The structure of nanoparticles has been difficult to determine accurately because the traditional structure methods rely on large monocrystals. Here, we discuss the structure of nanoparticles based on real-space modeling of the pair distribution function obtained by a Fourier transformation of the high-energy X-ray scattering structure factor. In particular, we consider X-ray scattering data taken from colloidal manganese oxide nanoparticles used in Lithium-ion batteries, air-purification, and biomedical systems, which are known to exist in various nanometer-sized polymorphs. Insight is thus obtained into characterizing the structural relaxation of the MnO₆ octahedra, which are the key building blocks of oxide nanoparticles, important in many technologies.