Global Geometry Optimization Research Articles

Structure and Thermodynamics of Li+Arn Clusters beyond the Second Solvation Shell

Small Li+Arn clusters are employed in this work as model systems to study microsolvation. Although first and second solvation shells are expected to be the most relevant ones for this type of atomic solvents, it is also interesting to explore larger clusters in order to identify the influence of external atoms on structural and thermodynamic properties. In this work, we perform a global geometry optimization for Li+Arn clusters (with n = 41–100) and parallel tempering Monte Carlo (PTMC) simulations for some selected sizes. The results show that global minimum structures of large clusters always have 6 argon atoms in the first solvation shell while maintaining the number of 14 or 16 argon atoms in the second one. By contrast, third and fourth solvation shells vary significantly the number of argon atoms with the cluster size, and other shells can hardly be assigned due to the reduced influence of Li+ on the external argon atoms for large clusters. In turn, PTMC calculations show that the melting of the most external solvation shells of large microsolvation clusters occurs at T∼50K, which is independent of cluster size. Structural transitions can be observed between quasi-degenerated structures at low temperatures. Moreover, the present results highlight the fluxional character of the external solvation shells of these large Li+Arn clusters, which may be seen as typical “snowball” structures.

Tree Parzen estimator for global geometry optimization: A benchmark and database of experimental gas-phase structures of organic molecules.

Finding global and local minima on the potential energy surface is a key task for most studies in computational chemistry. Having a set of possible conformations for chemical structures and their corresponding energies, one can judge their chemical activity, understand the mechanisms of reactions, describe the formation of metal-ligand and ligand-protein complexes, and so forth. Despite the fact that the interest in various minima search algorithms in computational chemistry arose a while ago (during the formation of this science), new methods are still emerging. These methods allow to perform conformational analysis and geometry optimization faster, more accurately, or for more specific tasks. This article presents the application of a novel global geometry optimization approach based on the Tree Parzen Estimator method. For benchmarking, a database of small organic molecule geometries in the global minimum conformation was created, as well as a software package to perform the tests.

IrO_{2} Surface Complexions Identified through Machine Learning and Surface Investigations.

A Gaussian approximation potential was trained using density-functional theory data to enable a global geometry optimization of low-index rutile IrO_{2} facets through simulated annealing. Ab initio thermodynamics identifies (101) and (111) (1×1) terminations competitive with (110) in reducing environments. Experiments on single crystals find that (101) facets dominate and exhibit the theoretically predicted (1×1) periodicity and x-ray photoelectron spectroscopy core-level shifts. The obtained structures are analogous to the complexions discussed in the context of ceramic battery materials.

Electrostatics-Assisted Building-Up Procedure for Capturing Energy Minima of Metal Clusters: Test Case of Agn Clusters.

Global geometry optimization of metal clusters is an important problem in nanophysics. The starting geometries of the clusters generated with empirical or other model potentials are generally optimized further by density functional theory (DFT)-based energy minimization. For this purpose, several algorithms such as simulated annealing, genetic algorithms, basin hopping, etc. are used. Our building-up procedure generates putative lower-energy structures of metal (M) clusters, Mn+1, Mn+2, etc., by anchoring one or more metal atoms in the vicinity of the minima of the molecular electrostatic potential (MESP) of Mn. Here, we report an application of this method to Agn clusters, for 5 ≤ n ≤ 20, followed up by DFT-based geometry optimization, generating several lower-energy structures than those reported in the literature. New low-energy isomers are obtained by applying the same procedure to the test case of mixed-metal clusters, NinAgm, for n + m = 4 and 5. In conclusion, our MESP-based building-up procedure offers a new general methodology for generating lower-energy geometries of metal clusters.

Global Geometry Optimization and magnetic properties of Pt and FePt Clusters

Abstract The ground state geometry and the electronic and magnetic structure of small FePtn, n = 3,4,5 and 6, clusters are reported. The optimization of the geometry is carried out by means of graph theory, and the electronic energy is calculated selfconsitently within the ab initio density functional theory that includes spin-orbit coupling. In particular we present in detail the geometry optimization procedure and present, as particular examples, the evolution of those properties as a function of the cluster size.

