Fast evaluation of spherical harmonics with sphericart.

Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from geology and atmospheric sciences to signal processing and computer graphics. More recently, they have become a key component of rotationally equivariant models in geometric machine learning, including applications to atomic-scale modeling of molecules and materials. We present an elegant and efficient algorithm for the evaluation of the real-valued spherical harmonics. Our construction features many of the desirable properties of existing schemes and allows us to compute Cartesian derivatives in a numerically stable and computationally efficient manner. To facilitate usage, we implement this algorithm in sphericart, a fast C++ library that also provides C bindings, a Python API, and a PyTorch implementation that includes a GPU kernel.

scikit-matter : A Suite of Generalisable Machine Learning Methods Born out of Chemistry and Materials Science.

Easy-to-use libraries such as scikit-learn have accelerated the adoption and application of machine learning (ML) workflows and data-driven methods. While many of the algorithms implemented in these libraries originated in specific scientific fields, they have gained in popularity in part because of their generalisability across multiple domains. Over the past two decades, researchers in the chemical and materials science community have put forward general-purpose machine learning methods. The deployment of these methods into workflows of other domains, however, is often burdensome due to the entanglement with domainspecific functionalities. We present the python library scikit-matter that targets domain-agnostic implementations of methods developed in the computational chemical and materials science community, following the scikit-learn API and coding guidelines to promote usability and interoperability with existing workflows.

Unified theory of atom-centered representations and message-passing machine-learning schemes.

Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-centered environments, which are associated with an atomic property or with an atomic contribution to an extensive macroscopic quantity. Frameworks in this class can be understood in terms of atom-centered density correlations (ACDC), which are used as a basis for a body-ordered, symmetry-adapted expansion of the targets. Several other schemes that gather information on the relationship between neighboring atoms using "message-passing" ideas cannot be directly mapped to correlations centered around a single atom. We generalize the ACDC framework to include multi-centered information, generating representations that provide a complete linear basis to regress symmetric functions of atomic coordinates, and provide a coherent foundation to systematize our understanding of both atom-centered and message-passing and invariant and equivariant machine-learning schemes.

Efficient implementation of atom-density representations.

Physically motivated and mathematically robust atom-centered representations of molecular structures are key to the success of modern atomistic machine learning. They lie at the foundation of a wide range of methods to predict the properties of both materials and molecules and to explore and visualize their chemical structures and compositions. Recently, it has become clear that many of the most effective representations share a fundamental formal connection. They can all be expressed as a discretization of n-body correlation functions of the local atom density, suggesting the opportunity of standardizing and, more importantly, optimizing their evaluation. We present an implementation, named librascal, whose modular design lends itself both to developing refinements to the density-based formalism and to rapid prototyping for new developments of rotationally equivariant atomistic representations. As an example, we discuss smooth overlap of atomic position (SOAP) features, perhaps the most widely used member of this family of representations, to show how the expansion of the local density can be optimized for any choice of radial basis sets. We discuss the representation in the context of a kernel ridge regression model, commonly used with SOAP features, and analyze how the computational effort scales for each of the individual steps of the calculation. By applying data reduction techniques in feature space, we show how to reduce the total computational cost by a factor of up to 4 without affecting the model's symmetry properties and without significantly impacting its accuracy.

DUBS: A Framework for Developing Directory of Useful Benchmarking Sets for Virtual Screening.

Benchmarking is a crucial step in evaluating virtual screening methods for drug discovery. One major issue that arises among benchmarking data sets is a lack of a standardized format for representing the protein and ligand structures used to benchmark the virtual screening method. To address this, we introduce the Directory of Useful Benchmarking Sets (DUBS) framework, as a simple and flexible tool to rapidly create benchmarking sets using the protein databank. DUBS uses a simple input text based format along with the Lemon data mining framework to efficiently access and organize data to the protein databank and output commonly used inputs for virtual screening software. The simple input format used by DUBS allows users to define their own benchmarking data sets and access the corresponding information directly from the software package. Currently, it only takes DUBS less than 2 min to create a benchmark using this format. Since DUBS uses a simple python script, users can easily modify this to create more complex benchmarks. We hope that DUBS will be a useful community resource to provide a standardized representation for benchmarking data sets in virtual screening. The DUBS package is available on GitHub at https://github.com/chopralab/lemon/tree/master/dubs.

Modelling of framework materials at multiple scales: current practices and open questions.

The last decade has seen an explosion of the family of framework materials and their study, from both the experimental and computational points of view. We propose here a short highlight of the current state of methodologies for modelling framework materials at multiple scales, putting together a brief review of new methods and recent endeavours in this area, as well as outlining some of the open challenges in this field. We will detail advances in atomistic simulation methods, the development of material databases and the growing use of machine learning for the prediction of properties. This article is part of the theme issue 'Mineralomimesis: natural and synthetic frameworks in science and technology'.

Ab Initio Derived Force Fields for Zeolitic Imidazolate Frameworks: MOF-FF for ZIFs.

