Computing energy barriers for rare events from hybrid quantum/classical simulations through the virtual work principle

Hybrid quantum/classical techniques can flexibly couple ab initio simulations to an empirical or elastic medium to model materials systems that cannot be contained in small periodic supercells. However, due to electronic non-locality a total energy cannot be defined, meaning energy barriers cannot be calculated. We provide a general solution using the principle of virtual work in a modified nudged elastic band algorithm. Our method enables the first ab initio calculations of the kink formation energy for edge dislocations in molybdenum and lattice trapping barriers to brittle fracture in silicon

Hybrid quantum/classical study of hydrogen-decorated screw dislocations in tungsten : ultrafast pipe diffusion, core reconstruction, and effects on glide mechanism

The interaction of hydrogen (H) with dislocations in tungsten (W) must be understood in order to model the mechanical response of future plasma-facing materials for fusion applications. Here, hybrid quantum mechanics/molecular mechanics (QM/MM) simulations are employed to study the ⟨111⟩ screw dislocation glide in W in the presence of H, using the virtual work principle to obtain energy barriers for dislocation glide, H segregation, and pipe diffusion. We provide a convincing validation of the QM/MM approach against full DFT energy-based methods. This is possible because the compact core and relatively weak elastic fields of ⟨111⟩ screw dislocations allow them to be contained in periodic DFT supercells. We also show that H segregation stabilizes the split-core structure while leaving the Peierls barrier almost unchanged. Furthermore, we find an energy barrier of less than 0.05 eV for pipe diffusion of H along dislocation cores. Our quantum-accurate calculations provide important reference data for the construction of larger-scale material models

f90wrap : an automated tool for constructing deep Python interfaces to modern Fortran codes

Abstract: f90wrap is a tool to automatically generate Python extension modules which interface to Fortran libraries that makes use of derived types. It builds on the capabilities of the popular f2py utility by generating a simpler Fortran 90 interface to the original Fortran code which is then suitable for wrapping with f2py, together with a higher-level Pythonic wrapper that makes the existance of an additional layer transparent to the final user. f90wrap has been used to wrap a number of large software packages of relevance to the condensed matter physics community, including the QUIP molecular dynamics code and the CASTEP density functional theory code

Development of an exchange–correlation functional with uncertainty quantification capabilities for density functional theory

This paper presents the development of a new exchange–correlation functional from the point of view of machine learning. Using atomization energies of solids and small molecules, we train a linear model for the exchange enhancement factor using a Bayesian approach which allows for the quantification of uncertainties in the predictions. A relevance vector machine is used to automatically select the most relevant terms of the model. We then test this model on atomization energies and also on bulk properties. The average model provides a mean absolute error of only 0.116 eV for the test points of the G2/97 set but a larger 0.314 eV for the test solids. In terms of bulk properties, the prediction for transition metals and monovalent semiconductors has a very low test error. However, as expected, predictions for types of materials not represented in the training set such as ionic solids show much larger errors

A preconditioning scheme for minimum energy path finding methods

Popular methods for identifying transition paths between energy minima, such as the nudged elastic band and string methods, typically do not incorporate potential energy curvature information, leading to slow relaxation to the minimum energy path for typical potential energy surfaces encountered in molecular simulation. We propose a preconditioning scheme which, combined with a new adaptive time step selection algorithm, substantially reduces the computational cost of transition path finding algorithms. We demonstrate the improved performance of our approach in a range of examples including vacancy and dislocation migration modeled with both interatomic potentials and density functional theory

Sensitivity and dimensionality of atomic environment representations used for machine learning interatomic potentials

Faithfully representing chemical environments is essential for describing materials and molecules with machine learning approaches. Here, we present a systematic classification of these representations and then investigate (i) the sensitivity to perturbations and (ii) the effective dimensionality of a variety of atomic environment representations and over a range of material datasets. Representations investigated include atom centered symmetry functions, Chebyshev Polynomial Symmetry Functions (CHSF), smooth overlap of atomic positions, many-body tensor representation, and atomic cluster expansion. In area (i), we show that none of the atomic environment representations are linearly stable under tangential perturbations and that for CHSF, there are instabilities for particular choices of perturbation, which we show can be removed with a slight redefinition of the representation. In area (ii), we find that most representations can be compressed significantly without loss of precision and, further, that selecting optimal subsets of a representation method improves the accuracy of regression models built for a given dataset

Modelling defects in Ni-Al with EAM and DFT calculations

We present detailed comparisons between the results of embedded atom model (EAM) and density functional theory (DFT) calculations on defected Ni alloy systems. We find that the EAM interatomic potentials reproduce low-temperature structural properties in both the γ and ${{\gamma}^{\prime}}$ phases, and yield accurate atomic forces in bulk-like configurations even at temperatures as high as  ~1200 K. However, they fail to describe more complex chemical bonding, in configurations including defects such as vacancies or dislocations, for which we observe significant deviations between the EAM and DFT forces, suggesting that derived properties such as (free) energy barriers to vacancy migration and dislocation glide may also be inaccurate. Testing against full DFT calculations further reveals that these deviations have a local character, and are typically severe only up to the first or second neighbours of the defect. This suggests that a QM/MM approach can be used to accurately reproduce QM observables, fully exploiting the EAM potential efficiency in the MM zone. This approach could be easily extended to ternary systems for which developing a reliable and fully transferable EAM parameterisation would be extremely challenging e.g. Ni alloy model systems with a W or Re-containing QM zone

A Posteriori Error Estimate and Adaptivity for QM/MM Models of Crystalline Defects

Hybrid quantum/molecular mechanics models (QM/MM methods) are widely used in material and molecular simulations when pure MM models cannot ensure adequate accuracy but pure QM models are computationally prohibitive. Adaptive QM/MM coupling methods feature on-the-fly classification of atoms, allowing the QM and MM subsystems to be updated as needed. The state-of-art "machine-learned interatomic potentials (MLIPs)" can be applied as the MM models for consistent QM/MM methods with rigorously justified accuracy. In this work, we propose a robust adaptive QM/MM method for practical material defect simulation, which is based on a developed residual-based error estimator. The error estimator provides both upper and lower bounds for the approximation error, demonstrating its reliability and efficiency. In particular, we introduce three minor approximations such that the error estimator can be evaluated efficiently without losing much accuracy. To update the QM/MM partitions anisotropically, a novel adaptive algorithm is proposed, where a free interface motion problem based on the proposed error estimator is solved by employing the fast marching method. We implement and validate the robustness of the adaptive algorithm on numerical simulations for various complex crystalline defects