Function Of Cluster Size Research Articles

Prediction of Structures and Atomization Energies of Coinage Metals, (M)n, n < 20: Extrapolation of Normalized Clustering Energies to Predict the Cohesive Energy.

The geometries of the group 11 coinage metals (n = 2-20) were optimized to determine the lowest energy isomers for each cluster size, singlets for even numbers and doublets for odd numbers. For copper and silver, 2-D (planar) geometries were favored up to n = 6. For gold, 2D (planar) geometries were favored up to n = 13. Normalized clustering energies were plotted as a function of cluster size (n-1/3, for n = 4-20) with various DFT functionals and the CCSD(T)-F12b method and were extrapolated to predict the bulk cohesive energy. In the case of copper and silver, there is excellent agreement between the cohesive energies predicted at the CCSD(T)-F12b level of theory and the experimental values. For gold, the CCSD(T)-F12b values needed to be corrected for spin-orbit relativistic effects to obtain good agreement with experiment. Electronic properties including the HOMO-LUMO gaps for the even clusters and the spin densities for the odd clusters were calculated. The lowest gap is predicted to occur for n = 16 where the HOMO and LUMO are very similar in shape.

Structure and electronic properties of AunPt (n = 1–8) nanoalloy clusters: the density functional theory study

The study of bimetallic nanoalloy clusters is of considerable interest due to its interesting electronic, optical, magnetic and catalytic properties. The geometrical structure and electronic properties of AunPt (n = 1–8) nanoalloy clusters are studied by using the density functional theory methodology. The result exhibits that the ground-state configurations of AunPt clusters favour planar confirmation in this molecular range. The most stable cluster is Au3Pt, which is having rhombus structure with symmetry group C2v and can be considered as building blocks for developing large clusters. The computed HOMO-LUMO energy gap of Au3Pt nanoalloy cluster is 1.741 eV. The energy gap in this particular range supports the use of bimetallic clusters as nonlinear optical devices and optoelectronic materials. The DFT-based global descriptors viz. HOMO-LUMO energy gap, electronegativity, hardness, softness and electrophilicity index are also studied. The computed HOMO-LUMO energy gap and chemical hardness exhibit a pronounced odd-even oscillation behaviour as a function of cluster size, n.

A comparative study of structure, stabilities and electronic properties of neutral and cationic [AuSin]λ and [Sin+1]λ (λ = 0, +1; n = 1–12) nanoalloy clusters

Structure, stabilities and electronic properties of [AuSin]λ and [Sin+1]λ (λ = 0, +1; n=1-12) nanoalloy clusters are studied invoking Density Functional Theory methodology. To understand the chemical stability of the lowest energy structure of cluster, chemical parameters like, Binding Energy, Fragmentation Energy, Second Order Difference in Energy and HOMO-LUMO energy gap are studied with the variation of cluster size. The binding energy of neutral and cationic Sin+1 and AuSin clusters is gradually increasing along with the cluster size n. The second order difference in energy for pure Sin+1 and doped cluster AuSin shows an interesting odd-even alternation behavior. It is found that Si7, AuSi5, [Si5]+ and [AuSi7]+ are the most stable clusters. The HOMO-LUMO energy gap of neutral and cationic AuSin cluster is high as compare to their corresponding neutral and cationic Sin+1 cluster. It indicates that doping of Au atom enhances the energy gap of silicon clusters. The computed HOMO-LUMO gap of neutral and cationic AuSin clusters are in the range of 1.35–2.94 eV, which is suitable for microelectronics, optoelectronic devices and photovoltaics applications. Density Functional Theory based descriptors viz. Electronegativity, Hardness, Softness and Electrophilicity Index are also reported. The HOMO-LUMO energy gap of pure Si and doped cluster AuSin displays odd-even oscillation behavior as a function of cluster size, n. The close agreement between theoretical and experimental results supports and validates our computational analysis.

