Magnetism of single-doped paramagnetic tin clusters studied using temperature-dependent Stern-Gerlach experiments with enhanced sensitivity: impact of the diamagnetic ligand field and paramagnetic dopant.

In this work, the magnetic properties of tetrel clusters SnNTM, which are singly doped with transition metals (TM), are investigated. On the one hand, the number of tetrel atoms (N = 11, 12, 14 and 17 with TM = Mn) is varied; on the other hand, different transition metals (N = 14, TM = Cr, Mn, Fe) are studied. Magnetic deflection experiments under cryogenic conditions show that the variation of the number of tetrel atoms strongly changes the magnetic properties of the Mn-doped clusters. It is observed that Sn12Mn, Sn11Mn and Sn14Mn partially show super-atomic behaviour, while spin relaxation occurs in Sn17Mn. Magnetic deflection experiments at higher nozzle temperatures were carried out for the first time enhanced by a second parallel-aligned Stern-Gerlach magnet to achieve larger deflections. The resulting temperature-dependent one-sided deflections are quantitatively analysed using Curie's law and show that Sn17Mn possesses the highest magnetic moment of these clusters, followed by Sn12Mn and Sn11Mn. Sn14Mn shows the lowest magnetic moment. The replacement of Mn by Cr in Sn14Mn leads to a diamagnetic singlet, i.e., the magnetic moment of Cr in Sn14Cr is completely quenched. The replacement of Mn by Fe in turn leads to a paramagnetic species, whereby Sn14Fe is most likely present as a triplet. On this basis, the geometrical and electronic structures are analysed using quantum chemical calculations, indicating an arachno-type structure for Sn14Cr, Sn14Mn and Sn14Fe, which has already been predicted in the literature for Si14Cr. This is experimentally confirmed by deflection of molecular beams with an electric field under cryogenic conditions, suggesting that the arachno-type geometry is crucial for the overall stability of the transition-metal-doped tetrel clusters Sn14TM with TM = Cr, Mn, Fe.

Dielectric Behavior and Prolate Growth Patterns of Silicon Clusters SiN with N = 12-30 by Cryogenic Electric Beam Deflection.

We present a comprehensive investigation of the dielectric behavior and geometric structures of cold neutral SiN clusters of intermediate size with N = 12-30 atoms. For this, cryogenic electric beam deflection experiments were carried out for the first time for Si clusters at nozzle temperatures below 30 K. In combination with quantum chemical calculations based on density functional theory and classical trajectory simulations of the rotational dynamics in the electric field, the geometric structures of the clusters are discriminated. Clusters with N < 15 favor a single-capped square antiprism as a nucleus for cluster growth, forming compact geometries in the molecular beam. Starting with 15 atoms, a prolate-like growth is observed. The prolate structures are based on stable building blocks which reappear for numerous sizes throughout the cluster growth. Finally, the transition from prolate to quasi-spherical shapes is shown to take place around Si29/Si30 as predicted theoretically by the literature. The influence of the exchange-correlation functional on the predicted structure and dielectric properties is discussed in detail for some clusters. Relaxation of the electric-dipole moment and therefore quenching of the observed electric response due to vibrational excitation and collisions with the background gas are also considered, which explains deviations between experiment and theory.

Correction: Optical absorption and shape transition in neutral SnN clusters with N ≤ 40: a photodissociation spectroscopy and electric beam deflection study.

Correction for 'Optical absorption and shape transition in neutral SnN clusters with N ≤ 40: a photodissociation spectroscopy and electric beam deflection study' by Andreas Lehr et al., Phys. Chem. Chem. Phys., 2022, 24, 11616-11635, https://doi.org/10.1039/D2CP01171A.

Scaling of the permanent electric dipole moment in isolated silicon clusters with near-spherical shape.

In silicon clusters a structural transition from prolate to near-spherical structures takes place at a size of about 25-30 atoms. While some of the prolate clusters are very polar, there has been no experimental evidence of the presence of dipole moments in larger silicon clusters with near-spherical shape. By means of electric molecular beam deflection experiments at cryogenic temperatures, it was possible to prove for the first time that SiN clusters with more than N = 30 atoms are also polar. Interestingly, the dipole moment per atom for clusters in the range between 30 and 80 or 90 atoms is almost constant and amounts to 0.02 D. This unusual behaviour manifests in effective polarizabilities increasing linearly with cluster size. The dipolar contribution to the polarizability means that SiN clusters with N = 80 atoms can be polarized more than twice as well as a correspondingly small sphere with the dielectric properties of bulk α-Si. This finding is analysed with quantum chemical calculations concerning the geometric structure as well as the charge distribution and is related to the dielectric behaviour of polar semiconductor nanocrystals.

