My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 5.
THE JELLIUM SLAB
Yan and his co-authors demonstrate that the various DFT methods all give
broadly the same values for the surface energy. More interestingly, these results
also agree with the DMC results obtained by Sottile and Ballone using finite jellium
spheres, but not with the extended-slab calculations of Acioli, Ceperley, Li et al.: the
extended-slab DMC surface energies appear too large. In a recent paper, Pitarke [71]
points out that Acioli and Ceperley incorrectly compared fixed-node slab energies
with release-node bulk energies, and therefore overestimated the surface energy. 3
He argues that using the fixed-node bulk energy brings the DMC results closer to
those obtained using DFT; however, they remain in disagreement, and the same
correction does not apply to the earlier work of Li et al. It seems increasingly likely
that the extended-slab DMC calculations were inaccurate.
Focusing on one density (r s = 2.07) which is very often studied, some different
values calculated for the surface energy are:
• −420 ± 80 erg cm −2 (Acioli and Ceperley [1], fixed-node DMC), corrected to
−554 ± 80 erg cm −2 (Pitarke [71]);
• −465 ± 50 erg cm −2 (Li et al. [53], fixed-node DMC);
• −610 erg cm −2 (Yan et al. [85], LDA);
• −533 erg cm −2 (Yan et al. [85], wave vector interpolation based on the GGA);
• −690 erg cm −2 (Perdew et al. [68], GGA);
• −567 erg cm −2 (Perdew et al. [68], meta-GGA);
• −553 erg cm −2 (Kurth and Perdew [44], combination of random phase approximation
and LDA);
• −587 erg cm −2 (Kurth and Perdew [44], combination of random phase approximation
and GGA).
3 The surface energy is negative; the ‘overestimate’ referred to here is a result which is insufficiently
negative, and therefore smaller in magnitude than the true value.
74