Tuning the electronic structure of gold cluster-assembled materials by altering organophosphine ligands

Superatomic clusters can be assembled to build bulk matter, where the individual characteristics are preserved. The main benefit of these materials over conventional bulk species is the capability to tailor their features by altering the physicochemical identities of individual clusters. Electronic properties of metal clusters can be modified by a protective shell of ligands that attach to the surface and make the whole nanoparticle soluble in organic or aqueous solvents. In the present work, we demonstrate that properly chosen ligands provide not only steric protection from aggregation but also tune the redox activity of metal clusters. We investigate the role of the ligands in electronic structure tunability and ligand-field splitting. Our first-principles calculations agree with the experiments, showing that phosphine-protected gold materials are small gap semiconductors. The obtained bandgaps strongly depend on the ligand used. Hence, using phosphine and organophosphine ligands should be feasible and promising while designing the novel superatom-based materials since the desired range of the bandgap might be achieved (by the proper choice of the ligand).

Dynamic sampling of liquid metal structures for theoretical studies on catalysis

Liquid metals have recently emerged as promising catalysts that can outcompete their solid counterparts for many reactions. Although theoretical modelling is extensively used to improve solid-state catalysts, there is currently no way to capture the interactions of adsorbates with a dynamic liquid metal. We propose a new approach based on ab initio molecular dynamics sampling of an adsorbate on a liquid catalyst. Using this approach, we describe time-resolved structures for formate adsorbed on liquid Ga-In, and for all intermediates in the methanol oxidation pathway on Ga-Pt. This yields a range of accessible adsorption energies that take into account the at-temperature motion of the liquid metal. We find that a previously proposed pathway for methanol oxidation on Ga-Pt results in unstable intermediates on a dynamic liquid surface, and propose that H desorption must occur during the path. The results showcase a more accurate way to treat liquid metal catalysts in this emerging field.

Dynamic Activation of Ga Sites by Pt Dopant in Low-Temperature Liquid-Metal Catalysts

Liquid GaPt catalysts with Pt concentrations as low as 1×10^-4  atomic % have recently been identified as highly active for the oxidation of methanol and pyrogallol under mild reaction conditions. However, almost nothing is known about how liquid state catalysts support these significant improvements in activity. Here, ab initio molecular dynamics simulations are employed to examine GaPt catalysts in isolation and interacting with adsorbates. We find that persistent geometric features can exist in the liquid state, given the correct environment. We postulate that the Pt dopant may not be limited to direct involvement in catalysis of reactions, but rather that its presence can also enable Ga atoms to become catalytically active.

Structural and electronic changes in Ga-In and Ga-Sn alloys on melting

The melting behaviour of surface slabs of Ga-In and Ga-Sn is studied using periodic density functional theory and ab initio molecular dynamics. Analysis of the structure and electronics of the solid and liquid phases gives insight into the properties of these alloys, and why they may act as promising CO₂ reduction catalysts. We report melting points for slabs of hexa-layer Ga-In (386 K) and Ga-Sn (349 K) that are substantially lower than the pure hexa-layer Ga system (433 K), and attribute the difference to the degree to which the dopant (In or Sn) disrupts the layered Ga network. In molecular dynamics trajectories of the liquid structures, we find that dopant tends to migrate from the centre of the slab towards the surface and accumulate there. Bader charge calculations reveal that the surface dopant atoms have increased positive charge, and density of states analyses suggest the liquid alloys maintain metallic electronic behaviour. Thus, surface In and Sn may provide good binding sites for intermediates in CO₂ reduction. This work contributes to our understanding of the properties of liquid metal systems, and provides a foundation for modelling catalysis on these materials.

Concentration dependent alloying behaviour of liquid GaAu

Liquid GaAu systems provide the possibility of developing dynamic and self-healing materials for a variety of applications, including catalysis. GaAu systems provide both dynamic capability by being liquid at just above room temperature, as a result of the Ga, and likely catalytic activity, resulting from the Au. While the formation of a Ga₂Au intermetallic is known, the behaviours that result from lower Au concentrations within a liquid Ga solvent are hitherto unknown. Here, ab initio molecular dynamics are used to understand how different low concentrations of Au operate within a liquid Ga solvent. We determine that Au concentrations of between 15% Au wt and 25% Au wt will give rise to the highest abundance of stabilised single Au atoms.

