Molecular dynamics simulations of molecular beam deflection experiments

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.

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.

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.

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

We present molecular beam electric deflection experiments on neutral gold-doped tin clusters. The experimental Sn_NAu (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.

Doping effects on the geometric and electronic structure of tin clusters

In depth analysis of doping effects on the geometric and electronic structure of tin clusters via electric beam deflection, numerical trajectory simulations and density functional theory.

Multiferroic rhodium clusters

Simultaneous magnetic and electric deflection measurements of rhodium clusters (Rh(N), 6 ≤ N ≤ 40) reveal ferromagnetism and ferroelectricity at low temperatures, while neither property exists in the bulk metal. Temperature-independent magnetic moments (up to 1 μ(B) per atom) are observed, and superparamagnetic blocking temperatures up to 20 K. Ferroelectric dipole moments on the order of 1D with transition temperatures up to 30 K are observed. Ferromagnetism and ferroelectricity coexist in rhodium clusters in the measured size range, with size-dependent variations in the transition temperatures that tend to be anticorrelated in the range n = 6-25. Both effects diminish with size and essentially vanish at N = 40. The ferroelectric properties suggest a Jahn-Teller ground state. These experiments represent the first example of multiferroic behavior in pure metal clusters.

Beam broadening of polar molecules and clusters in deflection experiments

A beam of rotating dipolar particles (molecules or clusters) will broaden when passed through an electric or magnetic field gradient region. This broadening, which is a common experimental observable, can be expressed in terms of the variance of the distribution of the resulting polarization orientation (the direction cosine). Here, the broadening for symmetric-top and linear rotors is discussed. These two types of rotors have qualitatively different low-field orientation distribution functions, but behave similarly in a strong field. While analytical expressions for the polarization variance can be derived from first-order perturbation theory, for experimental guidance it is important to identify the applicability and limitations of these expressions, and the general dependence of the broadening on the experimental parameters. For this purpose, the analytical results are compared with the full diagonalization of the rotational Stark-effect matrices. Conveniently for experimental estimations, it is found that for symmetric tops, the dependence of the broadening parameter on the rotational constant, the axial ratio, and the field strength remains similar to the analytical expression even outside of the perturbative regime. Also, it is observed that the shape envelope, the centroid, and the width of the orientation distribution function for a symmetric top are quite insensitive to the value of its rotational constant (except at low rotational temperatures).

Mass spectrometry and beam deflection studies of tin-lead nanoalloy clusters

Photo-ionization mass spectrometry and electric beam deflection experiments were used to study isolated Sn(M)Pb(N) clusters (7 <or=N + M<or= 13 for tin-rich clusters, 7 <or=N + M<or= 15 for lead-rich clusters) in a molecular beam apparatus. The observed mass spectra reveal a broad abundance distribution of the bimetallic clusters in which all possible cluster compositions can be identified within the investigated size ranges. Comparison of the relative cluster intensities between pure tin or lead clusters (Sn(N+M) and Pb(N+M)) and mixed Sn(M)Pb(N) clusters indicate quite similar relative abundance distributions which can be smoothly shifted from one to the other extreme by changing the composition. The mass spectroscopic findings could be explained by assuming a substitution "alloy" formation in the Sn(M)Pb(N) cluster system. In combination, the dielectric properties were determined by passing the bimetallic clusters through an inhomogeneous electric field. The observed polarizabilities are significantly increased for most of the bimetallic clusters. This can be explained in an adiabatic polarization model by the presence of permanent electric dipole moments. These observations demonstrate how the electronic properties are not only crucially influenced by the cluster size but also by the composition of this nanoalloy model system. In addition to the enhanced polarizability, most of the measured beam profiles for tin-rich clusters show detectable beam broadenings due to the permanent dipole moments, in contrast to lead-rich clusters which possess considerable smaller dipole moments. Molecular dynamic simulations of the measured beam profile for Sn(6)Pb(1) taking theoretically calculated isomeric structures and dipole moments into account yields no completely satisfying outcome. Therefore we discuss possible reasons for the discrepancy between experimental and theoretical results.

Electric susceptibility of sodium-doped water clusters by beam deflection

The electric susceptibility of neutral sodium-doped water clusters Na(H(2)O)(N), N = 6-33, was determined by beam electric deflection. The clusters behave as polarizable particles; their intensity profiles exhibit global shifts toward the high-field region without the occurrence of broadening. In the conditions of the experiment, sodium-water clusters have a "floppy" structure and hence the electric susceptibility presents both electronic and orientacional terms. Measured susceptibilities are somewhat higher than those of pure water clusters, and the contribution per water molecule is similar for both cluster types.