No Arabic abstract
We present a comprehensive methodology to enable addition of van der Waals (vdW) corrections to machine learning (ML) atomistic force fields. Using a Gaussian approximation potential (GAP) [Bartok et al., Phys. Rev. Lett. 104, 136403 (2010)] as baseline, we accurately machine learn a local model of atomic polarizabilities based on Hirshfeld volume partitioning of the charge density [Tkatchenko and Scheffler, Phys. Rev. Lett. 102, 073005 (2009)]. These environment-dependent polarizabilities are then used to parametrize a screened London-dispersion approximation to the vdW interactions. Our ML vdW model only needs to learn the charge density partitioning implicitly, by learning the reference Hirshfeld volumes from density functional theory (DFT). In practice, we can predict accurate Hirshfeld volumes from the knowledge of the local atomic environment (atomic positions) alone, making the model highly computationally efficient. For additional efficiency, our ML model of atomic polarizabilities reuses the same many-body atomic descriptors used for the underlying GAP learning of bonded interatomic interactions. We also show how the method enables straightforward computation of gradients of the observables, even when these remain challenging for the reference method (e.g., calculating gradients of the Hirshfeld volumes in DFT). Finally, we demonstrate the approach by studying the phase diagram of C$_{60}$, where vdW effects are important. The need for a highly accurate vdW-inclusive reactive force field is highlighted by modeling the decomposition of the C$_{60}$ molecules taking place at high pressures and temperatures.
Phase diagrams are an invaluable tool for material synthesis and provide information on the phases of the material at any given thermodynamic condition. Conventional phase diagram generation involves experimentation to provide an initial estimate of thermodynamically accessible phases, followed by use of phenomenological models to interpolate between the available experimental data points and extrapolate to inaccessible regions. Such an approach, combined with first-principles calculations and data-mining techniques, has led to exhaustive thermodynamic databases albeit at distinct thermodynamic equilibria. In contrast, materials during their synthesis, operation, or processing, may not reach their thermodynamic equilibrium state but, instead, remain trapped in a local free energy minimum, that may exhibit desirable properties. Mapping these metastable phases and their thermodynamic behavior is highly desirable but currently lacking. Here, we introduce an automated workflow that integrates first principles physics and atomistic simulations with machine learning (ML), and high-performance computing to allow rapid exploration of the metastable phases of a given elemental composition. Using a representative material, carbon, with a vast number of metastable phases without parent in equilibrium, we demonstrate automatic mapping of hundreds of metastable states ranging from near equilibrium to those far-from-equilibrium. Moreover, we incorporate the free energy calculations into a neural-network-based learning of the equations of state that allows for construction of metastable phase diagrams. High temperature high pressure experiments using a diamond anvil cell on graphite sample coupled with high-resolution transmission electron microscopy are used to validate our metastable phase predictions. Our introduced approach is general and broadly applicable to single and multi-component systems.
Traditionally, phase transitions are explored using a combination of macroscopic functional characterization and scattering techniques, providing insight into average properties and symmetries of the lattice but local atomic level mechanisms during phase transitions generally remain unknown. Here we explore the mechanisms of a phase transition between the trigonal prismatic and distorted octahedral phases of layered chalogenides in the MoS2 ReS2 system from the observations of local degrees of freedom, namely atomic positions by Scanning Transmission Electron Microscopy (STEM). We employ local crystallographic analysis based on machine learning of atomic environments to build a picture of the transition from the atomic level up and determine local and global variables controlling the local symmetry breaking. In particular, we argue that the dependence of the average symmetry breaking distortion amplitude on global and local concentration can be used to separate local chemical and global electronic effects on transition. This approach allows exploring atomic mechanisms beyond the traditional macroscopic descriptions, utilizing the imaging of compositional fluctuations in solids to explore phase transitions over a range of realized and observed local stoichiometries and atomic configurations.
The enormous structural and chemical diversity of metal-organic frameworks (MOFs) forces researchers to actively use simulation techniques on an equal footing with experiments. MOFs are widely known for outstanding adsorption properties, so precise description of host-guest interactions is essential for high-throughput screening aimed at ranking the most promising candidates. However, highly accurate ab initio calculations cannot be routinely applied to model thousands of structures due to the demanding computational costs. On the other side, methods based on force field (FF) parametrization suffer from low transferability. To resolve this accuracy-efficiency dilemma, we apply the machine learning (ML) approach. The trained models reproduce atom-in-material quantities, including partial charges, polarizabilities, dispersion coefficients, quantum Drude oscillator and electron cloud parameters within the accuracy of underlying density functional theory method. The aforementioned FF precursors make it possible to thoroughly describe non-covalent interactions typical for MOF-adsorbate systems: electrostatic, dispersion, polarization, and short-range repulsion. The presented approach can also significantly facilitate hybrid atomistic simulations/ML workflows.
Machine-learning force fields (MLFF) should be accurate, computationally and data efficient, and applicable to molecules, materials, and interfaces thereof. Currently, MLFFs often introduce tradeoffs that restrict their practical applicability to small subsets of chemical space or require exhaustive datasets for training. Here, we introduce the Bravais-Inspired Gradient-Domain Machine Learning (BIGDML) approach and demonstrate its ability to construct reliable force fields using a training set with just 10-200 geometries for materials including pristine and defect-containing 2D and 3D semiconductors and metals, as well as chemisorbed and physisorbed atomic and molecular adsorbates on surfaces. The BIGDML model employs the full relevant symmetry group for a given material, does not assume artificial atom types or localization of atomic interactions and exhibits high data efficiency and state-of-the-art energy accuracies (errors substantially below 1 meV per atom) for an extended set of materials. Extensive path-integral molecular dynamics carried out with BIGDML models demonstrate the counterintuitive localization of benzene--graphene dynamics induced by nuclear quantum effects and allow to rationalize the Arrhenius behavior of hydrogen diffusion coefficient in a Pd crystal for a wide range of temperatures.
We present an approach to generate machine-learned force fields (MLFF) with beyond density functional theory (DFT) accuracy. Our approach combines on-the-fly active learning and $Delta$-machine learning in order to generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on-the-fly during DFT based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces and stress tensors. Thanks to the relatively smooth nature of the differences, the expensive RPA calculations are performed only on a small number of representative structures of small unit cells. These structures are determined by a singular value decomposition rank compression of the kernel matrix with low spatial resolution. This dramatically reduces the computational cost and allows us to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia.