Spatial quenching of a molecular charge-transfer process in a quantum fluid: the Csx-C60 reaction in superfluid helium nanodroplets

Support effects on conical intersections of Jahn-Teller fluxional metal clusters on the sub-nanoscale

The concept of fluxionality has been invoked to explain the enhanced catalytic properties of atomically precise metal clusters of subnanometer size. Cu3 isolated in the gas phase is a classical case of a fluxional metal cluster where a conical intersection leads to a Jahn-Teller (JT) distortion resulting in a potential energy landscape with close-lying multiminima and, ultimately, fluxional behavior. In spite of the role of conical intersections in the (photo)stability and (photo)catalytic properties of surface-supported atomic metal clusters, they have been largely unexplored. In this work, by applying a high-level multi-reference ab initio method aided with dispersion corrections, we analyze support effects on the conical intersection of Cu3 considering benzene as a model support molecule of carbon-based surfaces. We verify that the region around the conical intersection and the associated Jahn-Teller (JT) distortion is very slightly perturbed by the support when the Cu3 cluster approaches it in a parallel orientation: Two electronic states remain degenerate for a structure with C3 symmetry consistent with the D3h symmetry of unsupported Cu3 at the conical intersection. It extends over a one-dimensional seam that characterizes a physisorption minimum of the Cu3-benzene complex. The fluxionality of the Cu3 cluster, reflected in large fluctuations of relaxed Cu-Cu distances as a function of the active JT mode, is kept unperturbed upon complexation with benzene as well. In stark contrast, for the energetically favored perpendicular orientation of the Cu3 plane to the benzene ring plane, the conical intersection (CI) is located 12 100 cm-1 (∼1.5 eV) above the chemisorption minimum, with the fluxionality being kept at the CI's nearby and lost at the chemisorption well. The first excited state at the perpendicular orientation has a deep well (>4000 cm-1), being energetically closer to the CI. The transition dipole moment between ground and excited states has a significant magnitude, suggesting that the excited state can be observed through direct photo-excitation from the ground state. Besides demonstrating that the identity of an isolated Jahn-Teller metal cluster can be preserved against support effects at a physisorption state and lifted out at a chemisorption state, our results indicate that a correlation exists between conical intersection topography and fluxionality in the metal cluster's Cu-Cu motifs.

A practical post-Hartree-Fock approach describing open-shell metal cluster-support interactions. Application to Cu3 adsorption on benzene/coronene

Current advances in synthesizing and characterizing atomically precise monodisperse metal clusters (AMCs) at the subnanometer scale have opened up fascinating possibilities in designing new heterogeneous (photo)catalysts as well as functional interfaces between AMCs and biologically relevant molecules. Understanding the nature of AMC-support interactions at molecular-level is essential for optimizing (photo)catalysts performance and designing novel ones with improved properties. Møller-Plesset second-order perturbation theory (MP2) is one of the most cost-efficient single-reference post-Hartree-Fock wave-function-based theories that can be applied to AMC-support interactions considering adequate molecular models of the support, and thus complementing state-of-the-art dispersion-corrected density functional theory. However, the resulting AMC-support interaction is typically overestimated with the MP2 method and must be corrected. The coupled MP2 (MP2C) scheme replacing the uncoupled Hartree-Fock dispersion energy by a coupled dispersion contribution, has been proven to describe accurately van-der-Waals (vdW)-dominated interactions between closed-shell AMCs and carbon-based supports. In this work, the accuracy of a MP2C-based scheme is evaluated in modelling open-shell AMC-cluster interactions that imply charge transfer or other strong attractive energy contributions beyond vdW forces. For this purpose, we consider the interaction of Cu3 with molecular models of graphene of increasing size (benzene and coronene). In this way, it is shown that subchemical precision (within 0.1 kcal mol-1) is achieved with the modified MP2C scheme, using the explicitly correlated coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)-F12] as a benchmark method. It is also revealed that the energy difference between uncoupled and coupled dispersion terms closely follows benchmark values of the repulsive intramonomer correlation contribution. The proposed open-shell MP2C-based approach is expected to be of general applicability to open-shell atomic or molecular species interacting with coronene for regions of the potential landscape where single-reference electronic structure descriptions suffice.

