Bond-distance-dependent decay probability of the N 1s π core-excited state in N 2

Transcription

1 J. Phys. B: At. Mol. Opt. Phys. 33 (2000) Printed in the UK PII: S (00) Bond-distance-dependent decay probability o the N 1s π core-excited state in N 2 M N Piancastelli, R F Fink, R Feiel, M Bässler +, S L Sorensen, C Miron +, H Wang +, I Hjelte, O Björneholm, A Ausmees, S Svensson #, P Sałek, F Kh Gel mukhanov and H Ågren Department o Physics, Uppsala University, Box 530, S Uppsala, Sweden Department o Synchrotron Radiation Research, Institute o Physics, University o Lund, Box 118, S Lund, Sweden Theoretical Chemistry, Teknikringen 30, Royal Institute o Technology, S Stockholm, Sweden Svante.Svensson@ysik.uu.se Received 10 January 2000, in inal orm 15 March 2000 Abstract. We report the observation o the unusually weak decay o the N 1s π coreexcited N 2 molecule to the B 2 u + inal state o N+ 2, which is only detectable in an experiment with high sensitivity. The resonant Auger spectra exhibit an unexpected dependence on the selected vibrational level o the intermediate state. Theoretical calculations show that the intererence between direct and resonant photoemission as well as a strong geometry dependence o the decay probability on the bond distance give rise to the observed eatures. Until now the description o the main eatures in electronic decay spectra o core-to-valence excited states has relied on the participator spectator classiication o the transitions [1]. The designations participator and spectator transitions reer to the role o the orbital that was occupied by the excitation process. In participator transitions, the excited electron does not remain in the initially unoccupied orbital, and the de-excitation produces one-hole states. In spectator transitions, the excited electron remains in the initially unoccupied orbital, and the de-excitation produces two-hole one-particle states. One particularly interesting eature in these spectra is the vibrational structure which is strongly aected by the lietime vibrational intererence (LVI) phenomenon [2 4]. To date the interpretation o the vibrational structures was almost exclusively based on the Franck Condon approximation, in which the excitation and de-excitation transition probabilities are assumed to be independent o the bond distance. In this paper we report an experimental observation o the electron decay o the N 1s π core-excited level in N 2 to the B 2 u + inal state o N+ 2. Several studies o the participator transitions to the X and à valence states exist, but the B state had not yet been Permanent address: Department o Chemical Sciences and Technologies, University Tor Vergata, Rome, Italy. Also at: Theoretical Chemistry, University o Bochum, D Bochum, Germany and Theoretical Chemistry, University o Lund, Box 124, S Lund, Sweden. + Also at: MAX-Lab, University o Lund, S Lund, Sweden. Also at: Institute o Physics, University o Tartu, Riia 142, EE Tartu, Estonia. # Author to whom correspondence should be addressed /00/ $ IOP Publishing Ltd 1819

2 1820 M N Piancastelli et al Figure 1. Let: experimental resonant Auger decay spectra o N 1s π excited N 2 to the B 2 u + inal state o N+ 2 measured at photon energies (bottom to top): , , , , , and ev, corresponding to excitation to the v = 0 6 vibrational components o the core-excited state. For the sake o comparison, the spectra are scaled such that the intensity o the lowest binding energy peak is always the same. Right: N 1s π absorption curve plotted to show the one-to-one connection between the decay spectra and the vibrational peaks in the intermediate state. observed due to the low sensitivity o previous experiments [2, 5]. However, this relatively low decay intensity reveals some especially interesting dynamical phenomena. The spectra show a peculiar vibrational intensity distribution that cannot be explained using the standard LVI ramework [4]. Instead, a model must be used which takes into account the strong inluence o the molecular geometry in determining the decay probability when bond lengths ar rom the Franck Condon region are reached. We will show that such a model implies a breakdown o the participator/spectator picture or this radiative decay. Furthermore, the Franck Condon principle does not hold, since the Auger transition amplitudes depend explicitly on the internuclear distance. With the advent o third-generation synchrotron radiation sources the experimental conditions or observing very weak processes have improved remarkably. The present experiments were perormed at the recently commissioned undulator beam line I 411 [6] at the MAX II storage ring at the Swedish National Synchrotron Radiation Facility in Lund, Sweden. This beam line provides photons in the ev energy range. It is equipped with a modiied high-resolution SX 700 monochromator and with a rotatable hemispherical SES 200 high-resolution electron analyser. The monochromator resolution used in the present

