(482d) Mapped-Averaging Formulations for Evaluation of Singlet and Multibody Density Distributions

We show that two recently proposed methods for computing singlet and pair density distributions without histograms are particular implementations of the general mapped-averaging framework for deriving alternative ensemble averages for physical properties. We then go on to use mapped averaging develop additional expression for singlet and multibody density distributions, and examine their performance in molecular simulation in application to several systems, including those that are inhomogeneous due to an external field (e.g., particles in a pore), as well as those that form microstructure spontaneously (e.g., crystals). We consider application also to systems with discontinuous potentials, such as hard spheres, and describe the manner in which these force-based methods are applied in these cases.