Publications by Edgar Albert Engel

A data-driven interpretation of the stability of organic molecular crystals

Michele Ceriotti, Edgar Albert Engel, Maria Pakhnova

Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A particularly active and fruitful approach involves classifying the different combinations of interacting chemical moieties, as understanding the relative energetics of different interactions enables the design of molecular crystals and fine-tuning of their stabilities. While this is usually performed based on the empirical observation of the most commonly encountered motifs in known crystal structures, we propose to apply a combination of supervised and unsupervised machine-learning techniques to automate the construction of an extensive library of molecular building blocks. We introduce a structural descriptor tailored to the prediction of the binding (lattice) energy and apply it to a curated dataset of organic crystals, exploiting its atom-centered nature to obtain a data-driven assessment of the contribution of different chemical groups to the lattice energy of the crystal. We then interpret this library using a low-dimensional representation of the structure-energy landscape and discuss selected examples of the insights into crystal engineering that can be extracted from this analysis, providing a complete database to guide the design of molecular materials.

ROYAL SOC CHEMISTRY2023

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Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free energy differences are sensitively affected by the description of electronic structure, the statistical mechanics of the nuclei and the cell, and thermal expansion. The importance of these effects has been individually established, but rigorous free energy calculations for general molecular compounds, which simultaneously account for all effects, have hitherto not been computationally viable. Here we present an efficient "end to end" framework that seamlessly combines state-of-the art electronic structure calculations, machine-learning potentials, and advanced free energy methods to calculate ab initio Gibbs free energies for general organic molecular materials. The facile generation of machine-learning potentials for a diverse set of polymorphic compounds-benzene, glycine, and succinic acid-and predictions of thermodynamic stabilities in qualitative and quantitative agreement with experiments highlight that predictive thermodynamic studies of industrially relevant molecular materials are no longer a daunting task.

NATL ACAD SCIENCES2022

Local Kernel Regression and Neural Network Approaches to the Conformational Landscapes of Oligopeptides

Michele Ceriotti, Edgar Albert Engel, Raimon Fabregat I De Aguilar-Amat, Alberto Fabrizio, Veronika Juraskova, Benjamin André René Meyer

The application of machine learning to theoretical chemistry has made it possible to combine the accuracy of quantum chemical energetics with the thorough sampling of finite-temperature fluctuations. To reach this goal, a diverse set of methods has been proposed, ranging from simple linear models to kernel regression and highly nonlinear neural networks. Here we apply two widely different approaches to the same, challenging problem: the sampling of the conformational landscape of polypeptides at finite temperature. We develop a local kernel regression (LKR) coupled with a supervised sparsity method and compare it with a more established approach based on Behler-Parrinello type neural networks. In the context of the LKR, we discuss how the supervised selection of the reference pool of environments is crucial to achieve accurate potential energy surfaces at a competitive computational cost and leverage the locality of the model to infer which chemical environments are poorly described by the DFTB baseline. We then discuss the relative merits of the two frameworks and perform Hamiltonian-reservoir replica-exchange Monte Carlo sampling and metadynamics simulations, respectively, to demonstrate that both frameworks can achieve converged and transferable sampling of the conformational landscape of complex and flexible biomolecules with comparable accuracy and computational cost.

2022

Importance of Nuclear Quantum Effects for NMR Crystallography

Michele Ceriotti, Edgar Albert Engel, Venkat Kapil

The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of computational predictions of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy. To test the limits of this approximation, we systematically study the importance of finite-temperature and quantum nuclear fluctuations for H-1, C-13, and N-15 shieldings in polymorphs of three paradigmatic molecular crystals: benzene, glycine, and succinic acid. The effect of quantum fluctuations is comparable to the typical errors of shielding predictions for static nuclei with respect to experiments, and their inclusion improves the agreement with measurements, translating to more reliable assignment of the NMR spectra to the correct candidate structure. The use of integrated machine-learning models, trained on first-principles energies and shieldings, renders rigorous sampling of nuclear fluctuations affordable, setting a new standard for the calculations underlying NMR structure determinations.

AMER CHEMICAL SOC2021

Importance of Nuclear Quantum Effects for NMR Crystallography

Michele Ceriotti, Edgar Albert Engel, Venkat Kapil

2021

Improving sample and feature selection with principal covariates regression

Michele Ceriotti, Edgar Albert Engel, Benjamin Aaron Helfrecht, Sergei Kliavinek

Selecting the most relevant features and samples out of a large set of candidates is a task that occurs very often in the context of automated data analysis, where it improves the computational performance and often the transferability of a model. Here we focus on two popular subselection schemes applied to this end: CUR decomposition, derived from a low-rank approximation of the feature matrix, and farthest point sampling (FPS), which relies on the iterative identification of the most diverse samples and discriminating features. We modify these unsupervised approaches, incorporating a supervised component following the same spirit as the principal covariates (PCov) regression method. We show how this results in selections that perform better in supervised tasks, demonstrating with models of increasing complexity, from ridge regression to kernel ridge regression and finally feed-forward neural networks. We also present adjustments to minimise the impact of any subselection when performing unsupervised tasks. We demonstrate the significant improvements associated with PCov-CUR and PCov-FPS selections for applications to chemistry and materials science, typically reducing by a factor of two the number of features and samples required to achieve a given level of regression accuracy.

