Evidence for oscillations in the C70 valence photoionization cross sections

14 November 1997

ELSEVIER

CHEMICAL PHYSICS LETTERS Chemical Physics Letters 279 (1997) 197-202

Evidence for oscillations in the C70 valence photoionization cross sections T. Liebsch, R. Hentges, A. Riidel, J. Viefhaus, U. Becker, R. SchliSgl Fritz-Haber-lnstitut der Max-Planck-Gesellschafi, D-14195 Berlin, Germany

Received 23 June 1997; in final form 10 September 1997

Abstract Photoelectron spectra of molecular C70 were recorded in the photon energy range from 20 to 60 eV to investigate the photoionization cross section behavior of the outermost molecular orbitals. As in the case of C6o, these photolines exhibit photon energy-dependent intensity oscillations, thus corroborating a quantum oscillation model based on the fullerene's unique shape. The photoelectron angular distribution parameter/3 measured during the same experiment shows, similarly to C6o, no pronounced oscillations, rather rising continuously as the photon energy is increased, a fullerene-unspecific behavior also known from other carbon-containing molecules, such as CO. © 1997 Elsevier Science B.V.

1. Introduction Since the exploration of the various forms of fullerenes, which started a decade ago, most of the work on fullerenes has been carried out in the condensed phase [1], whereas only very few gas-phase experiments have been performed to date. Photoelectron spectroscopy (PES) studies revealed a surprising correspondence of the electronic structure of the two phases. At first glance, the photoelectron spectra and consequently the electronic energy levels match approximately [2-5] because band dispersion, vibronic structure and possible vibronic coupling are of the same order of magnitude, causing a line broadening thus making it difficult to reveal the small band dispersion in the solid phase because molecules in the crystal behave in many respects like free molecules. The photoionization cross section behavior of these two phases also appears to be very similar. Previous PES results [5-8] gave evidence

for photon energy-dependent oscillations in the partial photoionization cross sections of the two (C-2p derived) highest occupied molecular orbitals HOMO and HOMO-I of C60. Different interpretations were suggested to explain this unexpected phenomenon. The first interpretation of the gas-phase results was proposed only recently [9]. Its quintessence is the following. When the molecule is photoionized, the photoelectron may leave the molecule directly or may be emitted through the inner part of the molecule being affected by the sudden change of the potential at the spherical shell. This diffraction effect may be visualized by the formation of spherical 'standing waves' within the inner part of the molecule. The amplitude of this photoelectron standing wave at the spherical shell r = R changes periodically with its 'wave number' and thus with photon energy. The C-2p derived molecular orbitals are assumed to be basically delocalized within the fullerene shell [10,11]. Since the partial photoionization cross sec-

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tion is proportional to the square of the photoionization matrix element between this initial state and the oscillating final state, it also oscillates. This situation corresponds in a scattering picture to the boundary conditions for a standing wave (or a quasi-stationary state) inside a spherical three-dimensional box potential - - a textbook example of quantum mechanics. The solutions of this eigenvalue problem are l-dependent spherical Bessel functions [12], forming quasi-'standing waves' inside the molecule. The zeros and the maxima of its squares at the sphere of the initial charge distribution r = R determine the positions of the minima and the maxima of the partial cross sections, respectively. Therefore, the alternating maxima and minima depend on the different angular momenta / of these orbitals [9], rather than on their different symmetry. The positions of the cross section maxima and minima depend only very weakly on the actual shape of the potential step perceived by the outgoing photoelectron because they depend, in our approximation, on the kinetic energy of the photoelectron at the spherical shell. Further systematic measurements on other fullerenes, especially C70, were suggested to validate this model. Such experimental data are presented in this work, and similar, but less pronounced, oscillations are found. The condition which determines the minima positions of the partial cross section, i.e. the vanishing overlap between the initially spherical distributed valence electrons and the outgoing photoelectron wave, is not fulfilled exactly, thereby reducing the observed oscillations compared to C60.

