Spectral Analysis of Local Atomic Environments

Abstract

The representation of local environments is a cornerstone challenge in computational materials science, with profound implications for property prediction and materials discovery. This thesis presents a comprehensive investigation of spectral descriptors constructed from spherical harmonic expansions to represent the geometries of local atomic environments. Systematic computational experiments evaluate the robustness of these descriptors to geometric perturbations and their capacity to differentiate structurally similar configurations. The findings reveal a clear performance hierarchy, with higher-order descriptors offering increased geometric expressivity and reconstruction accuracy in resolving challenging structural cases. This research further examines methods for inverting spectral representations back to atomic coordinates, demonstrating that directly optimizing three-dimensional positions through gradient-based techniques yields markedly better reconstruction accuracy than approaches operating in Fourier space. Dimensionality reduction via latent space embeddings is also explored, showing that essential geometric features can be preserved in significantly compressed representations. Through methodical analysis of descriptor limitations, performance boundaries, and sensitivity to hyperparameters, this work establishes practical benchmarks and implementation guidelines for spectral descriptors. These contributions strengthen the foundation for reliable machine learning models in computational materials science, advancing both the accuracy and efficiency of atomic-scale modeling for materials design and discovery.