How many spheres can be arranged around a unit sphere in Euclidian space? This mathematical problem seems trivial at first, but until today, no general solution could be found. For the special case that all spheres are the same size, the maximum coordination number is 12 for a closest packing. Larger coordination numbers can be realized with larger central spheres.

It is known that tin clusters can form stable cages, which can endohedrally accommodate another atom in their center. This is quite commonnly known for cages of 12 tin atoms, so-called stannaspherene. In this study, structures and the electrical and magnetic properties of gadolinium-doped tin clusters were investigated experimentally and with quantum chemical methods. Unusually high coordination numbers were found. Up to 19 tin atoms can be arranged around an endohedral gadolinium atom in the first coordination sphere (green in Figure). If the number of tin atoms is further increased, a second shell is formed. From 21 tin atoms on, this is directly visible at the cluster structures (orange).

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The level of theory which is applied to simulate molecular spectra depends on the complexity of the underlying system, but also on the resolvable degrees of freedom in the experimental spectra that serve as a comparison. Sufficiently large metal and semiconductor clusters often exhibit a high density of states, which is why a resolution of the vibronic transitions opens a playground for modern methods of quantum chemistry.

In cooperation with the group of Prof. Dr. Graham Worth of University College London, the Multiconfigurational Time-Dependent Hartree (MCTDH) method was used to calculate quantum dynamical properties for the heterocycle maleimide and to simulate vibrationally-resolved absorption spectra. A vibronic coupling Hamiltonian was constructed, which is able to describe both a strongly-coupled, broad and a weakly-coupled, fine-structured absorption band. While already a few decisive vibrational modes are sufficient for a quantitative detection of the spectral signature, it could be shown that the whole manifold of normal modes is essential for a complete dynamic characterisation of the system.

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Almost 100 years ago, Otto Stern and Walther Gerlach demonstrated the directional quantization of angular momentum by deflecting a silver atom beam in an inhomogeneous magnetic field. The conclusions from this experimental observation were groundbreaking for modern physics. However, the determined magnetic moments are subject to a relatively large inaccuracy in the range of a few percent. A much more precise method for the determination of magnetic moments of isolated particles was developed some years later with the molecular beam magnetic resonance (MBMR) method, which is basically an electron spin resonance experiment.

The Stern-Gerlach experiment, named after its inventors, is still used today to study the magnetic properties of metal clusters. However, resonance experiments could not be performed on heavy metal clusters until today, because the additional rotational and vibrational degrees of freedom facilitate spin relaxation which makes the measurement of spin resonance difficult or impossible. The discovery of superatomic clusters a few years ago, however, opens up new possibilities. For this reason, an apparatus for a resonance experiment is described in this publication. The magnetic fields were optimized by means of electrostatic simulations, so that magnetic field fluctuations could be minimized. Furthermore, the challenge of measuring spin resonance in pulsed molecular beams is discussed. The apparatus was successfully validated on an atomic europium beam. The Figure shows (a) an intensity profile of the molecular beam in the Stern-Gerlach experiment and (b) an electron spin resonance spectrum for two isotopes of europium.

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