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

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.

Phase-Dependent Properties of Manganese Oxides and Applications in Electrovoltaics

This study reports first-principles predictions as well as experimental synthesis of manganese oxide nanoparticles under different conditions. The theoretical part of the work comprised density functional theory (DFT)-based calculations and first-principles molecular dynamics (MD) simulations. The extensive research efforts and the current challenges in enhancing the performance of the lithium-ion battery (LIB) provided motivation to explore the potential of these materials for use as an anode in the battery. The structural analysis of the synthesized samples carried out using X-ray diffraction (XRD) confirmed the tetragonal structure of Mn3O4 on heating at 450 and 550 °C and the cubic structure of Mn2O3 on heating at 650 °C. The structures are found in the form of nanoparticles at 450 and 550 °C, but at 650 °C, the material appeared in the form of a nanoporous structure. Further, we investigated the electrochemical functionality of Mn2O3 and Mn3O4 as anode materials for utilization in LIBs via MD simulations. Based on the investigations of their electrical, structural, diffusion, and storage behavior, the anodic character of Mn2O3 and Mn3O4 is predicted. The findings indicated that 10 lithium atoms adsorb on Mn2O3, whereas 5 lithium atoms adsorb on Mn3O4 when saturation is taken into account. The storage capacities of Mn2O3 and Mn3O4 are estimated to be 1697 and 585 mAh g-1, respectively. The maximum value of lithium insertion voltage per Li in Mn2O3 is 0.93 and 0.22 V in Mn3O4. Further, the diffusion coefficient values are found as 2.69 × 10-9 and 2.65 × 10-10 m2 s-1 for Mn2O3 and Mn3O4, respectively, at 300 K. The climbing image nudged elastic band method (Cl-NEB) was implemented, which revealed activation energy barriers of Li as 0.30 and 0.75 eV for Mn2O3 and Mn3O4, respectively. The findings of the work revealed high specific capacity, low Li diffusion energy barrier, and low open circuit voltage for the Mn2O3-based anode for use in LIBs.

Improved Initialization of Optimal Path Calculations Using Sequential Traversal over the Image-Dependent Pair Potential Surface

In reaction path optimization, such as the calculation of a minimum energy path (MEP) between given reactant and product configurations of atoms, it is advantageous to start with an initial guess where the close proximity of atoms is avoided and bonds are not unnecessarily broken only to be reformed later. When the configurations of the atoms are described with Cartesian coordinates, a linear interpolation between the end points can be problematic, and a better option is provided by the so-called image dependent pair potential (IDPP) approach where interpolated pairwise distances are generated to form an objective function that can be used to construct an improved initial path. When started with a linear interpolation, this method can, however, still lead to unnecessary bond breaking in, for example, reactions in which a molecular subgroup undergoes significant rotation. In the method presented here, this problem is addressed by constructing the path gradually, introducing images sequentially starting from the vicinity of the end points while the distance between images in the central region is larger. The distribution of images is controlled by systematically scaling the tightness of springs acting between the images until the desired number of images is obtained, and they are evenly spaced. This procedure generates an initial path on the IDPP surface, a task that requires negligible computational effort, as no evaluation of the energy of the system is needed. The calculation of the MEP, typically using electronic structure calculations, is then subsequently carried out in a way that makes efficient use of parallel computing with the nudged elastic band method. Several examples of reactions are given where the linear interpolation IDPP (LI-IDPP) method yields problematic paths with unnecessary bond breaking in some of the intermediate images, while the sequential IDPP (S-IDPP) method yields paths that are significantly closer to realistic MEPs.

Computational Design of Antiperovskite Solid Electrolytes

In the face of the current climate emergency and the performance, safety, and cost limitations current state-of-art Li-ion batteries present, solid-state batteries are widely anticipated to revolutionize energy storage. The heart of this technology lies in the substitution of liquid electrolytes with solid counterparts, resulting in potential critical advantages, such as higher energy density and safety profiles. In recent years, antiperovskites have become one of the most studied solid electrolyte families for solid-state battery applications as a result of their salient advantages, which include high ionic conductivity, structural versatility, low cost, and stability against metal anodes. This Review highlights the latest progress in the computational design of Li- and Na-based antiperovskite solid electrolytes, focusing on critical topics for their development, including high-throughput screening for novel compositions, synthesizability, doping, ion transport mechanisms, grain boundaries, and electrolyte-electrode interfaces. Moreover, we discuss the remaining challenges facing these materials and provide our perspective on their possible future advances and applications.

Pushing Forward Simulation Techniques of Ion Transport in Ion Conductors for Energy Materials

Simulation techniques are crucial to establish a firm link between phenomena occurring at the atomic scale and macroscopic observations of functional materials. Importantly, extensive sampling of space and time scales is paramount to ensure good convergence of physically relevant quantities to describe ion transport in energy materials. Here, a number of simulation methods to address ion transport in energy materials are discussed, with the pros and cons of each methodology put forward. Emphasis is given to the stochastic nature of results produced by kinetic Monte Carlo, which can adequately account for compositional disorder across multiple sublattices in solids.

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.

Perspective: Path Sampling Methods Applied to Enzymatic Catalysis

This Perspective reviews the use of Transition Path Sampling methods to study enzymatically catalyzed chemical reactions. First applied by our group to an enzymatic reaction over 15 years ago, the method has uncovered basic principles in enzymatic catalysis such as the protein promoting vibration, and it has also helped harmonize such ideas as electrostatic preorganization with dynamic views of enzyme function. It is now being used to help uncover principles of protein design necessary to artificial enzyme creation.

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.

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.

Modified Single Iteration Synchronous-Transit Approach to Bound Diffusion Barriers for Solid-State Reactions

Herein, we detail an approach to accelerate the computational screening of materials for properties dictated by the kinetics of solid-state diffusion through reliably and rapidly identifying upper and lower bounds to the transition state (TS) energy through our proposed modified single iteration synchronous-transit (MSIST) approach. While this sacrifices providing detailed information of the explicit TS structure, it requires only 30% of the force evaluations of a full nudged elastic band (NEB) TS search and reduces the computational demand to compute estimated diffusion barriers by ∼70% on average. In all 53 cases in which we explicitly compared our results to those of an NEB calculation, the upper and lower bounds identified using this approach bracketed the TS energy calculated with explicit NEB calculations. We use the applications of diffusion of Na⁺ in potential sodium-ion battery electrodes and oxygen vacancy diffusion in solid-oxide fuel cell electrodes and redox mediators for solar thermochemical hydrogen production to demonstrate the power of MSIST for analyzing the kinetics of bulk diffusion. For Na⁺ diffusion through 13 proposed electrode materials in which the average diffusion barrier was 0.28 eV, the average difference between the upper and lower bounds was 0.08 eV. An iterative application of this approach to the three materials with the largest difference between their upper and lower bounds further narrowed the average range of the bounded TS energies to 0.04 eV while still requiring fewer force evaluations than an NEB TS calculation. When applied in a high-throughput manner to study 514 diffusion pathways in 97 different materials, the average difference between the upper and lower bounds was 0.33 eV and the average barrier, as calculated by the average of all upper and lower bounds, was ∼1.7 eV. Because the MSIST approach produces explicit errors, i.e., the difference between the upper and lower bounds energies, even predicted barrier ranges with large errors can be reliably modeled with weighted regression techniques. MSIST enables the analysis of the kinetics of solid-state diffusion across larger sets of materials and can thus efficiently provide data to train statistically learned models of diffusion and to develop physical insights into the diffusion process.

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.