BIGDML-Towards accurate quantum machine learning force fields for materials.

Machine-learning force fields (MLFF) should be accurate, computationally and data efficient, and applicable to molecules, materials, and interfaces thereof. Currently, MLFFs often introduce tradeoffs that restrict their practical applicability to small subsets of chemical space or require exhaustive datasets for training. Here, we introduce the Bravais-Inspired Gradient-Domain Machine Learning (BIGDML) approach and demonstrate its ability to construct reliable force fields using a training set with just 10-200 geometries for materials including pristine and defect-containing 2D and 3D semiconductors and metals, as well as chemisorbed and physisorbed atomic and molecular adsorbates on surfaces. The BIGDML model employs the full relevant symmetry group for a given material, does not assume artificial atom types or localization of atomic interactions and exhibits high data efficiency and state-of-the-art energy accuracies (errors substantially below 1 meV per atom) for an extended set of materials. Extensive path-integral molecular dynamics carried out with BIGDML models demonstrate the counterintuitive localization of benzene-graphene dynamics induced by nuclear quantum effects and their strong contributions to the hydrogen diffusion coefficient in a Pd crystal for a wide range of temperatures.

Structure, Energetics, and Thermal Behavior of Bimetallic Re-Pt Clusters.

Bimetallic Re-Pt is a widely used catalyst in petroleum reforming to obtain high-octane gasoline, but experimental and theoretical information of such systems at the subnanometer scale-namely, as cluster aggregates-is currently lacking. Thus, in this work, we performed a density functional theory-based global optimization study to determine the physicochemical properties of the most stable Re-Pt gas-phase clusters up to six atoms for all compositions. Our results indicate that in these putative global minima (GM) geometries, Re atoms tend to aggregate, while most Pt atoms remain separated from each other. This is even observed in Pt-rich clusters-an indication of the strength of the Re-Re and Re-Pt bonds over pure Pt-Pt ones-due to a strong, directional hybridization of the Re half-filled 5d and the nearly full Pt 5d states. We observe that doping monometallic Pt clusters even with a single Re atom increases their binding energy values and widens the bimetallic cluster highest occupied molecular orbital-lowest unoccupied molecular orbital gap. As catalysis occurs at elevated temperatures, we explore the concept of cluster fluxionality for Re-Pt minima in terms of the calculated isomer occupation probability, P(T). This allows us to quantify the abundance of GM and low-energy isomer configurations as a function of temperature. This is done at size 5 atoms due to the wide isomer observed variety. Our calculations indicate that for pure Re5, the P(T) of the GM configuration substantially decreases after 750 K. Especially, for Re4Pt1, the GM is the dominant structure up to nearly 700 K when the second-energy isomer becomes the stable one. Although no ordering changes are seen for Re3Pt2, Re2Pt3, and Re1Pt4, we do observe a structural transition-between the GM and the second isomer-for pure Pt5 above 1000 K. We expect this type of combined first-principles analysis to add to the overall, continuous understanding of the stability and energetics of ultrafine and highly-dispersed Re-Pt petroleum-reforming catalysts and the scarce available information on this particular bimetallic system.

Effect of the Metal-Ligand Interface on the Chiroptical Activity of Cysteine-Protected Nanoparticles.

Gold, silver, and copper small nanoparticles (NPs), with average size ≈2 nm, are synthesized and afterward protected with l- and d-cysteine, demonstrating emergence of chiroptical activity in the wavelength range of 250-400 nm for all three metals with respect to the bare nanoparticles and ligands alone. Silver-cysteine (Ag-Cys) NPs display the higher anisotropy factor, whereas gold-cysteine (Au-Cys) NPs show optical and chiroptical signatures slightly more displaced to the visible range. A larger number of circular dichroism (CD) bands with smaller intensity, as compared to gold and silver, is observed for the first time for copper-cysteine (Cu-Cys) NPs. The manifestation of optical and chiroptical responses upon cysteine adsorption and the differences between the spectra corresponding to each metal are mainly dictated by the metal-ligand interface, as supported by a comparison with calculations of the oscillatory and rotatory strengths based on time-dependent density functional theory, using a metal-ligand interface motif model, which closely resembles the experimental absorption and CD spectra. These results are useful to demonstrate the relevance of the interface between chiral ligands and the metal surfaces of Au, Ag, and Cu NPs, and provide evidence and further insights into the origin of the transfer mechanisms and induction of extrinsic chirality.

Structures, stabilities and aromatic properties of endohedrally transition metal doped boron clusters M@B22, M = Sc and Ti: a theoretical study.

