Electronic properties and collision cross sections of AgOkHm± (k, m = 1-4) aerosol ionic clusters

Experimental evidence shows that hydroxylated metal ions are often produced during cluster synthesis by atmospheric pressure spark ablation. In this work, we predict the ground state equilibrium structures of AgOkHm± clusters (k and m = 1-4), which are readily produced when spark ablating Ag, using the coupled cluster with singles and doubles (CCSD) method. The stabilization energy of these clusters is calculated with respect to the dissociation channel having the lowest energy, by accounting perturbative triples corrections to the CCSD method. The interatomic interactions in each of the systems have been investigated using the frontier molecular orbital (FMO), natural bond orbital (NBO) and quantum theory of atoms in molecules (QTAIM) methods. Many of the ground states of these ionic clusters are found to be stable, corroborating experimental observations. We find that clusters having singlet spin states are more stable in terms of dissociation than the clusters that have doublet or triplet spin states. Our calculations also indicate a strong affinity of the ionic and neutral Ag atom towards water and hydroxyl radicals or ions. Many 3-center, 4-electron (3c/4e) hyperbonds giving rise to more than one resonance structure are identified primarily for the anionic clusters. The QTAIM analysis shows that the O-H and O-Ag bonds in the clusters of both polarities are respectively covalent and ionic. The FMO analysis indicates that the anionic clusters are more reactive than the cationic ones. Using the cluster structures predicted by the CCSD method, we calculate the collision cross sections of the AgOkHm± family, with k and m ranging from 1 to 4, by the trajectory method. In turn, we predict the electrical mobilities of these clusters when suspended in helium at atmospheric pressure and compare them with experimental measurements.

Where are the Excess Electrons in Subvalent Compounds? The Case of Ag7Pt2O7

Subvalent compounds raise the question of where those valence electrons not belonging to chemical bonds are. In the limiting case of Ag7Pt2O7, there is just one-electron excess in the chemical formula requiring the presence of Ag atoms with oxidation states below +1, assuming conventional Pt4+ and O2- ions. Such a situation challenges the understanding of the semiconducting and diamagnetic behavior observed in this oxide. Previous explanations that localize pairwise the electron excess in tetrahedral Ag4 interstices do not suffice in this case, since there are six silver tetrahedral voids and only an excess of nine electrons in the unit cell. Here, we provide an alternative explanation for the subvalent nature of this compound by combining interatomic distances, electron density-based descriptors, and orbital energetic analysis criteria. As a result, Ag atoms that do not participate in their valence electron are revealed. We identify excess electrons located in isolated subvalent silver clusters with electron-deficient multicenter bonds resembling pieces of metallic bonding in fcc-Ag and Ag7Pt2 alloy. Our analysis of the electronic band structure also supports the multicenter bonding picture. This combined approach from the real and reciprocal spaces reconciles existing discrepancies and is key to understanding the new chemistry of silver subvalent compounds.

Reactivity of cationic silver clusters with O2: a probe of interplay between clusters' geometric and electronic structures

We explored the size-dependent reactivity of Agn+ (n = 2-22) with O2 under mild conditions and found that only a few sizes of Agn+, with even values of n = 4, 6, 12, 16, 18, and 22, are reactive. Possible structures of Agn+ (n = 2-22) were determined using a genetic algorithm with incomplete local optimizations at the DFT level, and the calculated bonding strengths of O2 on these structures are consistent with experimental observations. Analyses revealed a close relationship between the reactivity of Agn+ with O2 and its HOMO-LUMO gap: cationic silver clusters with a small HOMO-LUMO gap are reactive, which can be rationalized by the covalent character of chemical bonds between Agn+ and O2 involving their frontier orbitals. The peculiar size-dependent HOMO-LUMO gaps and reactivity with O2 correlate with the subtle interplay between the electronic configurations and geometric structures of these silver cluster cations.

