A genetic algorithm for first principles global structure optimization of supported nano structures

Adventures in DFTB: Toward an Automatic Parameterization Scheme

As we push forward on understanding the fate of chemicals in the environment, we need a method that will allow for the simulation of the inherent heterogeneity. Density functional tight binding (DFTB) is a methodology that allows for a detailed electronic description and would be ideal for this problem. While many parameters can be derived directly from DFT, empirical parameters still exist in the confinement and repulsion potentials. In this manuscript, we examine these potentials and present solutions that will minimize the degree of empiricism. Our results show that it is possible to construct confinement potentials from examining the atomic radial wavefunctions. Moreover, we found that the heterogeneous repulsion potentials can be derived from using only homogeneous repulsion curves.

Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization

Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low-energy structures of Pd_n (n = 1-21) clusters supported on CeO₂(111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pd_n clusters of any structure. Low-energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters, and large cluster isomers share similarities in both shape and energy. The findings elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure-energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.

Reliability of semiempirical and DFTB methods for the global optimization of the structures of nanoclusters

In this work, we explore the possibility of using computationally inexpensive electronic structure methods, such as semiempirical and DFTB calculations, for the search of the global minimum (GM) structure of chemical systems. The basic prerequisite that these inexpensive methods will need to fulfill is that their lowest energy structures can be used as starting point for a subsequent local optimization at a benchmark level that will yield its GM. If this is possible, one could bypass the global optimization at the expensive method, which is currently impossible except for very small molecules. Specifically, we test our methods with clusters of second row elements including systems of several bonding types, such as alkali, metal, and covalent clusters. The results reveal that the DFTB3 method yields reasonable results and is a potential candidate for this type of applications. Even though the DFTB2 approach using standard parameters is proven to yield poor results, we show that a re-parametrization of only its repulsive part is enough to achieve excellent results, even when applied to larger systems outside the training set.

Experimental study on classical and metaheuristics algorithms for optimal nano-chitosan concentration selection in surface coating and food packaging

In this study the Lagrange interpolation optimization algorithm based on two variables with respect to all experimental replicates (POA), was compared with two other heuristics methods (WOA and GOA). Modification of the apple surface by an edible nano coating solution in food packaging was used as case study. The experiment was performed as a factorial test based on completely randomized design by 100 permutations data sets. Results showed a significant difference between the three optimization methods (POA, WOA and GOA) which indicates the necessity of optimization and also efficiency of the present POA. The optimum result by POA, similar to a rose petal property, could rise 72% in surface contact angle (CA). The scanning electron microscopy (SEM) images of the derived surfaces showed almost a uniform spherical nanoparticles morphology. Remarkable advantages of this new approach are no additional material requirement, healthful, easy, inexpensive, fast and affordable technique for surface improvement.

Structure prediction of surface reconstructions by deep reinforcement learning

We demonstrate how image recognition and reinforcement learning combined may be used to determine the atomistic structure of reconstructed crystalline surfaces. A deep neural network represents a reinforcement learning agent that obtains training rewards by interacting with an environment. The environment contains a quantum mechanical potential energy evaluator in the form of a density functional theory program. The agent handles the 3D atomistic structure as a series of stacked 2D images and outputs the next atom type to place and the atomic site to occupy. Agents are seen to require 1000-10 000 single point density functional theory evaluations, to learn by themselves how to build the optimal surface reconstructions of anatase TiO2(001)-(1 × 4) and rutile SnO2(110)-(4 × 1).

Synthetic Biology: A Solution for Tackling Nanomaterial Challenges

Bioengineers have mastered practical techniques for tuning a biomaterial's properties with only limited information on the relationship between the material's structure and function. These techniques have been quintessential to engineering proteins, which are most often riddled with ill-defined structure-function relationships. In this Perspective, we review bioengineering approaches aimed at overcoming the elusive protein structure-function relation. We extend these principles to engineering synthetic nanomaterials, specifically applying the underlying theory to optical sensors based on single-stranded DNA-wrapped single-walled carbon nanotubes (ssDNA-SWCNTs). Bioengineering techniques such as directed evolution, computational design, and noncanonical synthesis are reviewed in the broader context of nanomaterials engineering. We further provide an order-of-magnitude analysis of empirical approaches that rely on random or guided searches for designing new nanomaterials. The underlying concepts presented in these approaches can be further extended to a broad range of engineering fields confronted with empirical design strategies, including catalysis, metal-organic frameworks (MOFs), pharmaceutical dosing, and optimization algorithms.

