An automated nudged elastic band method

Exploring potential energy surfaces to reach saddle points above convex regions

Saddle points on high-dimensional potential energy surfaces (PES) play a determining role in the activated dynamics of molecules and materials. Building on approaches dating back more than 50 years, many open-ended transition-state search methods have been developed to follow the direction of negative curvature from a local minimum to an adjacent first-order saddle point. Despite the mathematical justification, these methods can display a high failure rate: using small deformation steps, up to 80% of the explorations can end up in a convex region of the PES, where all directions of negative curvature vanish, while if the deformation is aggressive, a similar fraction of attempts lead to saddle points that are not directly connected to the initial minimum. In high-dimension PES, these reproducible failures were thought to only increase the overall computational cost, without having any effect on the methods' capacity to find all saddle points surrounding a minimum. Using activation-relaxation technique nouveau (ARTn), we characterize the nature of the PES around minima, considerably expanding on previous knowledge. We show that convex regions can lie on activation pathways and that not exploring beyond them can introduce significant bias in the saddle-point search. We introduce an efficient approach for traversing the convex regions, almost eliminating exploration failures, while multiplying by almost 10 the number of identified unique and connected saddle points as compared to the standard ARTn, thus underlining the importance of correctly handling convex regions for completeness of saddle point explorations.

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

A novel approach to study multi-domain motions in JAK1's activation mechanism based on energy landscape

The family of Janus Kinases (JAKs) associated with the JAK-signal transducers and activators of transcription signaling pathway plays a vital role in the regulation of various cellular processes. The conformational change of JAKs is the fundamental steps for activation, affecting multiple intracellular signaling pathways. However, the transitional process from inactive to active kinase is still a mystery. This study is aimed at investigating the electrostatic properties and transitional states of JAK1 to a fully activation to a catalytically active enzyme. To achieve this goal, structures of the inhibited/activated full-length JAK1 were modelled and the energies of JAK1 with Tyrosine Kinase (TK) domain at different positions were calculated, and Dijkstra's method was applied to find the energetically smoothest path. Through a comparison of the energetically smoothest paths of kinase inactivating P733L and S703I mutations, an evaluation of the reasons why these mutations lead to negative or positive regulation of JAK1 are provided. Our energy analysis suggests that activation of JAK1 is thermodynamically spontaneous, with the inhibition resulting from an energy barrier at the initial steps of activation, specifically the release of the TK domain from the inhibited Four-point-one, Ezrin, Radixin, Moesin-PK cavity. Overall, this work provides insights into the potential pathway for TK translocation and the activation mechanism of JAK1.

CO2 on Graphene: Benchmarking Computational Approaches to Noncovalent Interactions

Designing and optimizing graphene-based gas sensors in silico entail constructing appropriate atomistic representations for the physisorption complex of an analyte on an infinite graphene sheet, then selecting accurate yet affordable methods for geometry optimizations and energy computations. In this work, diverse density functionals (DFs), coupled cluster theory, and symmetry-adapted perturbation theory (SAPT) in conjunction with a range of finite and periodic surface models of bare and supported graphene were tested for their ability to reproduce the experimental adsorption energies of CO2 on graphene in a low-coverage regime. Periodic results are accurately reproduced by the interaction energies extrapolated from finite clusters to infinity. This simple yet powerful scheme effectively removes size dependence from the data obtained using finite models, and the latter can be treated at more sophisticated levels of theory relative to periodic systems. While for small models inexpensive DFs such as PBE-D3 afford surprisingly good agreement with the gold standard of quantum chemistry, CCSD(T), interaction energies closest to experiment are obtained by extrapolating the SAPT results and with nonlocal van der Waals functionals in the periodic setting. Finally, none of the methods and models reproduce the experimentally observed CO2 tilted adsorption geometry on the Pt(111) support, calling for either even more elaborate theoretical approaches or a revision of the experiment.