Liquid metal synthesis solvents for metallic crystals

In nature, snowflake ice crystals arrange themselves into diverse symmetrical six-sided structures. We show an analogy of this when zinc (Zn) dissolves and crystallizes in liquid gallium (Ga). The low-melting-temperature Ga is used as a "metallic solvent" to synthesize a range of flake-like Zn crystals. We extract these metallic crystals from the liquid metal solvent by reducing its surface tension using a combination of electrocapillary modulation and vacuum filtration. The liquid metal-grown crystals feature high morphological diversity and persistent symmetry. The concept is expanded to other single and binary metal solutes and Ga-based solvents, with the growth mechanisms elucidated through ab initio simulation of interfacial stability. This strategy offers general routes for creating highly crystalline, shape-controlled metallic or multimetallic fine structures from liquid metal solvents.

Molecular crystals vs. superatomic lattice: a case study with superalkali-superhalogen compounds

Using a first-principles approach, we study the assembly of atomically-precise cluster solids with atomic precision. The aims are to create binary assemblies of clusters through charge transfer between neutral molecular clusters, and employing intercluster electrostatic attraction as a driving force for co-assembly. We combined pairs of complementary clusters in which one cluster is electron-donating (superalkali) and the other is electron-accepting (superhalogen). From the analysis of the binding energy between superatomic counterparts, charge transfer, and the relative size of the clusters, we analyze the resulting structures as either molecular crystals or superatomic lattices. We demonstrate that the substitution of a single atom can result in minor changes to the crystal structure of the binary solids or entirely new packing structures. The [N₄Mg₆Li]⁺[AlCl₄]^-, [N₄Mg₆Na]⁺[AlCl₄]^-, [N₄Mg₆K]⁺[AlCl₄]^-, [N₄Mg₆Li]⁺[AlF₄]^-, [N₄Mg₆Na]⁺[AlF₄]^-, and [N₄Mg₆K]⁺[AlF₄]^- compounds all form the same close-packed superatomic lattice structure through halogen bonding, with subtle differences in the orientation of the superatoms. These salts may also form molecular crystals where clusters are held to one another by electrostatic interactions. Our results emphasize how the structure of superatomic solids can be tuned upon single atom substitution.

Catalytic potential of post-transition metal doped graphene-based single-atom catalysts for the CO2 electroreduction reaction

Catalysts are required to ensure electrochemical reduction of CO₂ to fuels proceeds at industrially acceptable rates and yields. As such, highly active and selective catalysts must be developed. Herein, a density functional theory study of p‐block element and noble metal doped graphene‐based single‐atom catalysts in two defect sites for the electrochemical reduction of CO₂ to CO and HCOOH is systematically undertaken. It is found that on all of the systems considered, the thermodynamic product is HCOOH. Pb/C₃, Pb/N₄ and Sn/C₃ are identified as having the lowest overpotential for HCOOH production while Al/C₃, Al/N₄, Au/C₃ and Ga/C₃ are identified as having the potential to form higher order products due to the strength of binding of adsorbed HCOOH.

Clustering of metal dopants in defect sites of graphene-based materials

Single-atom catalysts are promising candidates for many industrial reactions. However, making true single-atom catalysts is an experimental dilemma, due to the difficulty of keeping dopant single atoms stable at temperature and under pressure. This difficulty can lead to clustering of the metal dopant atoms in defect sites. However, the electronic and geometric structure of sub-nanoscale clusters in single-atom defects has not yet been explored. Furthermore, recent studies have proven sub-nanoscale clusters of dopants in single-atom defect sites can be equally good or better catalysts than their single-atom counterparts. Here, a comprehensive DFT study is undertaken to determine the geometric and electronic structure effects that influence clustering of noble and p-block dopants in C₃- and N₄-defect sites in graphene-based systems. We find that the defect site is the primary driver in determining clustering dynamics in these systems.

