Recommended by

Indexed by

Accurate fourth-generation machine learning potentials by electrostatic embedding

Tsz Wai Ko1*, Jonas A. Finkler2*, Stefan Goedecker2*, Jörg Behler1,3*

1 Universität Göttingen, Institut für Physikalische Chemie, Theoretische Chemie, Tammannstraße 6, 37077 Göttingen, Germany

2 Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland

3 Lehrstuhl für Theoretische Chemie II, Ruhr-Universität Bochum, 44780 Bochum, Germany, and Research Center Chemical Sciences and Sustainability, Research Alliance Ruhr, 44780 Bochum, Germany

* Corresponding authors emails: tko@chemie.uni-goettingen.de, jonas.finkler@unibas.ch, stefan.goedecker@unibas.ch, joerg.behler@ruhr-uni-bochum.de
DOI10.24435/materialscloud:g3-07 [version v1]

Publication date: May 23, 2023

How to cite this record

Tsz Wai Ko, Jonas A. Finkler, Stefan Goedecker, Jörg Behler, Accurate fourth-generation machine learning potentials by electrostatic embedding, Materials Cloud Archive 2023.77 (2023), doi: 10.24435/materialscloud:g3-07.


In recent years, significant progress has been made in the development of machine learning potentials (MLPs) for atomistic simulations with applications in many fields from chemistry to materials science. While most current MLPs are based on environment-dependent atomic energies, the limitations of this locality approximation can be overcome, e.g., in fourth-generation MLPs, which incorporate long-range electrostatic interactions based on an equilibrated global charge distribution. Apart from the considered interactions, the quality of MLPs crucially depends on the information available about the system, i.e., the descriptors. In this work we show that including — in addition to structural information — the electrostatic potential arising from the charge distribution in the atomic environments significantly improves the quality and transferability of the potentials. Moreover, the extended descriptor allows to overcome current limitations of two- and three-body based feature vectors regarding artificially degenerate atomic environments. The capabilities of such an electrostatically embedded fourth-generation high-dimensional neural network potential (ee4G-HDNNP), which is further augmented by pairwise interactions, are demonstrated for NaCl as a benchmark system. Employing a data set containing only neutral and negatively charged NaCl clusters, even small energy differences between different cluster geometries can be resolved, and the potential shows an impressive transferability to positively charged clusters as well as the melt.

Materials Cloud sections using this data

No Explore or Discover sections associated with this archive record.


File name Size Description
4.2 KiB Detailed description of different files
155.8 MiB Input data file for constructing HDNNPs using RuNNer program
5.1 KiB Basic input file for DFT calculations using FHI-aims
459.7 KiB Zipped folder containing different local minima of NaCl clusters predicted by ee4G-HDNNP


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

Journal reference (Paper where the data is discussed for constructing and benchmarking non-local machine learning potentials)
T. W. Ko, J. A. Finkler, S. Goedecker, J. Behler, J. Chem. Theory Comput., Accepted


DFT Machine Learning Potentials Electrostatics

Version history:

2023.77 (version v1) [This version] May 23, 2023 DOI10.24435/materialscloud:g3-07