  We describe the quantitative refinement of nanoparticle structures from gold
nanoparticles probed by ultrafast electron crystallography (UEC). We establish
the equivalence between the modified radial distribution function employed in
UEC and the atomic pair distribution function (PDF) used in x-ray and neutron
powder diffraction analysis. By leveraging PDF refinement techniques, we
demonstrate that UEC data are of sufficient quality to differentiate between
cuboctahedral, decahedral and icosahedral nanoparticle models. Furthermore, we
identify the signatures of systematic errors that may occur during data
reduction and show that atomic positions refined from UEC are robust to these
errors. This work serves as a foundation for reliable quantitative structural
analysis of time-resolved laser-excited nanoparticle states.
