Feature optimization for atomistic machine learning yields a data-driven construction of the periodic table of the elements

Machine-learning of atomic-scale properties amounts to extracting correlations between structure, composition and the quantity that one wants to predict. Representing the input structure in a way that best reflects such correlations makes it possible to improve the accuracy of the model for a given amount of reference data. When using a description of the structures that is transparent and well-principled, optimizing the representation might reveal insights into the chemistry of the data set. Here we show how one can generalize the SOAP kernel to introduce a distance-dependent weight that accounts for the multi-scale nature of the interactions, and a description of correlations between chemical species. We show that this improves substantially the performance of ML models of molecular and materials stability, while making it easier to work with complex, multi-component systems and to extend SOAP to coarse-grained intermolecular potentials. The element correlations that give the best performing model show striking similarities with the conventional periodic table of the elements, providing an inspiring example of how machine learning can rediscover, and generalize, intuitive concepts that constitute the foundations of chemistry. In the last few years, statistical regression techniques have gained an important place in the toolbox of atomic-scale modelling, making it possible to approximate effectively the properties of systems computed with accurate but demanding electronic structure methods based on a small number of reference calculations.1–3 It is fair to say that most of the recent progress in this field has been associated with the development of representations that encode the fundamental symmetries of the system.1,4–8 After symmetries have been accounted for, however, there is still considerable freedom in how to define the details of an atomic-scale representation. Optimizing the input representation can improve substantially the performance of the regression, by adapting it to the specific structure–property relations associated with a given problem. What is more, in the process one can often recognize correlations that rely on intuitive information on such structure–property relations. In this paper we consider the smooth overlap of atomic positions (SOAP) representation – a popular representation of atomic structure that has been successfully used to build interatomic potentials,9–11 predict molecular properties12 and visualize structural motifs13–15 – and extend it by adapting the representation to the intrinsic length scales of atomic interactions, and by considering “alchemical” correlations between chemical species, which make it possible for instance to exploit the similar behavior of different elements to accelerate learning in very chemically heterogeneous data sets. Not only do these extensions improve significantly the performance of SOAP representations, but they do indeed offer insights into the chemistry of the system, for instance providing a data-driven representation of the similarity between elements that is reminiscent of the periodic table of the elements.

Single-molecule-level characterization of supramolecular systems at surfaces

Dietmar Payer

This thesis deals with the self-organization of individual building blocks, specifically organic molecules and metal atoms, into supramolecular structures on metal surfaces under ultra high vacuum conditions (UHV). Self-organization of supramolecular systems is a promising candidate for a bottom-up approach in the fabrication of complex structures with specific properties. This process is steered by interactions between functional groups of the individual building blocks and is of apparent interest to gain a detailed understanding of the influence and the behavior of these functional groups enabling intermolecular binding. In the first part of the thesis, we investigate hydrogen bonded structures on metal surfaces. Of especial interest is the possibility of the formation of ionic hydrogen bonds, a special class of hydrogen bond which connects a charged donor (acceptor) and a neutral acceptor (donor) and is important in biological systems. By combined Scanning Tunneling Microscopy (STM), X-ray Photoelectron Spectroscopy (XPS) and Near Edge X-ray Absorption Fine Structure (NEXAFS) measurement we show the deprotonation of carboxylic functions in the molecules, forming carboxylate groups involved in intermolecular binding. With our complementary experimental and theoretical examinations we clearly show that the carboxylate groups are indeed still charged although adsorbed onto a conducting metal surface and that the observed structures can be computationally reproduced by using these charges in classical molecular dynamic calculations. Our investigations clearly reveal that all requirements for the formation of ionic hydrogen bonds in these samples at metal surfaces under solvent free conditions are fulfilled. In the second part, the confinement of surface state electrons in self-assembled hydrogen-bonded structures is investigated. The examined structure contains two-dimensional cavities, with different inner diameters in the periodic arrangement and in domain boundaries. Inside the cavities we detect a spatially localized modification in the local density of states (LDOS) of the Ag(111) surface state electrons. The energy of the peak correlates with the cavity area as predicted by a simple "particle in a box" model. This clearly shows that the surface state electrons form a confined state inside the cavities. Furthermore we examine self-assembled periodic structures as templates for binding single macrocyclic molecules. The macrocyclic molecules can be deposited by sublimation, as STM-topographs with submolecular resolution reflect the shape of the intact molecules and reveal a coverage dependent aggregation behavior. We show that it is possible to fabricate a structure in which at most one macrocyclic molecule per pore can be found in a defined binding position. In the last part of the thesis we investigate the influence of individual metal atoms on the chemical activity and the self-assembly process of molecules on metal surfaces. First, we demonstrate the high chemical reactivity of these metal atoms. In our experiments we address the chemical reactivity of static active sites, like kinks and step edges, and of dynamic active sites, like the metal atoms, separately. Doing this we show that a non-negligible amount of the chemical reactivity of a metal surface is due to this dynamic adatom gas. Furthermore the influence of metal atoms on the structure formation of organic molecules is investigated. We show that two-dimensional structures based on a complex formation between metal centers and ligands can be formed and that the coordination number is independent of the substrate symmetry. Furthermore, we show the possibility that on metal surfaces one can prepare three-fold coordinated Fe-centers, a coordination number which is rarely seen in three dimensional chemistry. In the last part we study catenanes, which consist of two interlocked macrocyclic molecules. Main interest is on the confirmation of a structural change of the catenanes adsorbed on a metal substrate. For our experiments we use the fact that the catenanes are designed to "trap" a Cu-atom by complex formation. As this reaction is associated with a structural change and a change in intermolecular interaction, we can verify a reaction of catenanes adsorbed onto a surface with Cu adatoms and therefore a structural alteration by simply imaging the formed structures. Our measurements show the possibility of depositing large molecules like catenanes by sublimation and of their potential for use as molecular machines adsorbed onto metal surfaces.

