Possible ground-state structure of Au26: A highly symmetric tubelike cage

Formation of pyramidal structures through mixing gold and platinum atoms: the AuxPty2+ clusters with x + y = 10

The geometric and electronic structures of a small series of mixed gold and platinum AuxPty2+ clusters, with x + y = 10, were investigated using quantum chemical methods. A consistent tetrahedral pyramid structure emerges, displaying two patterns of structural growth by a notable critical point at y = 5. This affects the clusters' electron population, chemical bonding, and stability. For the Pt-doped Au clusters with y values from 2 to 5, the bonds enable Pt atoms to assemble into symmetric line, triangle, quadrangle, and tetragonal pyramidal Pty blocks, respectively. For the Au-doped Pt clusters, with larger values of y > 5, the structures are more relaxed and the d electrons of Pt atoms become delocalized over more centers, leading to lower symmetry structures. A certain aromaticity arising from delocalization of d electrons over the multi-center framework in the doped Pt clusters contributes to their stability, with Pt102+ at y = 10 exhibiting the highest stability. While the ground electronic state of the neutral platinum atom [Xe]. 4f145d96s1 leads to a triplet state (3D3), the total magnetic moments of AuxPty2+ are large increasing steadily from 0 to 10 μB and primarily located on Pt atoms, corresponding to the increase of the number of Pt atoms from 0 to 10 and significantly enhancing the magnetic moments. An admixture of both Au and Pt atoms thus emerges as an elegant way of keeping a small pyramidal structure but bringing in a high and controllable magnetic moment.

Structural transformations in Cu, Ag, and Au metal nanoclusters

Finite-temperature structures of Cu, Ag, and Au metal nanoclusters are calculated in the entire temperature range from 0 K to melting using a computational methodology that we proposed recently [M. Settem et al., Nanoscale 14, 939 (2022)]. In this method, Harmonic Superposition Approximation (HSA) and Parallel Tempering Molecular Dynamics (PTMD) are combined in a complementary manner. HSA is accurate at low temperatures and fails at higher temperatures. PTMD, on the other hand, effectively samples the high temperature region and melts. This method is used to study the size- and system-dependent competition between various structural motifs of Cu, Ag, and Au nanoclusters in the size range 1-2 nm. Results show that there are mainly three types of structural changes in metal nanoclusters, depending on whether a solid-solid transformation occurs. In the first type, the global minimum is the dominant motif in the entire temperature range. In contrast, when a solid-solid transformation occurs, the global minimum transforms either completely to a different motif or partially, resulting in the co-existence of multiple motifs. Finally, nanocluster structures are analyzed to highlight the system-specific differences across the three metals.

New Insights into Adsorption Properties of the Tubular Au26 from AIMD Simulations and Electronic Interactions

Recently, we revealed the electronic nature of the tubular Au₂₆ based on spherical aromaticity. The peculiar structure of the Au₂₆ could be an ideal catalyst model for studying the adsorptions of the Au nanotubes. However, through Google Scholar, we found that no one has reported connections between the structure and reactivity properties of Au₂₆. Here, three kinds of molecules are selected to study the fundamental adsorption behaviors that occur on the surface of Au₂₆. When one CO molecule is adsorbed on the Au₂₆, the σ-hole adsorption structure is quickly identified as belonging to a ground state energy, and it still maintains integrity at a temperature of 500 K, where σ donations and π-back donations take place; however, two CO molecules make the structure of Au₂₆ appear with distortions or collapse. When one H₂ is adsorbed on the Au₂₆, the H-H bond length is slightly elongated due to charge transfers to the anti-bonding σ* orbital of H₂. The Au₂₆-H₂ can maintain integrity within 100 fs at 300 K and the H₂ molecule starts moving away from the Au₂₆ after 200 fs. Moreover, the Au₂₆ can act as a Lewis base to stabilize the electron-deficient BH₃ molecule, and frontier molecular orbitals overlap between the Au₂₆ and BH₃.

Tempering of Au nanoclusters: capturing the temperature-dependent competition among structural motifs

A computational approach to determine the equilibrium structures of nanoclusters in the whole temperature range from 0 K to melting is developed. Our approach relies on Parallel Tempering Molecular Dynamics (PTMD) simulations complemented by Harmonic Superposition Approximation (HSA) calculations and global optimization searches, thus combining the accuracy of global optimization and HSA in describing the low-energy part of configuration space, together with the PTMD thorough sampling of high-energy configurations. This combined methodology is shown to be instrumental towards revealing the temperature-dependent structural motifs in Au nanoclusters of sizes 90, 147, and 201 atoms. The reported phenomenology is particularly rich, displaying a size- and temperature-dependent competition between the global energy minimum and other structural motifs. In the case of Au₉₀ and Au₁₄₇, the global minimum is also the dominant structure at finite temperatures. In contrast, the Au₂₀₁ cluster undergoes a solid-solid transformation at low temperature (<200 K). Results indicate that PTMD and HSA very well agree at intermediate temperatures, between 300 and 400 K. For higher temperatures, PTMD gives an accurate description of equilibrium, while HSA fails in describing the melting range. On the other hand, HSA is more efficient in catching low-temperature structural transitions. Finally, we describe the elusive structures close to the melting region which can present complex and defective geometries, that are otherwise difficult to characterize through experimental imaging.