3 Decay probability o the N 1s π core-excited state in N Figure 2. (a) The potential energy curve or the N 1s π excited state, the binding energies and squares o the vibrational waveunctions o this state; (b) the Auger transition matrix elements Q pπ (ull curve) and Q dπ (dotted curve) or the decay to the B 2 u + state; (c) the Auger transition probabilities to the lower 1 2 u + (ull curve) and higher 2 2 u + (broken curve) inal states; and (d) the potential energy curve o these inal states in dependence o the N N bond distance. The vertical line at Å indicates the Franck Condon point. experiment was determined to be 85 mev. The chosen spectrometer resolution was 75 mev, thus yielding a total instrumental resolution o about 110 mev. The main axis o the spectrometer lens was at a 54.7 angle with respect to the plane o polarization. In igure 1 we show electron decay spectra related to the B 2 u + inal state. The spectra were measured at photon energies corresponding to the maxima o the v = 0 to 6 vibrational components o the intermediate state. When the lowest vibrational state o the core-excited N 2 is selected, in the decay spectrum (the bottom curve in igure 1, let-hand panel, marked by v = 0) we note only one group o vibrational peaks. When higher vibrational excitations are selected (decay spectra labelled v = 1 to 6), we note that the vibrational peaks become divided into two groups, one at a lower and one at a higher binding energy. Furthermore, in between the two groups o lines the spectra show less and less structure, eventually becoming totally lat at the excitation energy corresponding to v = 5. The simplest qualitative explanation which accounts or the gross eatures o the spectra relies on the relection principle and the possibility o mapping the intermediate state vibrational waveunctions. In igure 2(a) we show the potential curve or the intermediate state, the probability distribution, and the energies o the vibrational waveunctions. The latter is increased near the classical inner and outer turning points, where, classically speaking, the vibrational kinetic energy tends to zero and the system resides or a longer time. I the potential curve o the inal state is suiciently dierent rom that o the intermediate state, as is the case or the B state (see igure 2(d)), the resonant Auger decay will sample two dierent subregions o the vibrational envelope o the inal state, with a

4 1822 M N Piancastelli et al region in between where the amplitude is lower. This is o course a very simpliied picture but it is important to note that the position o the maxima o the two groups gives direct inormation about the classical turning points, thus a simple procedure to map the potential curve could be devised. O course, a realistic description o the spectra can only be done with the correct ormalism that we describe in the ollowing. Using the dipole length approximation or the photoemission and photoexcitation and Fermi s golden rule or the Auger transition rate, the cross section, σ, or the resonant Auger decay ater photoexcitation with photons that have an energy distribution P (hν) is given by [7, 8] 2π lm ˆ σ(ɛ) [ lm ˆr 0 + H E n n ˆr 0 2 ] lm n ɛ + E E n iɣ P(ɛ + E E 0 ) (1) where ɛ and hν are the electron and photon energies, respectively; Hˆ is the total Hamiltonian o the system including the kinetic energy o the electrons and nuclei and their Coulomb interaction; E is the total energy o the system and ˆr is the dipole operator; E 0, E n and E are the energies o the ground, intermediate and inal vibronic states, respectively; Ɣ is the lietime energy width o the core-excited state. The s are the corresponding total waveunctions where the indices lm designate the channels o the outgoing continuum Auger electron (i.e. lm includes the Auger electron). Note that all waveunctions in equation (1) explicitly include the electronic and vibrational coordinates. The irst matrix element on the right-hand side o the equation is the direct photoemission amplitude, whereas the ollowing raction represents the amplitude o the nth vibrational state. The latter is composed o the Auger decay and photon excitation amplitudes in the numerator. The denominator describes the rapid phase change o the resonant amplitude when the excitation energy is tuned through the energy dierence between the core-excited and ground states. This ormula includes the intererence between the direct photoemission channel and the vibrational (resonant) channels as well as or the intererence between the latter. In order to solve equation (1), it is convenient to apply the Born Oppenheimer approximation. Thus, the total waveunction is assumed to be a product unction o a nuclear waveunction χ(r), which depends only on the nuclear coordinates R, times an electronic waveunction (r, R), which depends urthermore on the electronic coordinates r (r, R) = (r, R)χ(R). (2) Then we obtain σ(ɛ) [ χ A lm χ 0 + lm n χ Q lm χ n χ n D χ 0 ɛ + E E n iɣ 2 ] P(ɛ + E E 0 ) (3) where we continue to designate the energies o the vibronic states with the labels 0, n and. The matrix elements A lm, Q lm and D are given by A lm = lm ˆr 0 (4) Q lm = 2π lm ˆ H E n (5) D = n ˆr 0. (6) We designate them as the direct photoemission, Auger transition and photoexcitation matrix elements, respectively.

