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.

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.

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.

On the Stability of Cu5 Catalysts in Air Using Multireference Perturbation Theory

An ab initio study of the interaction of O₂, the most abundant radical and oxidant species in the atmosphere, with a Cu₅ cluster, a new generation atomic metal catalyst, is presented. The open-shell nature of the reactant species is properly accounted for by using the multireference perturbation theory, allowing the experimentally confirmed resistivity of Cu₅ clusters toward oxidation to be investigated. Approximate reaction pathways for the transition from physisorption to chemisorption are calculated for the interaction of O₂ with quasi-iso-energetic trapezoidal planar and trigonal bipyramidal structures. Within the multireference approach, the transition barrier for O₂ activation can be interpreted as an avoided crossing between adiabatic states (neutral and ionic), which provides new insights into the charge-transfer process and gives better estimates for this hard to localize and therefore often neglected first intermediate state. For Cu₅ arranged in a bipyramidal structure, the O-O bond cleavage is confirmed as the rate-determining step. However, for planar Cu₅, the high energy barrier for O₂ activation, related to a very pronounced avoided crossing when going from physisorption to chemisorption, determines the reactivity in this case.

Increasing the optical response of TiO2 and extending it into the visible region through surface activation with highly stable Cu5 clusters

The decoration of semiconductors with subnanometer-sized clusters of metal atoms can have a strong impact on the optical properties of the support. The changes induced differ greatly from effects known for their well-studied, metallic counterparts in the nanometer range. In this work, we study the deposition of Cu5 clusters on a TiO2 surface and investigate their influence on the photon-absorption properties of TiO2 nanoparticles via the computational modeling of a decorated rutile TiO2 (110) surface. Our findings are further supported by selected experiments using diffuse reflectance and X-ray absorption spectroscopy. The Cu5 cluster donates an electron to TiO2, leading to the formation of a small polaron Ti3+ 3d1 state and depopulation of Cu(3d) orbitals, successfully explaining the absorption spectroscopy measurements at the K-edge of copper. A monolayer of highly stable and well fixated Cu5 clusters is formed, which not only enhances the overall absorption, but also extends the absorption profile into the visible region of the solar spectrum via direct photo-induced electron transfer and formation of a charge-separated state.

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.

Ab Initio Confirmation of a Harpoon-Type Electron Transfer in a Helium Droplet

An ab initio study of a long-range electron transfer or "harpoon"-type process from Cs and Cs₂ to C₆₀ in a superfluid helium droplet is presented. The heliophobic Cs or Cs₂ species are initially located at the droplet surface, while the heliophilic C₆₀ molecule is fully immersed in the droplet. First, probabilities for the electron transfer in the gas phase are calculated for reactants with velocities below the critical Landau velocity of 57 m/s to account for the superfluid helium environment. Next, reaction pathways are derived that also include the repulsive contribution from the extrusion of helium upon the approach of the two reactants. Our results are in perfect agreement with recent experimental measurements of electron ionization mass spectroscopy [ Renzler , M. ; et al., J. Chem. Phys. 2016 , 145 , 181101 ], showing a high possibility for the formation of a Cs₂-C₆₀ complex inside of the droplet through a direct harpoon-type electron transfer involving the rotation of the molecule but a negligibly low reactivity for atomic Cs.