--- geometry: top=3.18cm, bottom=3.18cm, left=2.54cm, right=2.54cm mainfont: Times New Roman CJKmainfont: FangSong fontsize: 12pt header-includes: - \usepackage{caption}\captionsetup{singlelinecheck=false,justification=centering} - \usepackage{setspace}\onehalfspacing - \usepackage{xcolor} - \usepackage{relsize} --- The *exact* asymptotic behavior of the exchange-energy density of any finite many-electron system is known, and is given by $$ \lim\limits_{r\to\infty} U_{X}^{\sigma} = -\mathlarger{\frac{1}{r}} $$ {#eq:asymptotic}