VOLUME 79, NUMBER 19 P H Y S I C A L R E V I E W L E T T E R S 10 NOVEMBER 1997

Core Level Energy Splitting in the C 1s Photoelectron Spectrum ofC2H2

B. Kempgens,1 H. Köppel,2 A. Kivimäki,1,* M. Neeb,1,† L. S. Cederbaum,2 and A. M. Bradshaw11Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany

2Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg,Im Neuenheimer Feld 253, 69120 Heidelberg, Germany

(Received 23 July 1997)

The partially resolved vibrational fine structure on the C1s photoelectron line of C2H2 clearlydiffers from that of other small hydrocarbon molecules such as CH4, C2H4, and C2H6. This isattributed to photoionization from the two1sg and1su core orbitals of C2H2, which can be describedas the symmetric and antisymmetric linear combinations of the C1s orbitals. According to ouranalysis they are split by105 6 10 meV, a result which is in good agreement with calculation.[S0031-9007(97)04424-4]

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In recent years there has been considerable progremolecularK-shell spectroscopy of small molecules. Cotinuous improvements in soft x-ray monochromator desfor synchrotron radiation sources [1] have led to a muhigher experimental resolution than has been possibleconventional sources [2]. This has yielded, for exampmore information on linewidth and on nuclear motion folowing the creation of aK-shell vacancy. It has recentlbecome possible, for example, to identify the excitatof nontotally symmetric modes and characteristic nonadbatic effects in systems with several equivalent core lev[3–8]. A phenomenon closely linked to the nonadiabaeffects in these systems is the occurrence of several ndegenerate core-hole configurations. Each of themresponds to a hole in a particular symmetry-adapted corbital, and the near degeneracy arises simply fromstrong spatial localization of the constituent atomic orbitof which the symmetry-adapted (molecular) orbitals acomposed. In principle, it should be possible to showperimentally that these states are not quite degenerate.splitting can occur in both ionization and absorption sptra, but for the latter case only one of the states mayobserved because of dipole selection rules. On the ohand, no such selection rules exist for photoelectron sptra where, in principle, the complete manifold of neadegenerate states should be seen. In the present Lettreport the first experimental identification of such a colevel energy splitting, namely, in the C1s photoelectronspectrum ofC2H2.

Ethyne (acetylene)C2H2, which is isoelectronic withCO andN2, is the simplest triply bonded hydrocarbon.has been extensively studied, both theoretically and expmentally, as the prototypical alkyne. Particular attenthas been paid to the valence level photoelectron spec[9]; the core level region has also been investigated bwith laboratory sources [10] as well as at variable enewith synchrotron radiation [11]. The ethyne moleculelinear and belongs to the point groupD`h. The C-C bondlength is1.204 6 0.002 Å [12] in the ground state.

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The photoelectron spectrum ofC2H2 was measured onthe X1B undulator beam line at the National SynchrotroLight Source (NSLS) in Brookhaven [13]. The photoelectron spectra were measured with a stationary, angresolving magic-angle cylindrical mirror analyzer (CMA)the axis of which is collinear with the incoming synchrotron radiation beam. In this geometry the total intensitintegrated over all angles around the axis, is independof the angular distribution of the photoelectrons and tdegree of light polarization. A description of the spetrometer has been published previously [14]. The hiresolution measurements of the C1s main line (over 20spectra at different photon energies) were recorded witconstant CMA pass energy of 10 eV, giving an electron knetic energy resolution of,80 meV. The photon energyresolution ranged from 60 to 80 meV, depending on tslit settings and photon energy. Figure 1 shows the mline C 1s21 photoelectron spectrum ofC2H2 measured at313 eV. At first sight, the spectrum resembles that of tdiatomics CO [15,16] andN2 [17], or of CH4 [18–20],and appears simple enough to be described using a si

FIG. 1. The C1s photoelectron line ofC2H2 measured at aphoton energy of 313 eV.

© 1997 The American Physical Society 3617

VOLUME 79, NUMBER 19 P H Y S I C A L R E V I E W L E T T E R S 10 NOVEMBER 1997

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vibrational progression. On the basis of the usual intepretation of photoelectron spectra based on the FranCondon principle, however, one would expect both thtotally symmetric C-C and C-H stretching modes to appear. In Fig. 1, the well resolved shoulder on the leftsituated about 240 meV from the peak maximum. This approximately the energy of the totally symmetric C-Cstretch in the ground state, 248 meV [21]; it is unlikely tbe due to the symmetric C-H stretch which has an enerof about 400 meV in small hydrocarbons.