Vibrational wave-packet dynamics of the silver pentamer probed by femtosecond NeNePo spectroscopy

Vibrational wave-packet dynamics on the ground electronic state of the neutral silver pentamer (Ag5) are studied by femtosecond (fs) pump-probe spectroscopy using the 'negative ion - to neutral - to positive ion' (NeNePo) excitation scheme. A vibrational wave packet is prepared on the 2A1 state of Ag5via photodetachment of mass-selected, cryogenically cooled Ag5- anions using a fs pump pulse. The temporal evolution of the vibrational wave packet is then probed by an ultrafast probe pulse via resonant multiphoton ionization to Ag5+. Frequency analysis of the fs NeNePo transients for pump-probe delay times from 0.2 to 8 ps reveals three primary beating frequencies at 157 cm-1, 101 cm-1 and 56 cm-1 as well as four weaker features. A comparison of these experimentally obtained beating frequencies to harmonic normal mode frequencies calculated from electronic structure calculations confirms that Ag5 in the gas phase adopts a planar trapezoidal geometry, similar to that previously observed in solid argon. The dependence of the ionization yield on the laser polarization indicates a s-d wave electron photodetachment from a 'p-type' occupied molecular orbital of Ag5. Franck-Condon analysis shows that both processes, photodetachment and subsequent photoionization determine the beating frequencies probed in the time-dependent cation yield. The present study extends the applicability of fs NeNePo spectroscopy to characterize the vibrational spectra in the far-IR frequency range in the absence of perturbations from a medium or a messenger atom to mass-selected neutral metal clusters with more than three atoms in the ground electronic states.

Probing the binding and activation of small molecules by gas-phase transition metal clusters via IR spectroscopy

Isolated transition metal clusters have been established as useful models for extended metal surfaces or deposited metal particles, to improve the understanding of their surface chemistry and of catalytic reactions. For this objective, an important milestone has been the development of experimental methods for the size-specific structural characterization of clusters and cluster complexes in the gas phase. This review focusses on the characterization of molecular ligands, their binding and activation by small transition metal clusters, using cluster-size specific infrared action spectroscopy. A comprehensive overview and a critical discussion of the experimental data available to date is provided, reaching from the initial results obtained using line-tuneable CO₂ lasers to present-day studies applying infrared free electron lasers as well as other intense and broadly tuneable IR laser sources.

Silver cluster interactions with Pterin: Complex structure, binding energies and spectroscopy

Metal nanoclusters (NCs) are widely present today in biosensing, bioimaging, and diagnostics due to their small size, great biocompatibility, and sensitivity to the biomolecular environment. Silver (Ag) NCs often possess intense fluorescence, photostability, and low photobleaching, which is in high demand during the detection of organic molecules. Pterins are small compounds, which are used in medicine as biomarkers of oxidative stress, cardiovascular diseases, neurotransmitter synthesis, inflammation and immune system activation. It is experimentally possible to detect pterin (Ptr) through the adsorption on Ag colloid. We optimized geometries and evaluated the binding energy in Ptr-Ag_n^q complexes (n = 1-6; q = 0, +1, +2) using quantum chemistry methods. Different Ptr atoms were preferential for silver attachment depending on NC charge and size. The highest E_b was obtained for the complexes between the Ptr⁰ and Ag₃²⁺ (-50.8 kcal mol^-1), between Ptr^-1 and Ag₃²⁺ (-64.8 kcal mol^-1), which means that these complexes should be formed preferably in aqueous solutions in acidic and alkaline media, respectively. The colorimetric detection of pterin with silver clusters does not seem to be promising. However, intense S_0→S₁ transitions of Ag₅⁺ complexes look promising for luminescent Ptr detection. SERS detection of pterin is better to be done at pH > 8 since deprotonated pterin Raman undergo more dramatic changes upon addition of Ag than the neutral pterin. The characteristics of absorption and vibrational spectra of silver-pterin should be exploited during biosensor development.