5 Decay probability o the N 1s π core-excited state in N Figure 3. Calculated spectra using equation (3) with R-dependent ab initio values or the Auger transition matrix elements (ull curves) and standard LVI theory (dotted curves). In our irst attempt we simulated the observed spectra with the standard LVI method, which is that Q lm and D are assumed to be independent o the bond distance (Franck Condon approximation), and A lm = 0. This means that only the intererence o the resonant vibrational channels is included and the direct photoemission amplitude is assumed to be negligible as compared to that o resonant photoemission. This method has almost exclusively been used to model vibrationally resolved Auger electron spectra [1 5, 9]. The vibrational waveunctions o all involved states were calculated with a time-dependent wavepacket method [9] on Morse potential energy curves. We use parameters o the ground and inal potential curves as given in [10]. The core-excited potential parameters come rom [11]. Calculations o the decay spectra that lead to the N + X 2 and à inal states show that these potentials are suicient to represent the observed spectral proile with respect to both energy and intensity distribution. Such results will be the subject o a orthcoming publication [12]. The result or the B-state is shown as the dotted curves in igure 3. While the splitting o the spectrum into two distinct groups o lines is reproduced, one immediately notices that the intensity o the lower binding energy group o vibrational peaks is underestimated and that the marked lattening in between the two groups o peaks could not be reproduced at all by such calculations.

