Long-range density-matrix-functional theory: Application to a modified homogeneous electron gas

Abstract

We propose a method that employs functionals of the one-electron reduced density matrix (density matrix) to capture long-range effects of electron correlation. The complementary short-range regime is treated with density functionals. In an effort to find approximations for the long-range density-matrix functional, a modified power functional is applied to the homogeneous electron gas with Coulomb interactions replaced by their corresponding long-range counterparts. For the power $\ensuremath{\beta}=1/2$ and the range-separation parameter $\ensuremath{\omega}=1/{r}_{s}$, the functional reproduces the correlation and the kinetic correlation energies with a remarkable accuracy for intermediate and large values of ${r}_{s}$. Analysis of the Euler equation corresponding to this functional reveals correct ${r}_{s}$ expansion of the correlation energy in the limit of large ${r}_{s}$. The first expansion coefficient is in very good agreement with that obtained from the modified Wigner-Seitz model.