Origin of hydroxyl pair formation on reduced anatase TiO2(101)

The interaction of water with metal oxide surfaces is of key importance to several research fields and applications. Because of its ability to photo-catalyze water splitting, reducible anatase TiO₂ (a-TiO₂) is of particular interest. Here, we combine experiments and theory to study the dissociation of water on bulk-reduced a-TiO₂(101). Following large water exposures at room temperature, point-like protrusions appear on the a-TiO₂(101) surface, as shown by scanning tunneling microscopy (STM). These protrusions originate from hydroxyl pairs, consisting of terminal and bridging OH groups, OH_t/OH_b, as revealed by infrared reflection absorption spectroscopy (IRRAS) and valence band experiments. Utilizing density functional theory (DFT) calculations, we offer a comprehensive model of the water/a-TiO₂(101) interaction. This model also explains why the hydroxyl pairs are thermally stable up to ∼480 K.

(2×1) Reconstruction Mechanism of Rutile TiO2(011) Surface

Understanding the reconstruction kinetics of solid surfaces involving an ensemble of atomic movements is practically important but challenging due to the complexity of high-dimensional potential energy surfaces. Herein, we develop a step-deciding technique incorporated with the nudged elastic band method, which enables multidirection pathway sampling and ensures the capture of a minimum energy path (MEP). Using this approach, the (2×1) reconstruction mechanism of a rutile-TiO₂(011) surface, a classic and long-standing open problem in the fields of surface science and heterogeneous catalysis, is quantified, and the MEP is explicitly identified and explained. Following the least-bond-breaking rule, it gives a stepwise Ti-O bond cleavage mechanism with a collection of decoupled local structural relaxation modes at an overall barrier of 1.25 eV critically affected by initial Ti-O bond opening, which is much lower than the common synergy mechanism. Moreover, the adsorption-induced reconstruction is rationalized considering practical reaction conditions, where H atom adsorbate is shown to effectively stabilize the labile one-fold O_1c intermediate and promote the reconstruction kinetics. This work reveals the reconstruction mechanism regarding multiatom movements and provides a general method for the structural exploration of other complicated systems.

Curvature-weighted nudged elastic band method using the Riemann curvature

The nudged elastic band (NEB) method is utilized to find reaction paths (RPs) using discretized intermediate structures called "images" between a reactant and a product. In fact, NEB calculations do not always converge because of the bent of RPs. Mathematically, more images are needed for complex curves, and here, we focused on the curvature. In this study, we propose a new method for calculating the curvature of the RPs as well as a method for weighting the spring constant of the NEB with the curvature, which we named the curvature weighted NEB (CW-NEB) method. In addition, we will propose the CW-NEB method with the climbing image (CI) method (CW-CI-NEB). To show the efficiency of our method, calculations for the ene-reaction of the CW-CI-NEB method were performed and compared with those of the CI-NEB methods. The CW-CI-NEB methods converged in shorter iteration times than the CI-NEB calculation, which was found by gathering the bent of RPs.

Expanding the Material Search Space for Multivalent Cathodes

Multivalent batteries are an energy storage technology with the potential to surpass lithium-ion batteries; however, their performance have been limited by the low voltages and poor solid-state ionic mobility of available cathodes. A computational screening approach to identify high-performance multivalent intercalation cathodes among materials that do not contain the working ion of interest has been developed, which greatly expands the search space that can be considered for material discovery. This approach has been applied to magnesium cathodes as a proof of concept, and four resulting candidate materials [NASICON V₂(PO₄)₃, birnessite NaMn₄O₈, tavorite MnPO₄F, and spinel MnO₂] are discussed in further detail. In examining the ion migration environment and associated Mg²⁺ migration energy in these materials, local energy maxima are found to correspond with pathway positions where Mg²⁺ passes through a plane of anion atoms. While previous studies have established the influence of local coordination on multivalent ion mobility, these results suggest that considering both the type of the local bonding environment and available free volume for the mobile ion along its migration pathway can be significant for improving solid-state mobility.