6 1824 M N Piancastelli et al The next step is to account or direct photoemission and its intererence to the resonant process, as considered recently by Carravetta et al [7]. Such an extension is important in the present case, since the resonant decay is very weak and the direct photoemission rather strong. Under the Franck Condon approximation, inclusion o the contribution rom the direct term as described in [7] improves the agreement between experiment and calculation or the relative intensities o the lower binding energy vibrational peaks. The strength o direct photoemission turns out to be about the same as resonant photoemission or the decay spectrum measured at the photon energy corresponding to v = 0 (bottom curve in igure 1). However, the inclusion o the direct term does not account or the very visible lattening o the intensity distribution between the two groups o lines. The next level o modelling has implied going beyond the Franck Condon approximation. Namely, we have included bond-distance-dependent Auger transition matrix elements (Q lm ). Such a procedure was proposed already in the 1970s by Kaspar et al [13], but since recently [14] it has not been included in a modelling o vibrationally resolved Auger electron spectra. We obtained the Q lm s rom ab initio calculations by describing the inal states with a conigurationinteraction (CI) approach. Then equation (5) becomes Q lm = 2π i where φi lm designates a coniguration rom which the inal-state electronic waveunctions are built up with the Auger electron in the channel lm coupled to it. The C i are the conigurationinteraction coeicients. In the ollowing we will show the behaviour o the matrix elements Q lm as calculated by an approach that is essentially the same as in [14], i.e. the Auger transition matrix elements were obtained within the ramework o the one-centre approximation [15, 16] using a valence CI description or the electronic waveunctions. At that level o theory only two channels with pπ and dπ symmetry contribute to the decay amplitudes. C i φi lm Hˆ E n (7) For the equilibrium bond distance o the N 2 molecule, the energetically lowest coniguration with 2 u + 1 symmetry is the single-hole, (2σu ) coniguration which is ollowed by two conigurations with the occupancy (3σg 1 1πu 11π g 1 ). In the ollowing we will restrict the discussion to the lower and more important o these conigurations in which the π electrons are triplet coupled. These conigurations dominate the two lowest 2 u + states o N+ 2. Note that the (2σu 1 ) and (3σg 1 1πu 11π g 1 ) conigurations are reached according to the deinition given above by a participator or a spectator transition, respectively. I the bond length is increased then the (2σu 1 ) coniguration becomes energetically more and more unavourable, as the 2σ u orbital corresponds in the dissociated N + 2 molecular ion to the antisymmetric linear combination o the 2s orbitals. On the other hand, the energy expectation values o the (3σg 1 1πu 11π g) conigurations are expected to decrease rapidly when the bond length is increased, since the hole orbital 1π u (and partially also the 3σ g orbital) are bonding, whereas the occupied 1π g orbital is antibonding. At a certain bond distance these conigurations have to change their energetic order and also the waveunction o the lower 2 u + inal state (this is the B 2 u + state o N+ 2 ) will change its electronic character, whereas it was dominated by the (2σu 1 ) coniguration at smaller bond distances, it is taken over by the (3σg 1 1πu 11π g 1 ) coniguration at larger bond distances. We ind this so-called avoided crossing point at about r = 1.35 Å. This can be seen rom the CI coeicients o the (2σ 1 and the (3σg 1 1πu 11π g 1 ) conigurations at dierent bond distances which are listed in table 1. In igure 2(b) we show the bond distance dependences o the Auger transition matrix elements and in igure 2(c) the Auger transition probabilities Q lm Q 2 (R) = lm u ) Q lm 2 (8)

7 Decay probability o the N 1s π core-excited state in N Table 1. The CI coeicients o the one-hole (2σu 1 ) and the two-hole one-particle (3σg 1 1πu 11π g 1) coniguration (C 1h and C 2h1p, respectively) or the two lowest 2 u + states o N+ 2 versus the bond distance (R). (1 2 + u ) (2 2 + u ) R(Å) C 1h C 2h1p C 1h C 2h1p a a Equilibrium bond distance o the N 2 X 1 g + ground state. rom the intermediate to the lower 1 2 u + (ull curve) and higher 2 2 u + (broken curve) inal states. Figure 2(d) presents the potential energy curves o these inal states. Clearly, the avoided crossing can also be seen in the behaviour o the Q 2 values and on the inal-state potential energy curves. Figure 2 indicates a simple qualitative interpretation o the spectral appearance: the higher the vibrational levels reached, the longer bond distances are populated. At these geometries the resonant Auger decay probability, which was extremely small at about the equilibrium bond distance o the intermediate state, increases by a actor o 20. This compensates or the decrease in strength o the resonant channel due to the reduced photoabsorption intensity (right-hand panel in igure 1). When the decay happens then at large bond distances it leads to a high point on the B 2 u + potential energy curve and thereore to highly excited vibrational states. Such a high point is not reachable in direct photoemission, where then such subtle eects cannot be observed. A simpliied explanation o the substantial change o the Auger transition probabilities Q 2 in igure 2(c) is that the Q2 1 value or the (2σu ) coniguration is small while that o the (3σg 1 1πu 11π g 1 ) coniguration is large. Then the transition rates change according to the relative weights o the conigurations in the total inal-state waveunction. A more detailed consideration [17] shows that apart rom this, the contribution o the (3σg 1 1πu 11π g 1) conigurations at the equilibrium bond distance o the N 2 molecule leads to destructive intererence or the amplitudes in equation (7). This causes the particularly small Auger transition rate to the B 2 u + inal state at the equilibrium bond distance. The details o the calculations perormed will be the subject o a separate paper [17]. The results o the calculation including the geometry dependence o the amplitudes (equation (3)) are given in igure 3, as a ull curve. The agreement with the experimental spectrum o igure 1 is remarkable. To summarize, we have ound that, based on our experimental observations and theoretical modelling, or the resonant decay o the N 1s π core-excited level in N 2 to the B 2 u + inal state, there is a strong inluence o the molecular geometry leading to a complete breakdown o both the spectator/participator model as well as o the Franck Condon approximation. In particular, the irst electronic state o 2 u + symmetry should be described as a superposition o at least two electronic conigurations, one one-hole and one two-hole one-particle states. Due to an avoided crossing, the CI coeicients depend substantially on the bond distance which, in turn, implies that the de-excitation transition probabilities are not independent o the bond distance as assumed in the Franck Condon approximation.