Bimetallic superalkali substitution in the CsPbBr3 perovskite: Pseudocubic phases and tunable bandgap

Perovskites attract attention as efficient light absorbers for solar cells due to their high-power conversion efficiency (up to 24%). The high photoelectric conversion efficiency is greatly affected by a suitable band structure. Cation substitution can be an effective approach to tune the electronic band structure of lead halide perovskites. In this work, superalkali cations were introduced to replace the Cs⁺ cation in the CsPbBr₃ material. The bimetallic superalkalis (LiMg, NaMg, LiCa, and NaCa) were inserted since they are structurally simple systems and have a strong tendency to lose one electron to achieve a closed-shell cation. The cation substitution in the lead halide perovskite leads to changes in the shape of both valence and conduction bands compared to CsPbBr₃. Introducing superalkali cations produces extra electronic states close to the Fermi level, which arise from the formation of alkali earth metal states at the top of the valence band. Our first-principles computations reveal that bimetallic superalkali substitution decreases the bandgap of the perovskite. The bandgaps of MgLi-PbBr₃ (1.35 eV) and MgNa-PbBr₃ (1.06 eV) are lower than the bandgap of CsPbBr₃ (2.48 eV) and within the optimal bandgap (i.e., 1.1-1.4 eV) for single-junction solar cells. Thus, the MgLi-PbBr₃ and MgNa-PbBr₃ inorganic perovskites are promising candidates for high-efficiency solar cells.

Emergent electronic properties in Co-deposited superatomic clusters

We report an intercluster compound based on co-deposition of the Au cluster [Au₉(PPh₃)₈](NO₃)₃ and the fulleride KC₆₀(THF). Electronic properties characteristic for a charge interaction between superatoms emerge within the solid state material [Au₉(PPh₃)₈](NO₃)_3-x(C₆₀)_x, as confirmed by UV-VIS and Raman spectroscopy and I-V measurements. These emergent properties are related to the superatomic electronic states of the initial clusters. The material is characterized by Fourier-transform infrared spectroscopy, x-ray diffraction, Raman spectroscopy, and electrical measurements. Structural optimization and ab initio band structure calculations are performed with density functional theory to interpret the nature of the electronic states in the material; Bader charge calculations assign effective oxidation states in support of the superatomic model of cluster interactions.

Structural, thermal, and electronic properties of two-dimensional gallium oxide(ß-Ga2O3) from first-principles design

Two-dimensional (2D) materials with exotic electronic, optical and mechanical properties have attracted tremendous attention in the last two decades, due to their potential applications in electronics, energy storage and conversion technologies. However, only a few dozen 2D materials have been successfully synthesized or exfoliated. Motivated by the recent discovery of 2D gallenene, we have explored new 2D allotropes of ß-Ga 2 O 3 , an emerging wide-band gap transparent conductive oxide (TCO) with a wide range of semiconducting applications. All the possible 2D allotropes of ß-Ga 2 O 3 with high energetic stability have been predicted using particle swarm optimization, combined with density functional theory calculations. The structural and dynamical stability of the predicted 2D allotropes has been analyzed. Although ß-Ga 2 O 3 is not a van der Waals material, results predict that one or two allotropes of ß-Ga 2 O 3 are stable. In addition, the accurate band structures of these 2D semiconducting oxides have been calculated using both the GGA and LDA-1/2 approach. Remarkably, monolayer Ga 2 O 3 (100) has a larger indirect band gap of 4 eV, demonstrating a new avenue for the discovery of 2D ß-Ga 2 O 3 based nano-devices with enhanced electronic properties.

Unique surface patterns emerging during solidification of liquid metal alloys

It is well-understood that during the liquid-to-solid phase transition of alloys, elements segregate in the bulk phase with the formation of microstructures. In contrast, we show here that in a Bi-Ga alloy system, highly ordered nanopatterns emerge preferentially at the alloy surfaces during solidification. We observed a variety of transition, hybrid and crystal-defect-like patterns, in addition to lamellar and rod-like structures. Combining experiments and molecular dynamics simulations, we investigated the influence of the superficial Bi and Ga₂O₃ layers during surface solidification and elucidated the pattern-formation mechanisms, which involve surface-catalysed heterogeneous nucleation. We further demonstrated the dynamic nature and robustness of the phenomenon under different solidification conditions and for various alloy systems. The surface patterns we observed enable high-spatial-resolution nanoscale-infrared and surface-enhanced Raman mapping, which reveal promising potential for surface- and nanoscale-based applications.