Structural, electronic and magnetic properties of NM-doped Ni clusters (NM=Cu, Ag, Au)

The lowest-energy structures of the noble metal atoms (NM=Cu, Ag, Au) doped into medium-scale Nin (n = 19–23) are obtained at the DFT-PBE level. The relative stability, electronic and magnetic properties of Nin-1NM clusters, in comparison with pure Nin clusters have been systematically investigated. The relative stability and chemical activity are analyzed based on the binding energy per atom, embedding energy and dissociation energy for the most stable clusters. It is found that only doping of Au atom can enhance the stability of Ni clusters. The weakening in the magnetic moment is obtained for Nin-1NM clusters compared to that of pure Ni clusters. The stability and the total magnetic moments of Nin-1NM are found to increase as a function of cluster size. And the charge transfer occurs from Ni clusters to the NM impurity. The Nin-1Au clusters both have larger AEA and AIP, which is due to the strong relativistic effects for Au clusters.

Photofragmentation of Bin+/- clusters (n = 2−19) in an electrostatic ion beam trap

Photofragmentation spectra for small bismuth-cluster cat- and anions are recorded for the investigation of their fragmentation pathways as a function of cluster size. To this end, the ions of interest are stored and size-selected in an electrostatic ion beam trap/a multi-reflection time-of-flight mass spectrometer with high resolving power. The subsequent photoexcitation is timed to their turn-around point in the trap’s mirror potential. In this novel approach, charged fragment clusters exhibit the same energy as the precursor ions and, thus, can be further stored and investigated with identical trap configurations. The results suggest a high stability of the neutral bismuth tetramer in accordance with previous reports, which is attributed to bismuth clusters exhibiting semimetal properties. Additionally, there is evidence for the loss of larger neutral fragments.

Making and breaking of small water clusters: A combined quantum chemical and molecular dynamics approach.

We present a combined quantum chemical and molecular dynamics study of cyclic and noncyclic water n-mers ([(H2 O]n , n = 2-6) at four different temperatures and showcase that the dynamics of small water clusters can reproduce the known properties of bulk water reasonably well. We investigate the making and breaking of the water clusters by computing the hydrogen bond strengths, average lifetimes, and relative stabilities, which are important to understand the complex solution dynamics. We compare the behavior of water clusters in the gas phase and in the solution phase as well as the variation in the properties as a function of cluster size and highlight the notably more interesting cluster dynamics of the water trimer when compared to the other water clusters. © 2019 Wiley Periodicals, Inc.

First-principles studies on the doping effect of Nin−1TM (n = 13, 19, 55)

The structural and electronic properties of different transition-metal atoms (TM = Cr, Mn, Fe, Co, Cu, Zn, Pd, Ag, Pt, Au) doped into Nin neutral and ionic clusters (n = 13, 19, 55) were investigated using density functional theory calculations with the PBE exchange-correlation energy functional. The properties of the Nin−1TM clusters differed substantially from those of Nin, implying that the substitution of a transition-metal atom (TMA) strongly affected the stability and electronic properties of the resultant clusters. The cluster size effect and element type influence are discussed. The stability and the total magnetic moments of Nin−1TM neutral and ionic clusters were found to increase as a function of cluster size. The size of the clusters had little effect on the amount of charge transferred. The AIP decreased with increasing cluster size, while the AEA is exhibited the opposite trend. All of the aforementioned electronic properties exhibited different degrees of variation due to doping of different TMAs.

Structural determination of neutral Con clusters (n = 4–10,13) through IR–UV two-color vibrational spectroscopy and DFT calculations

We recorded IR spectra for neutral cobalt clusters via two-color IR-UV ionization, using the Free Electron Laser for intracavity experiments (FELICE). Well-resolved IR spectra are presented for (n = 4–10, 13) and analyzed with the help of Density Functional Theory calculations using two different correlation exchange functionals: the revisited Tao–Perdew–Staroverov–Scuseria (revTPSS) and the frequently used Perdew–Burke–Ernzerhof (PBE) approaches. Although we have not performed an extensive structure search, we tentatively assign the spectra for all cluster sizes except for n = 7, and n = 10. We find that neither of the two functionals chosen clearly outperforms the other in predicting IR spectra, and that relatively low scaling factors of 0.82 (PBE) and 0.8 (revTPSS) are required. In contrast to the magnetic moments, the calculated electric dipole moments fluctuate strongly as a function of cluster size and could therefore be used as an indirect probe to the cluster structure.

