High-level ab initio evidence of bipyramidal Cu5 clusters as fluxional Jahn-Teller molecules.

The front cover artwork is provided by María Pilar de Lara-Castells, Head of the AbinitFot Group at IFF-CSIC (Madrid), Coordinator of the National Project "COSYES", and Chair of the COST Action CA21101 "COSY", and Alexander O. Mitrushchenkov from the Université Paris-Est. The image shows the connection between the Jahn-Teller effect featured by bypiramidal Cu5 clusters and the property of fluxionality. Cover design by Katarzyna Krupka. Read the full text of the Research Article at 10.1002/cphc.202300317.

Carbon vacancy-assisted stabilization of individual Cu5 clusters on graphene. Insights from ab initio molecular dynamics.

Recent advances in synthesis and characterization methods have enabled the controllable fabrication of atomically precise metal clusters (AMCs) of subnanometer size that possess unique physical and chemical properties, yet to be explored. Such AMCs have potential applications in a wide range of fields, from luminescence and sensing to photocatalysis and bioimaging, making them highly desirable for further research. Therefore, there is a need to develop innovative methods to stabilize AMCs upon surface deposition, as their special properties are lost due to sintering into larger nanoparticles. To this end, dispersion-corrected density functional theory (DFT-D3) and ab initio molecular dynamics (AIMD) simulations have been employed. Benchmarking against high-level post-Hartree-Fock approaches revealed that the DFT-D3 scheme describes very well the lowest-energy states of clusters of five and ten atoms, Cu5 and Cu10. AIMD simulations performed at 400 K illustrate how intrinsic defects of graphene sheets, carbon vacancies, are capable of confining individual Cu5 clusters, thus allowing for their stabilization. Furthermore, AIMD simulations provide evidence on the dimerization of Cu5 clusters on defect-free graphene, in agreement with the ab initio predictions of (Cu5)n aggregation in the gas phase. The findings of this study demonstrate the potential of using graphene-based substrates as an effective platform for the stabilization of monodisperse atomically precise Cu5 clusters.

Superfluid helium droplet-mediated surface-deposition of neutral and charged silver atomic species.

Experimental and theoretical work has delivered evidence of the helium nanodroplet-mediated synthesis and soft-landing of metal nanoparticles, nanowires, clusters, and single atoms on solid supports. Recent experimental advances have allowed the formation of charged metal clusters into multiply charged helium nanodroplets. The impact of the charge of immersed metal species in helium nanodroplet-mediated surface deposition is proved by considering silver atoms and cations at zero-temperature graphene as the support. By combining high-level ab initio intermolecular interaction theory with a full quantum description of the superfluid helium nanodroplet motion, evidence is presented that the fundamental mechanism of soft-deposition is preserved in spite of the much stronger interaction of charged species with surfaces, with high-density fluctuations in the helium droplet playing an essential role in braking them. Corroboration is also presented that the soft-landing becomes favored as the helium nanodroplet size increases.

Stability and Reversible Oxidation of Sub-Nanometric Cu5 Metal Clusters: Integrated Experimental Study and Theoretical Modeling.

Sub-nanometer metal clusters have special physical and chemical properties, significantly different from those of nanoparticles. However, there is a major concern about their thermal stability and susceptibility to oxidation. In situ X-ray Absorption spectroscopy and Near Ambient Pressure X-ray Photoelectron spectroscopy results reveal that supported Cu5 clusters are resistant to irreversible oxidation at least up to 773 K, even in the presence of 0.15 mbar of oxygen. These experimental findings can be formally described by a theoretical model which combines dispersion-corrected DFT and first principles thermochemistry revealing that most of the adsorbed O2 molecules are transformed into superoxo and peroxo species by an interplay of collective charge transfer within the network of Cu atoms and large amplitude "breathing" motions. A chemical phase diagram for Cu oxidation states of the Cu5 -oxygen system is presented, clearly different from the already known bulk and nano-structured chemistry of Cu.

Meta-stability through intermolecular interactions protecting the identity of atomic metal clusters: ab initio evidences in (Cu5-Cu5)n (n < 3) cases.

