Photoelectron Imaging Spectroscopy of the Small Sodium Cluster

Article pubs.acs.org/JPCA

Photoelectron Imaging Spectroscopy of the Small Sodium Cluster Anions Na3−, Na5−, and Na7− Christof Bartels,*,† Christian Hock,‡ Raphael Kuhnen,‡ and Bernd v. Issendorff‡ †

Institut für Physikalische Chemie, Universität Göttingen, 37077 Göttingen, Germany Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany

‡

ABSTRACT: We present a photoelectron imaging study of the small sodium cluster anions Na3−, Na5−, and Na7− at photon energies in the visible and near UV range (hv = 1.64−4.28 eV). The resulting angular distributions are remarkably diverse and exhibit a strong dependence on photon energy; only for hv > 3.5 eV do they evolve into more uniform distributions peaked in the direction of the laser polarization. We show that different energy dependencies of the distributions are related to different angular-momentum characters of the bound states. The jellium s-like character of the lowest single-particle states results in photoelectron emission parallel to the laser polarization at all photon energies, whereas the p-like character of the higher states leads to essentially isotropic distributions at threshold and a strong variation with photon energy. Close to the detachment threshold, the asymptotic angular distributions are attributed to the approximate validity of Wigner’s law, which states that the spectrum is dominated by the partial wave with the smallest angular momentum. For the planar cluster Na5−, we observe characteristically different behavior for electrons detached from the two in-plane p-like states, and we show how this correlates with the molecular symmetry. Our results indicate that a simple jellium-like description of the molecular orbitals is appropriate for the three-dimensional cluster Na7−, despite the energetic splitting of the normally triply degenerate 1p level. to model the experimental results.24−30 We contribute a study on small sodium clusters. Bulk sodium is known to be the best representative of a free-electron metal; to a good approximation, its valence electrons can be treated as a completely delocalized electron gas.31 The experimental observation of electron shells32,33 and supershells34 suggests that this concept remains valid for sodium nanoparticles and clusters, down to sizes with as few as eight atoms.35,36 For even smaller clusters, we expect more molecular behavior, and it is an interesting question how this will influence the PADs.

1. INTRODUCTION Photoelectron spectroscopy of gas-phase atoms and molecules is an invaluable tool for studying the electronic structure of small systems, and it has been widely used in cluster science.1−3 Its numerous important applications include, for example, the study of the evolution of metallicity with increasing cluster size,4,5 the investigation of solvation effects6,7 and sizedependent reactivity,8 or the determination of the geometries of many small and medium-sized clusters.9,10 The invention of velocity map photoelectron imaging11,12 made it possible to simultaneously measure the energy and angular distributions of the photodetached electrons. This technique can give new insight into the electronic structure of the investigated molecule because the angular distributions are related to the bound-state wave functions via the quantummechanical transition matrix elements.13 For symmetry reasons, the photoelectron angular distribution (PAD) of a nonoriented sample of molecules is restricted to the simple form 1 + β P2(cos θ), where P2 is the second-order Legendre polynomial, and θ is the angle between the light polarization and the direction of the emitted electron.14 The PADs are described by the single anisotropy parameter β, which assumes values in the range −1 to +2. The values β = −1, 0, and +2 correspond to perpendicular, isotropic, and parallel photoelectron emission proportional to sin2 θ, 1, and cos2 θ, respectively. During the last years, this technique has been used extensively for research on small molecules 15−17 and clusters,18−23 which also triggered significant theoretical efforts © 2014 American Chemical Society

2. EXPERIMENT The clusters are produced in a gas aggregation source by evaporating sodium from a crucible into a liquid-nitrogencooled helium atmosphere at a pressure of approximately 1 mbar and charged by a pulsed electric discharge. After exiting the aggregation tube, the cluster ions are transferred into a radio frequency 12-pole ion trap, which is cooled to 6 K by a helium refrigerator, and thermalized by collisions with helium buffer gas. The clusters are then accelerated into a doublereflectron time-of-flight mass spectrometer, and mass-selected by a multiwire mass gate positioned at the time-focusing point of the first reflector. An ion mirror is used to direct the ions Special Issue: A. W. Castleman, Jr. Festschrift Received: January 30, 2014 Revised: March 11, 2014 Published: March 11, 2014 8270

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distributions, and electrons detached from σu have isotropic to parallel emission distributions. For Na5−, detachment from 1a1 is parallel, and detachment from b1 and 2a1 is isotropic to parallel; for the smallest energies, weakly perpendicular emission is observed for electrons detached from b1. For Na7−, detachment from a1′ always results in parallel electron emission, whereas detachment from 1e1′, 2e1′, and a2″ results in approximately isotropic emission close to threshold, and parallel emission at higher energies. Note that, for all three cluster sizes, the electrons detached from the level with the highest binding energy show similar behavior, that is, parallel distributions that change only little with photon energy. In contrast, electrons detached from other levels exhibit more variation.

either into an Even-cup detector37 or into the imaging spectrometer, where the cluster beam is crossed at right angles with a laser beam for photodetachment. The laser-cluster interaction volume is approximately 2 × 2 × 2 mm3. An excimer-laser pumped dye laser provides laser light with wavelengths in the range λ = 290−755 nm, corresponding to photon energies of hv = 1.64−4.28 eV. Very low laser intensities on the order of 105 W/cm2 or less are used to ensure that two-photon absorption is completely negligible. The imaging spectrometer is oriented collinearly with the cluster beam. It uses an optimized velocity map imaging design with three acceleration regions. The electrons are amplified by a multichannel plate and converted to visible light by a phosphor screen, which is monitored by a high-sensitivity CCD camera from outside the vacuum chamber. For noise reduction, enhanced homogeneity and higher resolution, we employ an event counting algorithm.38 The velocity resolution of our spectrometer is v/Δv ≈ 120. For a typical spectrum, approximately 300 000 electron impacts are accumulated. The initial 3-dimensional photoelectron distribution is reconstructed from the projection using a modified version of the pbasex algorithm (with Legendre polynomials of order 0 and 2),39,40 and the β parameters for the individual transitions are extracted by fitting an appropriate number of Gaussian peaks to the reconstructed spectrum.

