My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 5.
THE JELLIUM SLAB
1.95
σ s
1.9
σ el
σ xc
σ
1.85
10 15 20 25 30
0.75
0.7
0.65
0.6
10 15 20 25 30
-2.9
-2.95
-3
-0.35
-0.4
-0.45
10 15 20 25 30
10 15 20 25 30
Slab width
Figure 5.6: The components of the LDA surface energy as a function of the slab width. All the
surface energies are given in mHa bohr −2 .
visible in figure 5.5 is around 3.88, which corresponds approximately to λ F /2. This
may be seen more clearly in figure 5.6, which shows the different components of the
surface energy. The oscillations in the kinetic, electrostatic and exchange-correlation
contributions to the surface energy largely cancel each other out. In particular, the
cusps which are present in all the individual components do not appear in the total
surface energy. The magnitude of the oscillations in the total surface energy is
around 0.03 mHa bohr −2 , or 10%, for a slab width of 10.
5.4 The jellium slab in QMC
The Kohn-Sham orbitals obtained from the DFT calculations are the foundation
for the QMC trial wave function (equation (3.77)); they are the components of the
Slater determinant. The usual procedure is then to improve on the determinantal
wave function by adding a Jastrow factor with a successively increasing number of
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