Transition from Water Wires to Bifurcated H-Bond Networks in 2-Pyridone·(H2O) n, n = 1-4 Clusters.

Mass-selective two-color resonant two-photon ionization (2C-R2PI), UV/UV hole-burning, and infrared (IR) depletion spectra of supersonic jet-cooled 2-pyridone·(H2O) n clusters with n = 1-4 have been measured to investigate the local hydration patterns around 2-pyridone (2PY) as a function of cluster size. As shown by others, the IR frequencies of the OH and NH stretches of the n = 1, 2 clusters are characteristic of water wires stretching from the NH to the C═O group of 2PY. We identify two isomers (3A and 3B) of the n = 3 cluster in the 2C-R2PI spectrum and separate them by IR/UV and UV/UV hole-burning techniques. Isomer 3A exhibits a three-membered water wire, extending the n = 1, 2 structural motif. Isomer 3B exhibits bifurcated water wires with the first H2O donating to two waters that form H-bonds to the C═O group. This increases the H-bond strength between the NH group of 2PY and the proximal H2O molecule, lowering the NH stretch to ∼2800 cm-1. The n = 4 cluster is also bifurcated with two water wires between the bifurcating H2O and the C═O group. The cluster-selective IR spectra are complemented with density-functional calculations using the PW91, B3LYP, B97-D, and M06-2X functionals, where the latter two include long-range dispersive interactions, and with the ab initio correlated SCS-CC2 method. The calculated IR spectra provide firm assignments of the structures of the n = 1-4 cluster structures and allow us to understand the evolution of individual H-bond strengths with increasing cluster size.

Vibrational Properties of Thiolate-Protected Gold Nanoclusters.

Over recent years, the field of thiolate-protected gold nanoclusters has made remarkable progress. The successful determination of the structure of some of these clusters by X-ray crystallography was a milestone in this field. X-ray crystallography is arguably the most important technique in the field up to now, and it enabled the study of structure evolution as a function of cluster size. It also shed light on the structure of the Au-S interface. Recently, it has been realized that thiolate-protected gold clusters are very dynamic systems. Metal atoms and ligands can exchange easily between clusters. Furthermore, the adsorbed ligands bear conformational dynamics. Such dynamic effects call for experimental methods that can cope with it. Future efforts in this field will be directed toward applications of thiolate-protected clusters, and many of them will rely on dissolved clusters. Therefore, structure determination in solution is an important issue, though it is very challenging. The structure of the metal core and the Au-S interface is not expected to change in solution with respect to the crystal. However, the structure of the adsorbed ligand itself is sensitive to the environment and may be different in the solid state and in solution, as has been shown in fact in the past. It is this (dynamic) structure of the ligand that determines the interaction between the cluster and its environment, which is crucial, for example, for sensing applications. Vibrational spectroscopy is a promising technique to characterize thiolate-protected clusters in different environments. A vibrational spectrum is sensitive to structure (conformation) although this information is often "hidden" in the spectrum, requiring detailed analysis and support from theory to be deciphered. Compared to other techniques like UV-vis spectroscopy and mass spectrometry, vibrational spectroscopy was not extensively used in the field of thiolate-protected clusters, but we believe that the technique will be very valuable for the future developments in the field. We have used vibrational spectroscopy to investigate thiolate-protected gold clusters for mainly two lines of research. In the first, we studied in detail the low energy region of the vibrational spectrum, in particular the Au-S vibrational modes, in order to understand the structure sensitivity. It emerges that the Au-S vibrational spectrum is indeed sensitive to the structure of the interface but also to other factors, especially the organic part of the thiol, in a complex way. The ability to directly correlate structure, from X-ray crystallography, and vibrational spectra for thiolate-protected clusters, should lead to a database that will help in the future the structure determination of the Au-S interface by vibrational spectroscopy for systems where direct structure determination is not possible, for example, for flat surfaces. A second line of research focused on the determination of the structure of the adsorbed ligands for dissolved clusters. Such information is mostly extracted by the comparison of theoretical and calculated spectra for different conformers. In this respect, vibrational circular dichroism (VCD) is particularly powerful as it strongly depends on the conformation, more than conventional infrared spectroscopy. VCD can be applied to chiral nonracemic compounds, and it is a sensitive probe for chirality. Using this method, it was possible to demonstrate that a cluster can transfer its chirality to achiral thiolate ligands. In this Account, we summarize the possibilities and challenges of vibrational spectroscopy in the field of thiolate-protected clusters.