4. ANALYSIS AND DISCUSSION To identify the peaks in the experimental spectra and to obtain a qualitative characterization of the valence-electron orbitals, we performed density functional theory (DFT) calculations.41 The exchange and correlation are taken from the Perdew−Burke− Ernzerhof generalized gradient approximation,42 and the electron-ion interaction is described by Troullier−Martins pseudopotentials.43 The relaxation of the geometries is performed using the Broyden−Fletcher−Goldfarb−Shanno algorithm.44 For comparison with the experiment, the entire spectrum is rigidly shifted to align the highest occupied Kohn− Sham orbital with the calculated vertical detachment energy, defined as the difference between the total energies of the anionic and the unrelaxed neutral cluster.45 The levels are broadened by Gaussian peaks with a width of 50 meV. Our ground-state geometries for Na3− and Na5− resemble those of previous calculations,46 but our bond lengths are systematically shorter by about 10%. One of our isomers for Na7− agrees with the results of a previous DFT study.45 The ground-state geometries and the occupied orbitals are summarized in Figure 3. The labeling of the orbitals reflects their behavior under the symmetry operations of the molecular point group. Na3− is a linear molecule with D∞h symmetry. Its valence-electron orbitals are σg and σu. Na5− is planar with a Wlike shape and C2v symmetry. Its lowest47 molecular orbital transforms like a1, the next state like b1, and the highest occupied molecular orbital again like a1; the orbitals are thus labeled 1a1, b1, and 2a1. For Na7−, we identify two quasidegenerate geometrical isomers (energy difference 1 s, pζ pη

pξ pη s, pζ

l>1 s, px py

pz pz s, pz

The orientation of the MF (molecular frame) is indicated.

The next step is to expand these final-state wave functions in angular momentum eigenstates and to determine the lowestorder nonvanishing contributions. As in the s&p model, we shall consider only terms with l ≤ 1 and neglect any higher angular momenta; this step is (partly) justified by the validity of the threshold law.51 Although s states always correspond to the totally symmetric irreducible representation a1, p states transform according to their orientation.56 Namely, the Cartesian orbitals pξ, pη, and pζ transform like b2, b1, and a1, respectively. Consequently, the nonvanishing contributions for the a1 final state are s and pζ; for the b1 final state, pη; and for the b2 final state, pξ. The a2 final state is antisymmetric with respect to both the ξ−ζ and the η−ζ plane, and thus the lowest nonvanishing contribution to its multipole expansion is a d wave, which is neglected. The resulting contributions are presented in the fifth and sixth columns of Table 1. According to the different orientations of the MF, these partial waves are then rereferenced to the LF. We find that electrons detached from the b1 state are likely to be emitted with isotropic or perpendicular distributions (s and px/py), whereas electrons detached from the 2a1 state are more likely emitted with isotropic or parallel distributions (s and pz). For excess energies of up to approximately 0.5 eV, these qualitative predictions are in excellent agreement with the experimental results, with the photoelectrons from the b1 state and the 2a1 state exhibiting negative and positive values of the β parameter, respectively. Although this model certainly is a crude approximation, it gives valuable insight into the origin of the different PADs observed for electron emission from b1 and 2a1. While these wave function are similar in the sense that their multipole expansion is dominated by the p terms, the fact that they transform like different symmetry species leads to different PADs at certain energies. For the three-dimensional cluster Na7−, the description of the valence orbitals by a phenomenological spherical shell model is fairly appropriate. For the detachment of the s-like a1′ (96.5% s) electron, the continuum state will essentially have p character with small deviations due to the higher angular momentum components. For the detachment of the p-like 1e1′, 2e1′, and a2″ (94.6%, 97.6%, 96.9% p) electrons, the continuum state will exhibit a clear s character close to threshold. The

5. CONCLUSIONS In conclusion, we have presented detailed experimental data for the evolution of photoelectron anisotropies with photon energy for the small sodium clusters Na3−, Na5−, and Na7−. We showed that the anisotropies close to threshold are correlated with the symmetry properties of the bound-state orbitals from which the electrons are detached, and that the asymptotic β parameters are in good agreement with the expectations from Wigner’s threshold law. For the planar cluster Na5− we observed clearly different anisotropies for electrons detached from the two p-like orbitals at small excess energies, and we presented a qualitative, symmetry-based explanation of this behavior. For the threedimensional cluster Na7−, the character of the four occupied orbitals agrees well with the expectation from a spherical shell 8274

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model, with an energetic splitting of the p states caused by the interaction with the nonspherical ionic background. We emphasize that for the systems presented here, the photoelectron angular distribution measured at a single photon energy does not contain enough information to draw definite conclusions about the character of the bound-state orbitals. In contrast, it turns out that the symmetry of the initial states is reflected in the evolution of the angular distributions with photon energy.

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AUTHOR INFORMATION

Corresponding Author

*C. Bartels: tel, +49 551-39-12605; e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Gustavo Garcia for providing the pbasex source code. The work was supported by the Deutsche Forschungsgemeinschaft.

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REFERENCES

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