Recent developments in new synthesis techniques have allowed the production of precise monodisperse metal clusters composed of a few atoms. These atomic metal clusters (AMCs) often feature a molecule-like electronic structure, which makes their physical and chemical properties particularly interesting in nanotechnology. Regarding potential applications, there is a major concern about the sintering of AMCs in nanoparticles due to the loss of their special properties. In this work, multireference ab initio theory is applied to demonstrate the formation of coupled AMC-AMC clusters in which the AMC partners maintain their 'identity' to a large extent in terms of their initial structures and atomic Mulliken charges, and their further oligomerization.

Aggregation and support effects in the oxidation of fluxional atomic metal clusters. The paradigmatic Cu5 case.

The recent development of new synthesis techniques has allowed the production of monodisperse metal clusters composed of a few atoms. Follow-up experimental spectroscopic characterization has indicated the stability of these atomic metal clusters (AMCs). Despite the common assumption that the occurrence of an irreversible oxidation becomes more likely as the cluster size decreases, its quenching and reversible nature has been experimentally identified in the particular case of Cu5 clusters, making them paradigmatic. This work aims to address the influence of aggregation and the effects of a chemically inert carbon-based support on the oxidation of AMCs, considering the case of Cu5 as a model system. For this purpose, we present an extended first-principles study of the oxidation of Cu5-Cu5 and circumpyrene-supported Cu5, comparing it with that of unsupported Cu5, and combine dispersion-corrected density-functionals, first principles thermochemistry, and ab initio molecular dynamics (AIMD) simulations within an adiabatic approach. Our results indicate that a molecular chemisorption/desorption model is sensible upon consideration of aggregation and support effects in such a way that the predicted (p-T)-phase diagrams do not differ significantly from those obtained for unsupported Cu5. We also provide insights into the decoupling of the Cu5-Cu5 dimer into Cu5 sub-units through activated fluxional rotational motion, upon heating, as well as the adsorption of multiple O2 molecules at high oxygen gas pressures. Furthermore, numerical evidence shows the likelihood of a support-mediated mechanism leading to the dissociation of chemisorbed peroxo O22- species, delivering states with very similar energies to those characterized by molecular chemisorption. A Boltzmann-weighted average of the free energies of formation is computed as well, coming up with a diagram of the dominant copper oxidation states as a function of temperature and oxygen gas pressure.

First-principles modelling of the new generation of subnanometric metal clusters: Recent case studies.

The very recent development of highly selective techniques making possible the synthesis and experimental characterization of subnanometric (subnanometer-sized) metal clusters (even single atoms) is pushing our understanding far beyond the present knowledge in materials science, driving these clusters as a new generation of quantum materials at the lower bounds of nanotechnology. When the size of the metal cluster is reduced to a small number of atoms, the d-band of the metal splits into a subnanometric d-type molecular orbitals network in which all metal atoms are inter-connected, with the inter-connections having the length of a chemical bond (1-2 Å). These molecular characteristics are at the very core of the high stability and novel properties of the smallest metal clusters, with their integration into colloidal materials interacting with the environment having the potential to further boost their performance in applications such as luminescence, sensing, bioimaging, theranostics, energy conversion, catalysis, and photocatalysis. Through the presentation of very recent case studies, this Feature Article is aimed to illustrate how first-principles modelling, including methods beyond the state-of-the-art and an interplay with cutting-edge experiments, is helping to understand the special properties of these clusters at the most fundamental level. Moreover, it will be discussed how superfluid helium droplets can act both as nano-reactors and carriers to achieve the synthesis and surface deposition of metal clusters. This concept will be illustrated with the quantum simulation of the helium droplet-assisted soft-landing of a single Au atom onto a titanium dioxide (TiO2) surface. Next, it will be shown how the application of first-principles methods have disclosed the fundamental reasons why subnanometric Cu5 clusters are resistant to irreversible oxidation, and capable of increasing and extending into the visible region the solar absorption of TiO2, of augmenting its efficiency for photo-catalysis beyond a factor of four, also considering the decomposition and photo-activation of CO2 as a prototypical (photo-) catalytic reaction. Finally, I will discuss how the modification of the same material with subnanometric Ag5 clusters has converted it into a "reporter" of a surface polaron property as well as a novel two-dimensional polaronic material.

Mini Review: Quantum Confinement of Atomic and Molecular Clusters in Carbon Nanotubes.

