Ab-initio thermodynamics with machine-learned force fields
Prof. Georg K. H. Madsen, PhD
Institute of Materials Chemistry, TU Wien, Vienna, Austria
16:15 - 17:15 Tuesday 31 October 2023 TUG Recent advances in machine learning provide access to highly accurate surrogate potential energy surfaces (PESs) at a fraction of the computational cost of ab-initio calculations. The computational efficiency opens the door to predictive calculation of thermodynamic properties with ab-initio accuracy. Here, we first describe our implementation of a neural-network force field (NNFF) based on the high-performance machine-learning library JAX.[1] We will illustrate its usage in predicting the temperature-dependent behavior of HfO2 using the effective harmonic potential (EHP) method.[2] The EHP relies on importance sampling of the PES and for the lower-symmetry monoclinic (m) and tetragonal (t) HfO2 phases, a DFT-backed approach incurs an unfeasible computational cost. We detail data acquisition for the low symmetry HfO2 phases and show how the NNFF-backed EHP gives temperature dependent lattice constants and phase transition temperatures of the m- and t-phases in excellent agreement with experimental data. In contrast, the lattice constants predicted for the studied cubic phases are substantially lower than the experimental and no cubic phase is found to be stable in the studied temperature range. It is hypothesized that cubic HfO2 is present only in a defect-stabilized form.
We then discuss a nested sampling study of the Silicon phase diagram.[3] The nested sampling algorithm in principle allows the prediction of the phase diagram without prior knowledge and the simulated phase diagram shows a good agreement with experimental results, closely reproducing the melting line and all of the experimentally stable structures. We point out the importance of the choice of exchange-correlation functional for the training data and show how the meta-GGA r2SCAN plays a pivotal role in achieving accurate thermodynamic behaviour. We perform a detailed analysis of the PES exploration and highlight the critical role of a diverse training data set.
For the study of the EHP study of the the phase-diagram of HfO2 approximately 2.5 10^6 atomic configuration were evaluated. For the unbiased exploration of the silicon phase diagram using nested sampling, more than 5 10^8 configuration were sampled.
[1] Montes-Campos, Carrete, Bichelmaier, Varela, Madsen J. Chem. Inf. Model “A Differentiable Neural-Network Force Field for Ionic Liquids” 62 (2022) p88
[2] S. Bichelmaier, J. Carrete, R. Wanzenböck, F. Buchner, G. K. H. Madsen
“A neural-network-backed effective harmonic potential study of the ambient pressure phases of hafnia” Phys. Rev. B 107 (2023) 184111 DOI: 10.1103/PhysRevB.107.184111
[3] N. Unglert, J. Carrete, L. B. Pártay, G. K. H. Madsen, “Neural-Network Force Field Backed Nested Sampling: Study of the Silicon p-T Phase Diagram” DOI: 10.48550/arXiv.2308.11426
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