statistical mechanics

Introduction In Ornstein and Zernike’s seminal work, Accidental deviations of density and opalescence at the critical point of a single substance, in: KNAW, Proceedings, 17 II, 1914, pp. 793-806, it was shown that the total correlation between molecules in a statistical mechanical system must obey an integral equation of the form,

This dissertation is founded on the central notion that structural correlations in dense fluids, such as dense gases, liquids, and …

The inverse problem of statistical mechanics is an unsolved, century-old challenge to learn classical pair potentials directly from …

While Bayesian inference is the gold standard for uncertainty quantification and propagation, its use within physical chemistry …

Structure-optimized potential refinement (SOPR) is a machine learning assisted iterative Boltzmann inversion method designed to predict accurate and transferable interaction potentials from a provided set of site-site partial radial distribution functions.

Structure and self-assembly are complex, emergent properties of matter that are often misrepresented by existing molecular simulation models. In this project, we use Bayesian optimization, an accurate and robust statistical method, to optimize novel force fields based on experimental neutron/X-ray diffraction data to better model the structural behavior of liquid state systems.

Neutron/X-ray diffraction measurements can be utilized to quantify many-body interactions at the same length scale as the interatomic interactions. We use a combination of electron structure theory and structure-optimized potential refinement to directly quantify the influence of third- and higher-order effects for real fluid ensembles.

The Henderson Inverse Theorem is an important result on the relationship between the radial distribution function and pairwise additive potential in a statistical ensemble. This theorem is the basis for the structure-optimized potential refinement algorithm and provides a variational solution to the statistical mechanical inverse problem.

The Kirkwood-Buff solution theory was presented in a landmark paper in 1951. The theory relates particle number fluctuations in the grand canonical ensemble to integrals of the radial distribution function. In this short introduction to the topic, we will introduce the statistical mechanics required to understand Kirkwood-Buff solution theory.

Deriving transferable pair potentials from experimental neutron and X-ray scattering measurements has been a longstanding challenge in …