My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 9.
ENERGY
A NEW CALCULATION OF THE JELLIUM SURFACE
0.2
0
0
Potential
-0.2
-0.4
V KS
(no image tail)
V KS
(z 0
=0.72)
V KS
(z 0
=1.49)
V XC
(no image tail)
V XC
(z 0
=0.72)
V XC
(z 0
=1.49)
electron density
-0.05
n(z)
s/2 s
z
Figure 9.1: The effect of including the image tail in V XC . The simple LDA form (shown for
comparison) is matched to the image potential outside the slab. The test system has density
parameter r s = 2.07 and slab width s = 17.64248; the simulation cell contains 600 electrons. In
addition to the exchange-correlation potential V XC , the Kohn-Sham potential V KS = V Ha +V B +V XC
is also plotted. The positions of the image planes are indicated by ticks on the z-axis.
region, the LDA potential decays exponentially, while the modified potentials have
the form described in equation (9.1). The electron density is plotted as a reference;
on this scale, the difference between the three density curves corresponding to the
different exchange-correlation potentials is not observable.
The effect on the single-electron orbitals is small; the greatest difference is observed
in the higher sub-bands, because these extend further into the vacuum region.
The highest occupied orbital for the current test system (the sixth sub-band) is plotted
in figure 9.2. Note that there is a very small correction to the nodes.
The overall correction to the wave function is small, and this is reflected in the
VMC energies listed in table 9.1. The wave functions calculated with the image
plane at z 0 = 1.49 give a slightly higher energy, and will not be used in the QMC
168