Efficient moves for global geometry optimization methods and their application to binary systems

MAGUS: machine learning and graph theory assisted universal structure searcher

Crystal structure predictions based on first-principles calculations have gained great success in materials science and solid state physics. However, the remaining challenges still limit their applications in systems with a large number of atoms, especially the complexity of conformational space and the cost of local optimizations for big systems. Here, we introduce a crystal structure prediction method, MAGUS, based on the evolutionary algorithm, which addresses the above challenges with machine learning and graph theory. Techniques used in the program are summarized in detail and benchmark tests are provided. With intensive tests, we demonstrate that on-the-fly machine-learning potentials can be used to significantly reduce the number of expensive first-principles calculations, and the crystal decomposition based on graph theory can efficiently decrease the required configurations in order to find the target structures. We also summarized the representative applications of this method on several research topics, including unexpected compounds in the interior of planets and their exotic states at high pressure and high temperature (superionic, plastic, partially diffusive state, etc.); new functional materials (superhard, high-energy-density, superconducting, photoelectric materials), etc. These successful applications demonstrated that MAGUS code can help to accelerate the discovery of interesting materials and phenomena, as well as the significant value of crystal structure predictions in general.

Principles of isomer stability in small clusters

In this work we study isomers of several representative small clusters to find principles for their stability. Our conclusions about the principles underlying the structure of clusters are based on a huge database of 44 000 isomers generated for 58 different clusters on the density functional theory level by Minima Hopping. We explore the potential energy surface of small neutral, anionic and cationic isomers, moving left to right across the third period of the periodic table and varying the number of atoms n and the cluster charge state q (X q n , with X = {Na, Mg, Al, Si, Ge}, q = -1, 0, 1, 2). We use structural descriptors such as bond lengths and atomic coordination numbers, the surface to volume ratios and the shape factor as well as electronic descriptors such as shell filling and hardness to detect correlations with the stability of clusters. The isomers of metallic clusters are found to be structure seekers with a strong tendency to adopt compact shapes. However certain numbers of atoms can suppress the formation of nearly spherical metallic clusters. Small non-metallic clusters typically also do not adopt compact spherical shapes for their lowest energy structures. In both cases spherical jellium models are not any more applicable. Nevertheless for many structures, that frequently have a high degree of symmetry, the Kohn-Sham eigenvalues are bunched into shells and if the available electrons can completely fill such shells, a particularly stable structure can result. We call such a cluster whose shape gives rise to shells that can be completely filled by the number of available electrons an optimally matched cluster, since both the structure and the number of electrons must be special and match. In this way we can also explain the stability trends for covalent silicon and germanium cluster isomers, whose stability was previously explained by the presence of certain structural motifs. Thus we propose a unified framework to explain trends in the stability of isomers and to predict their structure for a wide range of small clusters.

Biomolecular Simulations with the Three-Dimensional Reference Interaction Site Model with the Kovalenko-Hirata Closure Molecular Solvation Theory

The statistical mechanics-based 3-dimensional reference interaction site model with the Kovalenko-Hirata closure (3D-RISM-KH) molecular solvation theory has proven to be an essential part of a multiscale modeling framework, covering a vast region of molecular simulation techniques. The successful application ranges from the small molecule solvation energy to the bulk phase behavior of polymers, macromolecules, etc. The 3D-RISM-KH successfully predicts and explains the molecular mechanisms of self-assembly and aggregation of proteins and peptides related to neurodegeneration, protein-ligand binding, and structure-function related solvation properties. Upon coupling the 3D-RISM-KH theory with a novel multiple time-step molecular dynamic (MD) of the solute biomolecule stabilized by the optimized isokinetic Nosé-Hoover chain thermostat driven by effective solvation forces obtained from 3D-RISM-KH and extrapolated forward by generalized solvation force extrapolation (GSFE), gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties were obtained in this new quasidynamics protocol. The multiscale OIN/GSFE/3D-RISM-KH algorithm was implemented in the Amber package and well documented for fully flexible model of alanine dipeptide, miniprotein 1L2Y, and protein G in aqueous solution, with a solvent sampling rate ~150 times faster than a standard MD simulation in explicit water. Further acceleration in computation can be achieved by modifying the extent of solvation layers considered in the calculation, as well as by modifying existing closure relations. This enhanced simulation technique has proven applications in protein-ligand binding energy calculations, ligand/solvent binding site prediction, molecular solvation energy calculations, etc. Applications of the RISM-KH theory in molecular simulation are discussed in this work.