Modulating the thermal and structural stability of gallenene via variation of atomistic thickness

Using ab initio molecular dynamics, we show that a recently discovered form of 2D Ga-gallenene-exhibits highly variable thickness dependent properties. Here, 2D Ga of four, five and six atomic layers thick are found to be thermally stable to 457 K, 350 K and 433 K, respectively; all well above that of bulk Ga. Analysis of the liquid structure of 2D Ga shows a thickness dependent ordering both parallel and perpendicular to the Ga/vacuum interface. Furthermore, ground state optimisations of 2D Ga to 12 atomic layers thick shows a return to a bulk-like bonding structure at 10 atoms thick, therefore we anticipate that up to this thickness 2D Ga structures will each exhibit novel properties as discrete 2D materials. Gallenene has exciting potential applications in plasmonics, sensors and electrical contacts however, for the potential of 2D Ga to be fully realised an in depth understanding of its thickness dependent properties is required.

Two-dimensional aluminium, gallium, and indium metallic crystals by first-principles design

Rapidly emerging two-dimensional (2D) atomic layer crystals exhibit diverse, tunable electronic properties. They appear to be more flexible than 3D crystals with greater versatility and improved functionality in a wide range of potential applications. Among these 2D materials, metallic crystals are relatively unexplored although two allotropes of gallenene (2D gallium) have been synthesized on a range of substrates. Based on these experimental findings, we investigate systematically the group 13 metals using first-principles density functional theory calculations and an unbiased structural search. In this study, the electronic structure, bonding characteristics, and phonon properties of predicted 2D allotropes of group 13 metals are calculated, including the expected effects of strain induced by substrates on the dynamical stability. Theoretical results predict that most group 13 elements have one or more stable 2D allotropes with the preferred allotrope depending on the cell shape relaxation and strain, indicating that the substrate will determine the overall allotrope preferred. This demonstrates a new avenue for the discovery of thermodynamically stable 2D metallic layers, with properties potentially suitable for electronic and optoelectronic applications.

A mechanistic understanding of surface Bi enrichment in dilute GaBi systems

Experiment has shown that dilute GaBi systems produce a range of self-organised nanostructured patterns at the surface [Tang et al., Nat. Nanotechnol., 2021, 16, 431-439]. Using extensive ab initio molecular dynamics simulations, we elucidate the mechanisms underlying the formation of the Bi surface islands in Bi-doped Ga liquid metals. Here, we show that in order for internal Bi atoms to diffuse to the surface a lateral extension of the Ga surface network is required. Furthermore, the absence of surface Bi patterning perturbs the Ga surface network providing a preferred path for an internal Bi to diffuse. By understanding how and why Bi nucleates at a surface, we increase the ability to control, manipulate and design such systems for use in future electronic devices.