In this paper, we parametrized in a consistent way a new force field for a range of different zeolitic imidazolate framework systems (ZIF-8, ZIF-8(H), ZIF-8(Br), and ZIF-8(Cl)), extending the MOF-FF parametrization methodology in two aspects. First, we implemented the possibility to use periodic reference data in order to prevent the difficulty of generating representative finite clusters. Second, a new optimizer based on the covariance matrix adaptation evolutionary strategy (CMA-ES) was employed during the parametrization process. We confirmed that CMA-ES, as a state-of-the-art black box optimizer for problems on continuous variables, is more efficient and versatile for force field optimization than the previous genetic algorithm. The obtained force field was then validated with respect to some static and dynamic properties. Much effort was spent to ensure that the FF is able to describe the crucial linker swing effect in a large number of ZIF-8 derivatives. For this reason, we compared our force field to ab initio molecular dynamic simulations and found an accuracy comparable to those obtained by different exchange-correlation functionals.

Structure and Dynamics of Water Confined in Imogolite Nanotubes.

We have studied the properties of water adsorbed inside nanotubes of hydrophilic imogolite, an aluminum silicate clay mineral, by means of molecular simulations. We used a classical force field to describe the water and the flexible imogolite nanotube and validated it against the data obtained from first-principles molecular dynamics. With it, we observe a strong structuration of the water confined in the nanotube, with specific adsorption sites and a distribution of hydrogen bond patterns. The combination of number of adsorption sites, their geometry, and the preferential tetrahedral hydrogen bonding pattern of water leads to frustration and disorder. We further characterize the dynamics of the water, as well as the hydrogen bonds formed between water molecules and the nanotube, which is found to be more than 1 order of magnitude longer than water-water hydrogen bonds.

Forced intrusion of water and aqueous solutions in microporous materials: from fundamental thermodynamics to energy storage devices.

We review the high pressure forced intrusion studies of water in hydrophobic microporous materials such as zeolites and MOFs, a field of research that has emerged some 15 years ago and is now very active. Many of these studies are aimed at investigating the possibility of using these systems as energy storage devices. A series of all-silica zeolites (zeosil) frameworks were found suitable for reversible energy storage because of their stability with respect to hydrolysis after several water intrusion-extrusion cycles. Several microporous hydrophobic zeolite imidazolate frameworks (ZIFs) also happen to be quite stable and resistant towards hydrolysis and thus seem very promising for energy storage applications. Replacing pure water by electrolyte aqueous solutions enables to increase the stored energy by a factor close to 3, on account of the high pressure shift of the intrusion transition. In addition to the fact that aqueous solutions and microporous silica materials are environmental friendly, these systems are thus becoming increasingly interesting for the design of new energy storage devices. This review also addresses the theoretical approaches and molecular simulations performed in order to better understand the experimental behavior of nano-confined water. Molecular simulation studies showed that water condensation takes place through a genuine first-order phase transition, provided that the interconnected pores structure is 3-dimensional and sufficiently open. In an extreme confinement situations such as in ferrierite zeosil, condensation seem to take place through a continuous supercritical crossing from a diluted to a dense fluid, on account of the fact that the first-order transition line is shifted to higher pressure, and the confined water critical point is correlatively shifted to lower temperature. These molecular simulation studies suggest that the most important features of the intrusion/extrusion process can be understood in terms of equilibrium thermodynamics considerations.

Recent advances in the computational chemistry of soft porous crystals.

Here we highlight recent progress in the field of computational chemistry of nanoporous materials, focusing on methods and studies that address the extraordinary dynamic nature of these systems: the high flexibility of their frameworks, the large-scale structural changes upon external physical or chemical stimulation, and the presence of defects and disorder. The wide variety of behavior demonstrated in soft porous crystals, including the topical class of metal-organic frameworks, opens new challenges for computational chemistry methods at all scales.

Fermi resonance in CO2: Mode assignment and quantum nuclear effects from first principles molecular dynamics.

Vibrational spectroscopy is a fundamental tool to investigate local atomic arrangements and the effect of the environment, provided that the spectral features can be correctly assigned. This can be challenging in experiments and simulations when double peaks are present because they can have different origins. Fermi dyads are a common class of such doublets, stemming from the resonance of the fundamental excitation of a mode with the overtone of another. We present a new, efficient approach to unambiguously characterize Fermi resonances in density functional theory (DFT) based simulations of condensed phase systems. With it, the spectral features can be assigned and the two resonating modes identified. We also show how data from DFT simulations employing classical nuclear dynamics can be post-processed and combined with a perturbative quantum treatment at a finite temperature to include analytically thermal quantum nuclear effects. The inclusion of these effects is crucial to correct some of the qualitative failures of the Newtonian dynamics simulations at a low temperature such as, in particular, the behavior of the frequency splitting of the Fermi dyad. We show, by comparing with experimental data for the paradigmatic case of supercritical CO2, that these thermal quantum effects can be substantial even at ambient conditions and that our scheme provides an accurate and computationally convenient approach to account for them.