Graph-Driven Reaction Discovery: Progress, Challenges, and Future Opportunities

Graph-based descriptors, such as bond-order matrices and adjacency matrices, offer a simple and compact way of categorizing molecular structures; furthermore, such descriptors can be readily used to catalog chemical reactions (i.e., bond-making and -breaking). As such, a number of graph-based methodologies have been developed with the goal of automating the process of generating chemical reaction network models describing the possible mechanistic chemistry in a given set of reactant species. Here, we outline the evolution of these graph-based reaction discovery schemes, with particular emphasis on more recent methods incorporating graph-based methods with semiempirical and ab initio electronic structure calculations, minimum-energy path refinements, and transition state searches. Using representative examples from homogeneous catalysis and interstellar chemistry, we highlight how these schemes increasingly act as "virtual reaction vessels" for interrogating mechanistic questions. Finally, we highlight where challenges remain, including issues of chemical accuracy and calculation speeds, as well as the inherent challenge of dealing with the vast size of accessible chemical reaction space.

Elastic Image Pair Method for Finding Transition States on Potential Energy Surfaces Using Only First Derivatives

Herein, an elastic image pair (EIP) method is proposed to search transition states between two potential-energy minima using only first derivatives. In this method, two images are generated, and the spring forces are added to the images to control the distance between the two images. Transition states are reached when the force and the distance of the image pair are both converged. A set of test molecules is optimized using the EIP method, which shows its efficiency in transition state searching compared to other methods. This new method is more stable and reliable in finding transition states with much less computations.

Dimerization of dehydrogenated polycyclic aromatic hydrocarbons on graphene

Dimerization of polycyclic aromatic hydrocarbons (PAHs) is an important, yet poorly understood, step in the on-surface synthesis of graphene (nanoribbon), soot formation, and growth of carbonaceous dust grains in the interstellar medium (ISM). The on-surface synthesis of graphene and the growth of carbonaceous dust grains in the ISM require the chemical dimerization in which chemical bonds are formed between PAH monomers. An accurate and cheap method of exploring structure rearrangements is needed to reveal the mechanism of chemical dimerization on surfaces. This work has investigated the chemical dimerization of two dehydrogenated PAHs (coronene and pentacene) on graphene via an evolutionary algorithm augmented by machine learning surrogate potentials and a set of customized structure operators. Different dimer structures on surfaces have been successfully located by our structure search methods. Their binding energies are within the experimental errors of temperature programmed desorption measurements. The mechanism of coronene dimer formation on graphene is further studied and discussed.

Protocol for Directing Nudged Elastic Band Calculations to the Minimum Energy Pathway: Nurturing Errant Calculations Back to Convergence

The combination of density functional theory (DFT) and the nudged elastic band (NEB) method offers a practical tool for the discovery of underlying reaction mechanisms related to the synthesis of functional materials. However, in practice, the lack of a standardized protocol for minimum energy pathway determination too often leads to an inefficient and computationally intensive design process. To that end, we define a verifiable DFT+NEB protocol for efficiently locating and confirming the transition state of a reaction. To test this assertion, we curate 226 unique reactions within 14 classes of reactions and investigate their performance in terms of the number of NEB iterations they require to locate the transition state and an estimate of the associated mean absolute error. Leveraging this protocol, we demonstrate its application for an initial set of parameters: number of frames, N_frames = 11; maximum step size, S_max = 0.04 Å; optimizer = LBFGS; and spring constant, k_spr = 0.1 eV/Ų. We report a convergence rate of 73% and find that a root-mean-square force (F_RMS) of 0.01 eV/Å provides a "rule of thumb" below which NEB simulations are likely to converge. Venturing beyond this baseline enquiry, we delineate the effect on performance of altering the number of frames, maximum step size, choice of optimizer and spring constant. We find improvements in performance with increasing N_frames and S_max, ostensibly approaching some asymptotic limit. We also see substantial improvement in efficiency with the LBFGS optimizer and a clear minimum in performance for the spring constant value of 0.1 eV/Ų. Finally, we provide five case studies that demonstrate typical convergence issues for NEB simulations and suggest methods to overcome them. Our results provide specific and transferable recommendations, offering a transparent and practical tool for beginner and expert researchers alike toward a more rational NEB simulation design.