Electronic Structure, Stability, and Electrical Mobility of Cationic Silver Oxide Atomic Clusters

Silver oxide cluster cations (Ag_nO_m⁺) can readily be produced by a number of methods including atmospheric-pressure spark ablation of pure silver electrodes when trace amounts of oxygen are present in the carrier gas. Here we determine the equilibrium geometries of Ag_nO_m⁺ clusters (n = 1-4; m = 1-5) using accurate coupled cluster with singles and doubles (CCSD) method, while the stabilization energies are calculated with additional perturbative triples correction (CCSD(T)). Although a number of stable states have been identified, our results show that the Ag_nO_m⁺ clusters with m = 1 are more stable than those with m ≥ 2 due to the absence of the terminally attached O₂ molecule, corroborating recent observations by mass spectrometry. Using the computed structures, we calculate the electrical mobilities of the Ag_nO_m⁺ clusters and label the values on a respective experimentally determined spectrum in an attempt to better interpret the occurrence of the peaks and troughs in the measurements.

An Algorithmic Approach Based on Data Trees and Genetic Algorithms to Understanding Charged and Neutral Metal Nanocluster Growth

Metal nanocluster growth pathways are challenging to study due to the number of possible species involved and the branching nature of possible mechanisms. We present a data tree-based approach to mapping these reaction pathways based on structures and energies obtained from Density Functional Theory (DFT) computations and including positive, negative, and neutral clusters in a continuum solvent of water. We also develop a genetic algorithm to study the relative stability of the clusters, which we combine with the data tree method to determine the effects that favorable decomposition reactions have on the reaction pathways. Introducing data tree pruning based on the exothermicity of each reaction, and including the first and second most important paths for each cluster up to five atoms including positive, neutral, and negative clusters, is then implemented to determine the cluster growth paths. These most favorable Ag-Ag reaction pathways are in agreement with more limited prior theoretical and experimental results, but they provide more systematic results that include predictions about the importance of clusters not previously identified. A key feature of the data tree approach is that it provides a comprehensive sampling of possible clusters, but without needing to generate the entire reaction tree. Additionally, the data tree-based approach allows for flexibility in the analysis based on restricting reactant charge or size, selecting a starting species to mimic an experimental precursor, and choosing a maximum allowable final cluster size or charge of interest.

Interactions of Nitric Oxide Molecules with Pure and Oxidized Silver ClustersAgn{plus minus}/AgnO{plus minus} (n=11-13). A Computational Study

In this work we studied, within DFT, the interaction of NO with pure and oxidized Agn, both anionic and cationic, composed from11 to 13 Ag atoms. In that size interval, shell closing effects are not expected, and structural and electronic odd-even effects will determine the strength of interaction. We obtained that species Agn{plus minus} and AgnO{plus minus} with odd number of electrons (n=12) adsorb NO with higher energy than their neighbours. This result agrees with the facts observed in recent mass spectroscopy measurements, which were performed at finite temperature. The adsorption energy is about twice for oxidized clusters compared to pure ones, and higher for anions than for cations. The adsorption of another NO molecule on AgnNO{plus minus} forms Agn(NO)2{plus minus}, with the dimer (NO)2 in cis configuration, and binding the two N atoms with two neigbour Ag atoms. The n=12 show the higher adsorption energy again. In absence of reaction barriers, Agn(NO)2{plus minus} dissociate spontaneously into AgnO{plus minus} and N2O, except the n= 12 anion. The máximum high barrier along the dissociation path of Ag13(NO)2- is about 0.7 eV. Further analysis of PDOS for Ag11-13 (NO)x{plus minus} (x=0,1,2) molecules shows that bonding between NO and Agn mainly occurs in the range between -3.0 eV and 3.0 eV. The overlap between 4 d of Ag and 2 p of N and O is larger for Ag12(NO)2{plus minus} than for neighbour sizes. For n=12, the d bands are close to the (NO)2 2π orbital, leading to extra back-donation charge from the 4 d of Ag to the closer 2π orbital of (NO)2.

