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We present an algorithm that combines quantum scattering calculations with probabilistic machine-learning models to predict quantum dynamics rate coefficients for a large number of state-to-state transitions in molecule–molecule collisions much faster than with direct solutions of the Schrödinger equation. By utilizing the predictive power of Gaussian process regression with kernels, optimized to make accurate predictions outside of the input parameter space, the present strategy reduces the computational cost by about 75%, with an accuracy within 5%. Our method uses temperature dependences of rate coefficients for transitions from the isolated states of initial rotational angular momentum j, determined via explicit calculations, to predict the temperature dependences of rate coefficients for other values of j. The approach, demonstrated here for rovibrational transitions of SiO due to thermal collisions with H2, uses different prediction models and is thus adaptive to various time and accuracy requirements. The procedure outlined in this work can be used to extend multiple inelastic molecular collision databases without exponentially large computational resources required for conventional rigorous quantum dynamics calculations.
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A neural network parametrized coagulation rate model for <3 nm titanium dioxide nanoclusters
Coagulation is a key factor governing the size distribution of nanoclusters during the high temperature synthesis of metal oxide nanomaterials. Population balance models are strongly influenced by the coagulation rate coefficient utilized. Although simplified coagulation models are often invoked, the coagulation process, particularly for nanoscale particles, is complex, affected by the coagulating nanocluster sizes, the surrounding temperature, and potential interactions. Toward developing improved models of nanocluster and nanoparticle growth, we have developed a neural network (NN) model to describe titanium dioxide (TiO 2 ) nanocluster coagulation rate coefficients, trained with molecular dynamics (MD) trajectory calculations. Specifically, we first calculated TiO 2 nanocluster coagulation probabilities via MD trajectory calculations varying the nanocluster diameters from 0.6 to 3.0 nm, initial relative velocity from 20 to 700 m s −1 , and impact parameter from 0.0 to 8.0 nm. Calculations consider dipole–dipole interactions, dispersion interactions, and short-range repulsive interactions. We trained a NN model to predict whether a given set of nanocluster diameters, impact parameter, and initial velocity would lead to the outcome of coagulation. The accuracy between the predicted outcomes from the NN model and the MD trajectory calculation results is >95%. We subsequently utilized both the NN model and MD trajectory calculations to examine coagulation rate coefficients at 300 and 1000 K. The NN model predictions are largely within the range 0.65–1.54 of MD predictions, and importantly NN predictions capture the local minimum coagulation rate coefficients observed in MD trajectory calculations. The NN model can be directly implemented in population balances of TiO 2 formation.
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- Award ID(s):
- 2038173
- PAR ID:
- 10429958
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 158
- Issue:
- 8
- ISSN:
- 0021-9606
- Page Range / eLocation ID:
- 084301
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0136592