2. Experimental

different angles (0 ° and 55 °) with respect to the polarization vector of the synchrotron light, after calibrating the electron kinetic energy dependent efficiency ratio of the two TOF detectors. Further details are given elsewhere [5]. The branching ratios of the photolines of interest were normalized to the total area of all lines. However, there are two processes resulting in doubly charged ions: valence Auger decay [16] and shake-off (simultaneous double photoionization) [17], the latter giving rise to a continuous energy distribution of the photoelectrons because the excess energy is shared by two photoelectrons. These two contributions, which cannot be separated at this stage, are accounted for by integrating the area of the binding energy spectra from the origin to a so-called cut-off energy, which is the arithmetic mean of the photon energy and the double ionization threshold (18.8 eV) [ 18].

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The experiment was carried out at the monochromator TGM5 of the undulator beamline U I of the synchrotron radiation facility in Berlin (BESSY) under single bunch condition, using the time-of-flight (TOF) technique [13,14] for the partial cross section measurements. C70 molecules were evaporated by a resistively heated oven running at about 600°C. A drawing of this oven is depicted in Fig. 8 of a recent review article on metal atomic beam sources [15]. The angular distribution anisotropy parameter /3 of the photoelectron peaks can be derived from the intensity ratio of the photoelectron line taken at

0 c/3_

10

20

30

40

Binding energy (eV) Fig. 1. Evolution of the photoelectron spectra of gaseous of C 70 in the photon energy range from 20 to 50 eV. The intensities of the two outermost molecular orbitals ' H O M O ' and ' H O M O - I ' are plotted as light and dark grey areas, respectively.

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3. Results

and

tions of the C-2s and C-2p orbitals of atomic carbon [241. A sequence of gas-phase photoelectron spectra is displayed in Fig. 1, showing the intensity variations of the two outermost photolines. Their branching ratios are plotted in Fig. 2 along with their relative intensities. The ratio of the partial cross section of a particular photoelectron line with respect to the total cross section is called branching ratio, as defined in the previous section. This quantity is independent from photon flux and target density variations. This comparison suggests the mechanism of the cross section modulations to be the same. Higher fullerenes, e.g. C84 [25], C78, C82, C86, C90 and C 9 6

discussion

The photoelectron spectra of C70 differ significantly from these of C60 [4,19-21] because the lower molecular symmetry of the C70 molecule [22] results in lower degeneracies of the energy levels and therefore more photoelectron lines [20]. The PES intensities of the first two series of photolines denoted tentatively as ' H O M O ' and ' H O M O - I ' [4,23] appear to oscillate similarly as in the case of C60. These levels are assigned as C-2p derived molecular orbitals [4,19]. Their PES branching ratios decrease strongly as the photon energy is increased. This trend corresponds to the well-known cross section func-

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Fig. 2. Comparison of the relative cross sections of gaseous C70 (circles, squares [20], triangles [4]) with two series of semi-empirical curves based on a simple three-dimensional square box potential [9] for the inner part of the molecule (solid and dotted lines). The dotted line represents a fit to the experimental data assuming an equal radius of R = 0.354 nm for C6o as well as for C70 but a different potential of Um = 20.5 eV, whereas the solid line is based on an effective radius of Rcff = 0.365 nm for C70 but joint potential depths of 17.5 eV for both molecules. The shaded area represents the corresponding data of C60 [5] adjusted by a scaling factor and an energy shift.

200

7". Liebsch et al. / Chemical Physics Letters 279 (1997) 197-202

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Fig. 3. Angular distribution anisotropy parameters /3 of the two outermost photolines, 'HOMO' (solid circles) and 'HOMO-I" (open circles) of C70 along with the corresponding data of C60 (shaded areas).

[26-28], showed evidence for similar photoemission intensity variations in the solid state. These results point to a fullerene-specific phenomenon, although quantitative calculations for these molecules are not yet available. The photoelectron angular distributions were measured using the double time-of-flight method to record photoelectron spectra at two different angles simultaneously. Fig. 3 displays the angular distribution anisotropy parameter /3 of the photoelectrons emitted from the two outermost molecular orbitals of C70. A comparison with the corresponding data of C6o [5] shows that the /3 behavior of the two fullerenes is basically the same. The angular anisotropy parameter increases continuously without any evidence for oscillations. The only difference with respect to C6o is a small energy shift of approximately 1 eV. The behavior is basically equivalent to photon energy-dependent /3 variations of other carbon-containing molecules, such as CO [29]. This is in accord with the interpretation of the cross section