Silver Cluster Interactions with Tyrosine: Towards Amino Acid Detection

Tyrosine (Tyr) is involved in the synthesis of neurotransmitters, catecholamines, thyroid hormones, etc. Multiple pathologies are associated with impaired Tyr metabolism. Silver nanoclusters (Ag NCs) can be applied for colorimetric, fluorescent, and surface-enhanced Raman spectroscopy (SERS) detection of Tyr. However, one should understand the theoretical basics of interactions between Tyr and Ag NCs. Thereby, we calculated the binding energy (Eb) between Tyr and Agnq (n = 1-8; q = 0-2) NCs using the density functional theory (DFT) to find the most stable complexes. Since Ag NCs are synthesized on Tyr in an aqueous solution at pH 12.5, we studied Tyr-1, semiquinone (SemiQ-1), and Tyr-2. Ag32+ and Ag5+ had the highest Eb. The absorption spectrum of Tyr-2 significantly red-shifts with the attachment of Ag32+, which is prospective for colorimetric Tyr detection. Ag32+ interacts with all functional groups of SemiQ-1 (phenolate, amino group, and carboxylate), which makes detection of Tyr possible due to band emergence at 1324 cm-1 in the vibrational spectrum. The ground state charge transfer between Ag and carboxylate determines the band emergence at 1661 cm-1 in the Raman spectrum of the SemiQ-1-Ag32+ complex. Thus, the prospects of Tyr detection using silver nanoclusters were demonstrated.

Theoretical study of the stability, structure, and optical spectra of small silver clusters and their formation using density functional theory

An understanding of the mechanism of formation of small clusters would help to identify efficient routes to their synthesis. Here, we apply density functional theory (DFT) to study the free energies and structure of ultra-small silver clusters, and time-dependent density functional theory (TDDFT) to calculate their UV-Vis spectra and provide a better understanding of the intermediate steps in cluster formation in the gas phase and solution. Our calculations of the optical properties of neutral and cationic clusters confirm the presence of charged and uncharged intermediates observed in pulse radiolysis experiments during the early stages of the growth of silver clusters. The free energies of formation of hydrated clusters extracted from DFT calculations reveal the greater thermodynamic stability of cationic clusters compared to the corresponding neutral clusters of the same composition. This is consistent with the predominance of kinetically stable cationic clusters observed in pulse radiolysis experiments. Our DFT and TDDFT calculations clarify the effects of ligand, hydration, and oxidation states on the structure, stability, and optical properties of silver clusters that elucidate the mechanism of silver cluster formation in solution and the gas phase.

Comment on 'Structural characterization, reactivity and vibrational properties of silver clusters: a new global minimum for Ag16' by P. L. Rodríguez-Kessler, A. R. Rodríguez-Domínguez, D. MacLeod Carey and A. Muñoz-Castro, Phys. Chem. Chem. Phys., 2020, 22, 27255, DOI: D0CP04018E

A recent paper by Rodríguez-Kessler et al., Phys. Chem. Chem. Phys., 2020, 22, 27255-27262, reported not only results of quantum chemical computations (using the PW91 density functional) on Ag₁₆ clusters as emphasized in the article's title, but also on the Ag₁₅ size. These authors confirmed previous results obtained by McKee and Samokhvalov (J. Phys. Chem. A, 2017, 121, 5018-5028 using the M06 density functional) that the most stable isomer of Ag₁₅ is a C_2v structure. We wish to point out that two low symmetry isomers of Ag₁₅ that have a similar energy content are even lower in energy than their reported C_2v global minimum. The relative energies between low-lying Ag₁₅ isomers were again found to be method-dependent, and within the expected accuracy of DFT and CCSD(T) methods they could be considered as energetically degenerate, and likely coexist in a molecular beam. The new lower-energy Ag₁₅ isomers appear to fit more consistently within the structural evolution of small silver clusters.