Chemical bonding in initial building blocks of semiconductors: Geometrical structures and optical absorption spectra of isolated and Cd2 species.

We present the first experimental optical absorption spectra of isolated and Cd2 species in the photon energy range ℏω = 1.9-4.9 eV. We probe the optical response by measuring photodissociation cross sections and combine our results with time-dependent density functional theory and equation-of-motion coupled cluster calculations. Structural candidates for the time-dependent excited state calculations are generated by a density functional theory based genetic algorithm as a global geometry optimization tool. This approach allows us to determine the cluster geometries present in our molecular beams by a comparison of experimental spectra with theoretical predictions for putative global minimum candidates. For , an excellent agreement between the global minimum and the experimental results is presented. We identify the global minimum geometry of Cd2 as a trapezium, which is built up of a neutral Se2 and a cationic unit, in contrast to what was previously proposed. We find an excellent overall agreement between experimental spectra and excited state calculations. We further study the influence of total and partial charges on the optical and geometric properties of Cd2Se2 and compare our findings to CdSe quantum dots and to bulk CdSe.

Metastable exohedrally decorated Borospherene B40

The experimental discovery of borospherene, the only non-carbon fullerene observed in nature, has generated a lot of interest in the scientific community and led to the theoretical prediction of various endohedrally and exohedrally decorated borospherene. We apply Minima Hopping Method (MHM), a global geometry optimization algorithm at the density functional level to check the stability of recently proposed exohedrally decorated borospherenes M6@B40 for (M = Li, Na, K, Rb, Be, Mg, Ca, Sr, Sc and Ti). By performing short MHM runs, we find that the proposed fullerene structures are not global minima. Our new lowest energy structures are significantly deformed and of much lower symmetry. These low energy structures spontaneously aggregate by forming chemical bonds when they are brought together. Therefore, it would be challenging to synthesize bulk materials made out of the theoretically postulated exohedrally decorated borospherenes such as B40M6 which might have technologically useful properties.

Modeling Coronene Nanostructures: Analytical Potential, Stable Configurations and Ab Initio Energies

Coronene is one of the basic polycyclic aromatic hydrocarbons (PAHs) used to test the reliabilty of a multidimensional potential energy surface (PES) and to assess its influence on the formation dynamics of PAH clusters with defined physical and chemical properties. We report an analytical potential energy surface for modeling the coronene–coronene interaction, whose parameters were fine-tuned on dispersion-corrected DFT estimations performed within the generalized gradient PBE approximation, that is suitable for describing molecular aggregates involving aromatic species. This model was used to build a potential function for coronene clusters (Corn) that was then applied in a detailed global geometry optimization study with an evolutionary algorithm. A large variety of low-energy structures were obtained for the Corn (n = 2–15) clusters ranging from columnar-type to two-stacked in a handshake association motifs. Moreover, it was found that a transition from a single-stack columnar regime to other more com...

Assessing the relative stability of copper oxide clusters as active sites of a CuMOR zeolite for methane to methanol conversion: size matters?

Copper-containing zeolites exhibit high activity in the direct partial oxidation of methane into methanol at relatively low temperatures. Di- and tricopper species have been proposed as active catalytic sites, with recent experimental evidence also suggesting the possibility of the formation of larger copper oxide species. Using density functional theory based global geometry optimization, we were able to identify a general trend of the copper oxide cluster stability increasing with size. For instance, the identified ground-state structures of tetra- and pentamer copper clusters of CunOn2+ and CunOn-12+ stoichiometries embedded in an 8-ring channel of mordenite exhibit higher relative stability compared to smaller clusters. Moreover, the aluminium content and localization in the zeolite pore influence the cluster's stability and its geometrical motif, which offers a perspective of tuning the properties of copper-exchanged zeolites by creating copper oxide clusters of a given structure and size. With the activity of the cluster towards methane being connected to its stability, such tuning will potentially allow the design of catalysts with engineered properties.