New strontium titanate polymorphs under high pressure

We report six new dynamically stable structures of SrTiO₃ at various pressures ranging from 0 to 200 GPa. These structures were found by exploring the enthalpy surface with the Minima Hopping structure prediction method. The potential energy surface was generated by a machine learned potential, the charge equilibration via neural network technique (CENT), based on an extensive training data set of highly diverse SrTiO₃ periodic and cluster structures. All our CENT structures were validated at the level of density functional theory. For our new structures, we performed phonon calculations and NVT molecular dynamics calculations to investigate their dynamical stability. Finally, X-ray diffraction patterns were simulated to help to identify our predicted structures in experiments.

Fingerprint-Based Detection of Non-Local Effects in the Electronic Structure of a Simple Single Component Covalent System

Using fingerprints used mainly in machine learning schemes of the potential energy surface, we detect in a fully algorithmic way long range effects on local physical properties in a simple covalent system of carbon atoms. The fact that these long range effects exist for many configurations implies that atomistic simulation methods, such as force fields or modern machine learning schemes, that are based on locality assumptions, are limited in accuracy. We show that the basic driving mechanism for the long range effects is charge transfer. If the charge transfer is known, locality can be recovered for certain quantities such as the band structure energy.

Finding Reaction Pathways with Optimal Atomic Index Mappings

Finding complex reaction and transformation pathways involving many intermediate states is, in general, not possible on the density-functional theory level with existing simulation methods, due to the very large number of required energy and force evaluations. For complex reactions, it is not possible to determine which atom in the reactant is mapped onto which atom in the product. Trying out all possible atomic index mappings is not feasible because of the factorial increase in the number of possible mappings. We use a penalty function that is invariant under index permutations to bias the potential energy surface in such a way that it obtains the characteristics of a structure seeker, whose global minimum is the reaction product. By performing a minima-hopping-based global optimization on this biased potential energy surface, we rapidly find intermediate states that lead into the global minimum and allow us to then extract entire reaction pathways. We first demonstrate for a benchmark system, namely, the Lennard-Jones cluster LJ_{38}, that our method finds intermediate states relevant to the lowest energy reaction pathway, and hence we need to consider much fewer intermediate states than previous methods to find the lowest energy reaction pathway. Finally, we apply the method to two real systems, C_{60} and C_{20}H_{20}, and show that the reaction pathways found contain valuable information on how these molecules can be synthesized.

Surface reconstructions and premelting of the (100) CaF2 surface

In this work, surface reconstructions on the (100) surface of CaF2 are comprehensively investigated. The configurations were explored by employing the Minima Hopping Method (MHM) coupled to a machine-learning interatomic potential, that is based on a charge equilibration scheme steered by a neural network (CENT). The combination of these powerful methods revealed about 80 different morphologies for the (100) surface with very similar surface formation energies differing by not more than 0.3 J m-2. To take into account the effect of temperature on the dynamics of this surface as well as to study the solid-liquid transformation, molecular dynamics simulations were carried out in the canonical (NVT) ensemble. By analyzing the atomic mean-square displacements (MSD) of the surface layer in the temperature range of 300-1200 K, it was found that in the surface region the F sublattice is less stable and more diffusive than the Ca sublattice. Based on these results we demonstrate that not only a bulk system, but also a surface can exhibit a sublattice premelting that leads to superionicity. Both the surface sublattice premelting and surface premelting occur at temperatures considerably lower than the bulk values. The complex behaviour of the (100) surface is contrasted with the simpler behavior of other low index crystallographic surfaces.

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.

Size-guided multi-seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size-guided multi-seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest-energy configurations of the cluster with n - 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.

First-Principles Study of Lithium Cobalt Spinel Oxides: Correlating Structure and Electrochemistry

Embedding a lithiated cobalt oxide spinel (Li₂Co₂O₄, or LiCoO₂) component or a nickel-substituted LiCo_{1- x}Ni _xO₂ analogue in structurally integrated cathodes such as xLi₂MnO₃·(1- x)LiM'O₂ (M' = Ni/Co/Mn) has been recently proposed as an approach to advance the performance of lithium-ion batteries. Here, we first revisit the phase stability and electrochemical performance of LiCoO₂ synthesized at different temperatures using density functional theory calculations. Consistent with previous studies, we find that the occurrence of low- and high-temperature structures (i.e., cubic lithiated spinel LT-LiCoO₂; or Li₂Co₂O₄ ( Fd3̅ m) vs trigonal-layered HT-LiCoO₂ ( R3̅ m), respectively) can be explained by a small difference in the free energy between these two compounds. Additionally, the observed voltage profile of a Li/LiCoO₂ cell for both cubic and trigonal phases of LiCoO₂, as well as the migration barrier for lithium diffusion from an octahedral (O_h) site to a tetrahedral site (T_d) in Fd3̅ m LT-Li_{1- x}CoO₂, has been calculated to help understand the complex electrochemical charge/discharge processes. A search of LiCo _xM_{1- x}O₂ lithiated spinel (M = Ni or Mn) structures and compositions is conducted to extend the exploration of the chemical space of Li-Co-Mn-Ni-O electrode materials. We predict a new lithiated spinel material, LiNi_0.8125Co_0.1875O₂ ( Fd3̅ m), with a composition close to that of commercial, layered LiNi_0.8Co_0.15Al_0.05O₂, which may have the potential for exploitation in structurally integrated, layered spinel cathodes for next-generation lithium-ion batteries.