Combined NMR and Computational Study of Cysteine Oxidation during Nucleation of Metallic Clusters in Biological Systems

The widespread biomedical applications of silver and gold nanoparticles (AgNPs and AuNPs, respectively) prompt the need for mechanistic evaluation of their interaction with biomolecules. In biological media, metallic NPs are known to transform by various pathways, especially in the presence of thiols. The interplay between metallic NPs and thiols may lead to unpredictable consequences for the health status of an organism. This study explored the potential events occurring during biotransformation, dissolution, and reformation of NPs in the thiol-rich biological media. The study employed a model system evaluating the interaction of cysteine with small-sized AgNPs and AuNPs. The interplay of cysteine on transformation and reformation pathways of these NPs was experimentally investigated by nuclear magnetic resonance (NMR) spectroscopy and supported by light scattering techniques and transmission electron microscopy (TEM). As the main outcome, Ag- or Au-catalyzed oxidation of cysteine to cystine was found to occur through generation of reactive oxygen species (ROS). Computational simulations confirmed this mechanism and the role of ROS in the oxidative dimerization of biothiol during NPs reformation. The obtained results represent valuable mechanistic data about the complex events during the transport of metallic NPs in thiol-rich biological systems that should be considered for the future biomedical applications of metal-based nanomaterials.

Stability of cationic silver doped gold clusters and the subshell-closed electronic configuration of AgAu14. J Chem Phys 2020;153:244304. [PMID: 33380086 DOI: 10.1063/5.0033487]

Silver doping is a valuable route to modulate the structural, electronic, and optical properties of gold clusters. We combine photofragmentation experiments with density functional theory calculations to investigate the relative stability of cationic Ag doped Au clusters, AgAu_N-1 ⁺ (N ≤ 40). The mass spectra of the clusters after photofragmentation reveal marked drops in the intensity of AgAu₈ ⁺, AgAu₁₄ ⁺, and AgAu₃₄ ⁺, indicating a higher relative stability of these sizes. This is confirmed by the calculated AgAu_N-1 ⁺ (N ≤ 17) dissociation energies peaking for AgAu₆ ⁺, AgAu₈ ⁺, and AgAu₁₄ ⁺. While the stability of AgAu₆ ⁺ and AgAu₈ ⁺ can be explained by the accepted electronic shell model for metal clusters, density of states analysis shows that the geometry plays an important role in the higher relative stability of AgAu₁₄ ⁺. For this size, there is a degeneracy lifting of the 1D shell, which opens a relatively large HOMO-LUMO gap with a subshell-closed 1S²1P⁴1P²1D⁶ electronic configuration.

The structures of cationic gold clusters probed by far-infrared spectroscopy

Determining the precise structures of small gold clusters is an essential step towards understanding their chemical and physical properties. Due to the relativistic nature of gold, its clusters remain planar (2D) up to appreciable sizes. Ion mobility experiments have suggested that positively charged gold clusters adopt three-dimensional (3D) structures from n = 8 onward. Computations predict, depending on the level of theory, 2D or 3D structures as putative energy-minimum for n = 8. In this work, far-infrared multiple photon dissociation spectroscopy, using Ar as tagging element, is combined with density-functional theory calculations to determine the structures of Au_n⁺ (n≤ 9) clusters formed by laser ablation. While the Au frameworks in Au₆Ar_m⁺ and Au₇Ar_m⁺ complexes are confirmed to be planar and that in Au₉Ar_m⁺ three-dimensional, we demonstrate the coexistence of 3D and planar Au₈Ar_m⁺ (m = 1-3) isomers. Thus, it is revealed that at finite temperatures, the formal 2D to 3D transition takes place at n = 8 but is not sharp.