For the analysis of the vibrational structure a fit routinwas optimized to take into account up to 3 vibrational progressions with 4 quanta for each. (TheC2H2 moleculepossesses 2 doubly degenerate bending modes,n4 andn5,with fundamental frequencies of 76 and 90 meV [21], respectively. These, in principle, could also play a role in thvibrational fine structure. Modesn4 andn5 have, however,P symmetry and to a first approximation are not expecteto appear in the C1s21 photoelectron spectrum.) To re-duce the number of free parameters in the fit, the C1sphotoelectron spectra of molecules showing distinct vibrtional structure, such as CH4 and CO, were measured undethe same experimental conditions. The photon energy athe electron energy resolution extracted from these specwere used in the fit routine. However, over a large photoenergy range the photoelectron spectrum ofC2H2 couldnot be fitted satisfactorily with 1, 2, or even 3 vibrationaprogressions. The results, contrary to all expectations,tually indicated the presence of another line contributingthe width of the lowest binding energy feature in the photoelectron spectrum, the 2 lines being separated by ab100 meV.

In order to study further the fine structure on the C1sphotoelectron line ofC2H2, it was compared with that ofCH4, C2H4, andC2H6. The 4 molecules were measureunder the same experimental conditions, i.e., identicphoton energy, the same slit settings of the monochromtor, the same pass energy, and almost the same numbecounts. These spectra recorded at 338 eV photon eneare presented in Fig. 2. The spectral features in the C1sspectrum ofC2H2 are broader than those in CH4, C2H4,and C2H6, all of which show a distinct peak about400 meV from the main line due to the excitation of thC-H stretching vibration. Its relative intensity appears tdecrease with the number of hydrogen atoms. TheC2H4

and C2H6 spectra also contain another, less conspicuovibrational feature about 200 meV from the main linwhich arises from the excitation of the C-C stretch. Icontrast to the C-H stretch, its intensity is greater inC2H4

than inC2H6. The spectrum ofC2H2 does not fit in withthe general trends in the series. In particular, its low bining energy flank is not coincident with those of the othe3 molecules, but gives rise to the maximum at a highrelative binding energy. Furthermore, spectra measurat other photon energies show an identical behavior.

The presence of 2 main lines follows from elementartheoretical considerations. There are 2 almost degener

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FIG. 2. Superposition of the C1s photoelectron spectraof C2H2, C2H4, C2H6, and CH4 measured under identicaexperimental conditions (the same photon energy 338 eV,same slit settings of the monochromator, the same pass enfor the analyzer, and almost the same number of counts). Tspectra are shown on a relative binding energy scale scalethe low binding energy flank.

core orbitals1sg and1su, which are associated with thesymmetric and antisymmetric linear combination of thatomic1s carbon orbitals, respectively.

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The core hole states of ethyne thus occur in pairsnearly degenerate states ofg andu symmetry. We havedetermined this energy splitting between the 2 core hstates in the C1s21 C2H2 ion by ab initio calculations,approximating the core hole energies by the negativethe corresponding molecular orbital energies (Koopmatheorem). Two different basis sets have been employedthe calculations, one being of double zeta type, includia set of polarization functions, the other belongingDunning’s improved “correlation consistent” basis sets aincluded up tof functions on carbon and up tod functionson hydrogen (cc-pVTZ basis [22]). The difference ithe core orbital energies obtained is 98 and 101 merespectively.

The experimental energy splitting has been extracfrom an elaborate fit procedure based on the minimiztion of a “reduced”x2 functionsx2

redd, which is similar tothat in the usual least squares fit procedure, but includa variable for the number of free parameters [23]. Thmethod provides results of higher precision by reducithe uncertainty of mutually correlated experimental prameters. For the final analysis of the C1s photoelectronline of C2H2, we selected 4 spectra measured at relativehigh photon energies (337, 347, 360, and 370 eV) andted them simultaneously keeping all the parameters excintensity fixed. Thex2

red was then determined at differ-ent values for the parameter of interest. The results

