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.

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.

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.

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.

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.

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.

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.

Ab initio ro-vibronic spectroscopy of the Π2 PCS radical and Σ+1PCS- anion.

Near-equilibrium potential energy surfaces have been calculated for both the PCS radical and its anion using a composite coupled cluster approach based on explicitly correlated F12 methods in order to provide accurate structures and spectroscopic properties. These transient species are still unknown and the present study provides theoretical predictions of the radical and its anion for the first time. Since these species are strongly suggested to play an important role as intermediates in the interstellar medium, the rotational and vibrational spectroscopic parameters are presented to help aid in the identification and assignment of these spectra. The rotational constants produced will aid in ground-based observation. Both the PCS radical and the PCS- anion are linear. In the PCS- anion, which has a predicted adiabatic electron binding energy (adiabatic electron affinity of PCS) of 65.6 kcal/mol, the P-C bond is stronger than the corresponding neutral radical showing almost triple bond character, while the C-S bond is weaker, showing almost single bond character in the anion. The PCS anion shows a smaller rotational constant than that of the neutral. The ω3 stretching vibrational frequencies of PCS- are red-shifted from the radical, while the ω1 and ω2 vibrations are blue-shifted with ω1 demonstrating the largest blue shift. The ro-vibronic spectrum of the PCS radical has been accurately calculated in variational nuclear motion calculations including both Renner-Teller (RT) and spin-orbit (SO) coupling effects using the composite potential energy near-equilibrium potential energy and coupled cluster dipole moment surfaces. The spectrum is predicted to be very complicated even at low energies due to the presence of a strong Fermi resonance between the bending mode and symmetric stretch, but also due to similar values of the bending frequency, RT, and SO splittings.

Nuclear Bound States of Molecular Hydrogen Physisorbed on Graphene: An Effective Two-Dimensional Model.

The interaction potential of molecular hydrogen physisorbed on a graphene sheet is evaluated using the ab initio-based periodic dlDF+Das scheme and its accuracy is assessed by comparing the nuclear bound-state energies supported by the H2(D2/HD)/graphite potentials with the experimental energies. The periodic dlDF+Das treatment uses DFT-based symmetry-adapted perturbation theory on surface cluster models to extract the dispersion contribution to the interaction whereas periodic dispersionless density functional (dlDF) calculations are performed to determine the dispersion-free counterpart. It is shown that the H2/graphene interaction is effectively two-dimensional (2D), with the distance from the molecule center-of-mass to the surface plane and the angle between the diatomic axis and the surface normal as the relevant degrees of freedom. The global potential minimum is found at the orthogonal orientation of the molecule with respect to the surface plane, with an equilibrium distance of 3.17 Å and a binding energy of -51.9 meV. The comparison of the binding energies shows an important improvement of our approach over the vdW-corrected DFT schemes when we are dealing with the very weak H2/surface interaction. Next, the 2D nuclear bound-state energies are calculated numerically. As a cross-validation of the interaction potential, the bound states are also determined for molecular hydrogen on the graphite surface (represented as an assembly of graphene sheets). With the largest absolute deviation being 1.7 meV, the theoretical and experimental energy levels compare very favorably.

Combining density functional and incremental post-Hartree-Fock approaches for van der Waals dominated adsorbate-surface interactions: Ag2/graphene.

A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag2/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag2/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.

Transferability and accuracy by combining dispersionless density functional and incremental post-Hartree-Fock theories: Noble gases adsorption on coronene/graphene/graphite surfaces.

The accuracy and transferability of the electronic structure approach combining dispersionless density functional theory (DFT) [K. Pernal et al., Phys. Rev. Lett. 103, 263201 (2009)] with the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)], are validated for the interaction between the noble-gas Ne, Ar, Kr, and Xe atoms and coronene/graphene/graphite surfaces. This approach uses the method of increments for surface cluster models to extract intermonomer dispersion-like (2- and 3-body) correlation terms at coupled cluster singles and doubles and perturbative triples level, while periodic dispersionless density functionals calculations are performed to estimate the sum of Hartree-Fock and intramonomer correlation contributions. Dispersion energy contributions are also obtained using DFT-based symmetry-adapted perturbation theory [SAPT(DFT)]. An analysis of the structure of the X/surface (X = Ne, Ar, Kr, and Xe) interaction energies shows the excellent transferability properties of the leading intermonomer correlation contributions across the sequence of noble-gas atoms, which are also discussed using the Drude oscillator model. We further compare these results with van der Waals-(vdW)-corrected DFT-based approaches. As a test of accuracy, the energies of the low-lying nuclear bound states supported by the laterally averaged X/graphite potentials (X = (3)He, (4)He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6-7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the accuracy of the combined DFT and post-HF incremental scheme is established for all the noble-gas atoms. With relative deviations smaller than 4% and 11%, good agreement is also achieved by applying the vdW-corrected DFT treatments PBE-D3 and vdW-DF2 for noble-gas atoms heavier than neon.