N4Mg6M (M = Li, Na, K) superalkalis for CO2 activation

Superatoms have exciting properties, including diverse functionalization, redox activity, and magnetic ordering, so the resulting cluster-assembled solids hold the promise of high tunability, atomic precision, and robust architectures. By utilizing adamantane-like clusters as building blocks, a new class of superatoms N₄Mg₆M (M = Li, Na, K) is proposed here. The studied superalkalis feature low adiabatic ionization energies, an antibonding character in the interactions between magnesium and nitrogen atoms, and highly delocalized highest occupied molecular orbital (HOMO). Consequently, the N₄Mg₆M superalkalis might easily lose their HOMO electrons when interacting with superhalogen electrophiles to form stable superatom [superalkali]⁺[superhalogen]^- compounds. Moreover, the studied superalkalis interact strongly with carbon dioxide, and the resulting N₄Mg₆M/CO₂ systems represent two strongly interacting ionic fragments (i.e., N₄Mg₆M⁺ and CO₂ ^-). In turn, the electron affinity of the N₂ molecule (of -1.8 eV) is substantially lower than that observed for carbon dioxide (EA = -0.6 eV) and consequently, the N₂ was found to form the weakly bound [N₄Mg₆M][N₂] complex rather than the desired ionic [N₄Mg₆M]⁺[N₂]^- product. Thus, the N₄Mg₆M superalkalis have high selectivity over N₂ when it comes to CO₂ reduction and also are themselves stable. We believe that the results described within this paper will be useful for understanding CO₂ activation, which is the first step for producing fuels from CO₂. Moreover, we demonstrate that designing novel superatomic systems and exploring their physicochemical features might be used to create desirable functional materials.

Design of superatomic systems: exploiting favourable conditions for the delocalisation of d-electron density in transition metal doped clusters

The incorporation of transition metals into superatomic species has led to the proposal of highly tailorable systems, with the transition metal atoms typically acting as magnetic dopants. However, the extent to which d-electrons are able to delocalise from their ionic cores has not been fully recognised. In this work a variety of systems have been explored using a range of exchange-correlation functionals commonly used to explore cluster species, to test the extent of d-electron delocalisation under favourable conditions. Early transition metals have been shown to readily delocalise their valence d-electrons for superatomic shell closing, with higher period atoms showing a greater tendency for delocalisation. Our findings also provide the framework for the design of superatomic systems with large numbers of electrons being contributed from a single atom.

Modified Lennard-Jones potentials for nanoscale atoms

A classical 6-12 Lennard-Jones (LJ) equation has been widely used to model materials and is the potential of choice in studies when the focus is on fundamental issues. Here we report a systematic study comparing the pair interaction potentials within solid-state materials (i.e., [Co₆ Se₈ (PEt₃ )₆ ][C₆₀ ]₂ , [Cr₆ Te₈ (PEt₃ )₆ ][C₆₀ ]₂ , [Ni₉ Te₆ (PEt₃ )₈ ][C₆₀ ]) using density functional theory (DFT) calculations and LJ parametrization. Both classical (6-12 LJ) and modified LJ (mLJ) models were developed. In the mLJ approach, the exponents 6 and 12 are replaced by different integer number n and 2n, respectively, and an additional parameter (α) is introduced to describe intermolecular distance shift arising within the geometric centers' approach (instead of the shortest interatomic distance between particles). A general LJ approach reexamination reveals that in the case of nanoatoms, the attractive term decays with distance as the inverse fourth power, and the dominating at short distances repulsive term decays as the inverse eighth power. The modification of the LJ equation is even more prominent for interaction profiles, where intermolecular distance corresponds to separation between geometric centers of particles. In this approach, the attractive term decays with distance as the inverse 12th power, while the repulsive term decays rapidly (as the inverse 24th power). Thus, the mLJ models (e.g., 4-8 LJ) rather than the 6-12 classical ones seem to be a better choice for the description of binary interactions of nanoatoms. The developed mLJ models and electronic structure characteristics give an insight into the explanation of the unique physicochemical properties of superatomic-based solid-state materials.

5-Fold symmetry in superatomic scandium clusters: exploiting favourable orbital overlap to sequester spin

The geometries and electronic structures of icosahedral A₁₃^C (A = Sc, Y; C = 0, ±1, ±2) clusters have been determined at a range of multiplicities at each cluster charge, using density functional theory methods. These clusters demonstrate a complex electronic structure which provides insight into the anomalously high magnetic moment of icosahedral group 3 clusters and further contextualises the role of transition metals and d-electrons within the superatomic model. Embedded deeply within the density of states for these clusters are typical superatom orbitals which are populated up to the 2S level. Above the 2S-state there are three states of apparent F symmetry, which are preferentially singly occupied, followed by an abundance of approximately degenerate P-, G-, D- and F-states at the Fermi energy, which are at most singly occupied. In spite of apparent angular symmetry and a nodal structure reminiscent of superatomic orbitals these states are actually formed from preferential overlap of the valence d-orbitals of the cluster atoms. This analysis was further contextualised through analysis of the Sc₁₉ cluster, which shows a similar construction of Kohn-Sham states, but with the breaking of 5-fold symmetry along one of its Cartesian axes. Finally, this work clearly demonstrates the ability of d-electrons to give rise to superatomic orbitals is not just constrained by atomic species but also by the local environment of the atoms.

