2D wave-vector analysis of the correlation surface energy of a jellium slab of thickness 7.21 rs (rs = 2.07). Black, red, green, and blue lines represent inhomogeneous-STLS (ISTLS), uniform-gasbased TDDFT, random-phase-approximation (RPA), and local-density-approximation (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 in units of erg/cm2. kF represents the magnitude of the Fermi wave vector. rs represents (in units of the Bohr radius) the radius of a sphere that encloses one electron on average. We observe that in the longwavelenght limit (small q) both ISTLS and TDDFT calculations coincide with the RPA, which is exact in this limit, while the LDA fails badly. In the large-q limit, both ISTLS and TDDFT calculations approach the LDA, as expected, while the RPA is wrong. Two independent schemes (the ISTLS approach, which does not use and isotropic xc kernel derived from the uniform gas, and the TDDFT approach, which uses a uniform-gas-based isotropic xc kernel) yield essentially the same wave-vector analysis of the correlation surface energy. This supports the conclusion that the local-density approximation for the particle-hole interaction is indeed adequate to describe simple metal surfaces.
Our work vindicates the use of uniform-gas-based nonlocal kernels in time-dependent density-functional theory.
DIPC 08/09 21