A genetic search algorithm in conjunction with density functional theory calculations was used to determine the lowest-energy minima of the pure B22 cluster and thereby to evaluate the capacity of its isomers to form endohedrally doped cages with two transition metal atoms M (M = Sc and Ti). An important charge transfer from metal atoms M to the boron cage takes place, stabilizing the endohedral compounds, as predicted with the genetic algorithm implemented. High-level coupled-cluster theory CCSD(T) calculations were carried out to confirm that the structures found are the lowest-energy isomers. For a deeper understanding of the doping effects and related charge transfer, the best structural motif of the B22 isomers was also determined when the bare cages are in anionic states, such as B222- and B224-. It was found that B22 has an appropriate size, geometric shape and electronic state to host the chosen metal atoms and, consequently, to form stable endohedrally doped compounds Ti@B22 (C2v, 4-Ti) and Sc@B22 (C2v, 5-Sc). The chemical bonding was analyzed in order to understand the molecular orbitals that these novel systems form. The cage aromaticity was evaluated by means of the nuclear independent chemical shift (NICS(0)iso) indices, the isochemical shielding surface (ICSSzz), the anisotropy of the current induced density (ACID) maps, and the magnetic ring current Gauge-Including Magnetically Induced Current (GIMIC) method, indicating that aromaticity plays a crucial role in the stabilization of endohedrally doped boron clusters. Finally, the thermodynamic stability of the latter, using parameters derived from density functional theory (DFT), was evaluated. Ab initio molecular dynamics (AIMD) simulations were performed to elucidate the stability, at high temperature, of the most stable endohedrally doped boron clusters 4-Ti and 5-Sc.

CeO2(111) electronic reducibility tuned by ultra-small supported bimetallic Pt-Cu clusters.

Controlling Ce4+ to Ce3+ electronic reducibility in a rare-earth binary oxide such as CeO2 has enormous applications in heterogeneous catalysis, where a profound understanding of reactivity and selectivity at the atomic level is yet to be reached. Thus, in this work we report an extensive DFT-based Basin Hopping global optimization study to find the most stable bimetallic Pt-Cu clusters supported on the CeO2(111) oxide surface, involving up to 5 atoms in size for all compositions. Our PBE+U global optimization calculations indicate a preference for Pt-Cu clusters to adopt 2D planar geometries parallel to the oxide surface, due to the formation of strong metal bonds to oxygen surface sites and charge transfer effects. The calculated adsorption energy values (Eads) for both mono- and bimetallic systems are of the order of 1.79 up to 4.07 eV, implying a strong metal cluster interaction with the oxide surface. Our calculations indicate that at such sub-nanometer sizes, the number of Ce4+ surface atoms reduced to Ce3+ cations is mediated by the amount of Cu atoms within the cluster, reaching a maximum of three Ce3+ for a supported Cu5 cluster. Our computational results have critical implications on the continuous understanding of the strong metal-support interactions over reducible oxides such as CeO2, as well as the advancement of frontier research areas such as heterogeneous single-atom catalysts (SAC) and single-cluster catalysts (SCC).

CO2 adsorption on gas-phase Cu4-xPtx (x = 0-4) clusters: a DFT study.

Transition and noble metal clusters have proven to be critical novel materials, potentially offering major advantages over conventional catalysts in a range of value-added catalytic processess such as carbon dioxide transformation to methanol. In this work, a systematic computational study of CO2 adsorption on gas-phase Cu4-xPtx (x = 0-4) clusters is performed. An exhaustive potential energy surface exploration is initially performed using our recent density functional theory basin-hopping global optimization implementation. Ground-state and low-lying energy isomers are identified for Cu4-xPtx clusters. Secondly, a CO2 molecule adsorption process is analyzed on the ground-state Cu4-xPtx configurations, as a function of cluster composition. Our results show that the gas-phase linear CO2 molecule is deformed upon adsorption, with its bend angle varying from about 132° to 139°. Cu4-xPtx cluster geometries remain unchanged after CO2 adsorption, with the exception of Cu3Pt1 and Pt4 clusters. For these particular cases, a structural conversion between the ground-state geometry and the corresponding first isomer configurations is found to be assisted by the CO2 adsorption. For all clusters, the energy barriers between the ground-state and first isomer structures are explored. Our calculated CO2 adsorption energies are found to be larger for Pt-rich clusters, exhibiting a volcano-type plot. The overall effect of a hybrid functional including dispersion forces is also discussed.

2D-3D structural transition in sub-nanometer PtN clusters supported on CeO2(111).

