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This work revises the concept of defects in crystalline solids and proposes a universal strategy for their characterization at the atomic scale using outlier detection based on statistical distances. The proposed strategy provides a generic measure that describes the distortion score of local atomic environments. This score facilitates automatic defect localization and enables a stratified description of defects, which allows to distinguish the zones with different levels of distortion within the structure. This work proposes applications for advanced materials modelling ranging from the surrogate concept for the energy per atom to the relevant information selection for evaluation of energy barriers from the mean force. Moreover, this concept can serve for design of robust interatomic machine learning potentials and high-throughput analysis of their databases. The proposed definition of defects opens up many perspectives for materials design and characterization, promoting thereby the development of novel techniques in materials science.

The GW approximation to the electronic self-energy is now a well-recognized approach to obtain the electron quasiparticle energies of molecules and, in particular, their ionization potential and electron affinity. Though much faster than the corresponding wavefunction methods, the GW energies are still affected by slow convergence with respect to the basis completeness. This limitation hinders a wider application of the GW approach. Here, we show that we can reach the complete basis set limit for the cumbersome GW calculations solely based on fast preliminary calculations with an unconverged basis set. We introduce a linear model that correlates the molecular orbital characteristics and the basis convergence error for a large database of approximately 600 states in 104 organic molecules that contain H, C, O, N, F, P, S, and Cl. The model employs molecular-orbital-based non-linear descriptors that encode efficiently the chemical space offering outstanding transferability. Using a low number of descriptors (17) the performance of this extrapolation procedure is superior to that of the earlier more physically motivated approaches. The predictive power of the method is finally demonstrated for a selection of large acceptor molecules.

Empirical potentials using embedded atom method are developed for Fe, mainly to study irradiation-induced defects such as self-interstitial atom clusters or dislocation loops. The potentials are fitted using experimental values of solid-state properties, ab initio formation energies of basic point defects and ab initio forces acting on the atoms in the liquid or random state configurations. Various bulk and defect properties are compared to validate the transferability of the new potential. In this paper, we also investigate the energetic landscape of C15 self-interstitial atom clusters. In order to simplify and to facilitate the construction of lowest energy configurations in the complex energy landscape of C15 clusters, we test and propose three selection rules.

The temperature variation of the defect densities in a crystal depends on vibrational entropy. This contribution to the system thermodynamics remains computationally challenging as it requires a diagonalisation of the system's Hessian which scales as O(N 3) for a crystal made of N atoms. Here, to circumvent such an heavy computational task and make it feasible even for systems containing millions of atoms the harmonic vibrational entropy of point defects is estimated directly from the relaxed atomic positions through a linear-in-descriptor machine learning approach of order O(N). With a size-independent descriptor dimension and fixed model parameters, an excellent predictive power is demonstrated on a wide range of defect configurations, supercell sizes and external deformations well outside of the training database. In particular, formation entropies in a range of 250 kB are predicted with less than 1.6 kB error from a training database whose formation entropies span only 25 kB (train error less than 1.0 kB). This exceptional transferability is found to hold even when the training is limited to a low energy superbasin in the phase space while the tests are performed for a different liquid-like superbasin at higher energies.

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