High-Level Correlated Approach to the Jellium Surface Energy, without Uniform-Gas Input

We resolve the long-standing controversy over the metal surface energy: Density-functional methods that require uniform-electron-gas input agree with each other, but not with high-level correlated calculations such as Fermi hypernetted chain and diffusion Monte Carlo calculations that predict the uniform-gas correlation energy. Here we apply the inhomogeneous Singwi-Tosi-Land-Sjölander method, and find that the density functionals are indeed reliable (because the surface energy is bulklike). Our work also vindicates the use of uniform-gas-based nonlocal kernels in time-dependent density-functional theory.

Figure 1

Wave vector analysis ${\gamma }_q^c$ of the correlation surface energy for a jellium slab of thickness $7.21r_s$ and $r_s=2.07$. Solid, thick dashed, thin dashed, and dotted lines represent ISTLS, uniform-gas-based TDDFT (as reported in Ref. 10), RPA, and LDA calculations, respectively. $q$ is the magnitude of the 2D wave vector (in the surface plane) of the density fluctuations. The area under each curve amounts to the correlation surface energy ${\sigma }^c$. ($1\mathrm{hartee}/{\mathrm{bohr}}^2=1.557\times {10}^6\mathrm{erg}/{\mathrm{cm}}^2$).