Density functional theory and surface reactivity study of bimetallic AgnYm (n+m = 10) clusters

Density functional theory calculations have been performed on pure silver (Agn), yttrium (Ym) and bimetallic silver yttrium clusters AgnYm (n + m = 2–10) for reactivity descriptors in order to realize sites for nucleophilic and electrophilic attack. The reactivity descriptors of the clusters, studied as a function of cluster size and shape, reveal the presence of different type of reactive sites in a cluster. The size and shape of the pure silver, yttrium and bimetallic silver yttrium cluster (n = 2–10) strongly influences the number and position of active sites for an electrophilic and/or nucleophilic attack. The trends of reactivities through reactivity descriptors are confirmed through comparison with experimental data for CO binding with silver clusters. Moreover, the adsorption of CO on bimetallic silver yttrium clusters is also evaluated. The trends of binding energies support the reactivity descriptors values. Doping of pure cluster with the other element also influence the hardness, softness and chemical reactivity of the clusters. The softness increases as we increase the number of silver atoms in the cluster, whereas the hardness decreases. The chemical reactivity increases with silver doping whereas it decreases by increasing yttrium concentration. Silver atoms are nucleophilic in small clusters but changed to electrophilic in large clusters.

A Model for Protostellar Cluster Luminosities and the Impact on the CO–H2 Conversion Factor

Abstract We construct a semianalytic model to study the effect of far-ultraviolet (FUV) radiation on gas chemistry from embedded protostars. We use the protostellar luminosity function (PLF) formalism of Offner &amp; McKee to calculate the total, FUV, and ionizing cluster luminosity for various protostellar accretion histories and cluster sizes. We2 compare the model predictions with surveys of Gould Belt star-forming regions and find that the tapered turbulent core model matches best the mean luminosities and the spread in the data. We combine the cluster model with the photodissociation region astrochemistry code, 3d-pdr, to compute the impact of the FUV luminosity from embedded protostars on the CO-to-H2 conversion factor, X CO, as a function of cluster size, gas mass, and star formation efficiency. We find that X CO has a weak dependence on the FUV radiation from embedded sources for large clusters owing to high cloud optical depths. In smaller and more efficient clusters the embedded FUV increases X CO to levels consistent with the average Milky Way values. The internal physical and chemical structures of the cloud are significantly altered, and X CO depends strongly on the protostellar cluster mass for small efficient clouds.

Application of a parallel genetic algorithm to the global optimization of medium-sized Au\u2013Pd sub-nanometre clusters

To contribute to the discussion of the high activity and reactivity of Au–Pd system, we have adopted the BPGA-DFT approach to study the structural and energetic properties of medium-sized Au–Pd sub-nanometre clusters with 11–18 atoms. We have examined the structural behaviour and stability as a function of cluster size and composition. The study suggests 2D–3D crossover points for pure Au clusters at 14 and 16 atoms, whereas pure Pd clusters are all found to be 3D. For Au–Pd nanoalloys, the role of cluster size and the influence of doping were found to be extensive and non-monotonic in altering cluster structures. Various stability criteria (e.g. binding energies, second differences in energy, and mixing energies) are used to evaluate the energetics, structures, and tendency of segregation in sub-nanometre Au–Pd clusters. HOMO–LUMO gaps were calculated to give additional information on cluster stability and a systematic homotop search was used to evaluate the energies of the generated global minima of mono-substituted clusters and the preferred doping sites, as well as confirming the validity of the BPGA-DFT approach.

Electron scattering in large water clusters from photoelectron imaging with high harmonic radiation.

