arXiv subjects

Max Veit

Publications and source records attributed to Max Veit.

4 recordsLinked to original sources

arXiv2021

Thermodynamics and dielectric response of $\text{BaTiO}_3$ by data-driven modeling

Modeling ferroelectric materials from first principles is one of the successes of density-functional theory, and the driver of much development effort, requiring an accurate description of the electronic processes and the thermodynamic equilibrium that drive the spontaneous symmetry breaking and the emergence of macroscopic polarization. We demonstrate the development and application of an integrated machine learning model that describes on the same footing structural, energetic and functional properties of barium titanate ($\text{BaTiO}_3$), a prototypical ferroelectric. The model uses ab initio calculations as reference and achieves accurate yet inexpensive predictions of energy and polarization on time and length scales that are not accessible to direct ab initio modeling. These predictions allow us to assess the microscopic mechanism of the ferroelectric transition. The presence of an order-disorder transition for the Ti off-centered states is the main driver of the ferroelectric transition, even though the coupling between symmetry breaking and cell distortions determines the presence of intermediate, partly-ordered phases. Moreover, we thoroughly probe the static and dynamical behavior of $\text{BaTiO}_3$ across its phase diagram, without the need to introduce a coarse-grained description of the ferroelectric transition. Finally, we apply the polarization model to calculate dielectric response properties of the material in a fully ab initio manner, again reproducing the correct qualitative experimental behaviour.

cond-mat.mtrl-sci↗

arXiv2021

Efficient implementation of atom-density representations

Physically-motivated and mathematically robust atom-centred representations of molecular structures are key to the success of modern atomistic machine learning (ML) methods. They lie at the foundation of a wide range of methods to predict the properties of both materials and molecules as well as to explore and visualize the chemical compound and configuration space. Recently, it has become clear that many of the most effective representations share a fundamental formal connection: that 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 the calculation of such representations. 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 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 set. 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 further reduce the total computational cost by at up to a factor of 4 or 5 without affecting the model's symmetry properties and without significantly impacting its accuracy.

physics.chem-ph↗

arXiv2020

Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles

The molecular dipole moment ($\boldsymbol{\mu}$) is a central quantity in chemistry. It is essential in predicting infrared and sum-frequency generation spectra, as well as induction and long-range electrostatic interactions. Furthermore, it can be extracted directly from high-level quantum mechanical calculations, making it an ideal target for machine learning (ML). In this work, we choose to represent this quantity with a physically inspired ML model that captures two distinct physical effects: local atomic polarization is captured within the symmetry-adapted Gaussian process regression (SA-GPR) framework, which assigns a (vector) dipole moment to each atom, while movement of charge across the entire molecule is captured by assigning a partial (scalar) charge to each atom. The resulting "MuML" models are fitted together to reproduce molecular $\boldsymbol{\mu}$ computed using high-level coupled-cluster theory (CCSD) and density functional theory (DFT) on the QM7b dataset. The combined model shows excellent transferability when applied to a showcase dataset of larger and more complex molecules, approaching the accuracy of DFT at a small fraction of the computational cost. We also demonstrate that the uncertainty in the predictions can be estimated reliably using a calibrated committee model. The ultimate performance of the models depends, however, on the details of the system at hand, with the scalar model being clearly superior when describing large molecules whose dipole is almost entirely generated by charge separation. These observations point to the importance of simultaneously accounting for the local and non-local effects that contribute to $\boldsymbol{\mu}$; further, they define a challenging task to benchmark future models, particularly those aimed at the description of condensed phases.

physics.chem-ph↗

arXiv2018

Equation of state of fluid methane from first principles with machine learning potentials

The predictive simulation of molecular liquids requires models that are not only accurate, but computationally efficient enough to handle the large systems and long time scales required for reliable prediction of macroscopic properties. We present a new approach to the systematic approximation of the first-principles potential energy surface (PES) of molecular liquids using the GAP (Gaussian Approximation Potential) framework. The approach allows us to create potentials at several different levels of accuracy in reproducing the true PES, which allows us to test the level of quantum chemistry that is necessary to accurately predict its macroscopic properties. We test the approach by building potentials for liquid methane (CH$_4$), which is difficult to model from first principles because its behavior is dominated by weak dispersion interactions with a significant many-body component. We find that an accurate, consistent prediction of its bulk density across a wide range of temperature and pressure requires not only many-body dispersion, but also quantum nuclear effects to be modeled accurately.

physics.chem-ph↗