Global structure search for molecules on surfaces: Efficient sampling with curvilinear coordinates.

Efficient structure search is a major challenge in computational materials science. We present a modification of the basin hopping global geometry optimization approach that uses a curvilinear coordinate system to describe global trial moves. This approach has recently been shown to be efficient in structure determination of clusters [C. Panosetti et al., Nano Lett. 15, 8044-8048 (2015)] and is here extended for its application to covalent, complex molecules and large adsorbates on surfaces. The employed automatically constructed delocalized internal coordinates are similar to molecular vibrations, which enhances the generation of chemically meaningful trial structures. By introducing flexible constraints and local translation and rotation of independent geometrical subunits, we enable the use of this method for molecules adsorbed on surfaces and interfaces. For two test systems, trans-β-ionylideneacetic acid adsorbed on a Au(111) surface and methane adsorbed on a Ag(111) surface, we obtain superior performance of the method compared to standard optimization moves based on Cartesian coordinates.

DNA-stabilized Ag-Au bimetallic clusters: the effects of alloying and embedding on optical properties.

Global geometry optimization and time-dependent density functional theory calculations have been used to study the structural evolution and optical properties of AgnAun (n = 2-6) nanoalloys both as individual clusters and as clusters stabilized with the fragments of DNA of different size. We show that alloying can be used to control and tune the level of interaction between the metal atoms of the cluster and the organic fragments of the DNA ligands. For instance, gold and silver atoms are shown to exhibit synergistic effects in the process of charge transfer from the nucleobase to the cluster, with the silver atoms directly connected to the nitrogen atoms of cytosine increasing their positive partial charge, while their more electronegative neighbouring gold atoms host the excess negative charge. This allows the geometrical structures and optical absorption spectra of small bimetallic clusters to retain many of their main features upon aggregation with relatively large DNA fragments, such as a cytosine-based 9-nucleotide hairpin loop, which suggests a potential synthetic route to such hybrid metal-organic compounds, and opens up the possibility of bringing the unique tunable properties of bimetallic nanoalloys to biological applications.

Global Materials Structure Search with Chemically Motivated Coordinates.

Identification of relevant reaction pathways in ever more complex composite materials and nanostructures poses a central challenge to computational materials discovery. Efficient global structure search, tailored to identify chemically relevant intermediates, could provide the necessary first-principles atomistic insight to enable a rational process design. In this work we modify a common feature of global geometry optimization schemes by employing automatically generated collective curvilinear coordinates. The similarity of these coordinates to molecular vibrations enhances the generation of chemically meaningful trial structures for covalently bound systems. In the application to hydrogenated Si clusters, we concomitantly observe a significantly increased efficiency in identifying low-energy structures and exploit it for an extensive sampling of potential products of silicon-cluster soft landing on Si(001) surfaces.

Molecular and Dissociative Adsorption of Water on (TiO2)n Clusters, n = 1-4.

