Robust Kirkwood–Buff inversion in complex mixtures via reciprocal-space methods

Abstract

Understanding the relationship between microscopic structure and macroscopic thermodynamic properties is a central challenge in the study of complex fluids. The Kirkwood–Buff (KB) theory offers an elegant and powerful framework for bridging this gap by relating integrals over pair correlation functions to measurable thermodynamic quantities. In multicomponent systems, KB integrals connect directly to derivatives of thermodynamic potentials, including chemical potentials derivatives, partial molar volumes, and isothermal compressibility. While several computational methods exist to estimate KB integrals from molecular simulations, their application often demands careful treatment of finite-size effects and explicit extrapolation to the thermodynamic limit. Recently, alternative strategies based on the analysis of partial structure factors in reciprocal space have been proposed. Unlike real-space approaches, reciprocal-space methods avoid the additional truncation artifacts associated with direct integration or fluctuations in subensemble. They evaluate density fluctuations across the entire simulation box, fully accounting for periodic boundary conditions rather than relying on subdomains. As a result, these methods offer a compelling alternative, providing enhanced numerical stability for estimating KB integrals in complex mixtures. In this work, we extend, compare and validate these methods using binary and quaternary Lennard-Jones mixtures, as well as realistic molecular systems such as hexane–ethanol, water–urea, and aqueous NaCl mixtures. Our results provide practical guidelines for computing KB integrals and associated thermodynamic properties from canonical ensemble simulations, including recommendations on reciprocal-space extrapolation, uncertainty estimation, and linear algebra formulations of thermodynamic derivatives.