Efficient Helium Separation with Two-Dimensional Metal-Organic Framework Fe/Ni-PTC: A Theoretical Study

Helium (He) is one of the indispensable and rare strategic materials for national defense and high-tech industries. However, daunting challenges have to be overcome for the supply shortage of He resources. Benefitted from the wide pore size distribution, sufficient intrinsic porosity, and high specific surface area, metal–organic framework (MOF) materials are prospective candidates for He purification in the membrane-based separation technology. In this work, through first-principles calculations and molecular dynamics (MD) simulations, we studied the permeability and filtration performance of He by the newly synthesized two-dimensional Fe-PTC MOF and its analogue Ni-PTC MOF. We found that both Fe-PTC and Ni-PTC have superior high performance for He separation. The selectivity of He over N₂ was calculated to be ~10¹⁷ for Fe-PTC and ~10¹⁵ for Ni-PTC, respectively, both higher than most of the previously proposed 2D porous membranes. Meanwhile, high He permeance (10⁻⁴~10⁻³ mol s⁻¹ m⁻² Pa⁻¹) can be obtained for the Fe/Ni-PTC MOF for temperatures ranging from 200 to 500 K. Therefore, the present study offers a highly prospective membrane for He separation, which has great potential in industrial application.

A modified nudged elastic band algorithm with adaptive spring lengths

We present a modified version of the nudged elastic band (NEB) algorithm to find minimum energy paths connecting two known configurations. We show that replacing the harmonic band-energy term with a discretized version of the Onsager-Machlup action leads to a NEB algorithm with adaptive spring lengths that automatically increase the resolution of the minimum energy path around the saddle point of the potential energy surface. The method has the same computational cost per optimization step of the standard NEB algorithm and does not introduce additional parameters. We present applications to the isomerization of alanine dipeptide, the elimination of hydrogen from ethane, and the healing of a 5-77-5 defect in graphene.

Nudged Elastic Band Method for Molecular Reactions Using Energy-Weighted Springs Combined with Eigenvector Following

The climbing image nudged elastic band method (CI-NEB) is used to identify reaction coordinates and to find saddle points representing transition states of reactions. It can make efficient use of parallel computing as the calculations of the discretization points, the so-called images, can be carried out simultaneously. In typical implementations, the images are distributed evenly along the path by connecting adjacent images with equally stiff springs. However, for systems with a high degree of flexibility, this can lead to poor resolution near the saddle point. By making the spring constants increase with energy, the resolution near the saddle point is improved. To assess the performance of this energy-weighted CI-NEB method, calculations are carried out for a benchmark set of 121 molecular reactions. The performance of the method is analyzed with respect to the input parameters. Energy-weighted springs are found to greatly improve performance and result in successful location of the saddle points in less than a thousand energy and force evaluations on average (about a hundred per image) using the same set of parameter values for all of the reactions. Even better performance is obtained by stopping the calculation before full convergence and complete the saddle point search using an eigenvector following method starting from the location of the climbing image. This combination of methods, referred to as NEB-TS, turns out to be robust and highly efficient as it reduces the average number of energy and force evaluations down to a third, to 305. An efficient and flexible implementation of these methods has been made available in the ORCA software.

TSNet: predicting transition state structures with tensor field networks and transfer learning