8 1826 M N Piancastelli et al This paper is an example o the recently available experimental possibility to observe decay processes involving highly excited intermediate states and leading to molecular geometries ar rom the Franck Condon region. Such a new opportunity is not restricted to the present case and will imply more and more the need to improve the modelling widely used to date, to adequately describe new levels o complexity in the dynamics o resonant Auger processes. Acknowledgments The authors want to thank Ing J-O Forsell, as well as the sta o the MAX laboratory or technical assistance during measurements. This work has been supported by the Swedish Research Council or the Natural Sciences (NFR) as well as by the Swedish Council or Technical Development (TFR) and by the Swedish Foundation or Strategic Research (SSF). One o the authors (MNP) wishes to thank the NFR or a Guest Chair in Atomic and Molecular Physics. The Wennergren oundation is acknowledged or inancial support o one o us (RFF). Reerences [1] Eberhardt W 1995 Applications o Synchrotron Radiation ed W Eberhardt (Berlin: Springer) and reerences therein [2] Neeb M, Rubensson J E, Biermann M and Eberhardt W 1994 J. Electron Spectrosc. Relat. Phenom [3] Osborne S J, Ausmees A, Svensson S, Kivimäki A, Sairanen O P, Naves de Brito A, Aksela H and Aksela S 1995 J. Chem. Phys [4] Gel mukhanov F Kh, Mazalov L N and Kondratenko A V 1977 Chem. Phys. Lett [5] Piancastelli M N, Kivimäki A, Kempgens B, Neeb M, Maier K, Hergenhahn U, Rüdel A and Bradshaw A M 1999 J. Electron Spectrosc. Relat. Phenom [6] Bässler M et al 2000 Nucl. Instrum. Methods submitted [7] Carravetta V, Gel mukhanov F Kh, Ågren H, Sundin S, Osborne S J, Naves de Brito A, Björneholm O, Ausmees A and Svensson S 1997 Phys. Rev. A [8] Åberg T 1980 Phys. Scr Åberg T 1992 Phys. Scr. T [9] Sałek P, Gel mukhanov F and Ågren H 1999 Phys. Rev. A [10] Huber K P and Herzberg G 1979 Molecular Spectra and Molecular Structure vol 4 (New York: Van Nostrand) [11] Rubensson J-E, Neeb M, Kempgens B, Köppe H M, Bradshaw A M and Feldhaus J 1995 Phys. Rev. A [12] Feiel R et al to be published [13] Kaspar F, Domcke W and Cederbaum L S 1979 Chem. Phys [14] Piancastelli M N, Neeb M, Kivimäki A, Kempgens B, Köppe H M, Maier K, Bradshaw A M and Fink R F 1997 J. Phys. B: At. Mol. Opt. Phys [15] Fink R 1995 J. Electron Spectrosc. Relat. Phenom [16] Siegbahn H, Asplund L and Kelve P 1975 Chem. Phys. Lett [17] Sałek P et al to be published