Ultra stable superatomic structure of doubly magic Ga13 and Ga13Li electrolyte

We report the extreme thermal stability of the superatomic electronic structure for 13-atom gallium clusters and the Ga₁₃Li electrolyte. Using previously-validated first-principles simulations, [K. G. Steenbergen and N. Gaston, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 88, 161402-161405] we show that the superatomic shell progression of doubly-magic Ga₁₃^- remains stable up to 1000 K, making this cluster an ideal candidate for high-temperature applications requiring an exceptionally stable electronic structure. Using the neutral and cationic clusters for comparison, we quantify the extent to which cluster stability (geometric and electronic) is modified through addition or subtraction of a single electron. Finally, combining 13-atom gallium with lithium, we illustrate that superatomic closed-shell Ga₁₃Li exhibits the same exceptionally high thermal stability as naked Ga₁₃^-. For technological use as a superatomic electrolyte, we demonstrate that Ga₁₃Li has a low affinity to water as well as a low Li⁺ binding energy.

On the influence of exact exchange on transition metal superatoms

The electronic structure of A7C (A = Hg, Pd, V, Cr, Mn, Fe, Ni, Cu; C = 0, ±1, ±2) clusters has been determined using density functional theory methods. The A7C (A = Hg, Pd, Cr, Cu; C = 0, ±1, ±2) clusters all conform to the existing superatomic model, with a sufficiently stabilised local structure to prevent perturbation upon the introduction of exact exchange to the exchange correlation functional. For the A7C (A = Mn, Fe, Ni; C = 0, ±1, ±2) clusters the incorporation of exact exchange separates the atomic s- and d-electrons, leading to a net increase in the number of superatomic electrons. Conversely the incorporation of exact exchange into the exchange correlation functional decreases the number of superatomic electrons for the V7C (C = 0, ±1, ±2) clusters, owing to the radial extension of the d-orbitals influencing their ability to contribute into superatomic shells.

On the involvement of d-electrons in superatomic shells: the group 3 and 4 transition metals

The geometries and electronic structures of small M₇^C (M = Sc, Y, La, Ti, Zr, Hf; C = 0, ±1, ±2) clusters have been calculated at a range of multiplicities at each cluster charge, using density functional theory methods. These clusters conform to the existing superatom model, with some contextual differences. There are a range of states which are populated by the outermost s and d-electrons of the constituent atoms, with an irregular Aufbau rule for the states formed from the atomic d-electrons. The states comprised of d-electrons present themselves as two states of P-symmetry and two states of F-symmetry, which are nearly degenerate, followed by states of D-symmetry, a shell ordering which arises due to the symmetry, and favourable overlap, of the contributing states. The effect of exact exchange in modulating the localisation of these states is also discussed. In addition, this study shows pseudo-superatomic states which arise due to the 5-fold symmetry of the clusters, materialising as either a ring or plane of electron density. In summary, these observations allow for an expansion of the role that early transition metals have within the existing superatom framework.

Thickness dependent thermal stability of 2D gallenene

Freestanding 2D metallic gallenene exhibits remarkable stability when the thickness is three atomic layers.

