Materials are often represented in machine learning applications by (chemical-)geometric descriptions of their atomic structure. In this work, we propose an alternative framework for representing materials using descriptions of their electronic structure called Spectral Operator Representations (SOREPs). This record contains the code and data used to study carbon nanotubes (CNTs), barium titanate polymorphs, and the accelerated screening of transparent conducting materials with SOREPs. A data set for each application is provided: pz tight binding band structures for the three CNT configurations studied; the structures, band dispersions, and SOREP features of 127 BaTiO₃ polymorphs; and the SOREP features and ML targets for the MC3D materials considered in the accelerated screening. Additionally, code including patch files for Quantum ESPRESSO, the "sorep" python package, and the set of scripts used to prepare these data, train ML models, and plot results is provided.