Structural optimization in TensErLEED using a parameter tree and R-factor gradients

Quantitative low-energy electron diffraction [LEED I ( V )] is a powerful method for surface-structure determination, based on a direct comparison of I ( V ) data between experiment and computations for a structure model. As the diffraction intensities I are highly sensitive to subtle structural changes, local structure optimization is essential for assessing the validity of a structure model and finding the best-fit structure. Even when using the tensor-LEED approximation—which accelerates optimization by applying a perturbative treatment of small deviations from a reference structure—the optimization process is computationally expensive. In the new tensor-LEED implementation presented in this work, the problem of surface-structure optimization is reformulated using a tree-based data structure, which helps to avoid redundant function evaluations. Intensities are computed on the fly, eliminating limitations of previous algorithms using grid-based search with precomputed values. This enables the use of state-of-the-art optimization algorithms. Implemented in Python with the JAX library, the method provides access to gradients of the R factor and supports execution on graphics processing units (GPUs). These developments reduce the computing time by more than an order of magnitude.