Understanding the structural diversity of freestanding Al2O3 ultrathin films through a DFTB-aided genetic algorithm

(Sub)nanometre-thin alumina films are frequently encountered due to the self-limited oxidation of Al and its alloys, and seem to display an even larger structural variety than bulk alumina itself. While the nature of the underlying substrate and the oxidation kinetics are known to modulate the structure of supported films, understanding the intrinsic stability of freestanding films constitutes an important first step in itself, especially when the interaction with the substrate is rather weak. Using a combined tight-binding/DFT genetic algorithm approach, we identify particularly stable θ(100)-type films along with a host of novel stable thin film structures. Several of these correspond to cuts from relatively high energy bulk structures, e.g. dehydrated boehmite, pseudo-CaIrO3, defective rocksalt and LuMnO3, which are not commonly associated with alumina. DFT calculations allow to rationalize this stability reversal with respect to α-Al2O3 in terms of low surface energies compared to α(0001) and to identify the underlying mechanisms: breaking a low density of relatively weak Al-O bonds, filling of Al surface vacancies, and polarity-induced relaxation of the whole film. These observations provide interesting insights into existing supported ultrathin films.

Efficient Global Structure Optimization with a Machine-Learned Surrogate Model

We propose a scheme for global optimization with first-principles energy expressions of atomistic structure. While unfolding its search, the method actively learns a surrogate model of the potential energy landscape on which it performs a number of local relaxations (exploitation) and further structural searches (exploration). Assuming Gaussian processes, deploying two separate kernel widths to better capture rough features of the energy landscape while retaining a good resolution of local minima, an acquisition function is used to decide on which of the resulting structures is the more promising and should be treated at the first-principles level. The method is demonstrated to outperform by 2 orders of magnitude a well established first-principles based evolutionary algorithm in finding surface reconstructions. Finally, global optimization with first-principles energy expressions is utilized to identify initial stages of the edge oxidation and oxygen intercalation of graphene sheets on the Ir(111) surface.

O2 activation by AuAg clusters on a defective (100)MgO surface

In the present work, we discuss the electronic properties of supported dispersed bimetallic clusters with respect to their size, geometry, and Au_n/Ag_m (n + m = 6) composition. We have studied with supercell-density functional theory calculations the role of the charge transfer from the MgO defective support toward the cluster in the activation of O₂ by Au_nAg_m clusters. We first considered gas-phase clusters with different atomic compositions; then, we deposited all of them on a pristine (100)MgO surface and finally on a more realistic (100)MgO F-center. We performed a global and unrestricted search of the (cluster + surface) geometry. The Mexican enhanced genetic algorithm has been used to exhaustively explore the potential energy surface. Our results show that O₂ activation depends on the Au_n/Ag_m ratio. It has been found that both metals involved play different and important roles toward (a) the actual O₂ dissociation and (b) weakening of the oxygen-cluster bond, which, in turn, may promote the possibility of a catalytic process to take place, such as the oxidation process of CO and NO_x among others.

Nanocluster and single-atom catalysts for thermocatalytic conversion of CO and CO2

We highlight different aspects of single-atom and nanocluster catalysts for CO₂ reduction and CO oxidation, including synthesis, dynamic restructuring, and trends in activity and selectivity.

Pt8 cluster on alumina under a pressure of hydrogen: Support-dependent reconstruction from first-principles global optimization

