My PhD thesis - Condensed Matter Theory - Imperial College London

LIST OF FIGURES
5.3 The LDA energy per electron as a function of the number of grid
points. Cells of size w ∼105 and w ∼210 are compared, both for
finite systems containing 360 electrons and for systems infinite in the
xy-direction. Note that the two vertical scales are offset. The slab
width is 17.64248; the density parameter is r s = 2.07. The length of
the cell in the z-direction varies slightly as a function of the number
of grid points; this is to ensure optimal sampling of the important
slab region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.4 The dependence of the LDA energy per electron on the slab width;
for this system, r s = 2.07, the number of electrons is 360 and the cell
size in the z-direction is around 105. . . . . . . . . . . . . . . . . . . 78
5.5 The surface energy as a function of slab width, calculated using different
values of the bulk energy. The middle curve uses the Perdew-
Wang parameterisation [69] of Ceperley and Alder’s early QMC results
[12], which was the functional employed in the slab calculation.
The upper curve is from the Perdew-Zunger [70] paremeterisation of
the same results; the lower curve is from the Perdew-Zunger parameterisation
of Ortiz and Ballone’s later QMC calculations [63]. . . . . 79
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 . . . . . . . . 80
5.7 The distribution of configuration energies, before and after variance
minimisation. 10000 configurations have been included; the Jastrow
factor was of the form introduced in section 3.4.1 and described in
detail in section 6.3. Optimisation of both u and χ terms was allowed;
The minimisation was performed without reweighting. . . . . . . . . . 81
6.1 The total VMC energy per electron as a function of system size,
comparing the Ewald and MPC interactions. The exchange energy
given by equation (6.25) is also plotted (note the different vertical
scale). Energies, as usual, are in Ha. . . . . . . . . . . . . . . . . . . 90
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