Density Functional Theory with Correct Long-Range Asymptotic Behavior

We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. Using a simple approximation, we develop an electronic structure theory that combines a new local correlation energy (based on Monte Carlo calculations applied to the homogeneous electron gas) and a combination of local and explicit long-ranged exchange. The theory is applied to several first-row atoms and diatomic molecules where encouraging results are obtained: good description of the chemical bond at the same time allowing for bound anions, reasonably accurate affinity energies, and correct polarizability of an elongated hydrogen chain. Further stringent tests of DFT are passed, concerning ionization potential and charge distribution under large bias.

Figure 1

The ratio $\eta ={\epsilon }_C^{\gamma }/{\epsilon }_C^{\mathrm{L}\mathrm{D}\mathrm{A}}$ as a function of $r_s$ for $\gamma =1a_0^{-1}$. Shown are the AFMC results (filled dots) and the analytical fit (dotted curve and empty circles).

Figure 2

Polarizability of a linear hydrogen chain, as a function of its length, calculated with LDA, HFT, and the present functional.