Enhanced Electronic g-Factors in Magic Number Main Group Bimetallic Nanoclusters.

We report the observation of large electronic g-factors in magic number main group bimetallic nanoclusters by performing Stern-Gerlach deflection experiments at 10 K. The clusters AlPb12 and InPb12 exhibit values of g = 3.5-4.0, whereas GaPb12 clusters surprisingly reveal a value of g < 2.0. Multireference ab initio methods are applied to unmask the origin of the g-factors and to gain insight into the electronic structure. The interplay of the pyritohedral molecular symmetry, a particularly strong spin-orbit coupling involved in the ground state, and the presence of low-lying degenerate excited states causes large positive g-factors in AlPb12 and InPb12. Contrarily, the spin-orbit coupling in the GaPb12 ground state is completely quenched. This is due to the d-block contraction lowering the nonbonding Ga 5s orbital and consequently forming an icosahedral ground state. Thus, endohedral p-doped tetrel clusters, composed of purely main group elements, state a novel and unique class of magnetic compounds and their study contributes to a more profound understanding of the metal-metal interaction in polynuclear clusters as well as magnetism at the molecular level.

Joint electric and magnetic beam deflection experiments and quantum chemical studies of MSn12 clusters (M = Al, Ga, In): on the interplay of geometric structure and magnetic properties in nanoalloys.

MSn12 clusters (M = Al, Ga, In) were studied in electric and magnetic beam deflection experiments at temperatures of 16 K and 30 K. For all three species, the results of the electric beam deflection experiments indicate the presence of two structural isomers of which one is considerably polar. The magnetic beam deflection experiments show atom-like beam splitting (superatomic behavior) with g-factors of 2.6-2.7 for a fraction of the clusters in the molecular beam, indicating significant spin-orbit coupling. On the one hand, we investigate by several experiments combining electric and magnetic deflectors how the superatomic and polar fractions are linked proving the correlation of the Stark and Zeeman effects. On the other hand, the magnetic deflection behavior is examined more thoroughly by performing quantum chemical calculations. By systematic distortion of an artificial icosahedral tin cage towards the global minimum structure, which has a pyritohedral geometry, the shifts in the magnitude of the g-factor are found to be mainly caused by a single dominant electronic excitation. This allows one to develop a semi-quantitative understanding of the magnetic behavior. On the basis of avoided crossings in the rotational Zeeman diagram, simulations of the magnetic beam deflection comprising computed rotational constants, vibrational modes, g-factors and spin-rotation coupling constants are performed which resemble our experimental findings in satisfactory agreement. With this, a better understanding of the magnetic properties of nanoalloy clusters can be achieved. However, the geometric structures of the polar isomers are still unknown.

Optical absorption and shape transition in neutral SnN clusters with N ≤ 40: a photodissociation spectroscopy and electric beam deflection study.

Neutral SnN clusters with N = 6-20, 25, 30, 40 are investigated in a joint experimental and quantum chemical study with the aim to reveal their optical absorption in conjunction with their structural evolution. Electric beam deflection and photodissociation spectroscopy are applied as molecular beam techniques at nozzle temperatures of 16 K, 32 K and 300 K. The dielectric response is probed following the approach in S. Schäfer et al., J. Phys. Chem A, 2008, 112, 12312-12319. It is improved on those findings and the cluster size range is extended in order to cover the prolate growth regime. The impact of the electric dipole moment, rotational temperature and vibrational excitation on the deflection profiles is discussed thoroughly. Photodissociation spectra of tin clusters are recorded for the first time, show similarities to spectra of silicon clusters and are demonstrated to be significantly complicated by the presence of multiphoton absorption in the low-energy region and large excess energies upon dissociation which is modelled by the RRKM theory. In both experiments two isomers for the clusters with N = 8, 11, 12, 19 need to be considered to explain the experimental results. Triple-capped trigonal prisms and double-capped square antiprisms are confirmed to be the driving building units for almost the entire size range. Three dominating fragmentation channels are observed, i.e. the loss of a tin atom for N < 12, a Sn7 fragment for N < 19 and a Sn10 fragment for N ≥ 19 with Sn15 subunits constituting recurring geometric motifs for N > 20. The prolate-to-quasispherical structural transition is found to occur at 30 < N ≤ 40 and is analyzed with respect to the observed optical behavior taking quantum chemical calculations and the Mie-Gans theory into account. Limitations of the experimental approach to study the geometric and electronic structure of the clusters at elevated temperatures due to vibrational excitation is also thoroughly discussed.

Influence of nuclear spins on electron spin coherence in isolated, p-doped tin clusters.