Alumina supported Pt nanoclusters under a hydrogen environment play a crucial role in many heterogeneous catalysis applications. We conducted grand canonical genetic algorithm simulations for supported Pt₈ clusters in a hydrogen gas environment to study the intracluster, cluster-support, and cluster-adsorbate interactions. Two alumina surfaces, α-Al₂O₃(0001) and γ-Al₂O₃(100), and two conditions, T = 600 °C, p_H2 = 0.1 bar and T = 25 °C, p_H2 = 1.0 bar, were considered corresponding to low and high hydrogen chemical potential μ_H, respectively. The low free energy ensemble of Pt₈ is decorated by a medium (2-12 H), respectively, high (20-30 H), number of hydrogen atoms under equilibrium at low μ_H, respectively, high μ_H, and undergoes different morphological transformations on the two surfaces. On α-Al₂O₃(0001), Pt₈ is mostly 3D but very fluxional in structure at low μ_H and converts to open one-layer 2D structures with minimal fluxionality at high μ_H, whereas on γ-Al₂O₃(100), the exact opposite occurs: Pt₈ clusters present one-layer 2D shapes at low μ_H and switch to compact 3D shapes under high μ_H, during which the Pt₈ cluster preserves moderate fluxionality. Further analysis reveals a similar Pt-Pt bond length increase when switching from low μ_H to high μ_H on both surfaces although morphological transformations are different. Electronic structure analysis shows the existence of bonding interactions between Pt and Lewis acidic Al³⁺ sites along with the Pt-O interaction, which implies the necessity to include Al neighbors to discuss the electronic structure of small Pt clusters.

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).

"Teamwork Makes the Dream Work": Tribal Competition Evolutionary Search as a Surrogate for Free-Energy-Based Structural Predictions

Crystal structure prediction has been a grand challenge in material science owing to the large configurational space that one must explore. Evolutionary (genetic) algorithms coupled with first principles calculations are commonly used in crystal structure prediction to sample the ground and metastable states of materials based on configurational energies. However, crystal structure predictions at finite temperature ( T), pressure ( P), and composition ( X) require a free-energy-based search that is often computationally expensive and tedious. Here, we introduce a new machine-learning workflow for structure prediction that is based on a concept inspired by the evolution of human tribes in primitive society. Our tribal genetic algorithm (GA) combines configurational sampling with evolutionary optimization to accurately predict entropically stabilized phases at finite ( T, P, X), at a computational cost that is an order of magnitude smaller than that required for a free-energy-based search. In a departure from standard GA techniques, the populations of individuals are divided into multiple tribes based on a bond-order fingerprint, and genetic operations are modified to ensure that cluster configurations are sampled adequately to capture entropic contributions. Team competition introduced into the evolutionary process allows winning teams (representing a better set of individuals) to expand their sizes; this translates into a more expanded search of the phase space allowing us to explore solutions near possible global minimum. Each team explores a specific section of the structural phase space and avoids bias on solutions arising from the use of individual populations in a purely energy-based search. We demonstrate the efficacy of our approach by performing the structural prediction of a representative two-dimensional two-body system as well as Lennard-Jones clusters over a range of temperatures up to its melting point. Our approach outperforms the standard GA approaches and enables structural search under "real nonambient conditions" on both bulk systems and finite-sized clusters.

Iron doped gold cluster nanomagnets: ab initio determination of barriers for demagnetization

Magnetic properties of small- and nano-sized iron doped gold clusters are calculated at the level of second order multireference perturbation theory. We first assess the methodology for small Au6Fe and Au7Fe clusters, which are representative of even and odd electron count systems. We find that larger active spaces are needed for the odd electron count system, Au7Fe, which exhibits isotropic magnetization behaviour. On the other hand, the even electron count system, Au6Fe, exhibits strong axial magnetic anisotropy. We then apply this methodology to the tetrahedral and truncated pyramidal nano-sized Au19Fe (with S = 3/2) and Au18Fe (with S = 2) clusters. We find that face substitutions result in the most stable structures, followed by edge and corner substitutions. However, for Au18Fe, corner substitution results in strong magnetic anisotropy and a large barrier for demagnetization while face substitution does not. Thus, although corner and face substituted Au18Fe have the same spin, only corner substituted Au18Fe can act as a single nanoparticle magnet.

Experimental and theoretical 2p core-level spectra of size-selected gas-phase aluminum and silicon cluster cations: chemical shifts, geometric structure, and coordination-dependent screening

We present 2p core-level spectra of size-selected aluminum and silicon cluster cations from soft X-ray photoionization efficiency curves and density functional theory. The experimental and theoretical results are in very good quantitative agreement and allow for geometric structure determination. New ground state geometries for Al₁₂⁺, Si₁₅⁺, Si₁₆⁺, and Si₁₉⁺ are proposed on this basis. The chemical shifts of the 2p electron binding energies reveal a substantial difference for aluminum and silicon clusters: while in aluminum the 2p electron binding energy decreases with increasing coordination number, no such correlation was observed for silicon. The 2p binding energy shifts in clusters of both elements differ strongly from those of the corresponding bulk matter. For aluminum clusters, the core-level shifts between outer shell atoms and the encapsulated atom are of opposite sign and one order of magnitude larger than the corresponding core-level shift between surface and bulk atoms in the solid. For silicon clusters, the core-level shifts are of the same order of magnitude in clusters and in bulk silicon but no obvious correlation of chemical shift and bond length, as present for reconstructed silicon surfaces, are observed.