Gas-Phase Infrared Spectroscopy of Neutral Peptides: Insights from the Far-IR and THz Domain

Gas-phase, double resonance IR spectroscopy has proven to be an excellent approach to obtain structural information on peptides ranging from single amino acids to large peptides and peptide clusters. In this review, we discuss the state-of-the-art of infrared action spectroscopy of peptides in the far-IR and THz regime. An introduction to the field of far-IR spectroscopy is given, thereby highlighting the opportunities that are provided for gas-phase research on neutral peptides. Current experimental methods, including spectroscopic schemes, have been reviewed. Structural information from the experimental far-IR spectra can be obtained with the help of suitable theoretical approaches such as dynamical DFT techniques and the recently developed Graph Theory. The aim of this review is to underline how the synergy between far-IR spectroscopy and theory can provide an unprecedented picture of the structure of neutral biomolecules in the gas phase. The far-IR signatures of the discussed studies are summarized in a far-IR map, in order to gain insight into the origin of the far-IR localized and delocalized motions present in peptides and where they can be found in the electromagnetic spectrum.

Dissociative chemisorption of O2 on Agn and Agn−1Ir (n = 3–26) clusters: a first-principle study

Lower dissociation barriers and higher reaction rates of O₂ on doped Ag_n−1Ir clusters, and a gradually weakened dopant effect.

Solvation of Silver Ions in Noble Gases He, Ne, Ar, Kr, and Xe

We use a novel technique to solvate silver cations in small clusters of noble gases. The technique involves the formation of large, superfluid helium nanodroplets that are subsequently electron ionized, mass-selected by deflection in an electric field, and doped with silver atoms and noble gases (Ng) in pickup cells. Excess helium is then stripped from the doped nanodroplets by multiple collisions with helium gas at room temperature, producing cluster ions that contain no more than a few dozen noble gas atoms and just a few (or no) silver atoms. Under gentle stripping conditions, helium atoms remain attached to the cluster ions, demonstrating their low vibrational temperature. Under harsher stripping conditions, some of the heavier noble gas atoms will be evaporated as well, thus enriching stable clusters of Ng_nAg_m⁺ at the expense of less stable ones. This results in local anomalies in the cluster ion abundance, which is measured in a high-resolution time-of-flight mass spectrometer. On the basis of these data, we identify specific "magic" sizes n of particularly stable ions. There is no evidence, however, for enhanced stability of Ng₂Ag⁺, in contrast to the high stability of Ng₂Au⁺ that derives from the covalent nature of the bond for heavy noble gases. "Magic" sizes are also identified for Ag₂⁺ dimer ions complexed with He or Kr. Structural models will be tentatively proposed. A sequence of magic numbers n = 12, 32, and 44, indicative of three concentric solvation shells of icosahedral symmetry, is observed for He_nH₂O⁺.

Adsorption Kinetics of Nitrogen Molecules on Size-Selected Silver Cluster Cations

We present adsorption processes of dinitrogen on size-selected silver cluster cations, Ag n + (n = 1–10), studied by kinetics measurement using an ion trap. The cluster ions showed sequential adsorption of N2 molecules when the ion trap was cooled down to 105 K, excluding n = 8 and 9 that were exceptionally inactive at this temperature. Termolecular rate coefficients of each adsorption step are determined by analyzing time-dependent changes in the reactant and product ion signals. The first-step rate coefficients were found to increase exponentially from n = 1 to 7 due to increased internal degrees of freedom at larger sizes, which are favorable for accommodating the adsorption energy in a free cluster. In contrast, the adsorption rate turned to decrease for n > 7 due to weaker binding of dinitrogen as revealed by density-functional-theory (DFT) calculation. Adsorption sites on Ag n + are further discussed on the basis of the maximum number of adsorbing N2 molecules observed in the experiment.