Another look at energetically quasi-degenerate structures of the gold cluster Au27 q with q = 1, 0, -1

Quantum chemical computations were used to reinvestigate the geometries, spectroscopic, and energetic properties of the gold clusters Au₂₇ ^q in three charge states (q = 1, 0, -1). Density functional theory (DFT) and the domain-based local pair natural orbital modification of the coupled-cluster theory DLPNO-CCSD(T) calculations revealed that, at variance with earlier reports in the literature, while the anion Au₂₇ ^- tends to exist in a tube-like form, both the lowest-energy Au₂₇ and Au₂₇ ⁺ isomers exhibit a pyramidal shape. However, several isomers were found to lie very close in energy, thus rendering a structural transition and their coexistence easy to occur. More specifically, the equilibrium geometry of the neutral Au₂₇ is a core-shell pyramid-like structure with one gold atom located inside. We also identified a novel ground state for the anion Au₂₇ ^- and located for the first time the global minimum of the cation Au₂₇ ⁺ . The vertical detachment energies of the neutral and anionic states were also computed and used to assign the available experimental photoelectron spectra. Although many Au₂₇ isomers were predicted to be energetically quasi-degenerate, the corresponding distinctive vibrational signatures can be used as fingerprints for the identification of cluster geometrical features.

Structural Evolution and Stability Trend of Small-Sized Gold Clusters Aun (n = 20-30)

Structural evolution and stability pattern of pure neutral gold clusters Au_n in the small size range of n = 20-30 are examined using density functional theory (DFT) calculations. The equilibrium geometries are either confirmed or determined, and some new ground state structures are identified. The most stable configurations of Au₂₁-Au₂₃ sizes are formed by adding extra gold atoms to the highly stable pyramidal structure of Au₂₀, while flat-cage shapes are the best candidates for the global minima of both Au₂₄ and Au₂₅. For larger sizes of n = 26-30, pyramidal motifs tend to dominate the lower-lying population rather than tubular conformations as previously reported. The energy gaps, excitation energies, and exciton binding energies are also computed to test out the performance of the computational methods employed. Accordingly, a density functional with long-range exchange effects is highly recommended to quantitatively investigate both the ground and excited states of pure gold clusters.

Electronic shells of a tubular Au26 cluster: a cage-cage superatomic molecule based on spherical aromaticity

Gold clusters, which display a variety of unusual geometric structures due to their strong relativistic effects, have attracted much attention. Among them, Au₂₆ has a high-symmetry tubular structure (D_6d) with a large HOMO-LUMO energy gap, but its electronic stability still remains unclear. In this paper, the electronic nature of the Au₂₆ cluster is investigated using the density functional theory method. Depending on the super valence bond model, the tubular Au₂₆ cluster with 26 valence electrons could be viewed as a superatomic molecule composed of two open cages based on spherical aromaticity, and its molecule-like electronic shell closure is achieved via a super triple bond (σ, 2π) between the two cages. Based on this new cage-cage superatomic structural model, a series of similar tubular clusters are predicted from the Au₂₆ skeleton. The two capped Au atoms are replaced by Cu, Ag and In atoms, respectively, to form tubular D_6d Au₂₄Cu₂ and Au₂₄Ag₂ (26e) and Au₂₄In₂ (30e) clusters, where the super triple bonds also exist. Moreover, tubular D_5d Au₂₀In₂ (26e) is obtained by replacing hexatomic Au₆ rings in the bulk of Au₂₄In₂ with pentagonal Au₅ rings. Chemical bonding analysis reveals that there is a super quintuple bond (σ, 2π, 2δ) between two open (Au₁₀In) cages, in accordance with the 26e Li₂₀Mg₃ superatomic molecule composed of two icosahedral superatoms. Our study proposes the new cage-cage structural model of superatomic molecules based on spherical aromaticity, which extends the range of the super valence bonding pattern and gives inferences for further study of superatomic clusters.

Stability of AumAgn (m + n = 1-6) clusters supported on a F-center MgO(100) surface

A theoretical study has been performed for deposited AumAgn (m + n = 1-6) clusters. The combined use of the Mexican Enhanced Genetic Algorithm (MEGA) and Density Functional Theory (DFT) calculations allows us to explore the potential energy surface and therefore, find the global minimum configuration for each composition. We have performed calculations of clusters deposited on defects (oxygen vacancies) known as F centers on MgO (100) surfaces. Our results show interesting differences in the geometries of the clusters upon deposition and as a consequence in their electronic properties. The combination of two metals with different electronegativities creates an inhomogeneous charge distribution on their exposed surface producing good conditions for a catalytic process to take place.

