree most intense features between 13.3 and 15eVhave a maximum at 0° and a minimum at about40°. If only the states situated between 11 and13.3 eV are taken into account, the angular depend-ence is compatible (Fig. 7(b».

The third distribution contains, as mentionedbefore, the CT satellites of the 40- orbital. Thisregion is centered at 17.4eV. The states from thetheoretical spectra which represent this feature arein the energy region from 15 to 18.7eV. As can beseen in Fig. 7(c) the angular dependence of thecalculated and the experimental data agree very well.

The fourth distribution is governed by the mostintense features of the whole spectrum and alsopossesses the largest intensity in the experimentaldata. It is centered at 20 eV and is totally domi-nated by three states. The highest transition rateis given by the (171"-1171"-171"*) 1 state. This is a singlet

coupled state having two holes in two "different"

l7r orbitals. The next intense state is a (17r-27r*)state. Here, in contrast to the previous state, bothholes are located in the same spatiall7r orbital. Thecluster which is used has Coov symmetry makingboth 17r orbitals equivalent. On the surface thesymmetry is reduced, so the two 17r derived orbi-tals are not necessarily equivalent any more; Forthis reason we have differentiated the two 17r states.The third state is of (17r-ISu-I7r*)1 type. The ratioof the calculated transition probabilities of thethree is 2.8 : 2 : 1. The angular dependence of thesefeatures is represented very well by the calculation.The maximum at 0° is totally governed by the(17r-27r*) state while the (17r-117r-17r*)1 is respon-sible for the ascendence after the minimum atabout 4So. The contribution of (l7r-ISu-I7r*)1results in the minimum being less deep (Fig. 7(d».From this information, one has to say that the mostintense feature of the spectrum consists of satelliteswith participation from the 17r orbitals.

The fifth, sixth and seventh distributions areshown in Fig. 7(e). The intensity of these peaks isgiven by (4u-117r-I7r*)1 configurations. The threedistributions have a large overlap so that thedescription of the angular dependence is difficultto obtain. They are placed at 22.S, 24.7 and26.4eV. The angular dependence of the wholeregion fits very well with the angular dependenceof the fifth distribution. However, there is nocorrespondence with the sixth and seventh distri-butions. The angular dependence of the sixthdistribution is weak.

The seventh ,distribution is intense and has astrong angular dependence. This angular depend-ence fits with the (Su-27r*) state but this state hasno significant intensity. As mentioned before, thisregion is modeled very well in comparison with thedata of Bjorneholm et al. [33].

The eighth distribution at 29.21 eV is governedby states of the (4u-117r-I7r*)3 type. The angulardependence fits very well with the calculated depend-ence as shown in Fig. 7(t). The ninth distri-bution is located at 30.6eV. The angulardistribution of this peak is difficult to interpretbecause there is a large overlap with the follow-ing distributions.

In summary, there is qualitative agreementbetween the experimental and calculated angular

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206 No Sauerwald et alojJoumal of Electron Spectroscopy and Related Phenomena 70 (1995) 197-206

resolve the spectra of the two chemically differentnitrogen atoms.

A comparison with a corresponding set of calcu-lations for CO on the same surface indicatesthe similarities expected for these two isoelec-tronic systems, emphasizing the difference betweenthe autoionization process of molecules in thegas phase and autoionization of molecules onmetallic surfaces.

Acknowledgments

The present work was financially supported inpart by the "Bundesministerium fur Forschungund Technologie" under project No. 05 432F ABO. The "Hochstleistungsrechenzentrum derKFA Jiilich" is gratefully acknowledged for provid-ing the necessary computer time on their Cray Y-MP computer. J .K. thanks the Graduiertenkol1eg"Dynamische Prozesse an Festkorperobertlachen"for financial support.

References

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1896.[21] A.I.H. Wachters, J. Chern. Phys., 52 (1970) 1033.[22] A. Veillard and C. Salez, Theor. Chim. Acta, II (1968) 441.[23] N. Sauerwald, Diplomarbeit, Ruhr-Universitat Bochum,

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