A. V. Shapeev

V. Ehrlacher, C. Ortner, A. V. Shapeev

Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline environment. This work develops a rigorous framework within which the accuracy of different types of boundary conditions can be precisely assessed. We formulate the equilibration of crystal defects as variational problems in a discrete energy space and establish qualitatively sharp regularity estimates for minimisers. Using this foundation we then present rigorous error estimates for (i) a truncation method (Dirichlet boundary conditions), (ii) periodic boundary conditions, (iii) boundary conditions from linear elasticity, and (iv) boundary conditions from nonlinear elasticity. Numerical results confirm the sharpness of the analysis.

C. Ortner, A. V. Shapeev

We introduce a general class of (quasi-)interpolants of functions defined on a Bravais lattice, and establish several technical results for these interpolants that are crucial ingredients in the analysis of atomistic models and atomistic/continuum multi-scale methods.

A. A. Solovykh, N. E. Rybin, I. S. Novikov et al.

Accounting for nuclear quantum effects (NQEs) can significantly alter material properties at finite temperatures. Atomic modeling using the path-integral molecular dynamics (PIMD) method can fully account for such effects, but requires computationally efficient and accurate models of interatomic interactions. Empirical potentials are fast but may lack sufficient accuracy, whereas quantum-mechanical calculations are highly accurate but computationally expensive. Machine-learned interatomic potentials offer a solution to this challenge, providing near-quantum-mechanical accuracy while maintaining high computational efficiency compared to density functional theory (DFT) calculations. In this context, an interface was developed to integrate moment tensor potentials (MTPs) from the MLIP-2 software package into PIMD calculations using the i-PI software package. This interface was then applied to active learning of potentials and to investigate the influence of NQEs on material properties, namely the temperature dependence of lattice parameters and thermal expansion coefficients, as well as radial distribution functions, for lithium hydride (LiH) and silicon (Si) systems. The results were compared with experimental data, quasi-harmonic approximation calculations, and predictions from the universal machine learning force field MatterSim. These comparisons demonstrated the high accuracy and effectiveness of the MTP-PIMD approach.