Predictive treatment of functionalising defects in 2D materials

Point defects play a key role in determining catalytic activity and transport properties and ab-initio methods have reached a maturity that means that they can be screened to computationally choose the optimal dopant before experimental realization. However, the defect structure can be a delicate balance between charge delocalization and formation of  localized bonds or lone-pairs. For example, in GaAs (see Figure) S tends to form a lone pair leads to a hole-doping broken-bond DX-center instead of the expected electron doping substitutional defect [1].

Predictive treatment of non-trivial defect structures are a challenge because they require mapping of the full defect potential energy surface (PES). The challenge must be met because non-trivial defect structures are prevalent in 2D structures such as graphene and MoS2 and defects are often the active sites in bonding single atom catalysts. At the same time defects in 2D materials offer the unique possibility of direct validation of defect structures, due to the imaging possibilities of STM/AFM. 

The structure and electron localization function (ELF) of the hole-doping broken bond DX-center for S doped GaAs

© Georg Madsen

The structure and electron localization function (ELF) of the hole-doping broken bond DX-center for S doped GaAs.


Complex defect structures are a situation where semi-empirical descriptions lack the necessary accuracy, but direct ab-initio methods cannot cope with the dimensions of the systems involved. We aim at using machine learning algorithms to develop “on-the-fly” potentials to enable global exploration algorithms to explore the search space in an efficient manner. The algorithm will be applied to predict stable structures of extrinsic defects, such as dopants or catalytic sites, and intrinsic defects, such as vacancies and grain boundaries. The direct comparison of the predicted atomic structures will make it possible to evaluate both the developed potentials and the search algorithms. The most relevant defect structures identified this way will then be compared to experimental data.


For the exploration of the PESs we will implement an active learning approach based on our implementation of the covariance matrix adaption evolutionary strategy [2] and automatically differentiable neural-network force field (NNFF) [3]. Since NNFFs only give reliable results within their training domain, an active learning strategy, where the training set is augmented whenever the exploration algorithm moves beyond its confines, is mandatory. The differentiable implementation means that training can be performed on both forces and energies such that relatively small datasets can be used. The uncertainty of the predictions necessary for an active learning strategy will be quantified through cross validation among an ensemble of NNs. We will go beyond previous work by coupling our NNFFs to global PES exploration algorithms which allow for evaluation of the partition function.


The Parkinson group will provide detailed experimental information on the atomic structures of single atom catalysts, which will be used for benchmarking the developed potentials. The methodology will also be applied to understand the defect structures observed in the Diebold group and the transport properties of semiconductor devices (scattering and charge trapping at defect sites) in collaboration with the Grasser group. Filipovic will also apply our results when modeling conductivity in MoS2 monolayers for sensing applications.


Georg Madsen is a theoretical materials chemist with a research focus on defects, transport properties and electronic structure theory. He has contributed to the widely used electronic structure codes WIEN2k and GPAW and to the BoltzTraP2 and almaBTE codes for predictive calculation of transport properties. Focus has been put on both point defects to predict optimal doping strategies and extended defects such as dislocations. Recently the group has been developing machine learning methods for the efficient exploration of potential energy surfaces.


Group of Prof. Madsen


  1. Ashis Kundu, Fabian Otte, Jesús Carrete, Paul Erhart, Wu Li, Natalio Mingo, and Georg K. H. Madsen, Effect of local chemistry and structure on thermal transport in doped GaAs, Phys. Rev. Materials 3, 094602, DOI: 10.1103/PhysRevMaterials.3.094602.
  2. M. Arrigoni and G. Madsen. Evolutionary computing and machine learning for discovering of
    low-energy defect configurations. npj Comp. Mat. 7, 71 (2021). DOI: 10.1038/s41524-021-00537-1.
  3. H. Montes-Campos, J. Carrete, S. Bichelmaier, L. M. Varela, and G. K. H. Madsen. A differen-
    tiable neural-network force field for ionic liquids. Journal of Chemical Information and Modeling
    62, 88–101 (2022). DOI: 10.1021/acs.jcim.1c01380.