Prediction of superconducting iron-bismuth intermetallic compounds at high pressure

We report the discovery of novel iron-bismuth compounds, FeBi₂ and FeBi₃, at high-pressure.

The synthesis of materials in high-pressure experiments has recently attracted increasing attention, especially since the discovery of record breaking superconducting temperatures in the sulfur–hydrogen and other hydrogen-rich systems. Commonly, the initial precursor in a high pressure experiment contains constituent elements that are known to form compounds at ambient conditions, however the discovery of high-pressure phases in systems immiscible under ambient conditions poses an additional materials design challenge. We performed an extensive multi component ab initio structural search in the immiscible Fe–Bi system at high pressure and report on the surprising discovery of two stable compounds at pressures above ≈36 GPa, FeBi₂ and FeBi₃. According to our predictions, FeBi₂ is a metal at the border of magnetism with a conventional electron–phonon mediated superconducting transition temperature of T_c = 1.3 K at 40 GPa.

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

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

Probing Potential Energy Surface Exploration Strategies for Complex Systems

The efficiency of minimum-energy configuration searching algorithms is closely linked to the energy landscape structure of complex systems, yet these algorithms often include a number of steps of which the effect is not always clear. Decoupling these steps and their impacts can allow us to better understand both their role and the nature of complex energy landscape. Here, we consider a family of minimum-energy algorithms based, directly or indirectly, on the well-known Bell-Evans-Polanyi (BEP) principle. Comparing trajectories generated with BEP-based algorithms to kinetically correct off-lattice kinetic Monte Carlo schemes allow us to confirm that the BEP principle does not hold for complex systems since forward and reverse energy barriers are completely uncorrelated. As would be expected, following the lowest available energy barrier leads to rapid trapping. This is why BEP-based methods require also a direct handling of visited basins or barriers. Comparing the efficiency of these methods with a thermodynamical handling of low-energy barriers, we show that most of the efficiency of the BEP-like methods lie first and foremost in the basin management rather than in the BEP-like step.

Structure prediction for multicomponent materials using biminima

The potential energy surface of a heteroparticle system will contain points that are local minima in both coordinate space and permutation space for the different species. We introduce the term biminima to describe these special points, and we formulate a deterministic scheme for finding them. Our search algorithm generates a converging sequence of particle-identity swaps, each accompanied by a number of local geometry relaxations. For selected binary atomic clusters of size N = N(A) + N(B) ≤ 98, convergence to a biminimum on average takes 3 N(A)N(B) relaxations, and the number of biminima grows with the preference for mixing. The new framework unifies continuous and combinatorial optimization, providing a powerful tool for structure prediction and rational design of multicomponent materials.

Isomerism and structural fluxionality in the Au26 and Au26(-) nanoclusters

Using the minima hopping global optimization method at the density functional level, we found low-energy nanostructures for neutral Au26 and its anion. The local-density and a generalized gradient approximation of the exchange–correlation functional predict different nanoscale motifs. We found a vast number of isomers within a small energy range above the respective putative global minima with each method. Photoelectron spectroscopy of Au26(-) under different experimental conditions revealed definitive evidence of the presence of multiple isomers, consistent with the theoretical predictions. Comparison between the experimental and simulated photoelectron spectra suggests that the photoelectron spectra of Au26(-) contain a mixture of three isomers, all of which are low-symmetry core–shell-type nanoclusters with a single internal Au atom. We present a disconnectivity graph for Au26(-) that has been computed completely at the density functional level. The transition states used to build this disconnectivity graph are complete enough to predict Au26(-) to have a possible fluxional shell, which facilitates the understanding of its catalytic activity.

Phycocyanobilin in solution – a solvent triggered molecular switch

The chromophore phycocyanobilin changes its spectroscopic behaviour upon solvent change. Our calculations trace this effect back to conformational switching, induced by changes in the hydrogen bonding pattern.