The low energy structures of the (TiO2)n(H2O)m (n ≤ 4, m ≤ 2n) and (TiO2)8(H2O)m (m = 3, 7, 8) clusters were predicted using a global geometry optimization approach, with a number of new lowest energy isomers being found. Water can molecularly or dissociatively adsorb on pure and hydrated TiO2 clusters. Dissociative adsorption is the dominant reaction for the first two H2O adsorption reactions for n = 1, 2, and 4, for the first three H2O adsorption reactions for n = 3, and for the first four H2O adsorption reactions for n = 8. As more H2O's are added to the hydrated (TiO2)n cluster, dissociative adsorption becomes less exothermic as all the Ti centers become 4-coordinate. Two types of bonds can be formed between the molecularly adsorbed water and TiO2 clusters: a Lewis acid-base Ti-O(H2) bond or an O···H hydrogen bond. The coupled cluster CCSD(T) results show that at 0 K the H2O adsorption energy at a 4-coordinate Ti center is ∼15 kcal/mol for the Lewis acid-base molecular adsorption and ∼7 kcal/mol for the H-bond molecular adsorption, in comparison to that of 8-10 kcal/mol for the dissociative adsorption. The cluster size and geometry independent dehydration reaction energy, ED, for the general reaction 2(-TiOH) → -TiOTi- + H2O at 4-coordinate Ti centers was estimated from the aggregation reaction of nTi(OH)4 to form the monocyclic ring cluster (TiO3H2)n + nH2O. ED is estimated to be -8 kcal/mol, showing that intramolecular and intermolecular dehydration reactions are intrinsically thermodynamically allowed for the hydrated (TiO2)n clusters with all of the Ti centers 4-coordinate, which can be hindered by cluster geometry changes caused by such processes. Bending force constants for the TiOTi and OTiO bonds are determined to be 7.4 and 56.0 kcal/(mol·rad(2)). Infrared vibrational spectra were calculated using density functional theory, and the new bands appearing upon water adsorption were assigned.

CO oxidation catalysed by Pd-based bimetallic nanoalloys.

Density functional theory based global geometry optimization has been used to demonstrate the crucial influence of the geometry of the catalytic cluster on the energy barriers for the CO oxidation reaction over Pd-based bimetallic nanoalloys. We show that dramatic geometry change between the reaction intermediates can lead to very high energy barriers and thus be prohibitive for the whole process. This introduces challenges for both the design of new catalysts, and theoretical methods employed. On the theory side, a careful choice of geometric configurations of all reaction intermediates is crucial for an adequate description of a possible reaction path. From the point of view of the catalyst design, the cluster geometry can be controlled by adjusting the level of interaction between the cluster and the dopant metal, as well as between the adsorbate molecules and the catalyst cluster by mixing different metals in a single nanoalloy particle. We show that substitution of a Pd atom in the Pd5 cluster with a single Ag atom to form Pd4Ag1 leads to a potential improvement of the catalytic properties of the cluster for the CO oxidation reaction. On the other hand, a single Au atom does not enhance the properties of the catalyst, which is attributed to a weaker hybridization between the cluster's constituent metals and the adsorbate molecules. Such flexibility of properties of bimetallic nanoalloy clusters illustrates the possibility of fine-tuning, which might be used for design of novel efficient catalytic materials.

Electronic structure of new superconductor La0.5Th0.5OBiS2: DFT study

We studied from first-principles the recently discovered BiS2-layered superconductor La0.5Th0.5OBiS2 and compared with LaO0.5F0.5BiS2. Firstly, we have performed a global geometry optimization in order to predict an accurate ground state. In contract to the parent semiconductor LaOBiS2 and according to other recent works, the band structure of both materials presents superconducting behavior, four bands of Bi-6p orbitals that cross a Fermi-level. Additionally, the systematic study of the electronic properties as a function of pressure shows the same behavior in both materials “Enhancement of superconductivity TC”, where the Fermi-level is shifted upward and the Fermi surface presents a similar dispersion. These similarities between tetravalent cation electron-doped via Th+4 substitution for La+3 (La0.5Th0.5OBiS2), and monovalent anion electron-doped via F− substitution for O2− (LaO0.5F0.5BiS2) may predict the same electronic properties.

Energetic and vibrational analysis of hydrogenated siliconmvacancies above saturation

We present a systematic study on hydrogenated silicon $m$ vacancies above saturation. For each system a global geometry optimization search for low-lying local minima is performed using a newly developed SiH tight binding model. Subsequently a large number of low-energy structures are examined by density functional calculations using a minimal basis set. Finally the energetically favorable structures are reexamined using a systematically extendable basis set with local, semilocal, and hybrid exchange-correlation functionals. Particular attention is paid to the divacancy to which the Raman peak at 3822 ${\mathrm{cm}}^{\ensuremath{-}1}$ associated with the ${\mathrm{H}}_{2}$ molecule had previously been assigned. Both the energetics and vibrational analysis of divacancy-related stable configurations suggest a revision of the above conclusion.