Transition states are among the most important molecular structures in chemistry, critical to a variety of fields such as reaction kinetics, catalyst design, and the study of protein function. However, transition states are very unstable, typically only existing on the order of femtoseconds. The transient nature of these structures makes them incredibly difficult to study, thus chemists often turn to simulation. Unfortunately, computer simulation of transition states is also challenging, as they are first-order saddle points on highly dimensional mathematical surfaces. Locating these points is resource intensive and unreliable, resulting in methods which can take very long to converge. Machine learning, a relatively novel class of algorithm, has led to radical changes in several fields of computation, including computer vision and natural language processing due to its aptitude for highly accurate function approximation. While machine learning has been widely adopted throughout computational chemistry as a lightweight alternative to costly quantum mechanical calculations, little research has been pursued which utilizes machine learning for transition state structure optimization. In this paper TSNet is presented, a new end-to-end Siamese message-passing neural network based on tensor field networks shown to be capable of predicting transition state geometries. Also presented is a small dataset of S_N2 reactions which includes transition state structures - the first of its kind built specifically for machine learning. Finally, transfer learning, a low data remedial technique, is explored to understand the viability of pretraining TSNet on widely available chemical data may provide better starting points during training, faster convergence, and lower loss values. Aspects of the new dataset and model shall be discussed in detail, along with motivations and general outlook on the future of machine learning-based transition state prediction.

Simple position and orientation preconditioning scheme for minimum energy path calculations

Minimum-energy path (MEP) calculations, such as those typified by the nudged elastic band method, require input of reactant and product molecular configurations at initialization. In the case of reactions involving more than one molecule, generating initial reactant and product configurations requires careful consideration of the relative position and orientations of the reactive molecules in order to ensure that the resulting MEP calculation proceeds without converging on an alternative reaction-path, and without requiring excessive numbers of optimization iterations; as such, this initial system set-up is most commonly performed "by hand," with an expert user arranging reactive molecules in space to ensure that the following MEP calculation runs smoothly. In this Article, we introduce a simple preconditioning scheme which replaces this labor-intensive, human-knowledge-based step with an automated deterministic computational scheme. In our approach, initial reactant and product configurations are generated such that steric hindrance between reactive molecules is minimized in the reactant and product configurations, while also simultaneously requiring minimal structural differences between the reactants and products. The method is demonstrated using a benchmark test-set of >3400 organic molecular reactions, where comparison of the reactant/product configurations generated using our approach compare very well to initial configurations which were generated on an ad hoc basis.

New insights on the ESIPT process based on solid-state data and state-of-the-art computational methods

Benzothiazole derivatives were used as models to study the excited-state intramolecular proton transfer (ESIPT) from an experimental and theoretical point of view. The experimental electronic and vibrational results were compared with a comprehensive selection of state-of-the-art computational methods in a workflow approach. The latter were performed based on modern techniques, such as DLPNO-CCSD(T), which gives the reference energies and current methodologies for ESIPT analysis, such as molecular dynamics and charge density difference testing. The theoretical vibrational results were focused on the stretch vibrational-mode of the hydroxyl group, which indicated a large increase in the intramolecular hydrogen bond strength, which facilitates the ESIPT process. Theoretically, the optimization of a large number of molecules shows that π-stacking plays a fundamental role in benzothiazole stabilization, with a remarkably strong intramolecular hydrogen bond. The potential energy surface of the ESIPT reactive benzothiazole (4HBS) has a clear transition state where ESIPT is easily observed with a large difference in energy between the enol and keto tautomer. Additionally, molecular dynamics showed that the ESIPT process occurs very fast. The tautomer appears around 8.7 fs and the enolic form is regenerated in just 24 fs, closing the Förster cycle. The calculated Stokes shift could be related to the ESIPT process and the experimental solid-state emission spectrum matched almost perfectly with the theoretical one. In contrast, for the non-ESIPT benzothiazole (4HBSN), the agreement between theory and experiment was limited, probably due to intermolecular interaction effects that are not considered in these calculations.

A computational study on the reduction of O2 to H2O2 using small polycyclic aromatic molecules

This work presents the complete autoxidation pathway for the anthraquinone process and one alternative catalyst that overcomes its kinetic challenges.