Physisorbed H2@Cu(100) surface: potential and spectroscopy.

Using an embedding approach, a 2-D potential energy function has been calculated to describe the physisorption interaction of H2 with a Cu(100) surface. For this purpose, a cluster model of the system calculated with highly correlated wavefunctions is combined with a periodic Density-Functional-Theory method using van der Waals-DF2 functional. Rotational and vibrational energy levels of physisorbed H2, as well as D2 and HD, are calculated using the 2D embedding corrected potential energy function. The calculated transitions are in a very good agreement with Electron-Energy-Loss-Spectroscopy observations.

Communication: unraveling the (4)He droplet-mediated soft-landing from ab initio-assisted and time-resolved density functional simulations: Au@(4)He300/TiO2(110).

An ab-initio-based methodological scheme for He-surface interactions and zero-temperature time-dependent density functional theory for superfluid (4)He droplets motion are combined to follow the short-time collision dynamics of the Au@(4)He300 system with the TiO2(110) surface. This composite approach demonstrates the (4)He droplet-assisted sticking of the metal species to the surface at low landing energy (below 0.15 eV/atom), thus providing the first theoretical evidence of the experimentally observed (4)He droplet-mediated soft-landing deposition of metal nanoparticles on solid surfaces [Mozhayskiy et al., J. Chem. Phys. 127, 094701 (2007) and Loginov et al., J. Phys. Chem. A 115, 7199 (2011)].

Assessing the performance of dispersionless and dispersion-accounting methods: helium interaction with cluster models of the TiO2(110) surface.

As a prototypical dispersion-dominated physisorption problem, we analyze here the performance of dispersionless and dispersion-accounting methodologies on the helium interaction with cluster models of the TiO2(110) surface. A special focus has been given to the dispersionless density functional dlDF and the dlDF+Das construction for the total interaction energy (K. Pernal, R. Podeswa, K. Patkowski, and K. Szalewicz, Phys. Rev. Lett. 2009, 109, 263201), where Das is an effective interatomic pairwise functional form for the dispersion. Likewise, the performance of symmetry-adapted perturbation theory (SAPT) method is evaluated, where the interacting monomers are described by density functional theory (DFT) with the dlDF, PBE, and PBE0 functionals. Our benchmarks include CCSD(T)-F12b calculations and comparative analysis on the nuclear bound states supported by the He-cluster potentials. Moreover, intra- and intermonomer correlation contributions to the physisorption interaction are analyzed through the method of increments (H. Stoll, J. Chem. Phys. 1992, 97, 8449) at the CCSD(T) level of theory. This method is further applied in conjunction with a partitioning of the Hartree-Fock interaction energy to estimate individual interaction energy components, comparing them with those obtained using the different SAPT(DFT) approaches. The cluster size evolution of dispersionless and dispersion-accounting energy components is then discussed, revealing the reduced role of the dispersionless interaction and intramonomer correlation when the extended nature of the surface is better accounted for. On the contrary, both post-Hartree-Fock and SAPT(DFT) results clearly demonstrate the high-transferability character of the effective pairwise dispersion interaction whatever the cluster model is. Our contribution also illustrates how the method of increments can be used as a valuable tool not only to achieve the accuracy of CCSD(T) calculations using large cluster models but also to evaluate the performance of SAPT(DFT) methods for the physically well-defined contributions to the total interaction energy. Overall, our work indicates the excellent performance of a dlDF+Das approach in which the parameters are optimized using the smallest cluster model of the target surface to treat van der Waals adsorbate-surface interactions.

Ab initio ro-vibronic spectroscopy of SiCCl (X̃(2)Π).