Aluminum oxo-fluoride clusters: A first principle investigation of stability, synthetic considerations, and the interaction with water

The introduction of the so called fluorolytic sol-gel synthesis in 2003 gave access to previously inaccessible aluminum oxo-fluorides, thus to nanoscopic materials and, more importantly, novel catalysts. The intermediate cluster structures synthesized and stabilized by Kemnitz and coworkers have mainly been protected by iso-propoxide groups. However, since catalytic reactions take place in a large variety of media, hydrophilic analogs of those clusters would be of interest. In this manuscript, we present a computational analysis for the fluorination reaction, which represents the second part of fluorolytic sol-gel synthesis, and a theoretical study of the synthesized Al₄ F₄ (μ₄ -O)(μ-Oⁱ Pr)₅ [H(Oⁱ Pr)₂ ] nanostructure's conversion to its hydroxylated analog Al₄ F₄ (μ₄ -O)(μ-OH)₅ [H(OH)₂ ] utilizing the nudged elastic band method. Furthermore, the role of the fluorine atoms of the cluster in an aqueous medium is evaluated by studying the incremental addition of water molecules to the cluster with and without fluorine atoms. In addition, NMR shifts of clusters exhibiting different substituents are compared. It has been found that the inclusion of an explicit solvent is necessary to capture the magnetic response of the individual cluster atoms in an aqueous solvent correctly. © 2018 Wiley Periodicals, Inc.

Cluster assemblies as superatomic solids: a first principles study of bonding & electronic structure

The synthesis of cluster based materials poses an exciting challenge for experimental chemistry. The main advantage of these materials compared to conventional bulk compounds is the simple tunability of the chemical and physical characteristics of individual clusters. As a consequence, cluster assemblies can theoretically be used for the creation of designer materials exhibiting specifically desired properties. Since superatoms reveal a large intrinsic thermodynamic stability and often very interesting tunable electronic characteristics, they seem to be an excellent choice as building blocks for the bulk. Here, we present a detailed first principles analysis of carefully chosen superatomic cluster binary and bulk assemblies, in order to determine which forces control the attractive interaction in superatomic solids, and how the individual cluster properties affect these assemblies. This study uses the highly tunable and stable Au₁₃(RS(AuSR)₂)₆ cluster with a variety of dopants as a model system, while the principles are likely transferable to other ligand protected systems with a straightforward superatomic electron count, such as aluminum or sodium clusters. Three different superatomic materials based on doped gold clusters, boranes and C₆₀s are constructed and evaluated. Beyond the verification that superatoms can be used to create materials that reveal emergent atom-based solid like properties, various factors influencing superatomic materials, such as the EA, IP and relative sizes of the clusters, have been identified and critically evaluated.

How robust is the metallicity of two dimensional gallium?

Atomically thin gallium layers have recently been experimentally produced via solid–melt exfoliation, and show promise as robustly metallic 2D materials for electronic applications.

Superatomic states in nickel clusters: Revising the prospects for transition metal based superatoms

The geometries and electronic structures of small Ni_n^z clusters (n = 8, 9, 10) (z = 0, ±1, 2) have been elucidated for a range of multiplicities for each cluster size and charge, using density functional theory methods. These clusters have been found to conform in part to the existing superatomic model, with each cluster having a filled superatomic S-orbital, filled or partially filled superatomic P-orbitals, and empty or partially filled superatomic D-orbitals. Despite local states of mixed symmetry being present in the immediate vicinity of the Fermi energy, the addition or removal of a single electron from these systems causes a significant shift in the relative energies of the superatomic orbitals. In addition, this study demonstrates the possibility for d-electrons to contribute into superatomic orbitals to a greater or lesser extent, depending on the local environment. In summary, these observations lead to the prospect of a predictive model for electronic shell closings in some transition metal cluster systems.

First-principles calculations of the electronic structure and bonding in metal cluster-fullerene materials considered within the superatomic framework

Inspired by recent success of synthesizing cluster assembled compounds we address the question to what extent the three new materials [Co₆Se₈(PEt₃)₆][C₆₀]₂, [Cr₆Te₈(PEt₃)₆][C₆₀]₂, and [Ni₉Te₆(PEt₃)₈]C₆₀, upon forming bulk compounds, imitate atomic analogues. Although experimental results suggest the latter, a theoretical approach is the method of choice for offering a conclusive answer and for studying the actual superatomic character. The concept of superatoms for describing atom-imitating clusters is very intriguing since it allows chemists to apply their chemical intuition - a useful tool for predicting new materials - when it comes to inter-cluster reactions. Thus, we systematically study the lattice structure, the intercluster binding, and the electronic structure by density functional theory and assess them in terms of their superatomic features. We show that collective properties arise upon bulk formation, which promotes arguments for the formation of solids in which the constituent clusters have a superatomic character that determines some form of chemical bonding. Additionally, we find evidence for the formation of superatomic states. Unfortunately, however, due to the mixing of electronic states of transition metals and chalcogen atoms, no typical electronic shell closing in the cluster cores can be identified.

