Time-dependent current-density functional theory for the friction of ions in an interacting electron gas

TL;DR

This paper introduces a reformulation of the friction coefficient calculation in electron gases using current-density functional theory, improving agreement with experimental data for slow ions.

Contribution

The authors reformulate the friction coefficient formula using tensorial xc kernels in current-density functional theory, overcoming limitations of the local-density approximation in TDDFT.

Findings

Better agreement with experimental stopping power data for Al and Au.

Rectified overestimation of friction coefficient for heavy ions.

Enhanced accuracy in modeling ion-electron interactions.

Abstract

Due to the strongly nonlocal nature of $f_{xc}({\bf r},{\bf r}',\omega)$ the {\em scalar} exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT), the formula for Q the friction coefficient of an interacting electron gas (EG) for ions tends to give a too large value of Q for heavy ions in the medium- and low-density EG, if we adopt the local-density approximation (LDA) to $f_{xc}({\bf r},{\bf r}',\omega)$, even though the formula itself is formally exact. We have rectified this unfavorable feature by reformulating the formula for Q in terms of the {\em tensorial} xc kernel of the time dependent current-density functional theory, to which the LDA can be applied without intrinsic difficulty. Our numerical results find themselves in a considerably better agreement with the experimental stopping power of Al and Au for slow ions than those previously obtained within the LDA to the TDDFT.