VOLUME 79, NUMBER 19 P H Y S I C A L R E V I E W L E T T E R S 10 NOVEMBER 1997

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the energy splitting of the main line doublet and lifetimbroadening of the core-ionized state are shown as a ctour plot in Fig. 3; the minimum corresponds to an energsplitting of 105 6 10 meV and a lifetime broadening of90 6 10 meV. The other parameters such as vibrationspacings were determined using the same procedure.first vibrational energy is found to be270 6 12 meV forthe C-C modesn2d and415 6 15 meV for the C-H modesn1d; the intensity of the latter is very low. The highevibrational frequency for the ionic state of 270 meV compared to 248 meV for the neutral ground state indicatthat the equilibrium internuclear distance is shorter in thionic state. The approximation of Nicholls [24] applied tthe resulting Franck-Condon factors gives an equilibriuinternuclear distance ofRe ­ 1.158 s60.004d Å betweenthe 2 carbon atoms which is 0.046 Å shorter than in tneutral ground state.

The photoelectron spectrum ofC2H2 at another photonenergy (338 eV) is presented in Fig. 4(a). The parametderived above were used; only the vibrational branchiratio were fitted. (Note the skewed line shapes which aused to account for the effect of post-collision interactio[25,26]; see, e.g., Refs. [15,17,18]. Another spectrumeasured near threshold at 298 eV and fitted usingsame set of parameters is shown in Fig. 4(b). The fit is nas good, although in this the monochromator bandwidand lifetime broadening were not fixed. As a result of thvarious above-threshold resonances [11,27] at this phoenergy it appears that the excitations from1sg and 1su

initial states are no longer of equal weight [28,29]; i.ethe intensity ratio of the 2 components of the doublis dictated by dipole selection rules. The fit shows ththe intensity of the low kinetic energy component of thdoublet is overestimated.

FIG. 3. Contour plot ofx2red curves with the energy splitting

varied along the abscissa and the lifetime broadening alongordinate. The contours show a clear minimum correspondito an energy splitting of105 6 10 meV and a lifetime broad-ening G of 90 6 10 meV. Four C1s photoelectron spectrameasured at photon energies well above threshold were fitsimultaneously.

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We now briefly compare these findings with othesystems containing near-degenerate core-hole states.reason for the different behavior of the C1s21 states ofethene and ethane, for example, can be found with theof ab initio calculations forC2H4 [7]. Owing to the longerC-C bond (1.337 Å) [12] compared to ethyne, the enersplitting between the 2 core-hole states turns out to bethe range 20–30 meV. For ethane with its even longerC bond (1.536 Å) [12] the splitting will be correspondinglysmaller. Thus, for both ethane and ethene the core enesplitting is well below the lifetime broadening, which is othe order of85 6 15 meV. In the case of the C1s ! pp

excitations in ethene [3,4,6,7] and ethyne [5,30] as wellthe O1s21 ionization in CO2 [8,31], emphasis has been puon the phenomenon of core-hole localization and excitatiof nontotally symmetric vibrational modes. It turns outhat these phenomena play only a minor role in the1s ionization of ethyne. Additionalab initio calculationshave been performed which reveal that the asymmetricH stretching mode as well as both bending modes (n4 andn5) are hardly excited in the C1s21 photoelectron band.

In conclusion, we have shown that the energy splting between nearly degenerate core orbitals cannot

FIG. 4. C 1s photoelectron spectrum ofC2H2 measured at(a) hn ­ 338 eV and (b) 298 eV. Note the high quality of thefit of spectrum (a) considering that, apart from the intensitieall parameters are fixed: energy splitting, lifetime broadeninmonochromator bandwidth, and vibrational spacings.

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VOLUME 79, NUMBER 19 P H Y S I C A L R E V I E W L E T T E R S 10 NOVEMBER 1997

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neglected, if the vibrational fine structure on a core levphotoelectron line is to be properly understood. InC2H2this core energy splitting amounts to105 6 10 meV,which, although smaller than the vibrational energiesthen1 andn2 stretching modes, exceeds the lifetime broaening of the C1s21 states90 6 10 meVd. Similar effects,but usually smaller, are also expected to occur in core ioization spectra of other molecules containing equivaleatoms.

We thank J. Feldhaus for very helpful discussionand gratefully acknowledge financial support from thDeutsche Forschungsgemeinschaft. The NationSynchrotron Light Source is supported by the U.SDepartment of Energy under Contract No. DE-AC0278CH00016.

*Present address: Department of Physical Sciences, Uversity of Oulu, 90570 Oulu, Finland.

†Present address: IFF, Forschungszentrum Jülich Gmb52425 Jülich, Germany.

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