oscillations as a quantum state effect of a three-dimensional box potential with no significant effect on the phase of the outgoing photoelectron wave. This insensitivity of the cross section oscillations to the phase shift should result in first approximation in unaffected angular distributions concerning their photon energy dependence. In the last part of this section, we will try to give a more quantitative comparison between our measurements and the model of Xu et al. [9]. For this purpose, the branching ratios of the C7o ' H O M O ' and ' H O M O - I ' were determined semi-empirically according to their model A [9]. As in the case of C60, the final states are given by the /-dependent spherical Bessel functions j4(kr) and j3 (kr) [ 12], respectively. Note that the (effective) angular momenta 1 of the corresponding molecular orbitals are not known so far. The electron's momentum is denoted as hk. The branching ratio is proportional to the square of the dipole matrix element, which is very easily calculated to be the spherical Bessel function taken at r = R, since the initial state may, in the roughest approximation, assumed to be proportional to 6 ( r R). The magnitude of the molecule's radius is R = 0.354 rim. One might object that this initial state is not an eigenstate of the Schr~idinger equation, since the second derivative of the initial wave function with respect to the radius r cannot be calculated. However, the spherical harmonics Yl,m(O,(~) solve the SchrSdinger equation, as shown by the free electron model [30,31], yielding a crude approximation for the energy levels of the 2p-derived molecular orbitals. In a more realistic approximation, the initial state is known to be antisymmetric and hence the radial derivative representing the dipole operator in the velocity form is a symmetric function with respect to r = R. To evaluate the spherical Bessel functions j~(kR), we only need to know the potential Um perceived by the photoelectron in the inner part of the molecule r < R. Assuming an equal radius of R = 0.354 nm for C60 and C70, the present experimental data are best described by a potential Um = 20.5 eV, which is 3.0 eV larger than the corresponding potential of C60. In this approach, the elliptic shape of the C70 molecule is not specifically accounted for. To do this, we calculated an effective radius of a freely rotating molecule of Rcff = 0.365 nm. The two small axes of the ellipsoid are the C 7 0

T. Liebsch et al. / Chemical Physics Letters 279 (1997) 197-202

same as in C6o, the larger one amounts to a = 0.399 nm [32]. The present experimental data are, in this case, consistent with an equal potential of Um = 17.5 eV [9] for both C6o and C70, but further measurements in smaller photon energy steps are necessary to decide which approach is the better one. In order to account for the declining partial cross section, the square of the matrix element was multiplied by a linear function of photon energy h ~o. Their coefficients were obtained from a least-squares fit. The result is depicted in Fig. 2. The above reasoning remains valid, even if the finite thickness of the shell is considered [9]. The results are equivalent to the more elaborate model B [9], with two different potentials inside the shell and in the inner part of the molecule as long as the kinetic energy gained by the electron by travelling through the molecule is the same for both potentials. Such a more realistic potential may be obtained by e.g. the jellium model. However, independent of the particular potential the wave function of a 2p-derived molecular orbital is always antisymmetric with respect to the fullerene shell ( r = R) and hence its radial derivative is symmetric, since a 2p atomic orbital is antisymmetric with respect to the nucleus. This seems to be in contrast to our earlier assumption of the delocalized nature of the valence electrons, but e.g. in aromatic molecules delocalization of 2p-derived molecular orbitals is consistent with the nodal structure of an antisymmetric wave function [33]. Under these conditions, the zeros and the maxima of the photoelectron wave function at the spherical shell determine the positions of the minima and the maxima of the partial cross section, respectively. Due to the random orientation of the target molecules, the periodicity of this oscillation represents the effective electron density distribution within a spherical shell independent of its complete delocalization. In contrast, experiments on oriented or fixed in space molecules would enable further studies of localized electron density distributions.

4. Conclusion We have measured partial cross sections and angular distribution anisotropy parameters /3 of the two outermost valence orbitals of C70. The results

201

are very similar to those of C60, in particular with respect to the periodicity of the partial cross section oscillations, indicating that this behavior is a fullerene-specific phenomenon. This interpretation is corroborated by the angular distribution behavior, which is largely unaffected by the cross section oscillations in both C60 and C70.

Acknowledgements This work was sponsored by the Bundesministerium ftir Bildung, Wissenschaft, Forschung und Technologie (BMBF) and by the EU.

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