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

Novel highly selective synthesis techniques have enable the production of atomically precise monodisperse metal clusters (AMCs) of subnanometer size. These AMCs exhibit 'molecule-like' structures that have distinct physical and chemical properties, significantly different from those of nanoparticles and bulk material. In this work, we study copper pentamer Cu5 clusters as model AMCs by applying both density functional theory (DFT) and high-level (wave-function-based) ab initio methods, including those which are capable of accounting for the multi-state multi-reference character of the wavefunction at the conical intersection (CI) between different electronic states and augmenting the electronic basis set till achieving well-converged energy values and structures. After assessing the accuracy of a high-level multi-multireference ab initio protocol for the well-known Cu3 case, we apply it to demonstrate that bypiramidal Cu5 clusters are distorted Jahn-Teller (JT) molecules. The method is further used to evaluate the accuracy of single-reference approaches, finding that the coupled cluster singles and doubles and perturbative triples CCSD(T) method delivers the results closer to our ab initio predictions and that dispersion-corrected DFT can outperform the CCSD method. Finally, we discuss how JT effects and, more generally, conical intersections, are intimately connected to the fluxionality of AMCs, giving them a 'floppy' character that ultimately facilitates their interaction with environmental molecules and thus enhances their functioning as catalysts.

Quantum dynamics of the Br2 (B-excited state) photodissociation in superfluid helium nanodroplets: importance of the recombination process

We have studied the Br₂ photodissociation dynamics (B ← X electronic transition) of Br₂(v = 0, X)@(⁴He)_N doped nanodroplets (T = 0.37 K) at zero angular momentum, with N in the 100-1000 interval. To do this, we have used a quantum mechanical hybrid strategy proposed by us and, as far as we know, this is the second quantum dynamics study available on the photodissociation of molecules in superfluid helium nanodroplets. While the results obtained for some properties are qualitatively similar to those reported previously by us for the Cl₂(B ← X) related case (in particular, the oscillating Br final velocity distribution which also arises from quantum interferences), large differences are evident in three key properties: the photodissociation mechanism and probability and the time scale of the process. This can be interpreted on the basis of the significantly lower excitation energy achieved by the Br₂(B ← X) transition and the higher reduced mass of Br-Br in comparison to the chlorine case. The Br₂(B) photodissociation dynamics is significantly more complex than that of Cl₂(B) and leads to the fragmentation of the initial wave packet. Thus, the probability of non-dissociation is equal to 17, 18, 51, 85 and 100% for N = 100, 200, 300, 500 and 1000, respectively, while for chlorine this probability is equal to zero. In spite of the very large experimental difficulties that exist for obtaining nanodroplets with a well defined size, we hope that these results will encourage experimentalists to investigate these interesting systems.

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.

Efficient Formation of Size-Selected Clusters upon Pickup of Dopants into Multiply Charged Helium Droplets

Properties of clusters often depend critically on the exact number of atomic or molecular building blocks, however, most methods of cluster formation lead to a broad, size distribution and cluster intensity anomalies that are often designated as magic numbers. Here we present a novel approach of breeding size-selected clusters via pickup of dopants into multiply charged helium nanodroplets. The size and charge state of the initially undoped droplets and the vapor pressure of the dopant in the pickup region, determines the size of the dopant cluster ions that are extracted from the host droplets, via evaporation of the helium matrix in a collision cell filled with room temperature helium or via surface collisions. Size distributions of the selected dopant cluster ions are determined utilizing a high-resolution time of flight mass spectrometer. The comparison of the experimental data, with simulations taking into consideration the pickup probability into a shrinking He droplet due to evaporation during the pickup process, provides a simple explanation for the emergence of size distributions that are narrower than Poisson.

An anisotropic dressed pairwise potential model for the adsorption of noble gases on boron nitride sheets

Development of empirical potentials with accurate parameterization is indispensable while modeling large-scale systems. Herein, we report accurate parameterization of an anisotropic dressed pairwise potential model (PPM) for probing the adsorption of noble gases, He, Ne, Ar and Kr on boron nitride sheets. For the noble gas binding on B₄₈N₄₈H₂₄, we carried out a least-squares fit analysis of the dispersion and dispersionless contributions of the interaction potential separately. The transferability of the parameters for a range of molecular model systems of boron nitride is further established. The dressed PPM is then used in conjunction with a global optimization technique, namely particle swarm optimization (PSO) to assess the possibility of performing large-scale simulations with the PPM-PSO methodology. The results obtained for the adsorption of 2-5 noble gases on BN sheets establish the proof-of-concept, encouraging the pursuit of large-scale simulations using the PPM-PSO approach.

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.

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.

Spectroscopy of a rotating hydrogen molecule in carbon nanotubes

Computing the energy levels of molecular hydrogen rotating in carbon nanotubes of increasing size.

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.

Electron ionization of helium droplets containing C60 and alcohol clusters

Alcoholic chemical reactions at similar conditions as the interstellar medium can be heavily hampered by the presence of C₆₀.

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

This study shows ab initio evidence for hexagonal close packing of D₂ molecules in carbon nanotubes, with a = 3.6 Å and .