Structures of Cu n+ ( n = 3-10) Clusters Obtained by Infrared Action Spectroscopy

Coinage metal clusters are of great importance for a wide range of scientific fields, ranging from microscopy to catalysis. Despite their clear fundamental and technological importance, the experimental structural determination of copper clusters has attracted little attention. We fill this gap by elucidating the structure of cationic copper clusters through infrared (IR) photodissociation spectroscopy of Cu _n⁺-Ar _m complexes. Structures of Cu _n⁺ ( n = 3-10) are unambiguously assigned based on the comparison of experimental IR spectra in the 70-280 cm^-1 spectral range with spectra calculated using density functional theory. Whereas Cu₃⁺ and Cu₄⁺ are planar, starting from n = 5, Cu _n⁺ clusters adopt 3D structures. Each successive cluster size is composed of its predecessor with a single atom adsorbed onto the face, giving evidence of a stepwise growth.

Relative Stability of Small Silver, Platinum, and Palladium Doped Gold Cluster Cations

The stability patterns of single silver, platinum, and palladium atom doped gold cluster cations, MAuN−1+ (M = Ag, Pt, Pd; N = 3–6), are investigated by a combination of photofragmentation experiments and density functional theory calculations. The mass spectra of the photofragmented clusters reveal an odd-even pattern in the abundances of AgAuN−1+, with local maxima for clusters containing an even number of valence electrons, similarly to pure AuN+. The odd-even pattern, however, disappears upon Pt and Pd doping. Computed dissociation energies agree well with the experimental findings for the different doped clusters. The effect of Ag, Pt, and Pd doping is discussed on the basis of an analysis of the density of states of the N = 3–5 clusters. Whereas Ag delocalizes its 5s valence electron in all sizes, this process is size-specific for Pt and Pd.

Structures and magnetic properties of small [Formula: see text] and Co n-1Cr+ (n = 3-5) clusters

Small cobalt clusters [Formula: see text] and their single chromium atom doped counterparts Co _n-1Cr⁺ (n  =  3-5) were studied mass spectrometrically by measuring the infrared multiple photon dissociation (IRMPD) spectra of the corresponding argon tagged complexes. The geometric and electronic structures of the [Formula: see text] and Co _n-1Cr⁺ (n  =  3-5) clusters as well as their Ar complexes were optimized by density functional theory (DFT) calculations. The obtained lowest energy structures were confirmed by comparing the IRMPD spectra of [Formula: see text] and [Formula: see text] (n  =  3-5, m  =  3 and 4) with the corresponding calculated IR spectra. The calculations reveal that the doped Co _n-1Cr⁺ clusters retain the geometric structures of the most stable [Formula: see text] clusters. However, the coupling of the local magnetic moments within the clusters is altered in a size-dependent way: the Cr atom is ferromagnetically coupled in Co₂Cr⁺ and Co₃Cr⁺, while it is antiferromagnetically coupled in Co₄Cr⁺.

Elucidation of the molecular and electronic structures of some magic silver clusters Agn (n = 8, 18, 20)

Density functional theory (DFT) calculations were carried out to explore the geometric, spectroscopic, and electronic properties of three magic silver clusters Ag_n (n = 8, 18, and 20) in detail. The computed results show that the global minima of these clusters are compact, near-spherical structures, while other low-lying isomers exhibit oblate or prolate shapes. Vertical ionization energies for the low-lying isomers were also computed and assigned with respect to available experimental values. Although several isomers were predicted to have similar energies, their electronic and vibrational signatures were quite distinctive, meaning that they could be used as fingerprint signals to distinguish between isomers. In addition, the electronic structures of these systems were explored using the phenomenological shell model. Calculations for the coinage metal clusters M₂₀ (M = Cu, Ag, Au) indicated that the structures and properties of the Ag cluster are similar to those of the Cu cluster in that both Cu₂₀ and Ag₂₀ prefer a compact structure whereas Au₂₀ prefers to adopt a tetrahedral form. Graphical abstract Shell Orbitals of Ag₈ Cluster.