Catalytic Mechanism of Processive GlfT2: Transition Path Sampling Investigation of Substrate Translocation

We applied the transition path sampling (TPS) method to study the translocation step of the catalytic mechanism of galactofuranosyl transferase 2 (GlfT2). Using TPS in the field of enzymatic reactions is still relatively rare, and we show its effectiveness on this enzymatic system. We decipher an unknown mechanism of the translocation step and, thus, provide a complete understanding of the catalytic mechanism of GlfT2 at the atomistic level. The GlfT2 enzyme is involved in the formation of the mycobacterial cell wall and transfers galactofuranose (Galf) from UDP-Galf onto a growing acceptor Galf chain. The biosynthesis of the galactan chain is accomplished in a processive manner, with the growing acceptor substrate remaining bound to GlfT2. The glycosidic bond formed by GlfT2 between the two Galf residues alternates between β-(1-6) and β-(1-5) linkages. The translocation of the growing galactan between individual additions of Galf residues is crucial for the function of GlfT2. Analysis of unbiased trajectory ensembles revealed that the translocation proceeds differently depending on the glycosidic linkage between the last two Galf residues. We also showed that the protonation state of the catalytic residue Asp372 significantly influences the translocation. Approximate transition state structures and potential energy reaction barriers of the translocation process were determined. The calculated potential reaction barriers in the range of 6-14 kcal/mol show that the translocation process is not the rate-limiting step in galactan biosynthesis.

CNT-Assembled Octahedron Carbon-Encapsulated Cu3P/Cu Heterostructure by In Situ MOF-Derived Engineering for Superior Lithium Storage: Investigations by Experimental Implementation and First-Principles Calculation

Conspicuously, metal-organic frameworks (MOFs) serve as homogenously and periodically atom-dispersed self-sacrificial template for in situ engineering of hierarchical porous carbon-encapsulated micro/nanoheterostructure materials, integrating the merits of micro/nanostructure to high-volumetric energy storage. Copper phosphide represents a promising candidate due to its compact material density compared to commercial graphite. Herein, micro/nanostructured Cu3P/Cu encapsulated by carbon-nanotube-assembled hierarchical octahedral carbonaceous matrix (Cu3P/Cu@CNHO) is constructed by an in situ MOF-derived engineering for novel anode material in LIBs, which achieves an extraordinary cycling stability (a well-maintained gravimetric/volumetric capacity of 463.2 mAh g-1/1878.4 mAh cm-3 at 1 A g-1 up to 1600 cycles) and distinguished rate capability (an ameliorated capacity of 317.7 mAh g-1 even at 10 A g-1), together with unprecedented heat-resistant capability (an elevated temperature of 50 °C for 1000 cycles maintaining 434.7 mAh g-1 at 0.5 A g-1). The superior electrochemical performance of Cu3P/Cu@CNHO is credited to the large specific surface area, conductive carbon matrix and metallic copper dopants, synergistic effects of the intrinsic Cu3P/Cu heterostructure, and well-defined micro/nanostructure, facilitating a boosted electrochemical conductivity and accelerated diffusion kinetics.

Globally optimal catalytic fields for a Diels-Alder reaction

In a previous paper [M. Dittner and B. Hartke, J. Chem. Theory Comput. 14, 3547 (2018)], we introduced a preliminary version of our GOCAT (globally optimal catalyst) concept in which electrostatic catalysts are designed for arbitrary reactions by global optimization of distributed point charges that surround the reaction. In this first version, a pre-defined reaction path was kept fixed. This unrealistic assumption allowed for only small catalytic effects. In the present work, we extend our GOCAT framework by a sophisticated and robust on-the-fly reaction path optimization, plus further concomitant algorithm adaptions. This allows smaller and larger excursions from a pre-defined reaction path under the influence of the GOCAT point-charge surrounding, all the way to drastic mechanistic changes. In contrast to the restricted first GOCAT version, this new version is able to address real-life catalysis. We demonstrate this by applying it to the electrostatic catalysis of a prototypical Diels-Alder reaction. Without using any prior information, this procedure re-discovers theoretically and experimentally established features of electrostatic catalysis of this very reaction, including a field-dependent transition from the synchronous, concerted textbook mechanism to a zwitterionic two-step mechanism, and diastereomeric discrimination by suitable electric field components.

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.

High-efficiency helium separation through an inorganic graphenylene membrane: a theoretical study

Appropriate interactions between an IGP membrane and He molecules result in efficient helium separation.