Magnetic double deflection experiments reveal that nuclear spins diminish electron spin coherence in isolated AlSn12 clusters. A temperature-dependent fraction of the endohedral cage clusters show superatomic response in Stern-Gerlach experiments which allows one to detect spin flips under controlled conditions in a double deflection arrangement. The concentration of nuclear spins in the tin cage is varied by using isotopically enriched tin samples. Hyperfine interaction, nuclear spin statistics and spin dynamics are discussed in detail. It is demonstrated that state-interference in the multistate Landau-Zener system AlSn12 explains why the spin decoherence is significantly increased when one or two nuclear spins are already present in the cluster, while the spin coherence no longer changes significantly with the addition of further nuclear spins.

Discriminating the influence of thermal excitation and the presence of structural isomers on the Stark and Zeeman effect of AlSn12 clusters by combined electric and magnetic beam deflection experiments.

AlSn12 clusters were studied in electric and magnetic beam deflection experiments at nozzle temperatures of Tnozzle = 16-100 K. For 16 K, spatial separation of two fractions of clusters in the molecular beam was achieved by deflection with both an electric and a magnetic field gradient. In the electric deflection experiment, about 76% of the clusters are identified as non-polar and the rest as highly-polar, while the magnetic deflection experiment demonstrates that 37% show an atom-like and 63% a Brillouin-like magnetic response. In order to probe the connection between these fractions in electric and magnetic beam deflection, a combination of these two experiments was performed. This clearly demonstrates that the highly-polar clusters show a Brillouin-like magnetic response and only the non-polar clusters can be deflected atom-like in a magnetic field. This observation suggests that two structural isomers are present in the molecular beam, one of which is highly-symmetric, and demonstrates that spatial isomer separation of metal clusters containing heavy elements is feasible. However, vibrational excitation must also be taken into account to explain the observed magnetic response. A stepwise increase of the cluster temperature shows that suppression of the superatomic response is more sensitive to vibrational excitation than the quenching of the permanent electric dipole moment.

Variation of the optical properties with size and composition of small, isolated Cdx Sey + clusters.

Global energy minimum structures and optoelectronic properties are presented for isolated Cdx Sey + clusters with x + y ≤ 26. The compositional- and size-dependent variation of optical, electronic and geometric properties is systematically studied within the framework of ground state and time-dependent density functional theory. The applied methods are justified by benchmarks with experimental data. It is shown that the optical gap can be tuned by more than 2 eV by only changing the composition for a fixed number of atoms. The stoichiometric species reveal an unexpected size-dependent behavior in comparison to larger colloidal CdSe quantum dots, that is, a redshift of the optical gap was observed with decreasing cluster size in contrast to predictions by quantum-size effects. This unexpected result is discussed in detail taking the positive charge of the clusters into account.

Local coordination numbers of up to 19 in gadolinium-tin alloy nanoclusters.

A combined approach based on quantum-chemical calculations and molecular beam experiments demonstrates that in isolated nanoalloy clusters of type GdSnN, a total number of N = 19 tin atoms can be arranged around a central gadolinium atom. While the formation of the first coordination shell is incomplete for clusters with less than 15 tin atoms, the second coordination sphere starts to form for cluster sizes of more than 20 tin atoms. The magnetic properties of the clusters reveal that the tin atoms not only provide a hollow cage for Gd but also are chemically bound to the central atom. The calculated spin densities imply that an electron transfer from Gd to the tin cage takes place, which is similar to what is observed for endohedral metallofullerenes. However, the measured electric dipole moments indicate that in contrast to metallofullerenes, the Gd atom is located close to the center of the tin cage.

Optical Absorption of Atomically-Precise Sn14 Nanoclusters: The Antagonistic Interplay of Ligand Stabilization, Molecular Symmetry, and Solvatochromism.

The synthesis of atomically precise clusters is nowadays well established. The study of isolated clusters in the gas phase has also become an approved field of research. Although both approaches examine the same research objects, namely nanoclusters, little is known about to what extent results from gas phase studies can be transferred to colloidal systems and vice versa. In particular, it is not yet sufficiently understood how ligands influence the geometric and electronic structure of clusters from an experimental point of view. By comparing a ligand-stabilized tin nanocluster in solution with an isolated species in the gas phase and considering different geometric arrangements with the same number of tin atoms, the impacts of ligand stabilization, molecular symmetry, and solvatochromism on the optical behavior are thoroughly worked out for the first time.

Strong permanent magnet gradient deflector for Stern-Gerlach-type experiments on molecular beams.

We describe the design, assembly, and testing of a magnet intended to deflect beams of paramagnetic nanoclusters, molecules, and atoms. It is energized by high-grade permanent neodymium magnets. This offers a convenient option in terms of cost, portability, and scalability of the construction while providing field and gradient values (1.1 T, 330 T/m), which are fully comparable with those of commonly used electromagnet deflectors.