Transition metal particles dispersed on oxide supports are used as heterogeneous catalysts in numerous applications. One example is platinum clusters supported on ceria which is used in automotive catalysis. Although control at the nm-scale is desirable to open new technological possibilities, there is limited knowledge both experimentally and theoretically regarding the geometrical structure and stability of sub-nanometer platinum clusters supported on ceria. Here we report a systematic, Density Functional Theory (DFT) study on the growth trends of CeO2(111) supported PtN clusters (N = 1-10). Using a global optimization methodology as a guidance tool to locate putative global minima, our results show a clear preference for 2D planar structures up to size Pt8. It is followed by a structural transition to 3D configurations at larger sizes. This remarkable trend is explained by the subtle competition between the formation of strong Pt-O bonds and the cluster internal Pt-Pt bonds. Our calculations show that the reducibility of CeO2(111) provides a mechanism to anchor PtN clusters where they become oxidized in a two-way charge transfer mechanism: (a) an oxidation process, where Osurface atoms withdraw charge from Pt atoms forming Pt-O bonds, (b) surface Ce4+ atoms are reduced, leading to Ce3+. The active role of the CeO2(111) support in modifying the structural and eventually the chemical properties of sub-nanometer PtN clusters is computationally demonstrated.

Efficient hydrogenation over single-site bimetallic RuSn clusters.

Hydrogenation of ethene to ethane over single-site RuN and (RuSn)N clusters is investigated using Density Functional Theory calculations. The critical transition state barrier, namely the last hydrogenation step, correlates linearly for RuN with the adsorption energies of the reactants. Addition of Sn to the Ru-clusters breaks this relation and allows for lower reaction barriers. In general, Sn is found to have pronounced effects on the geometrical and electronic properties of RuN clusters with N≤ 12. RuN clusters preferably adopt cubic conformations with high spin states, whereas (RuSn)N have low spin states and form compact Ru cores capped with Sn atoms.

Structural motifs, mixing, and segregation effects in 38-atom binary clusters.

Thirty eight-atom binary clusters composed of elements from groups 10 and 11 of the Periodic Table mixing a second-row with a third-row transition metal (TM) (i.e., clusters composed of the four pairs: Pd-Pt, Ag-Au, Pd-Au, and Ag-Pt) are studied through a combined empirical-potential (EP)/density functional (DF) method. A "system comparison" approach is adopted in order to analyze a wide diversity of structural motifs, and the energy competition among different structural motifs is studied at the DF level for these systems, mainly focusing on the composition 24-14 (the first number refers to the second-row TM atom) but also considering selected motifs with compositions 19-19 (of interest for investigating surface segregation effects) and 32-6 (also 14-24 and 6-32 for the Pd-Au pair). The results confirm the EP predictions about the stability of crystalline structures at this size for the Au-Pd pair but with decahedral or mixed fivefold-symmetric/closed-packed structures in close competition with fcc motifs for the Ag-Au or Ag-Pt and Pd-Pt pairs, respectively. Overall, the EP description is found to be reasonably accurate for the Pd-Pt and Au-Pd pairs, whereas it is less reliable for the Ag-Au and Ag-Pt pairs due to electronic structure (charge transfer or directionality) effects. The driving force to core-shell chemical ordering is put on a quantitative basis, and surface segregation of the most cohesive element into the core is confirmed, with the exception of the Ag-Au pair for which charge transfer effects favor the segregation of Au to the surface of the clusters.

Structures and energetics of 98 atom Pd-Pt nanoalloys: potential stability of the Leary tetrahedron for bimetallic nanoparticles.

The energetics of 98 atom bimetallic Pd-Pt clusters are studied using a combination of: a genetic algorithm technique (to explore vast areas of the configurational space); a basin-hopping atom-exchange routine (to search for lowest-energy homotops at fixed composition); and a shell optimisation approach (to search for high symmetry isomers). The interatomic interactions between Pd and Pt are modelled by the Gupta many-body empirical potential. For most compositions, the putative global minima are found to have structures based on defective Marks decahedra, but in the composition range from Pd46Pt52 to Pd63Pt35, the Leary tetrahedron (LT)--a structure previously identified for 98 atom Lennard-Jones clusters--is consistently found as the most stable structure. Based on the excess energy stability criterion, Pd56Pt42 represents the most stable cluster across the entire composition range. This structure, a Td-symmetry LT, exhibits multi-layer segregation with an innermost core of Pd atoms, an intermediate layer of Pt atoms and an outermost Pd surface shell (Pd-Pt-Pd). The stability of the Leary tetrahedron is compared against other low-energy competing structural motifs: the Marks decahedron (Dh-M), a "quasi" tetrahedron (a closed-packed structure) and two other closed-packed structures. The stability of LT structures is rationalized in terms of their spherical shape and the large number of nearest neighbours.