Despite extensive experimental studies of multi-walled nanotubes based on transition metal chalcogenides, there are few works on their theoretical modeling. However, simulations of their properties are necessary for interpreting the observed properties of known nanomaterials and predicting the properties of nanosystems that have not yet been synthesized. Due to the high computational requirements, the ab initio methods of quantum chemistry cannot be used to simulate multi-walled nanotubes with diameters close to the experimental values. In this regard methods based on force fields, remain relevant. Unfortunately, most of existing force fields are not designed for modeling multi-walled nanotubes and should be optimized.
In this work, we present the results of applying a genetic algorithm to fit force fields intended for modeling the properties of WS2-based multi-walled nanotubes. We applied NSGA-III , a multi-objective optimization algorithm, to tune force fields. It was used to explore the Pareto-optimal front of the force field parameters and select the best solutions according to different criteria. We have demonstrated the effectiveness of our method and shown that it can produce superior force fields compared to those obtained by other methods using the relatively simple potential models. The authors considered their experience in modeling multi-walled nanotubes based on MS2  and gallium monochalcogenides  when choosing the dependences of the contributions to the potential energy of the system.
The proposed procedure is linked to Gulp  program which can be used both for force -field fitting and molecular mechanics or molecular dynamic simulations. Training set includes experimental data, and results of ab initio calculations of bulk phases, nanolayers, and single-walled nanotubes.
Several variants of the parameterization of the force field were obtained by us, which satisfactorily reproduce the properties of training systems. The finest parameters were selected by comparing the properties of double-walled nanotubes with small diameters calculated using ab inito methods and those obtained by molecular mechanics modeling. The finally selected force field was applied to simulate multi-walled nanotubes WS2, and comparison of calculated results with experimental data shows good agreement.
Acknowledgements. This work was supported by the Russian Science Foundation (Grant no. 23-23-00040). The authors appreciate the assistance of Saint Petersburg State University Computer Center in high-performance computing.
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