A Two-Dimensional Liquid Structure Explains the Elevated Melting Temperatures of Gallium Nanoclusters

Melting in finite-sized materials differs in two ways from the solid-liquid phase transition in bulk systems. First, there is an inherent scaling of the melting temperature below that of the bulk, known as melting point depression. Second, at small sizes changes in melting temperature become nonmonotonic and show a size-dependence that is sensitive to the structure of the particle. Melting temperatures that exceed those of the bulk material have been shown to occur for a very limited range of nanoclusters, including gallium, but have still never been ascribed a convincing physical explanation. Here, we analyze the structure of the liquid phase in gallium clusters based on molecular dynamics simulations that reproduce the greater-than-bulk melting behavior observed in experiments. We observe persistent nonspherical shape distortion indicating a stabilization of the surface, which invalidates the paradigm of melting point depression. This shape distortion suggests that the surface acts as a constraint on the liquid state that lowers its entropy relative to that of the bulk liquid and thus raises the melting temperature.

Phosphine passivated gold clusters: how charge transfer affects electronic structure and stability

First principle calculations of small charged phosphine ligand-protected gold clusters have been performed in order to understand the major factors determining stability, including its size, shape, and charge dependence.

The dimeric nature of bonding in gallium: from small clusters to the α-gallium phase

We consider the structural similarity of small gallium clusters to the bulk structure of α-gallium, which has been previously described as a molecular metal, via density functional theory-based computations. Previous calculations have shown that the tetramer, the hexamer, and the octamer of gallium are all structurally similar to the α-phase. We perform an analysis of the bonding in these clusters in terms of the molecular orbitals and atoms in molecules description in order to assess whether we can see similarities at these sizes to the bonding pattern, which is ascribed to the co-existence of covalent and metallic bonding in the bulk. The singlet Ga4 and Ga8 clusters can be constructed in a singlet ground state from the Ga-dimers in the first excited triplet state of the Ga2-molecule, the (3)Σg(-) state. Molecular orbital (MO) analysis confirms that the dimer is an essential building block of these small clusters. Comparison of the AIM characteristics of the bonds within the clusters to the bonds in the bulk α-phase supports the identification of the covalent bond in the bulk as related to the (3)Σg(-) state of the dimer.

Weak interactions in Graphane/BN systems under static electric fields—A periodic ab-initio study

Ab-initio calculations via periodic Hartree-Fock (HF) and local second-order Møller-Plesset perturbation theory (LMP2) are used to investigate the adsorption properties of combined Graphane/boron nitride systems and their response to static electric fields. It is shown how the latter can be used to alter both structural as well as electronic properties of these systems.

Al20+ does melt, albeit above the bulk melting temperature of aluminium

Employing first principles parallel tempering molecular dynamics in the microcanonical ensemble, we report the presence of a clear solid–liquid-like melting transition in Al₂₀⁺ clusters, not found in experiments.

Method of increments for the halogen molecular crystals: Cl, Br, and I

Method of increments (MI) calculations reveal the n-body correlation contributions to binding in solid chlorine, bromine, and iodine. Secondary binding contributions as well as d-correlation energies are estimated and compared between each solid halogen. We illustrate that binding is entirely determined by two-body correlation effects, which account for >80% of the total correlation energy. One-body, three-body, and exchange contributions are repulsive. Using density-fitting (DF) local coupled-cluster singles, doubles, and perturbative triples for incremental calculations, we obtain excellent agreement with the experimental cohesive energies. MI results from DF local second-order Møller-Plesset perturbation (LMP2) yield considerably over-bound cohesive energies. Comparative calculations with density functional theory and periodic LMP2 method are also shown to be less accurate for the solid halogens.