  This doctoral thesis is founded on the central notion that structural
correlations in dense fluids, such as dense gases, liquids, and glasses, are
directly related to fundamental interatomic forces. This relationship was
identified early in the development of statistical theories of fluids through
the mathematical formulations of Gibbs in the 1910s. However, it took nearly 80
years before practical implementations of structure-based theories became
widely used for interpreting and understanding the atomic structures of fluids
from experimental X-ray and neutron scattering data. The breakthrough in
successfully applying structure-potential relations is largely attributed to
the advancements in molecular mechanics simulations and the enhancement of
computational resources. Despite advancements in understanding the relationship
between structure and interatomic forces, a significant gap remains. Current
techniques for interpreting experimental scattering measurements are widely
used, yet there is little evidence that they yield physically accurate
predictions for interatomic forces. In fact, it is generally assumed that these
methods produce interatomic forces that poorly model the atomistic and
thermodynamic behavior of fluids, rendering them unreliable and
non-transferable. This thesis aims to address these limitations by refining the
statistical theory, computational methods, and philosophical approach to
structure-based analyses, thereby developing more robust and accurate
techniques for characterizing structure-potential relationships.