We overview our recent developments on a computational approach addressing quantum confinement of light atomic and molecular clusters (made of atomic helium and molecular hydrogen) in carbon nanotubes. We outline a multi-scale first-principles approach, based on density functional theory (DFT)-based symmetry-adapted perturbation theory, allowing an accurate characterization of the dispersion-dominated particle-nanotube interaction. Next, we describe a wave-function-based method, allowing rigorous fully coupled quantum calculations of the pseudo-nuclear bound states. The approach is illustrated by showing the transition from molecular aggregation to quasi-one-dimensional condensed matter systems of molecular deuterium and hydrogen as well as atomic 4He, as case studies. Finally, we present a perspective on future-oriented mixed approaches combining, e.g., orbital-free helium density functional theory (He-DFT), machine-learning parameterizations, with wave-function-based descriptions.

A Path Integral Molecular Dynamics Simulation of a Harpoon-Type Redox Reaction in a Helium Nanodroplet.

We present path integral molecular dynamics (PIMD) calculations of an electron transfer from a heliophobic Cs2 dimer in its (3Σu) state, located on the surface of a He droplet, to a heliophilic, fully immersed C60 molecule. Supported by electron ionization mass spectroscopy measurements (Renzler et al., J. Chem. Phys.2016, 145, 181101), this spatially quenched reaction was characterized as a harpoon-type or long-range electron transfer in a previous high-level ab initio study (de Lara-Castells et al., J. Phys. Chem. Lett.2017, 8, 4284). To go beyond the static approach, classical and quantum PIMD simulations are performed at 2 K, slightly below the critical temperature for helium superfluidity (2.172 K). Calculations are executed in the NVT ensemble as well as the NVE ensemble to provide insights into real-time dynamics. A droplet size of 2090 atoms is assumed to study the impact of spatial hindrance on reactivity. By changing the number of beads in the PIMD simulations, the impact of quantization can be studied in greater detail and without an implicit assumption of superfluidity. We find that the reaction probability increases with higher levels of quantization. Our findings confirm earlier, static predictions of a rotational motion of the Cs2 dimer upon reacting with the fullerene, involving a substantial displacement of helium. However, it also raises the new question of whether the interacting species are driven out-of-equilibrium after impurity uptake, since reactivity is strongly quenched if a full thermal equilibration is assumed. More generally, our work points towards a novel mechanism for long-range electron transfer through an interplay between nuclear quantum delocalization within the confining medium and delocalized electronic dispersion forces acting on the two reactants.

Nonadiabatic Effects in the Molecular Oxidation of Subnanometric Cu5 Clusters.

The electronic structure of subnanometric clusters, far off the bulk regime, is still dominated by molecular characteristics. The spatial arrangement of the notoriously undercoordinated metal atoms is strongly coupled to the electronic properties of the system, which makes this class of materials particularly interesting for applications including luminescence, sensing, bioimaging, theranostics, energy conversion, catalysis, and photocatalysis. Opposing a common rule of thumb that assumes an increasing chemical reactivity with smaller cluster size, Cu5 clusters have proven to be exceptionally resistant to irreversible oxidation, i.e., the dissociative chemisorption of molecular oxygen. Besides providing reasons for this behavior in the case of heavy loading with molecular oxygen, we investigate the competition between physisorption and molecular chemisorption from the perspective of nonadiabatic effects. Landau-Zener theory is applied to the Cu5(O2)3 complex to estimate the probability for a switching between the electronic states correlating the neutral O2 + Cu5(O2)2 and the ionic O2- + (Cu5(O2)2)+ fragments in a diabatic representation. Our work demonstrates the involvement of strong nonadiabatic effects in the associated charge transfer process, which might be a common motive in reactions involving subnanometric metal structures.

Computational Characterization of the Intermixing of Iron Triade (Fe, Co, and Ni) Surfaces and Sub-nanometric Clusters with Atomic Gold.

