Metrics for measuring distances in configuration spaces

Feasibility of Activation Energy Prediction of Gas-Phase Reactions by Machine Learning

Machine learning based on big data has emerged as a powerful solution in various chemical problems. We investigated the feasibility of machine learning models for the prediction of activation energies of gas-phase reactions. Six different models with three different types, including the artificial neural network, the support vector regression, and the tree boosting methods, were tested. We used the structural and thermodynamic properties of molecules and their differences as input features without resorting to specific reaction types so as to maintain the most general input form for broad applicability. The tree boosting method showed the best performance among others in terms of the coefficient of determination, mean absolute error, and root mean square error, the values of which were 0.89, 1.95, and 4.49 kcal mol^-1 , respectively. Computation time for the prediction of activation energies for 2541 test reactions was about one second on a single computing node without using accelerators.

Integrated Reaction Path Processing from Sampled Structure Sequences

Sampled structure sequences obtained, for instance, from real-time reactivity explorations or first-principles molecular dynamics simulations contain valuable information about chemical reactivity. Eventually, such sequences allow for the construction of reaction networks that are required for the kinetic analysis of chemical systems. For this purpose, however, the sampled information must be processed to obtain stable chemical structures and associated transition states. The manual extraction of valuable information from such reaction paths is straightforward but unfeasible for large and complex reaction networks. For real-time quantum chemistry, this implies automatization of the extraction and relaxation process while maintaining immersion in the virtual chemical environment. Here, we describe an efficient path processing scheme for the on-the-fly construction of an exploration network by approximating the explored paths as continuous basis-spline curves.

Machine learning for the structure-energy-property landscapes of molecular crystals

Molecular crystals play an important role in several fields of science and technology. They frequently crystallize in different polymorphs with substantially different physical properties. To help guide the synthesis of candidate materials, atomic-scale modelling can be used to enumerate the stable polymorphs and to predict their properties, as well as to propose heuristic rules to rationalize the correlations between crystal structure and materials properties. Here we show how a recently-developed machine-learning (ML) framework can be used to achieve inexpensive and accurate predictions of the stability and properties of polymorphs, and a data-driven classification that is less biased and more flexible than typical heuristic rules. We discuss, as examples, the lattice energy and property landscapes of pentacene and two azapentacene isomers that are of interest as organic semiconductor materials. We show that we can estimate force field or DFT lattice energies with sub-kJ mol-1 accuracy, using only a few hundred reference configurations, and reduce by a factor of ten the computational effort needed to predict charge mobility in the crystal structures. The automatic structural classification of the polymorphs reveals a more detailed picture of molecular packing than that provided by conventional heuristics, and helps disentangle the role of hydrogen bonded and π-stacking interactions in determining molecular self-assembly. This observation demonstrates that ML is not just a black-box scheme to interpolate between reference calculations, but can also be used as a tool to gain intuitive insights into structure-property relations in molecular crystal engineering.

What is the best or most relevant global minimum for nanoclusters? Predicting, comparing and recycling cluster structures with WASP@N

Our WASP@N project is an open-access database of cluster structures with a web-assisted interface and toolkit for structure prediction.

Optimal Alignment of Structures for Finite and Periodic Systems

Finding the optimal alignment between two structures is important for identifying the minimum root-mean-square distance (RMSD) between them and as a starting point for calculating pathways. Most current algorithms for aligning structures are stochastic, scale exponentially with the size of structure, and the performance can be unreliable. We present two complementary methods for aligning structures corresponding to isolated clusters of atoms and to condensed matter described by a periodic cubic supercell. The first method (Go-PERMDIST), a branch and bound algorithm, locates the global minimum RMSD deterministically in polynomial time. The run time increases for larger RMSDs. The second method (FASTOVERLAP) is a heuristic algorithm that aligns structures by finding the global maximum kernel correlation between them using fast Fourier transforms (FFTs) and fast SO(3) transforms (SOFTs). For periodic systems, FASTOVERLAP scales with the square of the number of identical atoms in the system, reliably finds the best alignment between structures that are not too distant, and shows significantly better performance than existing algorithms. The expected run time for Go-PERMDIST is longer than FASTOVERLAP for periodic systems. For finite clusters, the FASTOVERLAP algorithm is competitive with existing algorithms. The expected run time for Go-PERMDIST to find the global RMSD between two structures deterministically is generally longer than for existing stochastic algorithms. However, with an earlier exit condition, Go-PERMDIST exhibits similar or better performance.

