Density-functional versus wave-function methods: Toward a benchmark for the jellium surface energy

Abstract

For the surface energy of jellium at alkali-metal densities, the local-density approximation ͑LDA͒ and more advanced density-functional methods disagree strongly with the wave-function-based Fermi hypernetted-chain and diffusion Monte Carlo methods. We present a wave-vector interpolation correction to the generalized gradient approximation which gives jellium surface energies consistent with two other estimates based on advanced density functionals. LDA makes compensating errors at intermediate and small wave vectors. Studies of small jellium clusters also support the density-functional estimate for the jellium surface energy.

Metal surface energy: Persistent cancellation of short-range correlation effects beyond the random phase approximation

“…Usually GGA works better than LDA, but not for the jellium surface energy where long-range effects are especially important. In the present work, as in four others, 10,31,34,35 we have found that the jellium xc surface energy is only a few percent higher than it is in LDA. These closely-agreeing methods include two different short-range corrections to RPA (present work using a non-local xc kernel and Ref.…”

“…A different (and less complete) error cancellation between long-and intermediate-range xc effects explains 10 why the LDA works for the surface energy. The GGA corrects only the intermediate-range contributions, 10 and so gives surface energies slightly lower and less accurate than those of LDA. Usually GGA works better than LDA, but not for the jellium surface energy where long-range effects are especially important.…”

“…31 using an additive GGA correction), a long-range correction to GGA (Ref. 10), extraction of a surface energy from DMC energies for jellium spheres (Ref. 34), and a meta-GGA density functional (Ref.…”

Jellium surface energy beyond the local-density approximation: Self-consistent-field calculations

“…Moreover, a GGA 49 for the short-range correlation not present in the RPA has yielded a small and negative contribution to the surface energy, 17 thereby suggesting that the RPA may be a much better approximation for the changes in correlation energy upon surface formation than for the total correlation energy. A recent wave-vector interpolation as a long-range correction to the GGA, 18 which has predicted surface energies that are smaller but close to our non-local RPA results, has indicated that the LDA should be accurate even within an exact treatment of electron correlation. This is in contrast with non-local correlation surface energies reported in Refs.…”

“…[5][6][7][8][9][10][11] Recently, the wave-function-based Fermi hypernetted-chain (FHNC) 12 and quantum Monte Carlo (QMC) 13,14 predictions have been found to disagree with modern densityfunctional calculations of jellium surface energies that go beyond a local-density approximation. [15][16][17][18] In this paper, we present extensive self-consistent calculations of jellium surface energies. The dynamical density-response function of a bounded free electron gas (FEG) is evaluated within the random-phase approximation (RPA), 19 from the knowledge of the non-interacting density-response function.…”