Correlation-energy functional and its high-density limit obtained from a coupling-constant perturbation expansion.

摘要: A perturbation theory is developed for the correlation energy ${\mathit{E}}_{\mathit{c}}$[n], of a finite-density system, with respect to coupling constant \ensuremath{\alpha} which multiplies electron-electron repulsion operator in ${\mathit{H}}^{\mathrm{\ensuremath{\alpha}}}$=T^+\ensuremath{\alpha}V${\mathrm{^}}_{\mathit{e}\mathit{e}}$+${\mathit{tsum}}_{\mathit{i}}$${\mathit{v}}_{\mathrm{\ensuremath{\alpha}}}$(${\mathbf{r}}_{\mathit{i}}$). The external potential ${\mathit{v}}_{\mathrm{\ensuremath{\alpha}}}$ constrained keep gound-state density n fixed all \ensuremath{\alpha}\ensuremath{\ge}0. given completely terms functional derivatives at full charge (\ensuremath{\alpha}=1), from ${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$]=${\mathit{e}}_{\mathit{c},2}$[n]+ ${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}1}$${\mathit{e}}_{\mathit{c},3}$[n]+${\ensuremath{\lambda}}^{\mathrm{\ensuremath{-}}2}$${\mathit{e}}_{\mathit{c},4}$[n]+..., where each ${\mathit{e}}_{\mathit{c},}$j[n] expressed integrals involving Kohn-Sham determinants. Here, ${\mathit{n}}_{\ensuremath{\lambda}}$(x,y,x)=${\ensuremath{\lambda}}^{3}$n(\ensuremath{\lambda}x,\ensuremath{\lambda}y,\ensuremath{\lambda}z) and \ensuremath{\lambda}=${\mathrm{\ensuremath{\alpha}}}^{\mathrm{\ensuremath{-}}1}$. identification ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$], high-density limit, as second-order ${\mathit{e}}_{\mathit{c},2}$[n] allows one compute bounds upon ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$]; imply that ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$]\ensuremath{\simeq}${\mathit{E}}_{\mathit{c}}$[n] large class small atoms molecules, suggest ${\mathrm{lim}}_{\ensuremath{\lambda}\ensuremath{\rightarrow}\mathrm{\ensuremath{\infty}}}$${\mathit{E}}_{\mathit{c}}$[${\mathit{n}}_{\ensuremath{\lambda}}$] should be same order magnitude ${\mathit{E}}_{\mathit{c}}$[n] finite insulators semiconductors.