Excess electrons in simple fluids. II. Numerical results for the hard sphere solvent

Abstract

The theory for solvated excess electrons described in an earlier paper is now applied numerically. For the simple model of an electron excluded from spherical regions of radius d surrounding each of the particles in a hard sphere fluid, our results exhibit a rich behavior. At all temperatures for which λ_e»σ, where λ_e is the thermal wavelength of the electron and σ is the diameter of the hard sphere fluid particles, we find a relatively narrow transition region of solvent densities below which the solvated electron is extended and above which the electron is localized. For λ_e=10σ and d=σ/2, localization occurs near the solvent density 0.15σ⁻³. Both the width and location of the transition region increase with decreasing λ_e (i.e., increasing temperature). When λ_e=6σ, the region is broad, barely discernible, and located near 0.3σ⁻³ when d=σ/2. For λ_e≲5σ, no precipitous behavior is found as density is increased and the electron passes from extended to localized behavior. The localized electron is characterized by a condition of ground state dominance, and this behavior leads to a density dependence of the electron-solvent pair structure that is very different than the dependence found when the electron is delocalized and extended. We estimate the behavior of the friction constant for the electron and find a change in direction of its temperature dependence as one passes from the localization to delocalized case. We discuss how the location of the localization depends upon model parameters and temperature, and we provide qualitative explanations of our results in terms of structural principles associated with the fact that the delocalized electron has a distribution of spatially large fluctuations while the localized electron does not fluctuate over large distances and is characterized by primarily one length scale, its range of self-correlations. The equations central to our theory embody these principles.