Size- and Charge-Dependent Optoelectronic Properties of CdSe Clusters: Evolution of the Optical Gap from Molecular to Bulk Behavior.

In the present work, the optical response of isolated (CdSe)n+ clusters with n = 3-6 is probed by measuring the photodissociation cross section in the photon energy range ℏω = 1.9-4.9 eV. In this joint experimental and theoretical study, the experimental observations are analyzed with time-dependent density functional theory and equation-of-motion coupled cluster theory. Structural candidates for the time-dependent excited-state calculations are obtained via global optimization by employing a genetic algorithm. The combined experimental and theoretical approach allows the discrimination of cluster geometries in the molecular beam experiments. From n ≥ 5, three-dimensional structures are found. Already for n = 6, light absorption in the red spectral range is observed. This observation is discussed with respect to the size dependence of the optical behavior of finite systems taking experimental and theoretical work on bare and ligated CdSe clusters and nanoparticles into account. Particularly, the influence of the net charge and ligands is considered. This allows a detailed discussion of the size-dependent evolution of the optical properties starting from molecular species over to nanoclusters and nanoparticles and finally to bulk CdSe.

Doping effects on the geometric and electronic structure of tin clusters.

Molecular beam electric deflection experiments on neutral single copper-doped tin clusters are presented at different cryogenic nozzle temperatures. The experimental cluster beam profiles SnNCu (N = 9-16) are compared with classical rotational dynamic simulations of globally optimized structures obtained by a genetic algorithm based on density functional theory. The formation of endohedral complexes with comparable geometry to manganese- and gold-doped tin is confirmed. Theoretical methods predict ionic structures of the type Cuδ-@SnNδ+ with electron transfer from the tin cage to the central copper dopant. This behaviour is discussed based on a molecular orbital picture particularly with respect to other transition metal tetrel complexes.

Gold doping of tin clusters: exo- vs. endohedral complexes.

We present molecular beam electric deflection experiments on neutral gold-doped tin clusters. The experimental SnNAu (N = 6-16) cluster beam profiles are interpreted by means of classical trajectory simulations supplied, with cluster structures generated by a genetic algorithm based on density functional theory. The combined experimental and theoretical analysis confirms that at least nine tin atoms are necessary to form a cage that is capable of encapsulating a gold atom, with high symmetry only marginally distorted by the gold atom. Two-component DFT calculations reveal that for some clusters spin-orbit effects are necessary to properly describe these species. Partial charge analysis methods predict the presence of charge transfer effects from the tin host to the dopant, resulting in a negatively charged gold atom.

GIGA: a versatile genetic algorithm for free and supported clusters and nanoparticles in the presence of ligands.

We present a versatile parallelised genetic algorithm, which is able to perform global optimisation from first principles for pure and mixed free clusters in the gas phase, supported on surfaces or in the presence of one or several atomic or molecular species (ligands or adsorbates). The genetic algorithm is coupled to different quantum chemical software packages in order to permit a large variety of methods for the global optimisation. The genetic algorithm is also capable of optimising different electronic spin multiplicities explicitly, which allows global optimisation on several potential energy hypersurfaces in parallel. We employ the genetic algorithm to study ligand-passivated clusters [Cd3Se3(H2S)3]+ and to investigate adsorption of [Pt6(H2O)2]+ supported on graphene. The explicit consideration of the electronic spin multiplicity during global optimisation is investigated for nanoalloy clusters Pt4V2.

N-Doping at the Sub-Nanoscale: Dielectric and Magnetic Response of Neutral Phosphorus-Doped Tin Clusters.

Doped semiconductors play a prevalent role in all aspects of modern technology. Because of the trend for smaller and smaller devices, we have investigated N-doping at the sub-nanoscale. For that purpose, we present molecular beam electric and magnetic deflection experiments on Sn NP ( N = 6-12) and Sn NP2 ( N = 7-12) clusters combined with quantum chemical calculations and classical beam deflection simulations. The theoretically identified and experimentally confirmed global minima structures resemble the valence-isoelectronic pure tin anions/dianions very closely, while each phosphorus dopant occupies the site of a tin atom. In Stern-Gerlach experiments, the single-doped clusters show a partial atom-like deflection behavior with total electronic angular momentum J = 1/2 whereas the results for the double-doped species suggest singlet states. This is in full agreement with quantum chemical results. The effect of vibrational excitation on magnetic and electric deflection experiments is examined. Our results provide insight into how the electric, magnetic, and structure properties are affected by n-doping at the sub-nanoscale.