My PhD thesis - Condensed Matter Theory - Imperial College London

CHAPTER 9.
ENERGY
A NEW CALCULATION OF THE JELLIUM SURFACE
Number of electrons Phase Fractional occupation of sub-band
1 2 3 4 5 6
600 0 0.297 0.23 0.223 0.15 0.083 0.017
600 π 0.28 0.253 0.2 0.173 0.08 0.013
1140 0 0.282 0.254 0.212 0.156 0.079 0.016
1140 π 0.274 0.260 0.211 0.154 0.091 0.011
1600 0 0.276 0.246 0.221 0.151 0.086 0.019
1600 π 0.27 0.26 0.205 0.15 0.095 0.02
∞ - 0.279 0.252 0.210 0.154 0.087 0.018
Table 9.3: The fractional occupation of each sub-band. This is simply the occupation number
divided by the total number of electrons, and allows the results of finite-cell calculations to be
compared with those obtained in the infinite-cell limit.
Number of electrons Phase VMC energy DFT correction Corrected energy
600 0 32.56 ± 0.11 -0.268 32.29
600 π 32.32 ± 0.11 -0.128 32.19
1140 0 32.75 ± 0.13 -0.117 32.63
1140 π 32.41 ± 0.14 0.210 32.62
1600 0 32.92 ± 0.14 -0.072 32.85
1600 π 32.73 ± 0.18 0.070 32.80
Table 9.4: Comparison of energies calculated with different versions of the exchange-correlation
potential. All energies are in mHa. The trial wave function for the VMC calculations contained
no Jastrow factor.
usual independent-particle finite-size error correction has been applied, the results
are identical to within the statistical error: this is reassuring, but shows that using
alternative boundary conditions cannot reduce the remaining finite-size error. The
results are in agreement with the hole-squashing model proposed in chapter 6 to
explain this error.
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