IOP PUBLISHING LTD2021

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Machine-learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale, and complexity. Given the interpolative nature of these models, the reliability of predictions depends on the position in phase space, and it is crucial to obtain an estimate of the error that derives from the finite number of reference structures included during model training. When using a machine-learning potential to sample a finite-temperature ensemble, the uncertainty on individual configurations translates into an error on thermodynamic averages and leads to a loss of accuracy when the simulation enters a previously unexplored region. Here, we discuss how uncertainty quantification can be used, together with a baseline energy model, or a more robust but less accurate interatomic potential, to obtain more resilient simulations and to support active-learning strategies. Furthermore, we introduce an on-the-fly reweighing scheme that makes it possible to estimate the uncertainty in thermodynamic averages extracted from long trajectories. We present examples covering different types of structural and thermodynamic properties and systems as diverse as water and liquid gallium.

2021

A Bayesian approach to NMR crystal structure determination

Andrea Anelli, Michele Ceriotti, David Lyndon Emsley, Edgar Albert Engel, Albert Hofstetter, Federico Maria Paruzzo

Nuclear Magnetic Resonance (NMR) spectroscopy is particularly well suited to determine the structure of molecules and materials in powdered form. Structure determination usually proceeds by finding the best match between experimentally observed NMR chemical shifts and those of candidate structures. Chemical shifts for the candidate configurations have traditionally been computed by electronic-structure methods, and more recently predicted by machine learning. However, the reliability of the determination depends on the errors in the predicted shifts. Here we propose a Bayesian framework for determining the confidence in the identification of the experimental crystal structure, based on knowledge of the typical errors in the electronic structure methods. We demonstrate the approach on the determination of the structures of six organic molecular crystals. We critically assess the reliability of the structure determinations, facilitated by the introduction of a visualization of the similarity between candidate configurations in terms of their chemical shifts and their structures. We also show that the commonly used values for the errors in calculated 13C shifts are underestimated, and that more accurate, self-consistently determined uncertainties make it possible to use 13C shifts to improve the accuracy of structure determinations. Finally, we extend the recently-developed ShiftML model to render it more efficient, accurate, and, most importantly, to evaluate the uncertainties in its predictions. By quantifying the confidence in structure determinations based on ShiftML predictions we further substantiate that it provides a valid replacement for first-principles calculations in NMR crystallography.

2019

Ab initio thermodynamics of liquid and solid water

Michele Ceriotti, Bingqing Cheng, Edgar Albert Engel

Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations, and proton disorder. This is made possible by combining advanced free-energy methods and state-of-the-art machine-learning techniques. The ab initio description leads to structural properties in excellent agreement with experiments and reliable estimates of the melting points of light and heavy water. We observe that nuclear-quantum effects contribute a crucial 0.2 meV/H2O to the stability of ice Ih, making it more stable than ice Ic. Our computational approach is general and transferable, providing a comprehensive framework for quantitative predictions of ab initio thermodynamic properties using machine-learning potentials as an intermediate step.

NATL ACAD SCIENCES2019

Assessment of Approximate Methods for Anharmonic Free Energies

Michele Ceriotti, Edgar Albert Engel, Venkat Kapil, Mariana Rossi Carvalho

Quantitative evaluation of the thermodynamic properties of materials—most notably their stability, as measured by the free energy—must take into account the role of thermal and zero-point energy fluctuations. While these effects can easily be estimated within a harmonic approximation, corrections arising from the anharmonic nature of the interatomic potential are often crucial and require computationally costly path integral simulations to obtain results that are essentially exact for a given potential. Consequently, different approximate frameworks for computing affordable estimates of the anharmonic free energies have been developed over the years. Understanding which of the approximations involved are justified for a given system, and therefore choosing the most suitable method, is complicated by the lack of comparative benchmarks. To facilitate this choice we assess the accuracy and efficiency of some of the most commonly used approximate methods: the independent mode framework, the vibrational self-consistent field, and self-consistent phonons. We compare the anharmonic correction to the Helmholtz free energy against reference path integral calculations. These benchmarks are performed for a diverse set of systems, ranging from simple weakly anharmonic solids to flexible molecular crystals with freely rotating units. The results suggest that, for simple solids such as allotropes of carbon, these methods yield results that are in excellent agreement with the reference calculations, at a considerably lower computational cost. For more complex molecular systems such as polymorphs of ice and paracetamol the methods do not consistently provide a reliable approximation of the anharmonic correction. Despite substantial cancellation of errors when comparing the stability of different phases, we do not observe a systematic improvement over the harmonic approximation even for relative free energies. We conclude that, at least for the classes of materials considered here, efforts toward obtaining computationally feasible anharmonic free energies should therefore be directed toward reducing the expense of path integral methods.

2019