Multidoping of Si Cages: High Spin States beyond the Single-Dopant Septet Limit

Density-functional theory based global geometry optimization is employed to systematically scrutinize the possibility of multi-doping of hydrogenated Si clusters in order to achieve high spin states beyond the septet limit of a single-atom dopant. While our unbiased configurational search reveals that the previously suggested Si18H12 double hexagonal prism structure is generally too small to accommodate two dopants in magnetized state, the larger Si24H24 cage turns out to be suitable for such applications. For dimer dopants M2+ = Cr2+, Mn2+ and CrMn+, the structural integrity of the host cage is conserved in the ground-state structure of corresponding M2+@Si24H24 aggregates, as is the unusually high spin state of the guest dopant, which in case of Cr2+ already exceeds the single-atom dopant septet limit by almost a factor of two. Moreover, the possibility of further increasing the cluster spin moment by encapsulating an even larger number of dopants into a suitably sized hydrogenated Si cage is illustrated for the example of a (CrMn+)2@Si28H28 aggregate with a total number of 18 unpaired electrons. These results strongly suggest multi-doping of Si clusters as a viable route to novel cluster-based materials for magneto-optic applications.

MSi20H20 Aggregates: From Simple Building Blocks to Highly Magnetic Functionalized Materials

Density-functional theory based global geometry optimization is used to scrutinize the possibility of using endohedrally-doped hydrogenated Si clusters as building blocks for constructing highly magnetic materials. In contrast to the known clathrate-type facet-sharing, the clusters exhibit a predisposition to aggregation through double Si-Si bridge bonds. For the prototypical CrSi$_{20}$H$_{20}$ cluster we show that reducing the degree of hydrogenation may be used to control the number of reactive sites to which other cages can be attached, while still preserving the structural integrity of the building block itself. This leads to a toolbox of CrSi$_{20}$H$_{20-2n}$ monomers with different number of double "docking sites", that allows building network architectures of any morphology. For (CrSi$_{20}$H$_{18}$)$_{2}$ dimer and [CrSi$_{20}$H$_{16}$](CrSi$_{20}$H$_{18}$)$_{2}$ trimer structures we illustrate that such aggregates conserve the high spin moments of the dopant atoms and are therefore most attractive candidates for cluster-assembled materials with unique magnetic properties. The study suggests that the structural completion of the individual endohedral cages within the doubly-bridge bonded structures and the high thermodynamic stability of the obtained aggregates are crucial for potential synthetic polymerization routes $via$ controlled dehydrogenation.

Foraging on the potential energy surface: A swarm intelligence-based optimizer for molecular geometry

We present a stochastic, swarm intelligence-based optimization algorithm for the prediction of global minima on potential energy surfaces of molecular cluster structures. Our optimization approach is a modification of the artificial bee colony (ABC) algorithm which is inspired by the foraging behavior of honey bees. We apply our modified ABC algorithm to the problem of global geometry optimization of molecular cluster structures and show its performance for clusters with 2-57 particles and different interatomic interaction potentials.

Interplay between Chemical and Magnetic Order in FeRh Clusters

The structure, chemical order, and magnetic behavior in small FeRh clusters having N ≤ 19 atoms have been investigated theoretically. For N ≤ 6 atoms, a thorough global geometry optimization is performed by considering all possible cluster topologies, while for 7 ≤ N ≤ 19 only a few representative structures are considered. In all cases, the starting structures are fully relaxed in the entire range of concentrations and spin polarizations. The calculations are based on a generalized-gradient approximation to density-functional theory. The results are analyzed systematically as a function of size and composition. The optimized cluster structures are compact with a clear tendency to maximize the number of nearest-neighbor FeRh pairs. For very small sizes, the low-lying isomers present usually a topology different from that of the optimal structure, while for larger clusters the lowest-energy isomerizations imply mainly changes in the chemical order. The most stable structures are in general ferromagnetic. A...