Local density functional for the short-range part of the electron-electron interaction

Motivated by recent suggestions—to split the electron-electron interaction into a short-range part, to be treated within the density functional theory, and a long-range part, to be handled by other techniques—we compute, with a diffusion Monte Carlo method, the ground-state energy of a uniform electron gas with a modified, short-range-only electron-electron interaction $\mathrm{erfc}\left(\mu r\right)∕r$, for different values of the cutoff parameter $\mu$ and of the electron density. After deriving some exact limits, we propose an analytic representation of the correlation energy which accurately fits our Monte Carlo data and also includes, by construction, these exact limits, thus providing a reliable “short-range local-density functional.”

Figure 1

Splitting of the Coulomb electron-electron repulsion $v_{ee}=1∕r$ into a short-range (SR) part and a long-range (LR) part, according to Eqs. (1, 2), with $\mu =1$.

Figure 2

Correlation energy per particle of the short-range interacting gas at $\mu =0.5r_s=1$, for different numbers of particles $N$. The fitting function of Eq. (8) (line) favorably compares with the VMC data (dots).

Figure 3

Correlation energy of the short-range interacting gas as a function of $\mu r_s$, for different densities. Our fitting function (lines) is compared with our DMC data (dots). The error bars are comparable with the symbol sizes.