The N(4S) + O2(X3Σ−g) ↔ O(3P) + NO(X2Π) reaction: thermal and vibrational relaxation rates for the 2A′, 4A′ and 2A′′ states

Cross sections, rates, equilibrium constants and vibrational relaxation times for the N(⁴S) + O₂(X³Σ−g) ↔ O(³P) + NO(X²Π) reaction from simulations on new, RKHS-based surfaces for the three lowest electronic states.

Accurate reproducing kernel-based potential energy surfaces for the triplet ground states of N2O and dynamics for the N + NO ↔ O + N2 and N2 + O → 2N + O reactions

Reproducing kernel-based potential energy surface based on MRCI+Q/aug-cc-pVTZ energies for the triplet states of N₂O and quasiclassical dynamical study for the reaction, dissociation and vibrational relaxation.

The mechanism of Mg2+ conduction in ammine magnesium borohydride promoted by a neutral molecule

Light weight and cheap electrolytes with fast multi-valent ion conductivity can pave the way for future high-energy density solid-state batteries, beyond the lithium-ion battery.

Scaled and Dynamic Optimizations of Nudged Elastic Bands

We present a modified nudged elastic band routine that can reduce the number of force calls by more than 50% for bands with nonuniform convergence. The method, which we call "dyNEB", dynamically and selectively optimizes images on the basis of the perpendicular PES-derived forces and parallel spring forces acting on that region of the band. The convergence criteria are scaled to focus on the region of interest, i.e., the saddle point, while maintaining continuity of the band and avoiding truncation. We show that this method works well for solid state reaction barriers-nonelectrochemical in general and electrochemical in particular-and that the number of force calls can be significantly reduced without loss of resolution at the saddle point.

R-NEB: Accelerated Nudged Elastic Band Calculations by Use of Reflection Symmetry

Many activated processes in materials science, physics, and chemistry, e.g. diffusion processes, have initial and final states related by symmetry. Identification of minimum energy paths in such systems with methods such as nudged elastic band (NEB) can gain substantial speed up if the symmetry is exploited. The identification of minimum energy paths and transition states for such processes constitute a large fraction of the CPU-usage within computational materials science; much of which is in essence redundant due to symmetry. Paths with a reflection symmetry can be calculated using about half the computational resources, and the activation energy can, for some transitions, be estimated with high precision with a speed up factor equal to the number of images used in a standard NEB calculation. We present the formal properties required for a system to guarantee a reflection symmetric minimum energy path and an implementation to prepare and effectively speed up nudged elastic band calculations through symmetry considerations. Five examples are given to show the versatility and effectiveness of the method and to validate the implementation. The method is implemented in the open source package Atomic Simulation Environment (ASE) and contains internal methods to identify symmetry relations between the given end point configurations.

Low-Scaling Algorithm for Nudged Elastic Band Calculations Using a Surrogate Machine Learning Model

We present the incorporation of a surrogate Gaussian process regression (GPR) atomistic model to greatly accelerate the rate of convergence of classical nudged elastic band (NEB) calculations. In our surrogate model approach, the cost of converging the elastic band no longer scales with the number of moving images on the path. This provides a far more efficient and robust transition state search. In contrast to a conventional NEB calculation, the algorithm presented here eliminates any need for manipulating the number of images to obtain a converged result. This is achieved by inventing a new convergence criteria that exploits the probabilistic nature of the GPR to use uncertainty estimates of all images in combination with the force in the saddle point in the target model potential. Our method is an order of magnitude faster in terms of function evaluations than the conventional NEB method with no accuracy loss for the converged energy barrier values.