Combined Automated Reaction Pathway Searches and Sparse Modeling Analysis for Catalytic Properties of Lowest Energy Twins of Cu13

In nanocatalysis, growing attention has recently been given to investigation of energetically low-lying structural isomers of atomic clusters, because some isomers can demonstrate better catalytic activity than the most stable structures. In this study, we present a comparative investigation of catalytic activity for NO dissociation of a pair of the energetically degenerated isomers of Cu₁₃ cluster having C₂ and C _s symmetries. It is shown that although these isomers have similar structural, electronic, and optical properties, they can possess very different catalytic activities. The effect of isomerization between cluster isomers is considered using state-of-the-art automated reaction pathway search techniques such as an artificial force induced reaction (AFIR) method as a part of a global reaction route mapping (GRRM) strategy. This method allows effectively to locate a large number of possible reaction pathways and transition states (TSs). In total, 12 TSs for NO dissociation were obtained for Cu₁₃, of C₂, C _s, as well as I _h isomers. Sparse modeling analysis shows that LUMO is strongly negatively correlated with total energy of TSs. For most TSs, LUMO has the antibonding character of NO, consisting of the interaction between π* of NO and SOMO of Cu₁₃. Therefore, an increase in the strength of interaction between NO molecule and Cu₁₃ cluster causes the rise in energy of the LUMO, resulting in lowering of the TS energy for NO dissociation. The combination of the automated reaction pathway search technique and sparse modeling represents a powerful tool for analysis and prediction of the physicochemical properties of atomic clusters, especially in the regime of structural fluxionality, where traditional methods based on random geometry search analyses are difficult.

Two-level stochastic search of low-energy conformers for molecular spectroscopy: implementation and validation of MM and QM models

The search for stationary points in the molecular potential energy surfaces (PES) is a problem of increasing relevance in molecular sciences especially for large, flexible systems featuring several large-amplitude internal motions.

TGMin: An efficient global minimum searching program for free and surface-supported clusters

In this article, we introduce an efficient global-minimum structural search program named Tsinghua Global Minimum 2 (TGMin-2), which is the successor of the original TGMin algorithm that was developed in our group in 2011. We have introduced a number of new features and improvements into TGMin-2, including a symmetric structure generation algorithm that can produce good initial seeds for small- and medium-size clusters, the duplicated structure identification algorithm, and the improved structure adaption algorithm that was implemented in the original TGMin code. To predict the simulated photoelectron spectrum (PE spectrum) automatically, we also implemented a standalone program named AutoPES (Auto Photoelectron Spectroscopy), which can be used to simulate PE spectra and compare them with experimental results automatically. We have demonstrated that TGMin-2 and AutoPES are powerful tools for studying free and surface-supported molecules, clusters, and nanoclusters. © 2018 Wiley Periodicals, Inc.

Stability of AumAgn (m + n = 1-6) clusters supported on a F-center MgO(100) surface

A theoretical study has been performed for deposited AumAgn (m + n = 1-6) clusters. The combined use of the Mexican Enhanced Genetic Algorithm (MEGA) and Density Functional Theory (DFT) calculations allows us to explore the potential energy surface and therefore, find the global minimum configuration for each composition. We have performed calculations of clusters deposited on defects (oxygen vacancies) known as F centers on MgO (100) surfaces. Our results show interesting differences in the geometries of the clusters upon deposition and as a consequence in their electronic properties. The combination of two metals with different electronegativities creates an inhomogeneous charge distribution on their exposed surface producing good conditions for a catalytic process to take place.

