3 problems

Exchange-energy conjecture. The exchange energy should be given by a term of the form

Let $E_{\scriptscriptstyle\rm X}[n]$ be the exact exchange energy of an $N$-electron system with density $n$, and let the two-electron spin-unpolarized lower-bound constant be…

Let $E_{\scriptscriptstyle\rm X}[n]$ denote the exact exchange energy of an $N$-electron, spin-unpolarized system with density $n({\bf r})$. Perdew–Ruzsinszky–Sun–Burke's conjectur…