Dispersion-corrected density functional theory (DFT-D3) is applied to model iron triade (Fe, Co, and Ni) surfaces upon exchange of surface atoms with atomic gold. One first goal is to analyze the contact problem at the triade surface-Au interface and to correlate our findings with recent observations on iron triade nanoparticles (with diameters of around 5 nm) passivated by a few layers of gold. For this purpose, we analyze: (1) the energies of substitution; (2) the restructuring of the iron triade surfaces upon the atomic exchange; (3) the density of the orbitals bearing the largest projection on d(Au) atomic orbitals and, particularly, their overlap with orbitals from neighboring atoms of the triade surfaces; (4) the modification of the electronic density of states; and (5) the redistribution of the electronic density upon intermixing of Au and triade atoms. Inspite of the similarities between Ni, Co, and Fe in the condensed phase, significant differences are found in the features characterizing the exchange process. In particular, we find a better integration of the Au atom on the substitutional site of the Ni(001) surface than on those of the Fe(001) and Co(001) surfaces. This is in agreement with the fact that the electronic density of states is almost indistinguishable before and after Ni-Au intermixing. This outcome is correlated with the experimental observation on the allowing transition of Ni-Au core-shell nanoparticles before reaching the melting temperature. Our second objective is to explore the Au-triade atom intermixing process in sub-nanometric clusters, finding that it is energetically more favored than at solid surfaces yet endothermic at 0 K. This feature is explained as the result of the structural fluxionality characterizing clusters at the sub-nanometer scale. Entropy contributions make mixed Au-Ni clusters more stable than the unmixed counterpart already at 650 K while unmixed Co clusters remain energetically more favored up to 1295 K and iron clusters are predicted to be stable against intermixing over the experimentally relevant range of temperatures (up to 1100 °C). Remarkably, the net charge donated from the three triade atoms to atomic gold upon intermixing is similar in triade sub-nanometeric clusters and at extended triade surfaces. Gold clusters are prone to host Fe, Co, and Ni atoms at the center of their structures and the exchange process is predicted to be exothermic at 0 K even for a small cluster made of 13 atoms. More generally, our work highlights the importance of the polarity of the chemical bond between unlike metal atoms in alloys.

A nuclear spin and spatial symmetry-adapted full quantum method for light particles inside carbon nanotubes: clusters of 3He, 4He, and para-H2.

We present a new nuclear spin and spatial symmetry-adapted full quantum method for light fermionic and bosonic particles under cylindrical carbon nanotube confinement. The goal is to address Fermi-Dirac and Bose-Einstein nuclear spin statistics on an equal footing and to deliver excited states with a similar accuracy to that of the ground state, implementing ab initio-derived potential models as well. The method is applied to clusters of up to four (three) 4He atoms and para-H2 molecules (3He atoms) inside a single-walled (1 nm diameter) carbon nanotube. Due to spin symmetry effects, the bound states energy landscape as a function of the angular momentum around the tube axis becomes much more complex and rich as the number of 3He atoms increase compared to the spinless 4He and para-H2 counterparts. Four bosonic 4He and para-H2 particles form pyramidal-like structures which are more compact as the particle mass and the strength of the inter-particle interaction increases. They feature stabilization of the collective rotational motion as bosonic quantum rings bearing persistent rotational motion and superfluid flow. Our results are brought together with two key experimental findings from the group of Jan-Peter Toennies: (1) the congestion of spectral profiles in doped 3He droplets as opposed to the case of 4He droplets (S. Gebenev, J. P. Toennies and A. F. Vilesov, Science, 1998, 279, 2083); (2) the onset of microscopic superfluidity in small doped clusters of para-H2 molecules (S. Grebenev, B. G. Sartakov, J. P. Toennies and A. F. Vilesov, Science, 2000, 289, 1532), but at the reduced dimensionality offered by the confinement inside carbon nanotubes.

From Molecular Aggregation to a One-Dimensional Quantum Crystal of Deuterium Inside a Carbon Nanotube of 1 nm Diameter.

The quantum motion of clusters of up to four deuterium molecules under confinement in a single-wall (1 nm diameter) carbon nanotube is investigated by applying a highly accurate full quantum treatment of the most relevant nuclear degrees of freedom and an ab initio-derived potential model of the underlying dispersion-dominated intermolecular interactions. The wave functions and energies are calculated using an ad hoc-developed discrete variable representation (DVR) numerical approach in internal coordinates, with the space grid approaching a few billion grid points. We unambiguously demonstrate the formation of a solid-like pyramidal one-dimensional chain structure of molecules under the cylindrical nanotube confinement. The onset of solid-like packing is explained by analyzing the potential minima landscape. The stabilization of collective rotational motion through "rigid rotations" of four deuterium molecules provides conclusive evidence for the onset of a quantum solid-like behavior resembling that of quantum rings featuring persistent current (charged particles) or persistent flow (neutral particles).

