Density matrix for an excess electron in a classical fluid: results for a one-dimensional system

Abstract

We extend the theory of Chandler, Singh, and Richardson [J. Chem. Phys. 81, 1975 (1984)] to calculate the density matrix for an excess electron in a classical liquid like bath. For a one-dimensional fluid of hard rods and for two model potentials representing the electron fluid atom interaction (one representing the excluded volume effect and the other attractive interaction), we calculate the density matrix using the values of solvent induced potential surfaces for the electron found from our earlier calculations [Phys. Rev. B 42, 6090 (1990)]. The resulting density matrix is diagonalized and values of energies and wavefunctions of the electron including the effective mass and root mean square (RMS) displacement R_β in imaginary time βℏ. The transition of the electron to a state of self-trapping is visualized through a sudden change in the value of R_β or the effective mass m^∗ at a value of β or solvent density ρ_s^∗. For a potential model of hard rods, we find that the RMS displacement R_β for a given solvent density varies as (βℏ)^ν. Values of ν are evaluated for several solvent densities.