Bismuth-Doped Tin Clusters: Experimental and Theoretical Studies of Neutral Zintl Analogues

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.

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.

From organotin hydrides to heteronuclear main group metal compounds: isolation of the first neutral bismuth/tin clusters

From conversions of Ar₂SnH₂ (Ar = Tripp, Dipp; Tripp = 2,4,6-Triisopropylphenyl, Dipp = 2,6-Diisopropylphenyl), and a bismuth(III) amide, Bi[N(SiMe₃)₂]₃, we isolated the first representatives of mixed, uncharged Bi/Sn clusters, Bi₈Sn₃Ar₆. Along with unprecedented bicyclo[2.2.0]hexanes, (HAr₂Sn)₂Sn₂Bi₄, these have been characterized by single crystal X-Ray diffraction, heteronuclear NMR, vibrational and UV-Vis spectroscopy. Quantum-chemical calculations were carried out in order to understand bonding within the isolated polyhedral compounds.

A method for predicting basins in the global optimization of nanoclusters with applications to AlxCuy alloys

The problem of obtaining the geometrical configuration of a molecule that minimizes its potential energy is a very complicated one for a series of applications, ranging from determining the structure of biological macromolecules to nanoclusters of atoms. Global optimization tools are available for this task, and many of them are based in performing successive local optimizations, where the starting geometries for these steps are determined by an intelligent algorithm. Here we develop a method to save computing time in the optimization of nanoclusters by predicting if a given minimum has been previously visited during local optimization steps. Our application to Cu-Al nanoalloys indicates that it is possible to save a substantial amount of computational cost. The application also reveals new promising Al_xCu_y clusters and explain their stabilities in terms of the jellium model.

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.

Structural, electronic and magnetic properties of stoichiometric cobalt oxide clusters (CoO)nq (n=3−10,q=0,+1): A modified basin-hopping Monte Carlo algorithm with spin-polarized DFT

The structural, electronic and magnetic properties of the neutral and cationic cobalt oxide clusters (CoO)[Formula: see text] ([Formula: see text], [Formula: see text]) have been studied using a modified basin-hopping Monte Carlo (BHMC) algorithm refined by spin-polarized DFT. A systematic search of global minimum structures predicts new global minima of (CoO)[Formula: see text] and reproduced other minima that are in excellent agreement with previous works. For most low-spin and high-spin states, the structural transition from planar-like to compact structure occurs at (CoO)[Formula: see text], which is in contrast with the general notion that the structural changes at (CoO)[Formula: see text]. Supported by the results of the binding energy, second-order total energy difference, chemical hardness, chemical potential and HOMO-LUMO gap confirms the stability of (CoO)4. Results of the spin magnetic moments for the global minima show that (CoO)4 and (CoO)8 spin configurations exhibit a fully antiferromagnetic (AFM) ordering, while (CoO)9 spin displays the highest ferromagnetic (FM) ordering. Interestingly, elongation of Co–Co bond in (CoO)4 causes O being polarized by the neighboring Co atoms that accordingly follows the Goodenough-Kanamori-Anderson rule of FM super-exchange coupling for the Co-O-Co structural rearrangement to 90∘ ([Formula: see text] structure) in order to accommodate the spin magnetic ordering changes. This rearrangement is a result of the valence band being shifted away from the Fermi level to lower energy causing high population of the spin-up density of state and leading to the asymmetrical polarization of the whole (CoO)4 structure. As far as the dissociation energy surfaces are concerned, the first ever such surfaces are constructed corresponding to [Formula: see text], which identify a complete dissociation pathway linking the cationic and neutral clusters and finally confirm (CoO)[Formula: see text] as the most stable cluster compared to the rest.

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.

Towards operando computational modeling in heterogeneous catalysis

An increased synergy between experimental and theoretical investigations in heterogeneous catalysis has become apparent during the last decade. Experimental work has extended from ultra-high vacuum and low temperature towards operando conditions. These developments have motivated the computational community to move from standard descriptive computational models, based on inspection of the potential energy surface at 0 K and low reactant concentrations (0 K/UHV model), to more realistic conditions. The transition from 0 K/UHV to operando models has been backed by significant developments in computer hardware and software over the past few decades. New methodological developments, designed to overcome part of the gap between 0 K/UHV and operando conditions, include (i) global optimization techniques, (ii) ab initio constrained thermodynamics, (iii) biased molecular dynamics, (iv) microkinetic models of reaction networks and (v) machine learning approaches. The importance of the transition is highlighted by discussing how the molecular level picture of catalytic sites and the associated reaction mechanisms changes when the chemical environment, pressure and temperature effects are correctly accounted for in molecular simulations. It is the purpose of this review to discuss each method on an equal footing, and to draw connections between methods, particularly where they may be applied in combination.

Pool-BCGA: a parallelised generation-free genetic algorithm for the ab initio global optimisation of nanoalloy clusters

The Birmingham cluster genetic algorithm is a package that performs global optimisations for homo- and bimetallic clusters based on either first principles methods or empirical potentials. Here, we present a new parallel implementation of the code which employs a pool strategy in order to eliminate sequential steps and significantly improve performance. The new approach meets all requirements of an evolutionary algorithm and contains the main features of the previous implementation. The performance of the pool genetic algorithm is tested using the Gupta potential for the global optimisation of the Au10Pd10 cluster, which demonstrates the high efficiency of the method. The new implementation is also used for the global optimisation of the Au10 and Au20 clusters directly at the density functional theory level.

Optical and electronic properties of mixed Ag-Au tetramer cations

We present experimental and theoretical studies of the optical response of mixed Ag(n)Au(+)(4-n) (n=1-3) clusters in the photon energy range ℏω = 1.9-3.5 eV. Absorption spectra are recorded by a newly built longitudinal molecular beam depletion spectroscopy apparatus providing lower limits to absolute photodissociation cross sections. The experimental data are compared to optical response calculations in the framework of long-range corrected time-dependent density functional theory with initial cluster geometries obtained by the unbiased Birmingham Cluster Genetic Algorithm coupled with density functional theory. Experiments and excited state calculations shed light on the structural and electronic properties of the mixed Ag-Au tetramer cations.

Structure prediction of nanoclusters; a direct or a pre-screened search on the DFT energy landscape?

Atomic structure prediction, using KLMC (Lamarckian evolutionary algorithm search), and properties comparison of (KF)_n, (MgO)_n, (ZnO)_n and (CdSe)_n nanoclusters.