Bias-Free Chemically Diverse Test Sets from Machine Learning

Current benchmarking methods in quantum chemistry rely on databases that are built using a chemist's intuition. It is not fully understood how diverse or representative these databases truly are. Multivariate statistical techniques like archetypal analysis and K-means clustering have previously been used to summarize large sets of nanoparticles however molecules are more diverse and not as easily characterized by descriptors. In this work, we compare three sets of descriptors based on the one-, two-, and three-dimensional structure of a molecule. Using data from the NIST Computational Chemistry Comparison and Benchmark Database and machine learning techniques, we demonstrate the functional relationship between these structural descriptors and the electronic energy of molecules. Archetypes and prototypes found with topological or Coulomb matrix descriptors can be used to identify smaller, statistically significant test sets that better capture the diversity of chemical space. We apply this same method to find a diverse subset of organic molecules to demonstrate how the methods can easily be reapplied to individual research projects. Finally, we use our bias-free test sets to assess the performance of density functional theory and quantum Monte Carlo methods.

Metastable exohedrally decorated Borospherene B40

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

The many-body expansion combined with neural networks

Fragmentation methods such as the many-body expansion (MBE) are a common strategy to model large systems by partitioning energies into a hierarchy of decreasingly significant contributions. The number of calculations required for chemical accuracy is still prohibitively expensive for the ab initio MBE to compete with force field approximations for applications beyond single-point energies. Alongside the MBE, empirical models of ab initio potential energy surfaces have improved, especially non-linear models based on neural networks (NNs) which can reproduce ab initio potential energy surfaces rapidly and accurately. Although they are fast, NNs suffer from their own curse of dimensionality; they must be trained on a representative sample of chemical space. In this paper we examine the synergy of the MBE and NN's and explore their complementarity. The MBE offers a systematic way to treat systems of arbitrary size while reducing the scaling problem of large systems. NN's reduce, by a factor in excess of 10⁶, the computational overhead of the MBE and reproduce the accuracy of ab initio calculations without specialized force fields. We show that for a small molecule extended system like methanol, accuracy can be achieved with drastically different chemical embeddings. To assess this we test a new chemical embedding which can be inverted to predict molecules with desired properties. We also provide our open-source code for the neural network many-body expansion, Tensormol.

An efficient genetic algorithm for structure prediction at the nanoscale

We have developed and implemented a new global optimization technique based on a Lamarckian genetic algorithm with the focus on structure diversity. The key process in the efficient search on a given complex energy landscape proves to be the removal of duplicates that is achieved using a topological analysis of candidate structures. The careful geometrical prescreening of newly formed structures and the introduction of new mutation move classes improve the rate of success further. The power of the developed technique, implemented in the Knowledge Led Master Code, or KLMC, is demonstrated by its ability to locate and explore a challenging double funnel landscape of a Lennard-Jones 38 atom system (LJ₃₈). We apply the redeveloped KLMC to investigate three chemically different systems: ionic semiconductor (ZnO)_1-32, metallic Ni₁₃ and covalently bonded C₆₀. All four systems have been systematically explored on the energy landscape defined using interatomic potentials. The new developments allowed us to successfully locate the double funnels of LJ₃₈, find new local and global minima for ZnO clusters, extensively explore the Ni₁₃ and C₆₀ (the buckminsterfullerene, or buckyball) potential energy surfaces.

Comparing molecules and solids across structural and alchemical space

A general procedure to compare molecules and materials powers insightful representations of energy landscapes and precise machine-learning predictions of properties.

Design strategies for self-assembly of discrete targets

Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks to hierarchical sequences of intermediates, all the way to the fully addressable limit in which each component is unique. In this paper, we introduce an idealized model of cubic particles with patterned faces that allows self-assembly strategies to be compared and tested. We consider a simple octameric target, starting with the minimal requirements for successful self-assembly and comparing the benefits and limitations of more sophisticated hierarchical and addressable schemes. Simulations are performed using a hybrid dynamical Monte Carlo protocol that allows self-assembling clusters to rearrange internally while still providing Stokes-Einstein-like diffusion of aggregates of different sizes. Our simulations explicitly capture the thermodynamic, dynamic, and steric challenges typically faced by self-assembly processes, including competition between multiple partially completed structures. Self-assembly pathways are extracted from the simulation trajectories by a fully extendable scheme for identifying structural fragments, which are then assembled into history diagrams for successfully completed target structures. For the simple target, a one-component assembly scheme is most efficient and robust overall, but hierarchical and addressable strategies can have an advantage under some conditions if high yield is a priority.

Computer simulations of glasses: the potential energy landscape

We review the current state of research on glasses, discussing the theoretical background and computational models employed to describe them. This article focuses on the use of the potential energy landscape (PEL) paradigm to account for the phenomenology of glassy systems, and the way in which it can be applied in simulations and the interpretation of their results. This article provides a broad overview of the rich phenomenology of glasses, followed by a summary of the theoretical frameworks developed to describe this phenomonology. We discuss the background of the PEL in detail, the onerous task of how to generate computer models of glasses, various methods of analysing numerical simulations, and the literature on the most commonly used model systems. Finally, we tackle the problem of how to distinguish a good glass former from a good crystal former from an analysis of the PEL. In summarising the state of the potential energy landscape picture, we develop the foundations for new theoretical methods that allow the ab initio prediction of the glass-forming ability of new materials by analysis of the PEL.

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.