Towards operando computational modeling in heterogeneous catalysis

An increased synergy between experimental and theoretical investigations in heterogeneous catalysis has become apparent during the last decade. Experimental work has extended from ultra-high vacuum and low temperature towards operando conditions. These developments have motivated the computational community to move from standard descriptive computational models, based on inspection of the potential energy surface at 0 K and low reactant concentrations (0 K/UHV model), to more realistic conditions. The transition from 0 K/UHV to operando models has been backed by significant developments in computer hardware and software over the past few decades. New methodological developments, designed to overcome part of the gap between 0 K/UHV and operando conditions, include (i) global optimization techniques, (ii) ab initio constrained thermodynamics, (iii) biased molecular dynamics, (iv) microkinetic models of reaction networks and (v) machine learning approaches. The importance of the transition is highlighted by discussing how the molecular level picture of catalytic sites and the associated reaction mechanisms changes when the chemical environment, pressure and temperature effects are correctly accounted for in molecular simulations. It is the purpose of this review to discuss each method on an equal footing, and to draw connections between methods, particularly where they may be applied in combination.

Explicit treatment of hydrogen bonds in the universal force field: Validation and application for metal-organic frameworks, hydrates, and host-guest complexes

A straightforward means to include explicit hydrogen bonds within the Universal Force Field (UFF) is presented. Instead of treating hydrogen bonds as non-bonded interaction subjected to electrostatic and Lennard-Jones potentials, we introduce an explicit bond with a negligible bond order, thus maintaining the structural integrity of the H-bonded complexes and avoiding the necessity to assign arbitrary charges to the system. The explicit hydrogen bond changes the coordination number of the acceptor site and the approach is thus most suitable for systems with under-coordinated atoms, such as many metal-organic frameworks; however, it also shows an excellent performance for other systems involving a hydrogen-bonded framework. In particular, it is an excellent means for creating starting structures for molecular dynamics and for investigations employing more sophisticated methods. The approach is validated for the hydrogen bonded complexes in the S22 dataset and then employed for a set of metal-organic frameworks from the Computation-Ready Experimental database and several hydrogen bonded crystals including water ice and clathrates. We show that the direct inclusion of hydrogen bonds reduces the maximum error in predicted cell parameters from 66% to only 14%, and the mean unsigned error is similarly reduced from 14% to only 4%. We posit that with the inclusion of hydrogen bonding, the solvent-mediated breathing of frameworks such as MIL-53 is now accessible to rapid UFF calculations, which will further the aim of rapid computational scanning of metal-organic frameworks while providing better starting points for electronic structure calculations.

Metastable Structures in Cluster Catalysis from First-Principles: Structural Ensemble in Reaction Conditions and Metastability Triggered Reactivity

Reactivity studies on catalytic transition metal clusters are usually performed on a single global minimum structure. With the example of a Pt₁₃ cluster under a pressure of hydrogen, we show from first-principle calculations that low energy metastable structures of the cluster can play a major role for catalytic reactivity and that hence consideration of the global minimum structure alone can severely underestimate the activity. The catalyst is fluxional with an ensemble of metastable structures energetically accessible at reaction conditions. A modified genetic algorithm is proposed to comprehensively search for the low energy metastable ensemble (LEME) structures instead of merely the global minimum structure. In order to reduce the computational cost of density functional calculations, a high dimensional neural network potential is employed to accelerate the exploration. The presence and influence of LEME structures during catalysis is discussed by the example of H covered Pt₁₃ clusters for two reactions of major importance: hydrogen evolution reaction and methane activation. The results demonstrate that although the number of accessible metastable structures is reduced under reaction condition for Pt₁₃ clusters, these metastable structures can exhibit high activity and dominate the observed activity due to their unique electronic or structural properties. This underlines the necessity of thoroughly exploring the LEME structures in catalysis simulations. The approach enables one to systematically address the impact of isomers in catalysis studies, taking into account the high adsorbate coverage induced by reaction conditions.

On-the-Fly Machine Learning of Atomic Potential in Density Functional Theory Structure Optimization

Machine learning (ML) is used to derive local stability information for density functional theory calculations of systems in relation to the recently discovered SnO_{2}(110)-(4×1) reconstruction. The ML model is trained on (structure, total energy) relations collected during global minimum energy search runs with an evolutionary algorithm (EA). While being built, the ML model is used to guide the EA, thereby speeding up the overall rate by which the EA succeeds. Inspection of the local atomic potentials emerging from the model further shows chemically intuitive patterns.