Spectroscopy of a rotating hydrogen molecule in carbon nanotubes.

A first-principles study of the spectroscopy of a single hydrogen molecule rotating inside and outside of carbon nanotubes is presented. Density functional theory (DFT)-based symmetry-adapted perturbation theory (SAPT) is applied to analyze the influence of the rotation in the dispersionless and dispersion energy contributions to the adsorbate-nanotube interaction. A potential model for the H2-nanotube interaction is proposed and applied to derive the molecular energy levels of the rotating hydrogen molecule. The SAPT-based analysis shows that a subtle balance between the dispersionless and dispersion contributions is key in determining the angular dependence of the H2-nanotube interaction, which is strongly influenced by the diameter of the carbon nanotubes. As a consequence, the structure of molecular energy levels is very different in wide and narrow nanotubes with the diameter above and below 1 nanometer, respectively. Strong anisotropy effects lead to a rather constrained rotation of molecular hydrogen inside narrow nanotubes.

Effects of the Core Location on the Structural Stability of Ni-Au Core-Shell Nanoparticles.

Structural changes of Ni-Au core-shell nanoparticles with increasing temperature are studied at atomic resolution. The bimetallic clusters, synthesized in superfluid helium droplets, show a centralized Ni core, which is an intrinsic feature of the growth process inside helium. After deposition on SiN x , the nanoparticles undergo a programmed temperature treatment in vacuum combined with an in situ transmission electron microscopy study of structural changes. We observe not only full alloying far below the actual melting temperature, but also a significantly higher stability of core-shell structures with decentralized Ni cores. Explanations are provided by large-scale molecular dynamics simulations on model structures consisting of up to 3000 metal atoms. Two entirely different diffusion processes can be identified for both types of core-shell structures, strikingly illustrating how localized, atomic features can still dictate the overall behavior of a nanometer-sized particle.

Ab initio design of light absorption through silver atomic cluster decoration of TiO2.

A first-principles study of the stability and optical response of subnanometer silver clusters Agn (n ≤ 5) on a TiO2(110) surface is presented. First, the adequacy of the vdW-corrected DFT-D3 approach is assessed using the domain-based pair natural orbital correlation DLPNO-CCSD(T) calculations along with the Symmetry-Adapted Perturbation Theory [SAPT(DFT)] applied to a cluster model. Next, using the DFT-D3 treatment with a periodic slab model, we analyze the interaction energies of the atomic silver clusters with the TiO2(110) surface. Finally, the hybrid HSE06 functional and a reduced density matrix treatment are applied to obtain the projected electronic density of states and photo-absorption spectra of the TiO2(110) surface, with and without adsorbed silver clusters. Our results show the stability of the supported clusters, the enhanced light absorbance intensity of the material upon their deposition, and the appearance of intense secondary broad peaks in the near-infrared and the visible regions of the spectrum, with positions depending on the size and shape of the supported clusters. The secondary peaks arise from the photo-induced transfer of electrons from intra-band valence 5s orbitals of the noble-metal cluster to 3d Ti band states of the supporting material.

Quantum confinement of molecular deuterium clusters in carbon nanotubes: ab initio evidence for hexagonal close packing.

An ab initio study of quantum confinement of deuterium clusters in carbon nanotubes is presented. First, density functional theory (DFT)-based symmetry-adapted perturbation theory is used to derive parameters for a pairwise potential model describing the adsorbate-nanotube interaction. Next, we analyze the quantum nuclear motion of N D2 molecules (N < 4) confined in carbon nanotubes using a highly accurate adsorbate-wave-function-based approach, and compare it with the motion of molecular hydrogen. We further apply an embedding approach and study zero-point energy effects on larger hexagonal and heptagonal structures of 7-8 D2 molecules. Our results show a preference for crystalline hexagonal close packing hcp of D2 molecules inside carbon nanotubes even at the cost of a reduced volumetric density within the cylindrical confinement.