Molecular hydrodynamic theory of the velocity autocorrelation function

Abstract

The velocity autocorrelation function (VACF) encapsulates extensive information about the molecular-structural and hydrodynamic properties of a fluid. We address the following fundamental question: How well can a purely hydrodynamic model recover the molecular properties of a fluid as exhibited by the VACF? To this end, we develop a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes are described by linear hydrodynamic equations obtained as velocity moments of a single-particle kinetic equation; the fluid’s static kinetic energy spectrum is identified as a necessary initial condition for the momentum current correlation. This leads to a natural physical interpretation of the molecular-hydrodynamic VACF as a superposition of quasinormal hydrodynamic modes weighted commensurately with the static kinetic energy spectrum. Our method yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals; moreover, our hydrodynamic formulation of the self-intermediate scattering function appears to extend the description to low densities where the Schmidt number is of order unity, enabling calculations for the vapor and supercritical phases.