Structure of the SnO_{2}(110)-(4×1) Surface

Using surface x-ray diffraction (SXRD), quantitative low-energy electron diffraction (LEED), and density-functional theory (DFT) calculations, we have determined the structure of the (4×1) reconstruction formed by sputtering and annealing of the SnO_{2}(110) surface. We find that the reconstruction consists of an ordered arrangement of Sn_{3}O_{3} clusters bound atop the bulk-terminated SnO_{2}(110) surface. The model was found by application of a DFT-based evolutionary algorithm with surface compositions based on SXRD, and shows excellent agreement with LEED and with previously published scanning tunneling microscopy measurements. The model proposed previously consisting of in-plane oxygen vacancies is thus shown to be incorrect, and our result suggests instead that Sn(II) species in interstitial positions are the more relevant features of reduced SnO_{2}(110) surfaces.

Development of a Transferable Reactive Force Field of P/H Systems: Application to the Chemical and Mechanical Properties of Phosphorene

We developed ReaxFF parameters for phosphorus and hydrogen to give a good description of the chemical and mechanical properties of pristine and defected black phosphorene. ReaxFF for P/H is transferable to a wide range of phosphorus- and hydrogen-containing systems including bulk black phosphorus, blue phosphorene, edge-hydrogenated phosphorene, phosphorus clusters, and phosphorus hydride molecules. The potential parameters were obtained by conducting global optimization with respect to a set of reference data generated by extensive ab initio calculations. We extended ReaxFF by adding a 60° correction term, which significantly improved the description of phosphorus clusters. Emphasis was placed on the mechanical response of black phosphorene with different types of defects. Compared to the nonreactive SW potential ( Jiang , J.-W. Nanotechnology 2015 , 26 , 315706 ), ReaxFF for P/H systems provides a significant improvement in describing the mechanical properties of the pristine and defected black phosphorene, as well as the thermal stability of phosphorene nanotubes. A counterintuitive phenomenon is observed that single vacancies weaken the black phosphorene more than double vacancies with higher formation energy. Our results also showed that the mechanical response of black phosphorene is more sensitive to defects in the zigzag direction than that in the armchair direction. In addition, we developed a preliminary set of ReaxFF parameters for P/H/O/C to demonstrate that the ReaxFF parameters developed in this work could be generalized to oxidized phosphorene and P-containing 2D van der Waals heterostructures. That is, the proposed ReaxFF parameters for P/H systems establish a solid foundation for modeling of a wide range of P-containing materials.

The atomic simulation environment-a Python library for working with atoms

The atomic simulation environment (ASE) is a software package written in the Python programming language with the aim of setting up, steering, and analyzing atomistic simulations. In ASE, tasks are fully scripted in Python. The powerful syntax of Python combined with the NumPy array library make it possible to perform very complex simulation tasks. For example, a sequence of calculations may be performed with the use of a simple 'for-loop' construction. Calculations of energy, forces, stresses and other quantities are performed through interfaces to many external electronic structure codes or force fields using a uniform interface. On top of this calculator interface, ASE provides modules for performing many standard simulation tasks such as structure optimization, molecular dynamics, handling of constraints and performing nudged elastic band calculations.

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.

Unraveling the Planar-Globular Transition in Gold Nanoclusters through Evolutionary Search

Au nanoclusters are of technological relevance for catalysis, photonics, sensors, and of fundamental scientific interest owing to planar to globular structural transformation at an anomalously high number of atoms i.e. in the range 12–14. The nature and causes of this transition remain a mystery. In order to unravel this conundrum, high throughput density functional theory (DFT) calculations, coupled with a global structural optimization scheme based on a modified genetic algorithm (GA) are conducted. More than 20,000 Au₁₂, Au₁₃, and Au₁₄ nanoclusters are evaluated. With any DFT functional, globular and planar structures coexist across the size range of interest. The planar-globular transition is gradual at room temperature rather than a sharp transition as previously believed. The effects of anionicity, s-d band hybridization and long range interactions on the dimensional transition are quantified by using the structures adjacent to the minima. Anionicity marginally changes the relative stability of the clusters. The degree of s-d hybridization is varied via changing the Hubbard U value which corroborate that s-d hybridization alone does not stabilize planar structures. van der Waals interactions, on the other hand, stabilize globular structures. These results elucidate the balance between the different reasons of the dimensional transition in gold nanoclusters.