EPFL2007

Atom-density representations for machine learning

Michele Ceriotti, Félix Benedito Clément Musil, Michael John Willatt

This has led to a proliferation of alternative ways to convert an atomic structure into an input for a machine-learning model. We introduce an abstract definition of chemical environments that is based on a smoothed atomic density, using a bra-ket notation to emphasize basis set independence and to highlight the connections with some popular choices of representations for describing atomic systems. The correlations between the spatial distribution of atoms and their chemical identities are computed as inner products between these feature kets, which can be given an explicit representation in terms of the expansion of the atom density on orthogonal basis functions, that is equivalent to the smooth overlap of atomic positions power spectrum, but also in real space, corresponding to n-body correlations of the atom density. This formalism lays the foundations for a more systematic tuning of the behavior of the representations, by introducing operators that represent the correlations between structure, composition, and the target properties. It provides a unifying picture of recent developments in the field and indicates a way forward toward more effective and computationally affordable machine-learning schemes for molecules and materials.

2019

Unsupervised machine learning in atomistic simulations, between predictions and understanding

Michele Ceriotti

Automated analyses of the outcome of a simulation have been an important part of atomistic modeling since the early days, addressing the need of linking the behavior of individual atoms and the collective properties that are usually the final quantity of interest. Methods such as clustering and dimensionality reduction have been used to provide a simplified, coarse-grained representation of the structure and dynamics of complex systems from proteins to nanoparticles. In recent years, the rise of machine learning has led to an even more widespread use of these algorithms in atomistic modeling and to consider different classification and inference techniques as part of a coherent toolbox of data-driven approaches. This perspective briefly reviews some of the unsupervised machine-learning methods—that are geared toward classification and coarse-graining of molecular simulations—seen in relation to the fundamental mathematical concepts that underlie all machine-learning techniques. It discusses the importance of using concise yet complete representations of atomic structures as the starting point of the analyses and highlights the risk of introducing preconceived biases when using machine learning to rationalize and understand structure-property relations. Supervised machine-learning techniques that explicitly attempt to predict the properties of a material given its structure are less susceptible to such biases. Current developments in the field suggest that using these two classes of approaches side-by-side and in a fully integrated mode, while keeping in mind the relations between the data analysis framework and the fundamental physical principles, will be key to realizing the full potential of machine learning to help understand the behavior of complex molecules and materials.

2019

Single-molecule-level characterization of supramolecular systems at surfaces

Dietmar Payer

EPFL2007