Low-energy electron scattering in water clusters (H2O)n with average cluster sizes of n < 700 is investigated by angle-resolved photoelectron spectroscopy using high harmonic radiation at photon energies of 14.0, 20.3, and 26.5 eV for ionization from the three outermost valence orbitals. The measurements probe the evolution of the photoelectron anisotropy parameter β as a function of cluster size. A remarkably steep decrease of β with increasing cluster size is observed, which for the largest clusters reaches liquid bulk values. Detailed electron scattering calculations reveal that neither gas nor condensed phase scattering can explain the cluster data. Qualitative agreement between experiment and simulations is obtained with scattering calculations that treat cluster scattering as an intermediate case between gas and condensed phase scattering.

Dynamic Stabilization of the Ligand–Metal Interface in Atomically Precise Gold Nanoclusters Au68 and Au144 Protected by meta-Mercaptobenzoic Acid

Ligand-stabilized, atomically precise gold nanoclusters with a metal core of a uniform size of just 1-3 nm constitute an interesting class of nanomaterials with versatile possibilities for applications due to their size-dependent properties and modifiable ligand layers. The key to extending the usability of the clusters in applications is to understand the chemical bonding in the ligand layer as a function of cluster size and ligand structure. Previously, it has been shown that monodispersed gold nanoclusters, stabilized by meta-mercaptobenzoic acid (m-MBA or 3-MBA) ligands and with sizes of 68-144 gold atoms, show ambient stability. Here we show that a combination of nuclear magnetic resonance spectroscopy, UV-vis absorption, infrared spectroscopy, molecular dynamics simulations, and density functional theory calculations reveals a distinct chemistry in the ligand layer, absent in other known thiol-stabilized gold nanoclusters. Our results imply a low-symmetry C1 ligand layer of 3-MBA around the gold core of Au68 and Au144 and suggest that 3-MBA protects the metal core not only by the covalent S-Au bond formation but also via weak π-Au and O═C-OH···Au interactions. The π-Au and -OH···Au interactions have a strength of the order of a hydrogen bond and thus are dynamic in water at ambient temperature. The -OH···Au interaction was identified by a distinct carbonyl stretch frequency that is distinct for 3-MBA-protected gold clusters, but is missing in the previously studied Au102(p-MBA)44 cluster. These thiol-gold interactions can be used to explain a remarkably low ligand density on the surface of the metal core of these clusters. Our results lay a foundation to understand functionalization of atomically precise ligand-stabilized gold nanoclusters via a route where weak ligand-metal interfacial interactions are sacrificed for covalent bonding.

Can Support Acidity Predict Sub-Nanometer Catalyst Activity Trends?

The effect of metal-oxide support on the activity of ethylene hydrogenation catalyzed by size-selected platinum clusters (8–20 atoms per cluster) is investigated. Size-selected clusters have been shown to possess unique catalytic properties which change as a function of the precise cluster size. The temperature-programmed reaction and isothermal pulsed molecular beam data both demonstrate a size-dependent reactivity on each support. However, predicted trends based on the acidic (SiO2) or basic (MgO) properties of the support are more subtle, with the influence of the support also being a function of the cluster size. Only the average hydrogenation activity of all sizes measured, as well as the CO stretching frequency on clean clusters, were observed to follow predicted trends, but atomic-level resolution demonstrates a much more complicated picture. Pt13 had the lowest hydrogenation activity of all sizes on amorphous SiO2, while being the most active size on MgO, and trends between the same cluster sizes ...

Impact of S doping on the structural, electronic and magnetic properties of Cr n (n = 2 − 6) clusters

The impact of sulphur doping on the geometrical and electronic properties of small chromium clusters with up to six atoms is investigated within the density functional theory in the generalized gradient approximation for exchange and correlation. Neutral and charged states are considered in order to analyze the behavior of the vertical ionization potential and adiabatic electron affinity as a function of cluster size. We find good agreement with experimental data for the above electronic indicators in the case of pure chromium clusters, and show that S doping enhances their absolute stability, without destroying for the smaller ones, or not completely for the larger ones, the dimerization pattern typical of small particles made of elements with exact half-band filling. Thus, the chromium skeleton is largely preserved in general. Moreover, S doping does not destroy the odd-even behavior of the electronic quantities either. We find lower relative stability in clusters with odd number of Cr atoms than in those with even number, while only odd-Cr clusters retain a total magnetic moment which results slightly quenched upon S doping. The moment of the anionic clusters remains unchanged upon doping. We show that doping with an S impurity is a way to increase the stability of small Cr nanoparticles, without substantially modifying their magnetic properties and other electronic indicators.