The full dimensional potential energy surfaces of the (2)A' and (2)A'' electronic components of X̃(2)Π SiCCl have been computed using the explicitly correlated coupled cluster method, UCCSD(T)-F12b, combined with a composite approach taking into account basis set incompleteness, core-valence correlation, scalar relativity, and higher order excitations. The spin-orbit and dipole moment surfaces have also been computed ab initio. The ro-vibronic energy levels and absorption spectrum at 5 K have been determined from variational calculations. The influence of each correction on the fundamental frequencies is discussed. An assignment is proposed for bands observed in the LIF experiment of Smith et al. [J. Chem. Phys. 117, 6446 (2002)]. The overall agreement between the experimental and calculated ro-vibronic levels is better than 7 cm(-1) which is comparable with the 10-20 cm(-1) resolution of the emission spectrum.

Communication: A combined periodic density functional and incremental wave-function-based approach for the dispersion-accounting time-resolved dynamics of 4He nanodroplets on surfaces: 4He/graphene.

In this work we propose a general strategy to calculate accurate He-surface interaction potentials. It extends the dispersionless density functional approach recently developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] to adsorbate-surface interactions by including periodic boundary conditions. We also introduce a scheme to parametrize the dispersion interaction by calculating two- and three-body dispersion terms at coupled cluster singles and doubles and perturbative triples (CCSD(T)) level via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. The performance of the composite approach is tested on (4)He/graphene by determining the energies of the low-lying selective adsorption states, finding an excellent agreement with the best available theoretical data. Second, the capability of the approach to describe dispersionless correlation effects realistically is used to extract dispersion effects in time-dependent density functional simulations on the collision of (4)He droplets with a single graphene sheet. It is found that dispersion effects play a key role in the fast spreading of the (4)He nanodroplet, the evaporation-like process of helium atoms, and the formation of solid-like helium structures. These characteristics are expected to be quite general and highly relevant to explain experimental measurements with the newly developed helium droplet mediated deposition technique.

Solvent states and spectroscopy of doped helium clusters as a quantum-chemistry-like problem.

The Full-Configuration-Interaction Nuclear-Orbital (FCI-NO) approach [J. Chem. Phys., 2009, 131, 19401], as the implementation of the quantum-chemistry ansatz, is overviewed and applied to (He)N-Cl2(X) clusters (N≤ 4). The ground and excited states of both fermionic (3)He and bosonic (4)He [see also, J. Phys. Chem. Lett., 2012, 2, 2145] clusters are studied. It is shown that the FCI-NO approach allows us to overcome three main difficulties: (1) the Fermi-Dirac (Bose-Einstein) nuclear statistics; (2) the wide (highly anharmonic) amplitudes of the He-dopant and He-He motions; and (3) both the weakly attractive (long-range) and the strongly repulsive (short-range) interaction between the helium atoms. Special emphasis is placed on the dependence of the cluster properties on the number of helium atoms, and on the comparison between the two helium isotopes. In particular, we analyze the analogies between quantum rings comprising electrons and (3)He atoms. The synthetic vibro-rotational Raman spectra of Cl2(X) immersed in ((3,4)He)N clusters (N≤ 4) are discussed as a function of the cluster size and the nuclear statistics. It is shown that the Coriolis couplings play a key role in modifying the spectral dopant profile in (3)He. Finally, we point out possible directions for future research using the quantum-chemistry ansatz.

Structural and spectroscopic study of the linear proton-bound complex of PN with HNP+.

This work reports the results of high level ab initio calculations of the PN-HNP(+) complex and the corresponding hydrogen migration transition state. The geometries, rotational constants, harmonic vibrational frequencies, and energetics of each species involved in the complex are reported. A reduced dimensional 2D and 4D potential energy surface is constructed and used to obtain 2D and 4D vibrational states. The results of this study show excellent correlation to available experimental data for PN. The presented results can facilitate both laboratory and interstellar observations of this novel and strongly interacting linear proton-bound complex.

Study of the X̃2Π state of the SiCN/SiNC Renner-Teller system.

The potential energy surfaces of both components of the X̃(2)Π electronic ground state of the double Renner-Teller SiCN/SiNC system are calculated using explicitly correlated coupled cluster approach. The SiNC minimum is found to lie at 628 cm(-1) above the SiCN one. The isomerization transition state is found at 7583 cm(-1) on the (2)A' surface and at 7936 cm(-1) on the (2)A(") surface. The cyclic local minimum on surface (2)A' is also reproduced by our potential energy surface and is located at 3901 cm(-1). The calculated potentials are used to simulate rovibrational spectroscopy employing the recently developed EVEREST variational code. It is shown that Renner-Teller interaction (ε = 0.3043 for SiCN and ε = 0.3874 for SiNC) and spin-orbit coupling are both very important for a correct description of the spectroscopy of this system. Comparison with available experimental measurement is reported.