Au26: a case of fluxionality/co-existence

BOMD simulations are performed on experimentally identified conformations of the fluxional Au26 cluster at finite temperature. Comprehensive analysis of structural, electronic and thermal properties indicates that the highest energy tubular cage conformation (till 500 K) outperforms the ground state conformation (till 400 K) in terms of thermal stability.

Au19M (M=Cr, Mn, and Fe) as magnetic copies of the golden pyramid

An investigation on structure, stability, and magnetic properties of singly doped Au19M (M=Cr, Mn, and Fe) clusters is carried out by means of density functional theory calculations. The studied clusters prefer forming magnetic versions of the unique tetrahedral Au20. Stable sextet Au19Cr is identified as the least reactive species and can be qualified as a magnetic superatom. Analysis on cluster electronic structures shows that the competition between localized and delocalized electronic states governs the stability and magnetic properties of Au19M clusters.

Superatom-atom super-bonding in metallic clusters: a new look to the mystery of an Au20 pyramid

Using the super valence bond model, a generalized chemical picture for the electronic shells of an Au20 pyramid is given. It is found that Au20 can be viewed to be a superatomic molecule, of which its superatomic 16c-16e core (T) is in D(3)S hybridization bonded with four vertical Au atoms for the molecule-like (TAu4) electronic shell-closure. Based on such a superatom-atom bonding model, TX4 (X = F, Cl, or Br) are predicted to be very stable. Such a superatom-atom T-Au/T-X bonding enriches the scope of chemistry.

Structural and electronic properties of tungsten nanoclusters by DFT and basin-hopping calculations

The structural and electronic properties of small tungsten nanoclusters W_n (n = 2–16) were investigated by density functional theory (DFT) calculations.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Growth mechanism and chemical bonding in scandium-doped copper clusters: experimental and theoretical study in concert

Size matters! The electronic structure and size-dependent stability of neutral and cationic scandium-doped copper clusters have been investigated by mass spectrometric studies (for the cations) and also quantum chemical computations. The proposed reaction paths ultimately lead to the most stable Frank-Kasper-shaped Cu(16)Sc(+) cluster (shown here), which could be the germ of a new crystallization process.Electronic structure and size-dependent stability of scandium-doped copper cluster cations, Cu(n)Sc(+), were investigated by using a dual-target dual-laser vaporization production scheme followed by mass spectrometric studies and also quantum chemical computations in the density functional theory framework. The neutral species also were studied by using computational methods. Enhanced abundances and dissociation energies were measured in the case of Cu(n)Sc(+) for n=4, 6, 8, 10 and 16, the last of these identified as being extraordinary stable. Neutral clusters are stable with n=5, 7, 9 and 15, which are isoelectronic with respect to the number of the valence s electrons with the stable cationic clusters; hence a simple electron count determines cluster properties to a great extent. The Cu(17)Sc cluster was found to be a superatomic molecule, containing Cu(16)Sc(+) and Cu(-) units; however, the charge separation is not as pronounced as in the case of CuLi. Cu(15)Sc was found to be a stable cluster with a large dissociation energy and a closed electronic structure; hence this can be regarded as a superatom, analogous to the noble gases. The main factors determining the growth patterns of these clusters are the central position of the scandium atom and the successive filling of the shell orbitals. For smaller clusters, the reaction paths appear to diverge yielding various products; however all paths ultimately lead to the most stable Frank-Kasper shaped Cu(16)Sc cluster, which in turn can be the germ of the crystallization process.

Size-Dependent Structural Evolution and Chemical Reactivity of Gold Clusters

Ground-state structures and other experimentally relevant isomers of Au(15) (-) to Au(24) (-) clusters are determined through joint first-principles density functional theory and photoelectron spectroscopy measurements. Subsequent calculations of molecular O(2) adsorption to the optimal cluster structures reveal a size-dependent reactivity pattern that agrees well with earlier experiments. A detailed analysis of the underlying electronic structure shows that the chemical reactivity of the gold cluster anions can be elucidated in terms of a partial-jellium picture, where delocalized electrons occupying electronic shells move over the ionic skeleton, whose geometric structure is strongly influenced by the directional bonding associated with the highly localized "d-band" electrons.

Dual Relationship between Large Gold Clusters (Antifullerenes) and Carbon Fullerenes: A New Lowest-Energy Cage Structure for Au50

Recent theoretical prediction and experimental confirmation of cage configurations for Au clusters have stimulated considerable interest in finding novel gold clusters exhibiting high stability. We use a dual relationship between gold antifullerene cages with all triangular faces and carbon fullerenes with all degree 3 vertices to construct a large number of Au50 antifullerene cages by omnicapping and dualization procedures. Among these cages we find a new D6d cage as the lowest-energy configuration of Au50. The unusual stability of this new Au50 cage is associated with spherical aromaticity and sp-d hybridization.