A Practical Guide to Surface Kinetic Monte Carlo Simulations

This review article is intended as a practical guide for newcomers to the field of kinetic Monte Carlo (KMC) simulations, and specifically to lattice KMC simulations as prevalently used for surface and interface applications. We will provide worked out examples using the kmos code, where we highlight the central approximations made in implementing a KMC model as well as possible pitfalls. This includes the mapping of the problem onto a lattice and the derivation of rate constant expressions for various elementary processes. Example KMC models will be presented within the application areas surface diffusion, crystal growth and heterogeneous catalysis, covering both transient and steady-state kinetics as well as the preparation of various initial states of the system. We highlight the sensitivity of KMC models to the elementary processes included, as well as to possible errors in the rate constants. For catalysis models in particular, a recurrent challenge is the occurrence of processes at very different timescales, e.g., fast diffusion processes and slow chemical reactions. We demonstrate how to overcome this timescale disparity problem using recently developed acceleration algorithms. Finally, we will discuss how to account for lateral interactions between the species adsorbed to the lattice, which can play an important role in all application areas covered here.

Fast screening of homogeneous catalysis mechanisms using graph-driven searches and approximate quantum chemistry

Automatic analysis of competing mechanisms.

Rotation and diffusion of naphthalene on Pt(111)

The behavior of naphthalene on Pt(111) surfaces is studied by combining insight from scanning tunneling microscopy (STM) and van der Waals enabled density functional theory. Adsorption, diffusion, and rotation are investigated by a series of variable temperature STM experiments revealing naphthalene ability to rotate on-site with ease with a rotational barrier of 0.69 eV. Diffusion to neighbouring sites is found to be more difficult. The experimental results are in good agreement with the theoretical investigations which confirm that the barrier for diffusion is slightly higher than the one for rotation. The theoretical barriers for rotation and translation are found to be 0.75 and 0.78 eV, respectively. An automatic mapping of the possible diffusion pathways reveals very detailed diffusion paths with many small local minima that would have been practically impossible to find manually. This automated procedure provides detailed insight into the preferred diffusion pathways that are important for our understanding of molecule-substrate interactions.

Exciting H2 Molecules for Graphene Functionalization

Hydrogen functionalization of graphene by exposure to vibrationally excited H₂ molecules is investigated by combined scanning tunneling microscopy, high-resolution electron energy loss spectroscopy, X-ray photoelectron spectroscopy measurements, and density functional theory calculations. The measurements reveal that vibrationally excited H₂ molecules dissociatively adsorb on graphene on Ir(111) resulting in nanopatterned hydrogen functionalization structures. Calculations demonstrate that the presence of the Ir surface below the graphene lowers the H₂ dissociative adsorption barrier and allows for the adsorption reaction at energies well below the dissociation threshold of the H-H bond. The first reacting H₂ molecule must contain considerable vibrational energy to overcome the dissociative adsorption barrier. However, this initial adsorption further activates the surface resulting in reduced barriers for dissociative adsorption of subsequent H₂ molecules. This enables functionalization by H₂ molecules with lower vibrational energy, yielding an avalanche effect for the hydrogenation reaction. These results provide an example of a catalytically active graphene-coated surface and additionally set the stage for a re-interpretation of previous experimental work involving elevated H₂ background gas pressures in the presence of hot filaments.

Supramolecular Corrals on Surfaces Resulting from Aromatic Interactions of Nonplanar Triazoles

Interaction forces between aromatic moieties, often referred to as π-π interactions, are an important element in stabilizing complex supramolecular structures. For supramolecular self-assembly occurring on surfaces, where aromatic moieties are typically forced to adsorb coplanar with the surface, the possible role of intermolecular aromatic interactions is much less explored. Here, we report on unusual, ring-shaped supramolecular corral surface structures resulting from adsorption of a molecule with nonplanar structure, allowing for intermolecular aromatic interactions. The discrete corral structures are observed using high-resolution scanning tunneling microscopy, and the energetic driving forces for their formation are elucidated using density functional theory calculations and Monte Carlo simulations. The individual corrals involve between 11 and 18 molecules bound through triazole moieties to a ring-shaped ensemble of bridge site positions on (111) surfaces of copper, silver, or gold. The curvature required to form the corrals is identified to result from the angle dependence of aromatic interactions between molecular phenanthrene moieties. The study provides detailed quantitative insights into triazole-surface and aromatic interactions and illustrates how they may be used to drive surface supramolecular self-assembly.

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.