Stability and Vapor Pressure of Aqueous Aggregates and Aerosols Containing a Monovalent Ion.

The incidence of charged particles on the nucleation and the stability of aqueous aggregates and aerosols was reported more than a century ago. Many studies have been conducted ever since to characterize the stability, structure, and nucleation barrier of ion-water droplets. Most of these studies have focused on the free-energy surface as a function of cluster size, with an emphasis on the role of ionic charge and radius. This knowledge is fundamental to go beyond the rudimentary ion-induced classical nucleation theory. In the present article, we address this problem from a different perspective, by computing the vapor pressures of (H2O)nLi+ and (H2O)nCl- aggregates using molecular simulations. Our calculations shed light on the structure, the critical size, the range of stability, and the role of ion-water interactions in aqueous clusters. Moreover, they allow one to assess the accuracy of the classical thermodynamic model, highlighting its strengths and weaknesses.

Multibody expansion of particle interactions: How many-body is a particular element in a cluster

The particle-particle interaction potential of an $N\text{-atom}$ cluster is expanded in $n\text{-body}$ contributions. The expansion allows us to determine the magnitude of each one of the $n\text{-body}$ terms, and consequently quantifies how $n\text{-body}$ a potential really is. This way we obtain bounds for the relative error due to truncation, a feature that could be applicable in several contexts like the search of minimal energy cluster conformations, to obtain adequate seeds for further ab initio refinement, or to speed up molecular dynamics computations. We develop the formalism, and test the procedure numerically for the Lennard-Jones, Murrel-Motram, Gupta, and Sutton-Chen potentials. The contributions of the $n\text{-body}$ terms for Ag, Al, Au, Co, Cu, Fe, Ir, Ni, Pb, Pd, Pt, and Rh clusters are computed up to $n=9$; they show that the importance and magnitude of the $ng2$ interaction terms depend on the particular element. The relevance of the $n\text{-body}$ corrections as a function of cluster size is also explored for $N\ensuremath{\le}50$, and for a linear chain of $N\ensuremath{\le}1000$ atoms.

Lieb-Liniger-like model of quantum solvation in CO-(4)HeN clusters.

Small (4)He clusters doped with various molecules allow for the study of "quantum solvation" as a function of cluster size. A peculiarity of quantum solvation is that, as the number of (4)He atoms is increased from N = 1, the solvent appears to decouple from the molecule which, in turn, appears to undergo free rotation. This is generally taken to signify the onset of "microscopic superfluidity." Currently, little is known about the quantum mechanics of the decoupling mechanism, mainly because the system is a quantum (N + 1)-body problem in three dimensions which makes computations difficult. Here, a one-dimensional model is studied in which the (4)He atoms are confined to revolve on a ring and encircle a rotating CO molecule. The Lanczos algorithm is used to investigate the eigenvalue spectrum as the number of (4)He atoms is varied. Substantial solvent decoupling is observed for as few as N = 5 (4)He atoms. Examination of the Hamiltonian matrix, which has an almost block diagonal structure, reveals increasingly weak inter-block (solvent-molecule) coupling as the number of (4)He atoms is increased. In the absence of a dopant molecule the system is similar to a Lieb-Liniger (LL) gas and we find a relatively rapid transition to the LL limit as N is increased. In essence, the molecule initially-for very small N-provides a central, if relatively weak, attraction to organize the cluster; as more (4)He atoms are added, the repulsive interactions between the identical bosons start to dominate as the solvation ring (shell) becomes more crowded which causes the molecule to start to decouple. For low N, the molecule pins the atoms in place relative to itself; as N increases the atom-atom repulsion starts to dominate the Hamiltonian and the molecule decouples. We conclude that, while the notion of superfluidity is a useful and correct description of the decoupling process, a molecular viewpoint provides complementary insights into the quantum mechanism of the transition from a molecular cluster to a quantum solvated molecule.